The room temperature compatibility of the negatively charged nitrogen-vacancy (NV) center in diamond makes it the ideal quantum system for a university teaching lab. Here, we describe a low-cost experimental setup for coherent control experiments on the electronic spin state of the NV center. We implement spin-relaxation measurements, optically detected magnetic resonance, Rabi oscillations, and dynamical decoupling sequences on an ensemble of NV centers. The relatively short times required to perform each of these experiments (<10 min) demonstrate the feasibility of the setup in a teaching lab. Learning outcomes include basic understanding of quantum spin systems, magnetic resonance, the rotating frame, Bloch spheres, and pulse sequence development.

The arrival of the second quantum revolution—technologies that exploit coherent quantum phenomenon, such as quantum computation, quantum communication, and quantum sensors—has elevated quantum physics from fundamental research to an applied science.1 A thorough understanding of quantum mechanics is not only desirable but quite often demanded of university graduates entering the job market in this field. Theoretical skills are easily taught with pen and paper, by deriving analytical solutions, or with a few lines of computer code running numerical simulations, but real hands-on experience in manipulating a quantum system is, unfortunately, much more difficult to convey. This is partly due to the sensitivity of quantum systems to environmental disturbances that often demands operation at cryogenic temperatures or inside vacuum chambers, and partly due to the high cost of specialized equipment.

The NV center in diamond is an especially advantageous quantum system for a teaching lab as its electron spins can be initialized, controlled, and read out at room temperature in ambient atmosphere,2 strongly reducing the complexity of the experimental apparatus. Hence it has previously been recommended for teaching lab setups for magnetic resonance and magnetometry by Zhang et al. in Ref. 3, and is even available as a commercial system.4 While the experimental apparatus required to extend the experiments to coherent control is more complex, it has been thoroughly described in literature by Bucher et al. in Ref. 5. However, coherent control has not been demonstrated in a convenient and cost-effective fashion targeted at a university teaching lab.

Here, we describe a teaching lab setup that allows students to learn about fundamental concepts of quantum mechanics by coherently controlling the electronic spin state of the NV center in diamond. In fact, students can adapt and design their own control sequences and experiments. The presented setup is robust to its environmental conditions, such that it can even be operated in broad daylight on a normal desk, and does not require the carefully controlled environment of a research laboratory. Finally, the setup can be assembled for a total cost of less than USD 20k.

This paper is organized as follows: in Sec. II, we will give an overview of the learning outcomes that can be conveyed with these experiments. In Sec. III, we will give a short introduction to the NV center in diamond, explaining how initialization, control, and readout of the electronic spin states is achieved. Section IV provides a detailed description of the experimental setup. More specifically, Sec. IV A describes the diamond sample we use, Sec. IV B describes the optical part of the setup, Sec. IV C describes the equipment required for delivery of a microwave (MW) field, and Sec. IV D describes the signal detection scheme using a lock-in amplifier in combination with digital pulse sequences. Finally, Sec. V discusses the various experiments that can be conducted with this setup, with special attention to the quantum mechanical concepts that these experiments convey.

At UNSW Sydney, the experiments described below have been incorporated into a course targeted at the 4th-year undergraduate level. At the time of writing, we have thus far run the course for one semester in which students have been able to successfully perform all experiments, and demonstrate the learning outcomes. A total of nine students were enrolled in that semester, and were divided into groups of two or three. Each group had two hours per week to perform the experiments, for four weeks in total. Due to the number of groups, two identical setups were built and were operated simultaneously during the lab times. Throughout the course of the labs, it was essential for students to demonstrate links between experimental results, and both quantitative and qualitative understanding of quantum theory. More specifically, these labs encourage students to achieve the following:

  1. Understand the NV center structure, the spin initialization and readout procedure, and the spectral features.

  2. Incrementally develop pulse sequences with increasing complexity, i.e., starting from purely optical spin-dynamics for T1 measurements, up to complex dynamical decoupling sequences for T2 measurements.

  3. Understand the rotating frame, magnetic resonance, two-axes control, and be able to follow the spin orientations along the Bloch sphere during pulse sequences.

  4. Understand the incremental steps required to implement dynamical decoupling pulse sequences, such as finding a spin transition in the spectrum, performing Rabi oscillations, and calibrating π-pulse lengths. Due to the short experimental run times, students can often perform all experiments in a single two-hour lab once they have obtained the expertise.

Concepts demonstrated with these experiments are transferable to other quantum systems,6 like electron spin qubits confined to donors or quantum dots,7,8 nuclear spin qubits,9 superconducting qubits,10 atoms in ion traps,11 and magnetic resonance imaging (MRI).12 Literature that is readily available on these systems frequently benchmarks quantum devices using the same methods as described below. Performing such experiments has, up until now, often only been available to research students in an expensive research lab.

The NV center in diamond consists of a substitutional nitrogen atom adjacent to a vacant lattice site, as schematically shown in Fig. 1(a). It can exist along four different crystallographic orientations ([111], [11¯1¯], [1¯11¯], and [1¯1¯1]), which are in principle equivalent, but lead to different alignments of their NV center axes with respect to an externally applied static or oscillating magnetic field.

Fig. 1.

(Color online) (a) Atomic structure of the NV center in diamond with a substitutional nitrogen atom adjacent to a vacant lattice site. The depicted NV center is oriented along the [111] lattice direction, however, due to the tetrahedral structure of the crystal lattice, the NV center axis can also be oriented along the [11¯1¯], [1¯11¯], and [1¯1¯1] lattice directions. (b) Energy levels and transitions of the NV, with ground state |g, excited state |e, and intermediate singlet states |s. The corresponding shaded regions represent continua of orbital and vibrational states. Thicker arrows represent high probability transitions, while thinner arrows represent low probability transitions.

Fig. 1.

(Color online) (a) Atomic structure of the NV center in diamond with a substitutional nitrogen atom adjacent to a vacant lattice site. The depicted NV center is oriented along the [111] lattice direction, however, due to the tetrahedral structure of the crystal lattice, the NV center axis can also be oriented along the [11¯1¯], [1¯11¯], and [1¯1¯1] lattice directions. (b) Energy levels and transitions of the NV, with ground state |g, excited state |e, and intermediate singlet states |s. The corresponding shaded regions represent continua of orbital and vibrational states. Thicker arrows represent high probability transitions, while thinner arrows represent low probability transitions.

Close modal

The static Hamiltonian of the NV center ground state, neglecting any interactions with nuclear spins or spin-strain interactions, and assuming that the NV-axis is oriented along the z-direction, is given by

H0=DSz2+γeB0Su,
(1)

where D = 2.87 GHz is the zero-field splitting of the ground state, γe=28 GHz/T is the electron gyromagnetic ratio, B0 is the magnetic field applied along an arbitrary direction u, and Sx,y,z,u are the spin matrices for S = 1 along the x,y,z-axes and the u-direction.13 In this paper, we will treat H0 in units of frequency, as this is more relevant for the experiments.

In order to achieve magnetic spin resonance and coherent control, we need an oscillating magnetic field B1 that induces transitions between the spin sublevels. For example, a resonant B1 field enables us to controllably rotate the ground state spin states from |0 to |±1 and back (termed Rabi oscillations). This field is usually created at the position of the NV centers using a MW signal generator and an antenna (discussed further in Sec. IV). We include the oscillating magnetic field in the Hamiltonian as a time-dependent term given by

H1=γeB1cos(2πν1t)Sv,
(2)

where B1 is the magnitude of the oscillating magnetic field at frequency ν1 applied along an arbitrary direction v, and Sv is the spin matrix along the v-direction.

Due to the exact way the sample is mounted in the setup, there can be an angle between the static magnetic field B0, the oscillating magnetic field B1, and the direction in which the crystal field acts [defined as the z-direction in Eq. (1)], as for example indicated in Fig. 4(d). In fact, due to the four possible orientations of the NV center axis in the tetrahedral crystal, NV centers with different orientations will, intrinsically, have different Zeeman splittings and Rabi frequencies.

The experiments described in this paper will only be concerned with the spin physics of the ground state described above, denoted |g in Fig. 1(b). However, in order to describe the spin initialization and readout mechanisms, we must consider the optically excited state |e and the intermediate singlet states |s, also depicted in Fig. 1(b). The ground state |g and excited state |e are both spin-carrying states with S = 1. In |g at B0=0 T, the |±1g states are at νD=2.87 GHz higher energy than the |0g state due to the zero-field splitting D. Green laser light at λ = 520 nm or λ = 532 nm can excite the NV electrons from the ground state |g into the continuum of orbital and vibrational excited states (shaded region near |e) above the excited state |e (referred to as off-resonant excitation), from which they rapidly relax into |e. From there the electrons can decay radiatively, either directly to |g by emitting a photon at λZPL=637 nm into the zero-phonon-line (ZPL), or by simultaneously emitting a phonon and a photon of longer wavelength into the phonon-sideband (PSB). In either case, there is a high probability that the spin state of the electron will remain unchanged during this optical cycling, due to spin-conservation. Alternatively, the NV electrons can decay nonradiatively via the singlet state |s. Decay from |e to |s is favoured by the |±1e states compared to the |0e state (as indicated by the thicker arrow), and decay from |s to |g favours the |0g spin orientation of |g. Overall, these transition rules have two effects:

  1. Electrons cycling between the |0g and |0e states emit 30% more photons than those cycling between the |±1g and |±1e states. This provides a readout mechanism for the ensemble electronic spin state.

  2. With continuous laser excitation, electrons cycling between |±1g and |±1e states will over time populate the |0g state. The electrons can therefore be spin-initialized into the |0g state.2 

In this section, we provide details about the experimental setup. All optical and electrical components were purchased off-the-shelf, while the printed circuit boards for the antenna [see Fig. 2(c)] and the laser current driver (more information in  Appendix B) can be commercially manufactured (Eagle CAD files are included in the supplementary material).15 A detailed list of all parts with part numbers and recent prices can be found in  Appendix A.

Fig. 2.

(Color online) (a) Electronics setup. (b) Optics setup. (c) CAD drawing of the PCB antenna designed to deliver the oscillating magnetic field B1 to the NV spins. The geometric parameters are d1 = 14 mm, d2 = 1.0 mm (for laser pass-through), l1 = 10.9 mm, l2 = 3.1 mm, and g = 0.1 mm. The bottom layer copper is shorted to the ground/shield of the SMA connector (not shown). The design is adapted from Ref. 14, and commercially fabricated on a 0.254 mm thick FR4 substrate with 36 μm of copper thickness on each side. (d) Magnitude of the magnetic field |B1| at +24 dBm of excitation at 2.57 GHz, around the 1 mm hole. Simulations were performed in CST Microwave Studio. (e) Comparison of simulated (labeled “Sim.,” left axis) and measured (labeled “Meas.,” left axis) power reflected from the antenna (S11), and simulated magnetic field magnitude |B1| (right axis).

Fig. 2.

(Color online) (a) Electronics setup. (b) Optics setup. (c) CAD drawing of the PCB antenna designed to deliver the oscillating magnetic field B1 to the NV spins. The geometric parameters are d1 = 14 mm, d2 = 1.0 mm (for laser pass-through), l1 = 10.9 mm, l2 = 3.1 mm, and g = 0.1 mm. The bottom layer copper is shorted to the ground/shield of the SMA connector (not shown). The design is adapted from Ref. 14, and commercially fabricated on a 0.254 mm thick FR4 substrate with 36 μm of copper thickness on each side. (d) Magnitude of the magnetic field |B1| at +24 dBm of excitation at 2.57 GHz, around the 1 mm hole. Simulations were performed in CST Microwave Studio. (e) Comparison of simulated (labeled “Sim.,” left axis) and measured (labeled “Meas.,” left axis) power reflected from the antenna (S11), and simulated magnetic field magnitude |B1| (right axis).

Close modal

The diamond sample is a single crystal Type 1b 111-oriented high-pressure, high-temperature (HPHT) diamond obtained from Sumitomo. In order to obtain a high NV concentration, the diamond was additionally electron-irradiated in-house with a density of 1018 electrons/cm2, and annealed in vacuum at 900° C for 2 h. The electron irradiation significantly increases the PL intensity but reduces the coherence times,16 which can be a limiting factor for some more advanced measurement protocols. All experiments measure the photoluminescence (PL) from a large ensemble of NV centers with all four possible orientations. While the sample used in this manuscript requires some processing, a 100-oriented HPHT diamond sample with high NV center density of a few ppm can be purchased from Scimed,17 and a 100-oriented chemically vapour-deposited (CVD) diamond sample (available from Element Six)18 is also sufficient for the experiments described herein and will contain a measurable number of NV centers, without any additional processing. In  Appendix C, we show a comparison between the HPHT diamond that was used for the experiments in this manuscript and the commercially available CVD diamond from Element Six for a zero-field spin resonance experiment (as in Sec. V B) and a Rabi experiment (as in Sec. V C). The CVD sample has a 1000 times lower PL signal, and while the spin signal decreases proportionally, we obtain high-quality data with only 10 times longer measurement times. In contrast, the CVD sample has a much longer coherence time than the HPHT sample that allows observation of effects originating from coupling to nuclear spins (not discussed in this work). The effect of the different crystal orientations with respect to the diamond surface on our experiment is described in Sec. V C and Ref. 19.

The setup was designed with the goal of keeping the optical components to a minimum while ensuring ease of alignment. This way, the setup can be easily incorporated onto a small optical breadboard (Thorlabs MB3045/M) for portability, and fully covered with an enclosure (Thorlabs XE25C7/M) to constrain laser scattering.

A schematic of the optics part of our setup is shown in Fig. 2(b). We use a single mode, fiber-coupled 520 nm green laser diode (Thorlabs LP520-SF15) as our excitation source. The beam is first collimated using an aspheric lens (Thorlabs C280TMD-A), and then reflected off a 550 nm long-pass dichroic mirror (Thorlabs DMLP550) and onto a microscope objective (Olympus MS Plan 50×/0.80NA). The objective lens focuses the laser to a focal spot of 1μm on the diamond sample, which results in an excitation volume over which B0 and B1 field are both relatively constant. The diamond sample is mounted on a 3-axis translation stage (Thorlabs MBT616D/M). Between the objective lens and the diamond sample, we place a printed circuit board (PCB) MW antenna to create the strong oscillating magnetic field (B1 field) for spin control. The antenna structure includes a 1 mm diameter hole, through which both the excitation laser and the PL emission from the diamond sample can pass. The design of the antenna is discussed in more detail in Sec. IV C.

The PL signal from the diamond sample is transmitted through the dichroic mirror and into the detection part of our setup. Here, a flip-mirror (Thorlabs PF10-03-P01 on Thorlabs TRF90/M) allows the signal to follow one of two paths:

  1. Through an achromatic doublet (Thorlabs AC254-125-A) onto a CMOS camera (Thorlabs DCC1545M) that allows for alignment of the sample and focusing of the laser using the 3-axis stage. A 600 nm longpass filter (Thorlabs FEL0600) and a 900 nm shortpass filter (Thorlabs FES0900) can be added here to view the PL signal instead of residual laser light.

  2. Via two silver-coated mirrors (Thorlabs PF10-03-P01) on separate kinematic mounts (Thorlabs KM100) and through an aspheric lens (Thorlabs C260TMD-B) into a 50 μm multi-mode fiber (Thorlabs M42L01) that guides the light to a photodiode (Thorlabs DET025AFC/M) for detection. A 600 nm longpass filter (Thorlabs FEL0600) and 900 nm shortpass filter (Thorlabs FES0900) are placed in this path to ensure that only the NV PL is detected.

A block diagram of the electronics part of our setup is shown in Fig. 2(a). The block labeled “Microwave Source & Amp” is discussed in this section. First, a PC communicates with the MW source (SignalCore SC800) to set the MW frequency between 0 and 6 GHz. The MW signal is fed into an I/Q modulator (Texas Instruments TRF370417EVM). The I (“in-phase”) input of the modulator controls the amplitude of a MW signal that has the same phase as the input MW signal. The Q (“quadrature”) input controls the amplitude of a MW signal that is 90° phase-shifted. The output of the modulator is the sum of these signals. For our experiments, it is sufficient to restrict the I and Q inputs to high/low signals (TTL high or low), which enable or disable the I and Q signal components. The modulator's output is therefore either a signal that is in-phase with the input MW signal (I high, Q low), 90° out of phase (I low, Q high), or 45° out of phase (I high, Q high). The modulator's output is then amplified by a MW amplifier (ZQL-2700MLNW+) to a MW power of +24 dBm (251 mW), and transmitted to the PCB antenna [shown in Fig. 2(c)] via a coaxial cable with SMA connectors on both ends.

The antenna is designed to produce the oscillating magnetic field B1 at the position of the NV centers. Figure 2(c) shows our antenna design with all geometrical parameters, adapted from Ref. 14. The antenna was designed and simulated in-house using Eagle CAD and CST MW Studio, respectively, and manufactured commercially by the PCB manufacturer Circuit Labs. The antenna geometry is referred to as a loop-gap resonator, where the “loop” in our case is a through hole, near which we can have a strong oscillating B1 field in the direction perpendicular to the plane of the PCB as shown in Fig. 2(d). This hole also allows for both the excitation laser and the PL of the diamond sample to pass through the PCB.

Simulations predict that the antenna has a resonance at 2.57 GHz, indicated by the minimum of the S11 reflection coefficient, shown by the curve labeled “Sim.” in Fig. 2(e). In the manufactured PCB, we measure the resonant S11 minimum to be at ∼2.49 GHz (curve labeled “Meas.”), which agrees well with our simulated value.20 The simulations also predict that with a MW power of +24 dBm (251 mW), the antenna produces a maximum oscillating magnetic field of B1=306μT, which would result in an electron spin Rabi frequency of ΩR=1/2γeB14.3 MHz.21 The diamond sample is placed as close to the top layer [Fig. 2(c)] of the PCB as possible (using tape as adhesive), and we align the excitation laser's focal spot to the center of the hole, where we can expect the greatest homogeneity of B1 in magnitude (||B1||=0.13μT/μm at +24 dBm of excitation power). While the antenna response peaks at ∼2.49 GHz, the bandwidth of the antenna is broad enough to perform the spin resonance measurements at 2.87 GHz (i.e., at B0=0 T), which will be discussed in Sec. V B.

As discussed in Sec. III, the NV center emits 30% more photons when decaying from the |0e states compared to the |±1e states. Under experimental conditions, where we collect emission from the four different NV orientations simultaneously, and spin control of the ensemble is far from ideal, the contrast of the spin signal is limited to a few percent. It is possible to extract the spin signal by using a power-stabilized laser source and sufficient averaging. However, to achieve a more robust implementation for a teaching lab, we employ a lock-in amplifier.

The operation of a phase-sensitive lock-in amplifier is well-known, and described in Ref. 22. Given a reference frequency, the lock-in amplifier will make a phase-sensitive measurement of signals present exactly at that frequency, with a bandwidth as narrow as 0.01 Hz (selectable). If the signal of choice can be modulated at the reference frequency, the lock-in amplifier can extract it with a good signal-to-noise ratio (SNR) from large background signals at other frequencies. For example, in an experiment where laser excitation provides a PL signal from an ensemble of NV centers, and a resonant MW source drives the spin from the |0g state to the |±1g states, the spin signal can be extracted with a lock-in amplifier when the MW field is amplitude- or frequency-modulated at the reference frequency, while any DC signal is rejected.

The experiments are clocked and triggered by a Pulse Blaster ESR Pro 250 pulse pattern generator that can be programmed to generate TTL pulse sequences on up to 24 channels. For the experiments described here, we require four channels:

  • “CH0” provides the reference frequency to a phase-sensitive lock-in amplifier (Ametek 5210 or alternatively Stanford Research Systems SR830).

  • “CH1” pulse-modulates the 520 nm laser diode via an in-house-designed high-speed current source (discussed in  Appendix B).

  • “CH2” provides the I input for the I/Q modulator (discussed in Sec. IV C).

  • “CH3” provides the Q input for the I/Q modulator.

We perform our experiments by programming pulse sequences onto the four channels, keeping in mind that we only modulate the signals at the lock-in reference frequency that we are interested in detecting (except for the T1 measurements in Sec. V A). Each experiment below has a specific pulse sequence associated with it. The software programming of each pulse sequence is done on a PC using matlab, and the pulse blaster is configured to generate the corresponding TTL pulses via USB serial interface.

At room temperature, without any laser, MW excitation, or external magnetic fields, the NV spins are completely depolarized and the spin states are very nearly equally populated, as described by a Boltzmann distribution for a two-level system with a 2.87 GHz level splitting at 300 K. Thus, all experiments discussed in this paper will start with spin initialization via an optical pulse as described above. As discussed in Sec. III, electrons decaying via the |s state will be initialized into the |0g state with a high probability. Hence, continuous 520 nm laser excitation, and therefore repeated optical cycling of the dynamics discussed in Sec. III, will result in the ensemble being initialized into the |0g state.

Readout of the NV spin states at the end of the experiment relies on the same process. A laser pulse is used to excite the NV centers to the |e state. As relaxation via the |s state is more likely for the |±1e state than for the |0e state, the |0e state will result in a larger number of photons being detected at the wavelengths of the ZPL and PSB.

The spin T1 decay time gives an idea of how long the spins remain in the prepared state, before longitudinal relaxation into a Boltzmann-distributed population occurs. Note, that a T1 experiment measures the spin decay time only, and is not sensitive to any dephasing of the system. There are two methods to measure the spin T1 decay time:

  1. By initializing the spins into the |0g state using a laser pulse, leaving them to relax for a time τdelay, and then measuring the resultant spin population with a second laser pulse. This is a fairly simple measurement that requires no MW control and works at zero B0 magnetic field. Furthermore, it results in a signal from all members of the ensemble, irrespective of the orientation of the NV axes.

  2. By additionally using a resonant MW pulse to coherently invert the spin population before the decay period τdelay. At non-zero B0 field, this method allows the selection of a specific spin transition and measurement of its corresponding T1 time. However, due to the different orientations of the NV center axes with respect to the B0 and B1 fields (see also Sec. III), a MW pulse will not be resonant with all the defects or lead to non-perfect inversion, producing a partial initialization of the spin ensemble and resulting in a smaller signal.

We choose the first method for the teaching labs. This method results in a stronger signal, and allows the introduction of spin initialization and readout independent of the concept of MW spin control.

Figure 3(a) describes the pulse sequence to implement the all-optical T1 measurement. CH0 sets the reference signal for the lock-in amplifier, while CH1 defines the laser pulse sequence. There are two initialization laser pulses in the sequence [denoted “i” in Fig. 3(a)], one at the beginning of each half-cycle. As they are separated by a π-phase shift with respect to the lock-in reference (CH0), the lock-in detection will cancel out this signal under the condition that τrefT1. The second initialization pulse is followed by a readout laser pulse (denoted “r”) of the same length, after a variable delay τdelay. The signal caused by the readout pulse is dependent on the T1 process, however since this laser pulse is only present in the second half-cycle of the reference, the readout pulse will additionally result in the detection of a PL signal that is independent of T1 (i.e., a background signal). In Fig. 3(b), we show the corresponding measurement. The signal decreases from 0.391 mV to 0.374 mV with a time constant of T1=1.64±0.25 ms. The 4.3% change in signal corresponds to the spin decay from the |0g state to the Boltzmann-distributed population. The 0.374 mV offset originates from the spin-independent PL signal caused by the readout pulse being present in only one of the two half-cycles.

Fig. 3.

(Color online) (a) Pulse sequences programmed to measure the spin T1 decay of the NV ground state, and a multi-spin representation showing the set of pure spin state vectors that constitute the NV spin ensemble at selected times along the pulse sequence. τref=15 ms, τlaser=5 μs, and τdelay is varied. (b) NV center T1 decay measured with lock-in detection. The total measurement time is ∼3 min.

Fig. 3.

(Color online) (a) Pulse sequences programmed to measure the spin T1 decay of the NV ground state, and a multi-spin representation showing the set of pure spin state vectors that constitute the NV spin ensemble at selected times along the pulse sequence. τref=15 ms, τlaser=5 μs, and τdelay is varied. (b) NV center T1 decay measured with lock-in detection. The total measurement time is ∼3 min.

Close modal

As discussed in Sec. III, an oscillating magnetic field B1 can be used to controllably rotate the NV ground-state electronic spin. To demonstrate this, we employ another channel of the Pulse Blaster (denoted “CH2”) to pulse-modulate the output of the MW source and create a sequence of oscillating B1 pulses, as shown in Fig. 4(a) (see also Secs. IV C and IV D for details of the setup). We start by measuring the spin transition spectrum of the NV center ensemble in zero magnetic field. As before, an initial laser pulse is used to initialize the NV into the |0 state. A subsequent MW pulse of fixed length τmw (T2*) then attempts to rotate the spins. When the MW frequency is equal to the |0g|±1g transition frequency, we rotate the spins about the +X axis.23 The next laser pulse will serve as the readout pulse. This procedure is referred to as optically detected magnetic resonance (ODMR), as the optical signal is reduced in magnitude when the spins are rotated from the |0g state into the |±1g state. Using a lock-in amplifier, the resonance condition will result in a large, positive magnitude reading, which represents the absolute value of the change in signal under resonance. Out of resonance the MW pulses have no effect on the lock-in magnitude. Figure 4(b) shows the zero magnetic field ODMR spectrum. The main peak is centered at D = 2.87 GHz, with a spin-strain splitting E = 7 MHz which lifts the degeneracy of the |0g|±1g transition. Additionally, the side peaks visible are a result of hyperfine interaction (A = 128 MHz) of the subset of NV spins that are also coupled to a nearest neighbor C13 nucleus. The side peaks are 3.3% of the center peak intensity, which corresponds to the probability of finding a C13 nucleus next to an NV site.

Fig. 4.

(Color online) (a) Pulse sequence to perform pulsed-ODMR spectroscopy and Rabi oscillations, and multi-spin representation showing the set of pure spin state vectors on a Bloch sphere for NV centers of one particular orientation (i.e., all spins are resonant with the MW frequency). τref=2.5 ms, τlaser=5μs, τpadding=1μs, τmw=5μs for pulsed-ODMR, and τmw is varied for Rabi oscillations. Laser and MW pulses sequences (CH1 and CH2) are repeated N = 250 times within each half-cycle to increase the signal strength. (b) Zero-field pulsed-ODMR spectrum. The main ODMR peak is centered at D = 2.87 GHz. The splitting E = 7 MHz is a result of lifting the |±1g degeneracy due to a spin-strain interaction [corresponding term not included in Eq. (1)]. The smaller side peaks are split by A = 128 MHz, and are due to the hyperfine interaction of the NV centers coupled to a nearest neighbor C13 nucleus with a nuclear spin of ±1/2 [corresponding term not included in Eq. (1)]. The total measurement time is ∼2 min. (c) Pulsed-ODMR signal obtained with a permanent magnet placed in 3 arbitrary locations within the vicinity of the sample. The B0 magnitudes follow B0A<B0B<B0C. The total measurement time is ∼6 min for each magnet position. (d) Peak from (c) for B0C at the resonant frequency of the MW antenna [compare Fig. 2(d)]. The peak fits to a Lorentzian centered at νODMR=2.49 GHz and linewidth ΓFWHM=14.2 MHz. (e) Rabi oscillations with MW frequency set to νODMR=2.49 GHz. Measurement time is ∼8 min.

Fig. 4.

(Color online) (a) Pulse sequence to perform pulsed-ODMR spectroscopy and Rabi oscillations, and multi-spin representation showing the set of pure spin state vectors on a Bloch sphere for NV centers of one particular orientation (i.e., all spins are resonant with the MW frequency). τref=2.5 ms, τlaser=5μs, τpadding=1μs, τmw=5μs for pulsed-ODMR, and τmw is varied for Rabi oscillations. Laser and MW pulses sequences (CH1 and CH2) are repeated N = 250 times within each half-cycle to increase the signal strength. (b) Zero-field pulsed-ODMR spectrum. The main ODMR peak is centered at D = 2.87 GHz. The splitting E = 7 MHz is a result of lifting the |±1g degeneracy due to a spin-strain interaction [corresponding term not included in Eq. (1)]. The smaller side peaks are split by A = 128 MHz, and are due to the hyperfine interaction of the NV centers coupled to a nearest neighbor C13 nucleus with a nuclear spin of ±1/2 [corresponding term not included in Eq. (1)]. The total measurement time is ∼2 min. (c) Pulsed-ODMR signal obtained with a permanent magnet placed in 3 arbitrary locations within the vicinity of the sample. The B0 magnitudes follow B0A<B0B<B0C. The total measurement time is ∼6 min for each magnet position. (d) Peak from (c) for B0C at the resonant frequency of the MW antenna [compare Fig. 2(d)]. The peak fits to a Lorentzian centered at νODMR=2.49 GHz and linewidth ΓFWHM=14.2 MHz. (e) Rabi oscillations with MW frequency set to νODMR=2.49 GHz. Measurement time is ∼8 min.

Close modal

Figure 4(c) shows further ODMR spectra recorded for arbitrary magnetic fields B0A,B0B,B0C, introduced by placing a permanent magnet in the proximity of the diamond crystal. The energy splitting of the |±1g state depends on the orientation of the B0 field with respect to the NV axis, allowing us to distinguish between the four different NV orientations in our ODMR spectra, and resolving a total of eight transitions for the field strengths B0A and B0C, and six transitions in B0B due to an overlap of two pairs of transitions (see also Sec. III).

The term Rabi oscillations refers to the driven evolution of a two-level system that manifests as the circular movement of the system's state vector around the Bloch sphere.6 Successful demonstration of Rabi oscillations means that we have achieved coherent control, an important step in demonstrating the viability of any quantum system (see also Sec. II). Figure 4(d) shows a detailed ODMR spectrum of the |0g|1g transition for B0C. For this particular field, we have roughly aligned the magnetic field from the permanent magnet such that its direction is parallel to one of the three [11¯1¯], [1¯11¯], [1¯1¯1] NV center axes, and from matching the spectrum in Fig. 4(c) to theory, we can extract B0=14.2 mT with an angle of 13.6° to the best-aligned NV axis (see Fig. 4(d) inset). Furthermore, the position of the permanent magnet was adjusted such that the |0g|1g ODMR transition frequency coincides with the resonant frequency of the PCB antenna (see Sec. IV C). This way, we subject our NV spins to the largest B1 field and hence achieve the fastest Rabi oscillation frequencies.19 This is important as short Rabi periods compared to the driven coherence time ensure a greater number of clearly observable oscillations, allowing us to perform the multi-pulse sequences described in Sec. V D. A larger B1 field will additionally result in an ODMR peak with the largest peak intensity and broadest linewidth.

To observe Rabi oscillations, we set the driving frequency νmw to be in resonance with the ODMR transition frequency νODMR=2.49 GHz, and vary the MW pulse length τmw while recording the lock-in signal. We observe oscillations in the spin signal as a function of pulse length, as shown in Fig. 4(e), indicating coherent rotations of the spin around the Bloch sphere. As we have selected only one of the eight visible transitions in Fig. 4(c), we are only coherently driving NV centers of a single axis orientation and only from the |0g to the |1g state. The oscillations can be fitted to an exponentially decaying sinusoid

VLI=A·sin(2πΩRτmw+ϕ)·exp(τmwT2Rabi)+Bτmw+C,
(3)

where A is the Rabi oscillation amplitude, B is a linear term included due to an observed increase in signal with increasing τmw (possibly due to heating of the sample due at long τmw), C is an offset, ΩR=2.69±0.02 MHz is the Rabi frequency, ϕ=1.24±0.09 radians is the phase-offset (π/2 for ideal Rabi oscillations), and T2Rabi=1.12±0.14μs is the driven coherence time of the spin.24,25 The T2Rabi coherence time describes how long the |0g|1g transition in the ensemble can be driven before the ensemble dephases into a mixed-state. This is due to both the inhomogeneity of the B1 field over the region of the sample in focus, and the inhomogeneous broadening of resonance frequencies over the NV centers being measured.

From the Rabi oscillations, we can calibrate the exact π/2- and π-pulse lengths as τπ/2=72 ns and τπ=144 ns. These pulse times will be important for the experiments in Sec. V D, where we construct dynamical decoupling pulse sequences out of π/2- and π-pulses.

In the next experiment, we measure the coherence time T2 of the NV centers. T2 is the time over which a well-defined phase relation between a quantum state and a reference clock can be preserved, before noise and coupling to the environment randomize it. Compared to quantum systems operating at colder temperatures, room temperature systems are subject to a large amount of thermal energy that leads to a particularly noisy environment. As it is much easier to contemplate practical room temperature quantum systems than those that require complex cooling mechanisms, it becomes especially interesting to investigate their room temperature coherence times. T2 is also one of the key metrics for comparing different quantum systems, however, as there are different definitions of T2, it important to use the same metric when comparing different quantum systems. One such coherence time was already determined in Fig. 4(e) and is the coherence time of the system while it is driven (T2Rabi). In the following experiments, we look at the coherence time during free precession of the spins using different dynamical decoupling sequences.

Dynamical decoupling methods make use of refocusing pulses, as in the Hahn-echo sequence26 [see also Fig. 5(a)], to refocus the phases of spins that precess at slightly different rates. Here, one differentiates between inhomogeneous dephasing, where the transition frequencies of individual NV centers are shifted due to their local environments, e.g., due to static inhomogeneities in the sample itself or in the applied B0 magnetic field, and homogeneous dephasing where the transition frequencies of all NV centers are broadened by similar amounts, e.g., due to dynamic noise or the finite lifetime of the quantum state. Sequences consisting of refocusing pulses are very good at refocusing static shifts in transition frequencies—a single refocusing pulse (as in the Hahn echo) is sufficient to decouple the quantum system from static noise.26 Noise of any frequency is refocused as long as its frequency is much lower or much higher than the refocusing pulse repetition frequency, which can be best understood in the filter function formalism as described in Refs. 27 and 28. In fact, changing the pulse repetition frequency changes the frequency spectrum the spin remains sensitive to, which allows conducting detailed investigations of the noise spectrum.28–31 

Fig. 5.

(Color online) (a) Dynamical decoupling pulse sequence, with one refocusing pulse, where either a Xπ-pulse, or Yπ-pulse can be chosen as the refocusing pulse. τdelay is varied, and the experiment is performed under the same experimental conditions as in Fig. 4(e), with τπ/2=72 ns and τπ=144 ns. Laser and MW pulses sequences (CH1, CH2, CH3) are repeated N = 100 times within each half-cycle to increase the signal strength. The multi-spin representation shows the evolution of a set of pure spin state vectors on the Bloch sphere throughout the sequence. (b) Coherence time measurement for the echo sequence as in (a) with the MW π-pulse applied along the +X (Hahn echo) or +Y axis (1-pulse CPMG). For long free precession times, the ensemble enters a mixed state, as can be seen from the convergence of the two spin signals to a common value. The solid lines are fits to an exponential decay. Measurement time is ∼4 min for each scan.

Fig. 5.

(Color online) (a) Dynamical decoupling pulse sequence, with one refocusing pulse, where either a Xπ-pulse, or Yπ-pulse can be chosen as the refocusing pulse. τdelay is varied, and the experiment is performed under the same experimental conditions as in Fig. 4(e), with τπ/2=72 ns and τπ=144 ns. Laser and MW pulses sequences (CH1, CH2, CH3) are repeated N = 100 times within each half-cycle to increase the signal strength. The multi-spin representation shows the evolution of a set of pure spin state vectors on the Bloch sphere throughout the sequence. (b) Coherence time measurement for the echo sequence as in (a) with the MW π-pulse applied along the +X (Hahn echo) or +Y axis (1-pulse CPMG). For long free precession times, the ensemble enters a mixed state, as can be seen from the convergence of the two spin signals to a common value. The solid lines are fits to an exponential decay. Measurement time is ∼4 min for each scan.

Close modal

In Fig. 5(a), we show the pulse sequence used to measure the Hahn echo coherence time T2Hahn, while the Bloch spheres at the bottom of the panel give an indication of the spin orientations at specific points of the sequence. A first Xπ/2-pulse rotates the spin to the +Y direction on the Bloch sphere. The spins are left to freely precess for a time τdelay, before a Xπ-pulse rotates them to the -Y direction. Any phase that they might have accumulated with respect to the rotating frame until then (as indicated by the coloured arrows) will be unwound in the second free precession time τdelay, before a final Xπ/2-pulse rotates them to the +Z direction for readout. We present the corresponding experimental data in Fig. 5(b). Here, τdelay is increased until any phase relation is randomized and the spin signal saturates, indicating a completely mixed state. The spin refocusing pulse can be applied along either the +X (Hahn echo) or +Y axis (using IQ modulation as described in Sec. IV C), with the system entering into the same mixed-state in either case as shown in Fig. 5(b). We fit the data to an exponential decay and extract a coherence time of T2Hahn=1.2±0.2μs.

Instead of a single refocusing pulse, multiple such refocusing pulses can be applied to further extend the spin coherence time. However, performing multiple refocusing pulses about the +X axis leads to an accumulation of pulse errors. Hence, refocusing pulses about the +Y axis – known as Carr-Purcell-Meiboom-Gill (CPMG) spin-echo pulse sequence32,33—are more advantageous. For the CPMG pulse sequence shown in Fig. 6(a), NCPMG is the total number of Yπ-pulses, and t=NCPMGτdelay is the total free precession time of the NV spin. The CPMG pulse sequence acts as a bandpass filter, increasing the number of refocusing pulses for a fixed τdelay sharpens the filter, whereas decreasing the time τdelay between refocusing pulses has the effect of shifting the center of the filter to higher frequency. The bandpass center frequency is given by π/τdelay.28 

Fig. 6.

(Color online) (a) Pulse sequences for the CPMG spin-echo sequence, where NCPMG is number of Yπ refocusing pulses. Laser and MW pulse sequences (CH1, CH2, CH3) are repeated N = 100 times within each half-cycle to increase the signal strength. (b) Examples of CPMG measurements for different NCPMG. The measurement time is ∼4 min for each scan. (c) Extracted T2CPMG for all CPMG scans.

Fig. 6.

(Color online) (a) Pulse sequences for the CPMG spin-echo sequence, where NCPMG is number of Yπ refocusing pulses. Laser and MW pulse sequences (CH1, CH2, CH3) are repeated N = 100 times within each half-cycle to increase the signal strength. (b) Examples of CPMG measurements for different NCPMG. The measurement time is ∼4 min for each scan. (c) Extracted T2CPMG for all CPMG scans.

Close modal

In Fig. 6(b), we plot the result of CPMG sequences with an increasing number of refocusing pulses NCPMG. For the same total free precession time, a larger NCPMG implies a shorter τdelay, and hence a larger center frequency of the CPMG filter function.34 The normalized lock-in signal as a function of total free precession time can be fitted to C(t)=Aexp[(t/T2CPMG)n]. In Fig. 6(c), we plot the extracted T2CPMG as a function of NCPMG and observe a clear correlation between T2CPMG(NCPMG) and NCPMG, suggesting that the noise spectral density of the NV electron's environment reduces towards higher frequencies. We were able to fit these data with a function of the form T2CPMG(NCPMG)=B(NCPMG)α with α=0.77±0.13, which is within the bounds experimentally determined in Ref. 34 for a CVD grown diamond with a large NV density (1016cm3).

We have presented a cost-effective experimental setup that is suitable for demonstrating coherent spin control concepts in an undergraduate teaching laboratory environment. The experiments implement the optically detected magnetic resonance technique at room temperature on NV centers in diamond, and the setup is constructed using the minimal necessary optics and electronics components. Students will develop an intuitive feeling for quantum spin physics, gain first-hand experience in controlling a quantum system, and have the freedom to develop unique pulse sequences and observe the results in real-time. The use of a high-density NV diamond sample provides a large signal, making the measurements insensitive to misalignment of the optics and exposure to high ambient light levels—as is desirable for an undergraduate lab setup.

The authors would like to thank Jean-Philippe Tetienne for useful discussions, and Ye Kuang, Meilin Song, and Yiwen Zhang for their contributions. The authors acknowledge support from the School of Electrical Engineering and Telecommunications at UNSW Sydney, and the Australian Research Council (No. CE170100012). H.R.F. acknowledges the support of an Australian Government Research Training Program Scholarship. J.J.P. was supported by an Australian Research Council Discovery Early Career Research Award (No. DE190101397).

Table I.

List of parts for “Optics” section of experimental set-up, shown in Fig. 2(b).

ItemSupplierPart numberApplicationPrice (USD) (December 17, 2019)QtyTotal (USD)
Housing 
Aluminum Breadboard Thorlabs MB3045/M Base plate 199.45 199.45 
Enclosure Thorlabs XE25C7/M Enclosure for all optics 199.11 199.11 
Optical Excitation 
SM Fiber-Pigtailed Laser Diode Thorlabs LP520-SF15 Excitation laser 717.45 717.45 
Laser Diode ESD Protection Thorlabs SR9HA Laser diode protection 54.11 54.11 
Fiber Adapter Plates Thorlabs SM1FC - FC/PC Laser fiber coupling 31.38 31.38 
Kinematic Mount Thorlabs KM100T Laser mounting 70.87 70.87 
50 mm Pedestal Pillar Post Thorlabs RS2P/M Laser mounting 28.95 28.95 
Aspheric Lens Thorlabs C280TMD-A Laser collimation lens 85.49 85.49 
SM1 to M9 Lens Cell Adapter Thorlabs S1TM09 Lens mounting 24.35 24.35 
SM1 Lens Tube 1.50in Thorlabs SM1L15 Lens mounting 16.17 16.17 
Longpass 550 nm dichroic mirror Thorlabs DMLP550 Excitation/detection filtering 182.88 182.88 
Kinematic Mount Thorlabs KM100 Dichroic mirror mount 39.86 39.86 
50 mm Pedestal Pillar Post Thorlabs RS2P/M Dichroic mirror mount 28.95 28.95 
Microscope Objective Olympus MS Plan 50×/0.80NA Excitation lens 744 744 
RMS Threaded Cage Plate Thorlabs CP42/M Objective lens mount 32.78 32.78 
50 mm Pedestal Pillar Post Thorlabs RS2P/M Objective lens mount 28.95 28.95 
5 mm Post Spacer Thorlabs RS5M Objective lens mount 8.17 8.17 
Sample Mount 
3-axis Sample Positioner Thorlabs MBT616D/M Stage for diamond sample 1184.92 1184.92 
Blank Device Mount Thorlabs HBB002 Sample mount 56.55 56.55 
Imaging 
Protected Silver Mirror Thorlabs PF10-03-P01 Imaging mirror 53.58 53.58 
Flip Mount Thorlabs TRF90/M Mirror mounting 88.73 88.73 
38 mm Pedestal Pillar Post Thorlabs RS1.5P4M Mirror mounting 25.21 25.21 
600 nm Longpass Filter (optional) Thorlabs FEL0600 Imaging filtering 80.62 80.62 
900 nm Shortpass filter (optional) Thorlabs FES0900 Imaging filtering 80.62 80.62 
SM1 Lens Tube 0.50in (optional) Thorlabs SM1L05 Filter mounting 12.97 25.94 
Achromatic Doublet Thorlabs AC254-125-A Imaging lens 81.16 81.16 
SM1 Lens Tube 1.50in Thorlabs SM1L15 Lens mounting 16.17 16.17 
CMOS Camera Thorlabs DCC1545M Imaging camera 387.92 387.92 
SM1 Lens Tube Spacer 3.50in Thorlabs SM1S35 Lens/camera mounting 25.53 25.53 
SM1 Cage Plate Thorlabs CP33/M Lens/camera mounting 16.89 33.78 
50 mm Pedestal Pillar Post Thorlabs RS2P/M Objective lens mount 28.95 57.9 
5 mm Post Spacer Thorlabs RS5M Objective lens mount 8.17 16.34 
Detection 
Protected Silver Mirror Thorlabs PF10-03-P01 Detection mirror 53.58 107.16 
Kinematic Mount Thorlabs KM100 Mirror mounting 39.86 79.72 
50 mm Pedestal Pillar Post Thorlabs RS2P/M Mirror mounting 28.95 57.9 
600 nm Longpass Filter Thorlabs FEL0600 Detection filtering 80.62 80.62 
900 nm Shortpass filter Thorlabs FES0900 Detection filtering 80.62 80.62 
SM1 Lens Tube 0.50in Thorlabs SM1L05 Filter mounting 12.97 25.94 
Aspheric Lens Thorlabs C260TMD-B Fiber coupling lens 85.49 85.49 
SM1 to M9 Lens Cell Adapter Thorlabs S1TM09 Lens mount 24.35 24.35 
XY-Axes Translation Mount Thorlabs ST1XY-D/M Fiber alignment 517.26 517.26 
38 mm Pedestal Pillar Post Thorlabs RS1.5P4M Fiber coupler mounting 25.21 25.21 
4 mm Post Spacer Thorlabs RS4M Fiber coupler mounting 7.9 7.9 
Z-Axis Translation Mount Thorlabs SM1Z Fiber alignment 205.6 205.6 
2-inch Rods Thorlabs ER2 Fiber alignment 6.28 25.12 
Fiber Adapter Plates Thorlabs SM1FC - FC/PC Fiber coupling 31.38 31.38 
50 micron FC/PC Multimode Fiber Thorlabs M42L01 Detection fiber 70.87 70.87 
Si Photodetector Thorlabs DET025AFC/M Signal detection 306 306 
Mounting 
M6 Clamping Fork Thorlabs CF125C/M Mounting 11.69 105.21 
Sample 
CVD Diamond Sample Element Six 145–500-0274–01 Sample 130 130 
(e.g., SC Plate CVD ⟨100⟩) 
B0 and B1 Magnetic Fields 
PCB Antennas (pack of 5) Circuit Labs B1 Microwave Excitation 72.16 72.16 
Neodymium Block Magnets 10 × 10 × 5 mm AMF Magnets B0 Static Magnetic Field 2.3 9.2 
Total Optics Cost: 6780.6 
ItemSupplierPart numberApplicationPrice (USD) (December 17, 2019)QtyTotal (USD)
Housing 
Aluminum Breadboard Thorlabs MB3045/M Base plate 199.45 199.45 
Enclosure Thorlabs XE25C7/M Enclosure for all optics 199.11 199.11 
Optical Excitation 
SM Fiber-Pigtailed Laser Diode Thorlabs LP520-SF15 Excitation laser 717.45 717.45 
Laser Diode ESD Protection Thorlabs SR9HA Laser diode protection 54.11 54.11 
Fiber Adapter Plates Thorlabs SM1FC - FC/PC Laser fiber coupling 31.38 31.38 
Kinematic Mount Thorlabs KM100T Laser mounting 70.87 70.87 
50 mm Pedestal Pillar Post Thorlabs RS2P/M Laser mounting 28.95 28.95 
Aspheric Lens Thorlabs C280TMD-A Laser collimation lens 85.49 85.49 
SM1 to M9 Lens Cell Adapter Thorlabs S1TM09 Lens mounting 24.35 24.35 
SM1 Lens Tube 1.50in Thorlabs SM1L15 Lens mounting 16.17 16.17 
Longpass 550 nm dichroic mirror Thorlabs DMLP550 Excitation/detection filtering 182.88 182.88 
Kinematic Mount Thorlabs KM100 Dichroic mirror mount 39.86 39.86 
50 mm Pedestal Pillar Post Thorlabs RS2P/M Dichroic mirror mount 28.95 28.95 
Microscope Objective Olympus MS Plan 50×/0.80NA Excitation lens 744 744 
RMS Threaded Cage Plate Thorlabs CP42/M Objective lens mount 32.78 32.78 
50 mm Pedestal Pillar Post Thorlabs RS2P/M Objective lens mount 28.95 28.95 
5 mm Post Spacer Thorlabs RS5M Objective lens mount 8.17 8.17 
Sample Mount 
3-axis Sample Positioner Thorlabs MBT616D/M Stage for diamond sample 1184.92 1184.92 
Blank Device Mount Thorlabs HBB002 Sample mount 56.55 56.55 
Imaging 
Protected Silver Mirror Thorlabs PF10-03-P01 Imaging mirror 53.58 53.58 
Flip Mount Thorlabs TRF90/M Mirror mounting 88.73 88.73 
38 mm Pedestal Pillar Post Thorlabs RS1.5P4M Mirror mounting 25.21 25.21 
600 nm Longpass Filter (optional) Thorlabs FEL0600 Imaging filtering 80.62 80.62 
900 nm Shortpass filter (optional) Thorlabs FES0900 Imaging filtering 80.62 80.62 
SM1 Lens Tube 0.50in (optional) Thorlabs SM1L05 Filter mounting 12.97 25.94 
Achromatic Doublet Thorlabs AC254-125-A Imaging lens 81.16 81.16 
SM1 Lens Tube 1.50in Thorlabs SM1L15 Lens mounting 16.17 16.17 
CMOS Camera Thorlabs DCC1545M Imaging camera 387.92 387.92 
SM1 Lens Tube Spacer 3.50in Thorlabs SM1S35 Lens/camera mounting 25.53 25.53 
SM1 Cage Plate Thorlabs CP33/M Lens/camera mounting 16.89 33.78 
50 mm Pedestal Pillar Post Thorlabs RS2P/M Objective lens mount 28.95 57.9 
5 mm Post Spacer Thorlabs RS5M Objective lens mount 8.17 16.34 
Detection 
Protected Silver Mirror Thorlabs PF10-03-P01 Detection mirror 53.58 107.16 
Kinematic Mount Thorlabs KM100 Mirror mounting 39.86 79.72 
50 mm Pedestal Pillar Post Thorlabs RS2P/M Mirror mounting 28.95 57.9 
600 nm Longpass Filter Thorlabs FEL0600 Detection filtering 80.62 80.62 
900 nm Shortpass filter Thorlabs FES0900 Detection filtering 80.62 80.62 
SM1 Lens Tube 0.50in Thorlabs SM1L05 Filter mounting 12.97 25.94 
Aspheric Lens Thorlabs C260TMD-B Fiber coupling lens 85.49 85.49 
SM1 to M9 Lens Cell Adapter Thorlabs S1TM09 Lens mount 24.35 24.35 
XY-Axes Translation Mount Thorlabs ST1XY-D/M Fiber alignment 517.26 517.26 
38 mm Pedestal Pillar Post Thorlabs RS1.5P4M Fiber coupler mounting 25.21 25.21 
4 mm Post Spacer Thorlabs RS4M Fiber coupler mounting 7.9 7.9 
Z-Axis Translation Mount Thorlabs SM1Z Fiber alignment 205.6 205.6 
2-inch Rods Thorlabs ER2 Fiber alignment 6.28 25.12 
Fiber Adapter Plates Thorlabs SM1FC - FC/PC Fiber coupling 31.38 31.38 
50 micron FC/PC Multimode Fiber Thorlabs M42L01 Detection fiber 70.87 70.87 
Si Photodetector Thorlabs DET025AFC/M Signal detection 306 306 
Mounting 
M6 Clamping Fork Thorlabs CF125C/M Mounting 11.69 105.21 
Sample 
CVD Diamond Sample Element Six 145–500-0274–01 Sample 130 130 
(e.g., SC Plate CVD ⟨100⟩) 
B0 and B1 Magnetic Fields 
PCB Antennas (pack of 5) Circuit Labs B1 Microwave Excitation 72.16 72.16 
Neodymium Block Magnets 10 × 10 × 5 mm AMF Magnets B0 Static Magnetic Field 2.3 9.2 
Total Optics Cost: 6780.6 
Table II.

List of parts for “Electronics” section of experimental set-up, shown in Fig. 2(a).

ItemSupplierPart numberApplicationPrice (USD) (December 17, 2019)QtyTotal (USD)
USB Pulse Blaster SpinCore PBESR-PRO-250-USB Pulse Sequences 4485 4485 
Dual Phase Lock-In Ametek 5210 Lock-in detection 2000 2000 
Windows PC 2000 2000 
6 GHz Microwave Source SignalCore SC800 Microwave Drive 1295 1295 
Benchtop 3-Channel PSU Newark HM7042-5.02 Microwave Drive Power 1155 1155 
RF Amplifier Mini-Circuits ZQL-2700MLNW+ Microwave Drive 304.95 304.95 
IQ Modulator Texas Instr. TRF370417EVM Microwave Drive 199 199 
12V DC Wall Adapter Thorlabs LDS12B Home-built current source 85.22 85.22 
RS232 Serial Adapter StarTech ICUSB232DB25 Lock-in detection 20.99 20.99 
BNC-BNC Coaxial Thorlabs 2249-C-48 TTL Signals 19.29 96.45 
SMA-SMA Coaxial 12-inch Thorlabs CA2912 Microwave interconnects 15.69 62.76 
SMA 50-ohm termination Mini-Circuits ANNE-50X IQ Modulator 15.95 31.9 
BNC-SMA Adapter Thorlabs T4290 IQ Modulator 14.07 28.14 
USB A-Mini B Cable Thorlabs USB-AB-72 Microwave Source 8.87 8.87 
USB A-B Cable Thorlabs USB-A-79 Pulse Blaster 8.87 8.87 
BNC-Banana Adapter Thorlabs T1452 Laser Diode ESD Protection 8.65 8.65 
Banana Patch Cable Thorlabs T13120(2) Microwave Drive Power 7.31 29.24 
Total Electronics Cost: 11820.04 
ItemSupplierPart numberApplicationPrice (USD) (December 17, 2019)QtyTotal (USD)
USB Pulse Blaster SpinCore PBESR-PRO-250-USB Pulse Sequences 4485 4485 
Dual Phase Lock-In Ametek 5210 Lock-in detection 2000 2000 
Windows PC 2000 2000 
6 GHz Microwave Source SignalCore SC800 Microwave Drive 1295 1295 
Benchtop 3-Channel PSU Newark HM7042-5.02 Microwave Drive Power 1155 1155 
RF Amplifier Mini-Circuits ZQL-2700MLNW+ Microwave Drive 304.95 304.95 
IQ Modulator Texas Instr. TRF370417EVM Microwave Drive 199 199 
12V DC Wall Adapter Thorlabs LDS12B Home-built current source 85.22 85.22 
RS232 Serial Adapter StarTech ICUSB232DB25 Lock-in detection 20.99 20.99 
BNC-BNC Coaxial Thorlabs 2249-C-48 TTL Signals 19.29 96.45 
SMA-SMA Coaxial 12-inch Thorlabs CA2912 Microwave interconnects 15.69 62.76 
SMA 50-ohm termination Mini-Circuits ANNE-50X IQ Modulator 15.95 31.9 
BNC-SMA Adapter Thorlabs T4290 IQ Modulator 14.07 28.14 
USB A-Mini B Cable Thorlabs USB-AB-72 Microwave Source 8.87 8.87 
USB A-B Cable Thorlabs USB-A-79 Pulse Blaster 8.87 8.87 
BNC-Banana Adapter Thorlabs T1452 Laser Diode ESD Protection 8.65 8.65 
Banana Patch Cable Thorlabs T13120(2) Microwave Drive Power 7.31 29.24 
Total Electronics Cost: 11820.04 
Fig. 7.

(Color online) Schematic of the custom current source used in this experiment, broken down into the three main blocks. (a) The circuitry supplying the current to the diode. U3 is an off-the-shelf current source integrated circuit that has the output current set by R3 and R4 to ∼165 mA. As U3 requires some time to settle to a steady state current, if we were to modulate this current directly, we would not be able to operate at the desired bandwidth of 10 MHz. Thus we construct a current mirror using Q6; a matched pair of N-channel MOSFETs. The mirror sources 165 mA through the diode, unless the connection is interrupted by Q8. This allows U3 to output a constant, stable current, circumventing the switching speed problems. (b) Power supplies required for the operation of the circuit. There are two options available for the operation of this circuit. In “Option 1,” an external 12 V input can be provided, which is then regulated down to Vss by U2. In “Option 2,” a lab power supply can be directly connected to the circuit to provide the power. Vss was set to −9 V as a safety feature. The case of the laser diode is at the electrical potential of the anode and thus, this potential was set to ground. As a consequence, a negative supply voltage is required. For the current source that was used to obtain the results in this paper, there was a soldering error with the power supply provided by U2 in “Option 1,” and thus “Option 2” was used. We have populated another PCB with “Option 1” for another teaching setup and confirmed that it functions correctly. (c) Input logic and a level shifter. This block takes the TTL input signal and level-shifts it between ground and Vss. Such voltage levels are required to correctly drive the MOSFETs in block (a), as standard TTL levels would not be able to switch Q8 due to the presence of negative supply voltages.

Fig. 7.

(Color online) Schematic of the custom current source used in this experiment, broken down into the three main blocks. (a) The circuitry supplying the current to the diode. U3 is an off-the-shelf current source integrated circuit that has the output current set by R3 and R4 to ∼165 mA. As U3 requires some time to settle to a steady state current, if we were to modulate this current directly, we would not be able to operate at the desired bandwidth of 10 MHz. Thus we construct a current mirror using Q6; a matched pair of N-channel MOSFETs. The mirror sources 165 mA through the diode, unless the connection is interrupted by Q8. This allows U3 to output a constant, stable current, circumventing the switching speed problems. (b) Power supplies required for the operation of the circuit. There are two options available for the operation of this circuit. In “Option 1,” an external 12 V input can be provided, which is then regulated down to Vss by U2. In “Option 2,” a lab power supply can be directly connected to the circuit to provide the power. Vss was set to −9 V as a safety feature. The case of the laser diode is at the electrical potential of the anode and thus, this potential was set to ground. As a consequence, a negative supply voltage is required. For the current source that was used to obtain the results in this paper, there was a soldering error with the power supply provided by U2 in “Option 1,” and thus “Option 2” was used. We have populated another PCB with “Option 1” for another teaching setup and confirmed that it functions correctly. (c) Input logic and a level shifter. This block takes the TTL input signal and level-shifts it between ground and Vss. Such voltage levels are required to correctly drive the MOSFETs in block (a), as standard TTL levels would not be able to switch Q8 due to the presence of negative supply voltages.

Close modal
Table III.

List of parts required to assemble current driver circuit in Fig. 7.

ComponentDescriptionSupplierPart numberPrice (USD) (December 17, 2019)QtyTotal (USD)
U1 LDO 3V3 Regulator Element 14 1469102 1.6 1.6 
U2 Integrated Power Supply RS Online 798–1290 19.05 19.05 
U3 Current Source RS Online 779–9615 5.58 5.58 
J1 J3 J4 BNC Connector Element 14 1169739 7.25 21.75 
J2 Barrel Jack Element 14 1854514 1.25 1.25 
Q1 PFET Element 14 1510765 0.27 0.27 
Q8 NFET Element 14 2317616 0.2 0.2 
Q6 Dual NFET Element 14 2706719 1.07 1.07 
R1 1 kΩ Resistor 0603 Element 14 2284191 0.14 0.14 
R3 16.5 kΩ Resistor 0805 Element 14 2483960 0.46 0.46 
R4 1 Ω Resistor 0805 Element 14 2813642 0.31 0.31 
R5 10 kΩ Resistor 0603 Element 14 1652827 0.19 0.19 
R6 205 kΩ Resistor 0603 Element 14 2303251 0.01 0.01 
R7 75 kΩ Resistor 0603 Element 14 1799354 0.01 0.01 
R8 102 kΩ Resistor 0603 Element 14 2336927 0.21 0.21 
C1 C4 10 μF Capacitor 1206 Element 14 2118134 0.61 1.22 
C2 C3 C7 1 μF Capacitor 0603 Element 14 1845736 0.16 0.48 
C6 C8 C9 C10 C11 100 μF Capacitor 0603 Element 14 1709958 0.02 0.1 
C5 100 μF Capacitor 0603 Element 14 2354734 1.57 1.57 
PCB Seeed Studio 57.86 57.86 
Total PCB Cost: 113.33 
ComponentDescriptionSupplierPart numberPrice (USD) (December 17, 2019)QtyTotal (USD)
U1 LDO 3V3 Regulator Element 14 1469102 1.6 1.6 
U2 Integrated Power Supply RS Online 798–1290 19.05 19.05 
U3 Current Source RS Online 779–9615 5.58 5.58 
J1 J3 J4 BNC Connector Element 14 1169739 7.25 21.75 
J2 Barrel Jack Element 14 1854514 1.25 1.25 
Q1 PFET Element 14 1510765 0.27 0.27 
Q8 NFET Element 14 2317616 0.2 0.2 
Q6 Dual NFET Element 14 2706719 1.07 1.07 
R1 1 kΩ Resistor 0603 Element 14 2284191 0.14 0.14 
R3 16.5 kΩ Resistor 0805 Element 14 2483960 0.46 0.46 
R4 1 Ω Resistor 0805 Element 14 2813642 0.31 0.31 
R5 10 kΩ Resistor 0603 Element 14 1652827 0.19 0.19 
R6 205 kΩ Resistor 0603 Element 14 2303251 0.01 0.01 
R7 75 kΩ Resistor 0603 Element 14 1799354 0.01 0.01 
R8 102 kΩ Resistor 0603 Element 14 2336927 0.21 0.21 
C1 C4 10 μF Capacitor 1206 Element 14 2118134 0.61 1.22 
C2 C3 C7 1 μF Capacitor 0603 Element 14 1845736 0.16 0.48 
C6 C8 C9 C10 C11 100 μF Capacitor 0603 Element 14 1709958 0.02 0.1 
C5 100 μF Capacitor 0603 Element 14 2354734 1.57 1.57 
PCB Seeed Studio 57.86 57.86 
Total PCB Cost: 113.33 
Fig. 8.

(Color online) (a) and (b) Performance characterization of the current driver, showing (a) turn-on and (b) turn-off of the laser. The curve corresponding to the left axis is a copy of the pulse blaster TTL output that is used as an input for the current driver. The curve corresponding to the right axis is the output of the current driver at its (a) falling edge and (b) rising edge, respectively. The traces were measured with a Tektronix TDS3052 oscilloscope with 250 MHz bandwidth. The input impedances of both oscilloscope channels were 50 ∼ ω. The fall time of the current source output (turn-on time) is 1.6 ns and the rise time (turn-off time) is 27.0 ns.

Fig. 8.

(Color online) (a) and (b) Performance characterization of the current driver, showing (a) turn-on and (b) turn-off of the laser. The curve corresponding to the left axis is a copy of the pulse blaster TTL output that is used as an input for the current driver. The curve corresponding to the right axis is the output of the current driver at its (a) falling edge and (b) rising edge, respectively. The traces were measured with a Tektronix TDS3052 oscilloscope with 250 MHz bandwidth. The input impedances of both oscilloscope channels were 50 ∼ ω. The fall time of the current source output (turn-on time) is 1.6 ns and the rise time (turn-off time) is 27.0 ns.

Close modal
Fig. 9.

(Color online) Measurements comparing the HPHT diamond used for all experiments in the main text and a CVD diamond purchased from Element Six, listed in Appendix A. Measurements were taken in current mode (similar signal-to-noise ratios were observed for voltage and current mode) of the EG&G 5210 lock-in amplifier listed in  Appendix A. The PL emitted was 705 nW by the HPHT diamond and 0.75 nW by the CVD diamond, as measured with a power meter for ∼15 mW excitation power at λexc = 520 nm. (a) Zero-field ODMR comparison. Measurement time was ∼2 min for the HPHT diamond and ∼9 min for the CVD diamond for a spectrum with 200 data points. (b) Rabi oscillations comparison at νODMR = 2.53 GHz. Measurement time was ∼2 min for the HPHT diamond and ∼13 min for the CVD diamond for 60 data points. Fits were performed with Eq. (3), which gives T2Rabi=310±60 ns and ΩR=7.2±0.1 MHz for the HPHT diamond, and T2Rabi=450±90 ns and ΩR=5.2±0.1 MHz for the CVD diamond. In these measurements, T2Rabi is limited by the inhomogeneous broadening of the ensemble linewidth, e.g., due to strain and hyperfine coupling to nuclear spins, and the inhomogeneity of the B1 field. The PCB antenna used to perform these measurements had the same dimensions as described in Fig. 2(c), except with the center hole diameter d = 0.6 mm, different from the d2 = 1.0 mm used in the main text. While a smaller hole delivers a larger B1 field (hence increasing ΩR), a shorter T2Rabi is expected due to the increased inhomogeneity of the B1 field at the center of the hole. The higher ΩR of the HPHT diamond compared to that of the CVD diamond can be explained by the different projections of the B1 vector onto the NV axes being measured (Ref. 19).

Fig. 9.

(Color online) Measurements comparing the HPHT diamond used for all experiments in the main text and a CVD diamond purchased from Element Six, listed in Appendix A. Measurements were taken in current mode (similar signal-to-noise ratios were observed for voltage and current mode) of the EG&G 5210 lock-in amplifier listed in  Appendix A. The PL emitted was 705 nW by the HPHT diamond and 0.75 nW by the CVD diamond, as measured with a power meter for ∼15 mW excitation power at λexc = 520 nm. (a) Zero-field ODMR comparison. Measurement time was ∼2 min for the HPHT diamond and ∼9 min for the CVD diamond for a spectrum with 200 data points. (b) Rabi oscillations comparison at νODMR = 2.53 GHz. Measurement time was ∼2 min for the HPHT diamond and ∼13 min for the CVD diamond for 60 data points. Fits were performed with Eq. (3), which gives T2Rabi=310±60 ns and ΩR=7.2±0.1 MHz for the HPHT diamond, and T2Rabi=450±90 ns and ΩR=5.2±0.1 MHz for the CVD diamond. In these measurements, T2Rabi is limited by the inhomogeneous broadening of the ensemble linewidth, e.g., due to strain and hyperfine coupling to nuclear spins, and the inhomogeneity of the B1 field. The PCB antenna used to perform these measurements had the same dimensions as described in Fig. 2(c), except with the center hole diameter d = 0.6 mm, different from the d2 = 1.0 mm used in the main text. While a smaller hole delivers a larger B1 field (hence increasing ΩR), a shorter T2Rabi is expected due to the increased inhomogeneity of the B1 field at the center of the hole. The higher ΩR of the HPHT diamond compared to that of the CVD diamond can be explained by the different projections of the B1 vector onto the NV axes being measured (Ref. 19).

Close modal
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Supplementary Material