Rydberg electromagnetically induced transparency based laser lock to Zeeman sublevels with 0.6 GHz scanning range

Many present-day atomic, molecular, or precision spectroscopy experiments require a frequency-stabilized laser source, engineered to some extent via the frequency and the linewidth to address a particular atomic or molecular transition.^1–3 Frequently, optical absorption,⁴ optical cavities,^2,5 or frequency combs⁶ are used as frequency references to stabilize the laser. Some of the most common techniques for frequency locking include saturated absorption spectroscopy (SAS),⁷ Pound–Drever–Hall (PDH) locking,⁸ modulation transfer spectroscopy (MTS),⁹ fluorescence spectroscopy,¹⁰ and dichroic atomic vapor laser locking (DAVLL).¹¹ Another technique, electromagnetically induced transparency (EIT) locking,^12–15 can be exploited to lock the relative frequency of two or more lasers. This method is useful if one needs to access a narrow transition when a direct absorption signal is not feasible, for example, in the excitation of neutral atoms to Rydberg states.^16–22 The particular interest in Rydberg atoms lies in their potential as a platform for quantum computation,^23–26 quantum simulation,^27,28 and quantum repeater²⁹ technologies, due to their particular properties, such as the long lifetime of Rydberg states, strong dipole–dipole interactions, and the Rydberg blockade phenomenon.^30–33 In most related experiments, reliable laser locking and frequency scanning techniques are needed to precisely control optical transitions to the Rydberg states as well as between Zeeman sublevels for the purpose of state preparation.

Some experiments require trapped Rydberg atoms, and most demonstrated traps rely on a magnetic potential,^34–36 the shape and depth of which strongly depend on the m_J quantum number, where m_J represents the Zeeman sublevels, each requiring a different transition wavelength. Hence, having control over Rydberg-state Zeeman sublevels and, therefore, any associated magnetic potential, requires a reference transition frequency for each of the sublevels. Rydberg atoms are also viewed as excellent tools for microwave sensing applications^37–40 due to their high sensitivity to electric fields. Controlling the microwave frequency detection range necessitates managing the optical transitions to Rydberg states as well as the separation between different Rydberg states or the various Zeeman sublevels within a particular Rydberg state.⁴¹ 

In this work, we demonstrated laser locking to Zeeman sublevel EIT peaks in a ⁸⁷Rb three-level, cascaded Rydberg system in the presence of an applied magnetic field [see Fig. 1(a)], in a manner analogous to the work by Bao et al.⁴² for Cs atoms. Our method allowed us to continuously shift the frequency of the 480 nm pump laser (ω_pump) by up to 300 MHz on either side of the locking position with zero applied magnetic field. We also demonstrated that, when the Earth’s and stray magnetic fields were not shielded from the system, the reference, single-peak EIT signal experienced a frequency shift due to the difference in the energy shift between two neighboring m_J states. The nondegenerate Zeeman sublevels were indistinguishable from the observed EIT signal. However, depending on the polarization of the 480 nm pump, the locking position shifted according to the most dominant m_J transition. This introduced a frequency uncertainty of 1.6 MHz between the extreme locking points which could be detrimental to spectroscopy or precision measurement experiments.

The experimental setup is shown in Fig. 1(b). We used a room-temperature ⁸⁷Rb-enriched vapor cell (TT-RB87-75-V-P, TRIAD Technology, Inc.) of diameter d = 25 mm and length l = 75 mm. An applied DC magnetic field was produced along the z-axis, transverse to the light beam propagation axis, by a pair of rectangular coils with dimensions 150 × 70 mm² and N = 50 turns connected in series. Each coil was ∼30 mm from the center of the cell. The magnetic field was measured at the center of the cell by a gaussmeter (HIRST Magnetic Instruments Ltd., GM08) for currents varying from I = 2.0–6.0 A with 0.1 G precision. The 780 nm laser (DL pro, Toptica), used as the probe in the two-photon EIT scheme [see Fig. 1(a)], was locked via SAS to the $Rb855S1/2,F=3→5P3/2,F′=3,4$ crossover peak. It was then shifted by 1.0662 GHz using an electro-optic modulator (EOM, NIR-NPX800 LN-10, Photline Technologies) to be resonant with the $Rb875S1/2,F=2→5P3/2,F′=3$ transition. For the purposes of this work, the EOM was not used to tune the lock and was driven with a fixed frequency of 1.0662 GHz. The 480 nm pump light was derived from a frequency-doubled, high power 960 nm laser (TA-SHG pro, Toptica). Approximately 1 μW of the 960 nm seed light was collected prior to the doubling cavity and was sent via an optical fiber to a wavemeter (HighFinesse Ångstrom WS-6/600) to measure the laser wavelength. Each wavelength measurement was obtained by taking an average of at least 200 values and then converted into frequency for the 480 nm light.

The power of the 780 nm laser was set to 300 μW, and that of the 480 nm laser was 300 mW. The 780 nm beam was split with a polarizing beam splitter, with one part sent through the vapor cell as a reference and the other counter-propagated with the 480 nm pump through the cell, thereby coupling the $5S1/2,F=2$ ground, $5P3/2,F′=3$ intermediate, and $32D5/2$ Rydberg states. In the presence of the applied magnetic field, the Zeeman sublevels were nondegenerate and are shown as m_F for the ground and intermediate states and as m_J for the Rydberg state [see Fig. 1(a)]. A λ/2 waveplate in the beam of the 480 nm laser controlled its polarization to satisfy the momentum conservation requirement, Δm_F = ±1, for transitions to various m_J levels of the Rydberg state. When the polarization was aligned along the x-axis, i.e., orthogonal to the applied magnetic field, the atoms experienced a linear combination of σ⁺ and σ⁻ fields. When the polarization was aligned along the z-axis, i.e., parallel to the applied magnetic field, the atoms experienced π polarized light. The 780 nm laser light polarization was set orthogonal to the applied magnetic field, optically pumping the atoms to the m_F = ±4 Zeeman sublevels.¹⁸ The two 780 nm beams were incident on a dual photodetector (Thorlabs PDB210A/M), where the reference, incident on PD1, was subtracted from the probe, incident on PD2, to get the EIT signal. The processed signal from the photodetectors was transmitted to the Toptica Digilock 110 module and monitored using the DigiLock software. As the 480 nm laser frequency was scanned, a spectrum was obtained. When the 480 nm laser was resonant with the Rydberg transition in the absence of the applied magnetic field, a single EIT peak was visible, as shown on the measured spectrum in Fig. 2(a).

In the initial set of experiments, no magnetic field was applied to the system, and the 480 nm laser was locked to the EIT signal recorded from the photodetector, as shown in Fig. 2(a). In this case, the Zeeman shifts from the Earth’s magnetic field and any additional stray magnetic fields were not enough for individual Zeeman levels to be distinguishable. We then rotated the 480 nm λ/2 waveplate in steps of 10° to change the polarization and recorded the wavelength, which we subsequently converted to frequency values [see Fig. 2(b)]. We observed a polarization-dependent frequency shift of the lock position with a peak-to-peak variation of 1.6 MHz. As we adjusted the 480 nm polarization, the dominant m_J Rydberg level also changed according to the angular momentum conservation selection rules $ΔmF=0,±1$ for π and σ^± polarization, respectively, $ΔmF=mI+ΔmJ$⁠, thereby changing the weighting of the transitions that determined the lock point. From these measurements, it can be seen that, in an environment with no magnetic shielding and zero applied magnetic field, the locking frequency can vary quite significantly depending on the laser polarization.

We next applied a magnetic field of 26 G to the system using the same laser conditions as before. We observed a splitting of the EIT peak [see Fig. 3(a)] corresponding to the different m_J levels. Depending on the polarization of the 480 nm laser, we observed different combinations of the m_J peaks with different amplitudes. We locked the 480 nm laser to the $5P3/2,mF′=3→32D5/2,mJ=−5/2$ transition and varied its polarization by rotating the λ/2 waveplate; see Fig. 3(b). One can see that the relative shift of the locking frequency is within $∼0.6$ MHz, which is almost three times less than when no magnetic field is applied [Fig. 2(b)]. The variation arose from the fact that, when the polarization was changed, the amplitude of the $5P3/2,mF′=3→32D5/2,mJ=−5/2$ transition peak changed.⁴³ At the same time, the neighboring $5P3/2,mF′=3→32D5/2,mJ=−3/2$ transition peak appeared, and its tail overlapped with the locking transition peak. This affects the locking frequency. If the scan of the waveplate angle, θ, were outside the range of 290°–340°, the m_J = −5/2 EIT peak signal disappeared and the lock was no longer possible. For the specific case where the 480 nm polarization was set such that the atoms experienced a linear combination of σ⁺ and σ⁻ circular polarizations, a suppression of the transitions to the m_J = ±3/2 sublevels was observed [see Fig. 3(a)] and the laser could be locked precisely to the m_J = ±5/2 transition frequency.

The frequency stability of the 480 nm laser when locked to the $5P3/2,mF′=3→32D5/2,mJ=−5/2$ transition was determined by recording its value for 70 min; see Fig. 5(a). The frequency separation between the most distant mean frequency values gave an estimation of the long-term laser lock drift. Thence, we plotted a histogram of the frequency drift over a 10-min recording; see Fig. 5(b). We fitted the histogram with a Gaussian function and extracted the full-width-at-half maximum (FWHM) to estimate the short-term lock stability. The long-term frequency drift was $≈0.5$ MHz, while the short-term lock stability was $≈0.15$ MHz, an improvement over that previously reported in the work of Rajasree et al.,¹⁵ where the long-term drift was $∼0.5$ MHz and the short-term stability was $∼0.4$ MHz. We also characterized the frequency stability by means of Allan variance,⁴⁴ defined by $σ2(τ)=12τ2∑n=1N−2(xn+2−2xn+1+xn)2$⁠, where x_n is the time series of the wavemeter frequency measurement spaced by the integration interval τ. We observed a minimum Allan deviation, $σ2(τ)$⁠, on the order of 10⁻¹¹ for an integration time of 7 s; see Fig. 5(c). To address the stability change for different detunings of the 480 nm laser, we measured the lock frequency using the wavemeter at two different magnetic field strengths and observed no change in the frequency drift. This could be explained by examining the amplitudes of the photodiode (PD) signal from the Zeeman-split EIT measurement. Once the m_j = 5/2 and m_j = −5/2 peaks become distinguishable in the signal, their amplitudes show minimal variation as the magnetic field is increased; see Fig. 4(b). In addition, we performed a heterodyne measurement by overlapping spatial modes of the target seed laser and a local oscillator via an optical fiber splitter. The local oscillator electric field was provided by a continuous wave (CW) Ti:Sapphire laser (MSquared), locked to a reference cavity yielding a spectral linewidth of 100 kHz. We introduced a frequency difference between the two lasers to observe a beat note signal. By performing a Fourier transform of the signal from time to the frequency domain, we extracted a combined linewidth. Knowing the estimated linewidth of the local oscillator allowed us to calculate the linewidth of the target laser. When locking was performed in the absence of the external magnetic field, the linewidth was ∼1.8 MHz. In contrast, applying the external magnetic field for the locking reduced the linewidth to about 0.8 MHz.

In conclusion, we have demonstrated a method to directly lock a 480 nm laser to the Zeeman sublevels of a Rydberg state, using the $5P3/2,F=3→32D5/2$ transition as an example. This locking technique allows one to continuously tune the laser frequency over a range from −280 to +280 MHz by controlling the strength of a transversely applied magnetic field. The scanning range could be increased further by increasing the maximum value of the applied magnetic field; however, in this case, care must be taken to avoid the quadratic Zeeman effect as the field gets larger.¹⁸ In the absence of an applied magnetic field, we have shown that the background magnetic fields introduce polarization-dependent locking uncertainty due to the small Zeeman shift. The described technique is relatively low-cost and is useful for studies with Rydberg atoms where large continuous tuning of the laser frequency is required. The lock stability is comparable to or better than similar locking methods, with a short-term frequency stability of 0.15 MHz and a long-term frequency drift of 0.5 MHz recorded. We have also demonstrated that using the Rydberg Zeeman level reduces the lock linewidth by a factor of two. The limit of the 480 nm pump laser scanning range using the Rydberg Zeeman level, while the probe laser is locked to the 5S_1/2 → 5P_3/2 transition, is one and a half times larger than that of a single-peak EIT locking scheme. The scanning range could be extended by heating the vapor cell to increase the Doppler width of the absorption spectrum for the 5S_1/2 → 5P_3/2 transition. In addition, the probe laser frequency can be matched with the Zeeman shift of a target laser via an EOM, in which case an arbitrary scanning range of the pump laser should be achievable.

This work was supported by the funding from the Okinawa Institute of Science and Technology Graduate University. D.J.B. and S.N.C. acknowledge the support from the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid Nos. 22K13986 (Early Career) and 24K08289, respectively.

The authors have no conflicts to disclose.

Alexey Vylegzhanin: Writing – original draft (lead); Writing – review & editing (equal). Síle Nic Chormaic: Writing – original draft (equal); Writing – review & editing (equal). Dylan J. Brown: Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.