Current controllers for optimizing laser cooling on cold atom experiments

It is not uncommon to stumble upon what has become a familiar sight in both new and old cold atom laboratories—a collection of multi-channel bench-top power supplies, typically two channel 24 V/3 A, often on the floor of a laboratory with water cooling present (!), directly supplying current to three pairs of quasi-Helmholtz electromagnets. They are held together with zipties, vinyl tape, and/or epoxy; sometimes the number of turns contained within these electromagnets is known, often it is not, and coincidentally neither is the inductance, calculated or empirical. While it is often the case that the atoms are sufficiently cold after sub-Doppler laser cooling to proceed to further intermediate cooling techniques or directly to optical or magnetic traps, the physical questions of optimizing the atom number and temperature, and so phase-space density, are often hastily dismissed as time consuming. This is a trade in time and efficiency for simplicity and poorly placed pragmatism, and it bellies the fact that new students arrive with a new and different set of skills from their predecessors.

Computer controllable commercial current controllers are available, but a series of simple electronics circuits are capable of fulfilling this role from a single low noise power supply of the user’s choice and at a more affordable cost, with student education as an added benefit. The design, construction, and testing of these electronics is a learning experience that new students of laser cooling and trapping should not dismiss—there is physics, electronics, and good system design to be found in this exercise.

Here, we focus on a key application within cold atom physics—controlling the background and stray magnetic fields for realizing one of the sub-Doppler cooling techniques commonly employed, red-detuned σ⁺–σ⁻ polarization gradient cooling.^2–6 A more modern example from laser cooling and trapping that requires current and therefore applied magnetic field precision would be gray molasses cooling.^7–10 This tutorial is motivated by the disparity in reported laser cooling results using the same atomic species and sub-Doppler technique, as well as the intransigence experienced in laboratories about the inadequacy of using bench-top power supplies directly. Nominally, the aforementioned techniques should leave cooled ensembles at only a few recoil energies above the recoil limit, often the μK level for heavier atomic species. Practically, these temperatures are only obtained when stray magnetic fields that would modulate or shift the m_F states relative to one another are carefully controlled; this has been pointed out succinctly and long ago in common undergraduate/master’s level texts;^11,12 however, a brief summary of the known physics is called for.

Equation (2) is clear—for example, an ensemble of ⁸⁷Rb cooled to 5 μK implies that B < 7.7 × 10⁻⁵ T, so 77 μT.¹⁴ For scale, this is an order of magnitude less than the Earth’s own magnetic field (⁠$∼5×10−5$ T) in the laboratory! This magnitude of magnetic field is not daunting to realize or to establish control over—a back-of-the-envelope calculation can help here; what is required to cancel Earth’s ambient field in the laboratory? In the Helmholtz configuration, the magnetic field produced by a running current I is $BHelm=453/2μ0nIR$⁠. With modest n = 50-turn electromagnets of radius R = 10 cm, to generate a local field to compete with Earth’s field of 77 μT requires about 172 mA (assuming the axis of the two magnets is parallel to that of Earth’s field). In addition to Earth’s magnetic field, stray magnetic fields can be introduced by magnetic optomechanics or screws in the vacuum chamber, permanent magnets from nearby ion pumps, Zeeman slowers, or 2D MOTs, or even nearby experiments.¹⁵ Stray magnetic fields from these devices lead to typical corrections ranging from around 10–200 μT, implying currents up to about 400 mA for electromagnets in or near Helmholtz configurations—a higher current will generally be required for pairs of electromagnets falling well outside the Helmholtz conditions.

For an atomic ensemble of a few 10⁸ atoms generated with 25 mm optics and typical magneto-optical trap parameters and a typical vacuum system, there is typically a relatively wide range of applied magnetic field values that allow for a sufficient state degeneracy in red-detuned polarization gradient cooling.¹⁶ This is in stark contrast to techniques like gray molasses that require high field accuracy to realize optimal cooling. Typical bench-top power supplies offer LED displays elucidating the current applied down to the 10 mA or even 1 mA level—most boast analog control knobs, but some offer digital control. It is in this way that many laboratories are able to establish some level of control over stray magnetic fields to obtain cooling results $<25μ$K but often bottoming out near 10 μK. The electromagnet radius being too small, non-Helmholtz configurations, the number of turns vs the current fine tuning capability of the current supply, and other banalities of the experiment can easily lead the control knobs of such a bench-top current supply to be insufficient for establishing sufficient magnetic field resolution zero-field conditions to complete sub-Doppler cooling at the μK level.

It is a happy coincidence that bench-top supplies are sometimes sufficient as a current supply for bias/shim electromagnets in laboratories, despite few students doing the calculation to realize how often their experiments are actually amenable to this shortcut—or not.¹⁷ Temperatures ranging from 1 to 3 μK employing red-detuned σ⁺–σ⁻ polarization gradient cooling on the ⁸⁷Rb D2 line have been reported.^18,19 These results are partially facilitated by the vast series of improvements to laser cooling systems and architectures under the auspice of the development of mobile quantum technologies. These systems employ automated magnetic field control to maintain magnetic field stability, ensuring the continuity of the cooling results throughout the lifetime and location of the instrument. We present a version of this type of circuit here, based on the results of recent theses that facilitated modern atom chip and atom interferometer experiments.^19–30 

We present an integrated solution based upon a single low-cost high voltage and high current bipolar operational amplifier for controlling bias/shim electromagnets on a cold atom experiment, originally adapted for driving current in atom chip wires^20,22 and further modified for driving bias electromagnets for Raman spectroscopy and laser cooling.³¹ The Texas Instrument’s (TI) Burr–Brown products OPA549,³² functioning as single channel current sources, are used in the results presented here [see (a) of Fig. 1 for a schematic used in experiments]. This power operational amplifier can continuously output 8 A with modest heat sinking.³³ They are amenable to a parallel output configuration for increased controllable current output³² and can offer voltages amenable to driving electromagnets with significant resistance, ∼±4 V at 8 A directly from the chip. The chip is protected against overtemperature conditions (operating from −40 to +125 °C) and current overloads, as well as providing simple logic for disabling the output should these conditions be met or by other set conditions. There is a simple connection for a user-selected current limit (critical for electromagnets!), as well as for thermal shutdown indication and/or forced shutdown—this chip, as a current driver, does not require a power resistor in series with the output current path, instead sensing the load indirectly. The chip contains simple resistor controlled current limit functionality—a resistor or potentiometer connected between pins 6 and 8 will suffice, or connect them to realize the full current of the device. A small offset in the current limit circuit may introduce a variation of ±0.25 A for small currents; low output current applications may be better suited to other members of the family, like the OPA547 or OPA548.

Control systems offering bipolar or unipolar voltage control, from 1 to 10 V, can easily integrate with this current driver with some basic electronics before the non-inverting input to realize the full range of the device; one can even design further safety limits by limiting the control voltage.³⁴ While such a device can be employed in an inverting configuration, typically such driving power electronics are non-inverting to allow for active filtering to suppress high frequency noise and a reduction in loading effects on the source (i.e., the chip), a common find in specialty commercial current supplies. The gain of the non-inverting amplifier and voltage control input are both easily scaled, so control system agnostic. An optocoupler between any control system and current driving electronics is always strongly recommended, especially when using FETs and MOSFETs. This said, the author has designed to use this circuit without such precautions, typically, and has found little cause for concern.

It is common to add in a TTL control for fast switching of the circuit—an example implementation can be found in Zou’s thesis, Fig. B.4 on pg. 128.²⁹ This circuit is amenable to inclusion into a PID loop, either for canceling ambient fields in conjunction with a Hall sensor or even just to feedback and stabilize the output current in an application—an example can be found in Sewell’s thesis, Fig. 3.10 on pg. 55²⁰—wherein current stabilization comes from feedback via a sense resistor, in turn, fed into a differential amplifier for comparison to the control voltage. Various indicators, like output enable, thermal shutdown, and current direction, among others, are possible if not encouraged. The current noise density (1 pA/$Hz$ at 1 kHz) is far below what is required of the current driver for bias electromagnets and is sufficient for precision applications like current carrying wires in atom chips and for electromagnets driving magnetic fields required for precision spectroscopy. This chip has a gain bandwidth product of 900 kHz; for rf modulation, one might consider a different family of chips,³⁵ but for driving bias magnets, this is sufficient, even for rapid turning of magnetic fields in typical spin-polarized quantum gas experiments. The gain-bandwidth decreases in an approximately linear relationship to 870 kHz at 125 °C as the chip heats; it is mostly flat over the useable temperature range before thermal shutdown is enabled.

For current supplies, one needs to consider the current stability as a function of temperature. Of note are the aforementioned current noise density as well as the thermal resistance of the chip—1.4°C/W with an adequate heatsink³² or 30 °C/W without any thermal sink.³⁶ Under maximum current output, the current limit as a function of temperature is flat; at the maximum, there is a slight non-linearity on the approach to the maximum operation temperature. The input bias current also suffers a decrease, changing over the operational temperature range but is somewhat flatter near room temperature. Furthermore, for a given voltage powering circuit, the quiescent current suffers a quasi-linear decrease from room temperature to the maximum operating temperature. It is important the chip be well sunk to reduce these effects, despite the excellent qualities of the chip. Good operating procedure is also important, waiting to take data until the chip is thermalized. Finally, with the output disabled, there is still a typical leakage current of around ±200 μA; an attached transistor, triggered by the output disabled, can ensure this current does not leak to the application.

Other chip families and manufacturers can be made into similar operational amplifier based current supply circuits of varying characteristics without having to resort directly to FETs and/or MOSFETs. From TI, for example, the OPA family includes the likes of the OPA541, OPA544, OPA547, and OPA548 or even friends of the family like the LM1876 and related. In the atomic sources of the MIGA infrastructure,^19,27–30 the OPA547³⁷ is used, two in parallel for each channel (the OPA 548 would suffice as well, as a single chip).³⁸ The LM1876 can be employed in pulsed operation atomic experiments that require reduced power consumption—when the amplifiers are idle, they switch to a power conservation mode with external logic. More expensive options come from the likes of the PA02, PA16, and PA75 and other high current chips from Apex Microtechnology.³⁹ While these devices would be underutilized for bias electromagnets given their cost and capabilities, such high current operational amplifiers can be used to drive precision inductive loads with a similar circuit to that presented here and without a sense resistor. Be mindful of their current noise level, power dissipation requirements, and bandwidth with respect to the applied application. Furthermore, the majority of these chips are designed to drive current across resistive loads, not necessarily inductive loads—be prepared to create a RC snubber for your inductive load applications. These circuits are easily incorporated into existing experiments with a few extra analog voltage outputs to control the setpoint and a few TTL lines for fast switching of the circuit, and so the electromagnets,⁴⁰ if required, are perfect for PID loops and are readily integrated with Hall effect sensors for complete active feedback of the ambient magnetic field around an experiment.

To demonstrate these circuits in action, we present a ⁸⁷Rb ensemble undergoing red-detuned polarization gradient cooling; the circuit shown in Fig. 1 formed the basis for a 2U 19″ rack unit (depth 10 cm) with four OPA549 inside, three for each axis of compensation, and an extra axis for bias in an atom interferometer experiment.^25,31 The sequence, designed to generate cold atoms rapidly (total sub-Doppler cooling sequence $<$5 ms instead of a more typical 10–25 ms seen on BEC machines), but without optimizing the phase-space density, is as follows: a 3D MOT is loaded from a 2D MOT with a push beam; the 3D MOT electromagnets are switched off; after a dwell time of 3 ms to allow eddy currents to subside,⁴¹ the cooling begins. This involves a linear sweep of the detuning from −2.5Γ to −25Γ⁴² in 500 µs followed immediately by a linear sweep of the light intensity from a few I_sat to zero in 500 µs.⁴³ To exhibit the optimization of the temperature of the ensemble via the applied magnetic field, an iteration is performed over scans of the applied magnetic field from three pairs of shim electromagnets, starting with the X shim magnet, see (a) of Fig. 2, with a fixed time-of-flight of 10 ms and a fixed cooling sequence. Note that the MOT electromagnets are oriented along the Z axis while XY are perpendicular. Fluorescence detection illuminates a CCD camera (Pike 505b), and a 2D Gaussian fit routine, written in Python, extracts the σ_x and σ_y⁴⁴ of the ensemble.

Typically complete after two iterations, to ascertain the temperature, a full time-of-flight expansion of the ensemble is then performed (b) of Fig. 2, realizing a minimum temperature of 3 μK⁴⁶ and without magnetic shielding. This experiment would collect a few 10⁹ atoms in the 3D MOT, a few 10⁸ after the magnets are turned off, and end up with a few 10⁶ atoms at 3 μK. Lower temperatures with similar atom numbers have been reported; they are realized due to improvements in specific implementations of the technique for the atomic/laser/control system.^19,27,30

In addition to a role in sub-Doppler cooling techniques, this circuit is capable of sufficiently stable and precise current output for precision laser spectroscopy requiring applied magnetic fields (see Fig. 3); they are otherwise amenable to current stabilization using a sense resistor.²⁰ To explore this application, a 3D MOT of ⁸⁷Rb is loaded from a 2D MOT with a push beam to realize a loading rate in excess of $∼109$ atoms/s. The atoms are subjected to red-detuned σ⁺–σ⁻ polarization gradient cooling applied over the six 3D MOT beams, reaching 3 μK. The atoms undergo a simple optical pumping routine before being probed via spectroscopy, wherein after polarization gradient cooling, they are assured to be in the F = 2 manifold (equally distributed due to no magnetic field gradients⁴⁷) by a precautionary illumination of the dark state for 100 µs. An applied magnetic field is stepped on along a direction of 45° from X or Y but within the XY plane. A two-photon Raman pulse is applied to the ensemble; the two-photon detuning δ is scanned to explore the occupation density of the Zeeman sublevels via Raman spectroscopy. There is no appreciable time-of-flight expansion for this test.

A schematic diagram of the various allowed transitions using two-photon Raman transitions,^12,48 see (a) of Fig. 3, between the two hyperfine ground states of ⁸⁷Rb are shown, and in the linear, or in the low field limit (i.e., small applied magnetic field) Zeeman splitting regime. These internal energy level transitions, (i)–(iii) in Fig. 3, are Doppler-insensitive co-propagating transitions, here shown from the F = 2 to the F = 1 ground states. The applied magnetic field can be determined with high precision, see (b) of Fig. 3, if all the Stark effects, i.e., light shifts,⁴⁹ are controlled.

With all precautions taken and the system calibrated, including good operating protocol of the circuits such that they are at their steady operational temperature—a few shots is usually sufficient, with good heat sinks—one can then determine the applied magnetic field at the position of the ensemble with high precision and accuracy. The measurement precision is limited by the frequency uncertainty of the laser system (for Raman systems used in atom interferometry, easily Hz level) and is certainly better than the current stability of the OPA549 current driver, while the measurement accuracy is limited by the frequency chain and metrology of the laser system; this is certainly far superior to the current stability of the OPA549. In (b) of Fig. 3, the values are rounded to the hundred nT level,⁵⁰ which is more than sufficient to determine the stability of the applied field. In this experiment, we observe an applied field of 51.8 μT.

The stability of the circuit was put to the ultimate test in a deterministic run pattern,⁵¹ essentially turning an atom interferometer experiment into a lock-in amplifier.^25,31 In 36 12-h datasets, a modulation pattern included the change in the direction of the applied current to an electromagnet pair providing an applied magnetic field for driving counter-propagating Raman transitions. The modulation pattern, when demodulated and analyzed for contributions from errors in the magnetic field, revealed two results—one, and obviously, that the modulation pattern allowed us to measure and subsequently remove any error from the applied magnetic field (such an error snowballs into an error in the measured atom interferometer phase), and two, that there was no appreciable error to remove, the contribution to the measured atomic phase being well below the 1 mrad level (that is the state-of-the-art at the time of this tutorial), nearing the few μrad level. This is entirely expected, considering the electromagnet characteristics with the scaling of current noise to noise in the applied field and finally the transfer of that error induced on measuring occupation density in the magnetically insensitive Zeeman sublevels (m_F = 0 states).

The single chip current sources presented are shown to be capable of consistently producing 3 μK ⁸⁷Rb ensembles when used to control stray magnetic fields and correct field biases as part of red-detuned σ⁺–σ⁻ polarization gradient cooling. We further show these devices are applicable to precision spectroscopy via their application to two-photon Raman spectroscopy, demonstrating no inhomogeneous broaden and so an applied field where the transitions are not smeared out to be larger than the applied Rabi frequency. This tutorial provides a quick reference for how, with what, and why students and postdocs on cold atom experiments should design, build, and operate these simple circuits to optimize their laser cooling as well as maintain a level of knowledge where tabletop physics directly meets electronics.

D.O.S. would like to thank all the combative graduate students that made it obvious to those concerned, those being almost exclusively the authors, that a tutorial such as this could be relevant and necessary. The author would like to thank Valerijus “Val” Gerulis for his electrical engineering support and suggestions, as well as Joseph Junca, Xinhao Zou, and Paul Robert for being patient and studious PhD candidates.

The author has no conflicts to disclose.

D. O. Sabulsky: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

For information on these devices please consult your local laboratory electronics support staff and/or open a copy of The Art of Electronics. For all other inquiries and comments contact the corresponding author.