1. Introduction

Lumino-frigoriques is a term originally used by A. Kastler to describe optical pumping (OP) of sodium atoms between hyperfine states to accumulate population in a dark state [1]. The effects of optical pumping “cool” the sample when the final (dark) state is at a lower energy than the initial state. OP is ubiquitous in the laser cooling of atoms [2,3], and has recently been adopted to produce samples of ground state molecules: it has been demonstrated for Cs₂ by pumping vibrational levels with a femtosecond laser [4] or with low power broad band cw light [5], and for molecular ions by pumping rotational states [6, 7].

Producing a sample of polar molecules in the rovibrational ground state is of significant current interest as a starting point for the creation of dipolar crystals [8, 9], quantum computation [10] and quantum chemistry [11]. So far, the approaches for accumulating heteronuclear molecules in the (ro)vibrational ground state either involve highly efficient yet technically challenging experimental techniques, or are relatively simple but inefficient. The earliest demonstration is a “pump-dump” procedure in RbCs [12] that transferred population in select vibrational levels to X¹Σ⁺(v=0) with an experimentally unconfirmed rotational distribution. Then, there is the efficient but technically challenging demonstration of magneto-association and coherent transfer of KRb [13] to the rovibrational ground state using laser system referenced to a frequency comb. Also, direct photoassociation yields rovibrational ground state LiCs [14] and vibrational ground state NaCs [15] but with the majority of the sample distributed across a range of excited rovibrational states.

In this work, we utilize the simple and effective process of luminorefrigeration to vibrationally cool a sample of highly polar NaCs molecules created by photoassociation. Specifically, we optically pump an initial distribution of rovibrational levels to the vibrational ground state, X¹Σ⁺(v=0, J=0–4). We describe a series of experiments that explore the pumping dynamics and discuss the applicability of this approach to other bialkali systems.

2. Experimental setup: molecule formation

During the experiment, we first photoassociate (PA) NaCs from dark-SPOT magneto-optical traps. Initially, we choose a PA resonance that is part of the (4)Ω=1 progression [20], detuned 32 GHz from the Cs 6²S_1/2 → 6²P_3/2 transition, and we lock the PA laser to within a few MHz. This channel has a high formation rate, estimated to be ∼10⁷ molecules/s determined from spectroscopic results [21], the wavefunction overlap of the PA resonance with the singlet ground state calculated using LEVEL 8.0 [22], and by considering the volume of the ionizer beam intersecting with the region of molecule formation. The ultracold molecules are not trapped and drift away from the formation/manipulation/detection region over a period of ∼10ms estimated from the measured kinetic temperature of ∼250 μK. To achieve vibrational cooling, the photoassociated NaCs sample is continuously exposed to OP light, driving the rovibrational distribution of molecules through the A¹Σ⁺ and b³Π electronic states (A–b complex). We then probe the populated vibrational states of the NaCs sample using Resonance Enhanced Multi-photon Ionization (REMPI) where the neutral molecules are ionized and subsequently detected by a channel electron multiplier (CEM) using time of flight mass spectroscopy, and these experiments are run at a 10 Hz repetition rate. Other spectroscopic techniques are employed to unambiguously determine the rovibrational state populations, such as pulsed depletion spectroscopy (PDS) [21] and cw depletion spectroscopy [23].

The initial population distribution created using the 32 GHz PA resonance has been shown to include X¹Σ⁺(v=4–6,8,9,11,13,15,17,19,21,23,25–27,31), determined using PDS [21]. This range of vibrational states exhibits an electric dipole moment of ∼4.6 Debye [24]. We expect that there is also population in higher singlet ground state vibrational levels from the Franck-Condon (FC) overlap of the potential energy curves (PECs) calculated using LEVEL 8.0 [22], though we have not yet directly confirmed population of these states using REMPI.

3. Experimental setup: molecule manipulation

The A–b complex is illustrated in Fig. 1. We choose it for OP because it minimizes the number of electronic states involved in the cycling transition, and because it is a well studied system [18]. From transition moment and transition energy calculations provided by A. Stolyarov et al. [25], we know that the singlet ground state and A–b complex PECs are well overlapped and similar in shape and depth. Therefore for the appropriate choice of OP light, we may drive a maximal number of ground state transitions with minimal spectral width. We note that the A–b complex has singlet and triplet spin components, therefore optical pumping can involve both the singlet and triplet ground states.

 

Fig. 1 Optical pumping pathways in NaCs. Ground state molecules are pumped through the A¹Σ⁺–b³Π complex using broadband light that is not energetic enough to drive molecules out of X¹Σ⁺(v=0). Excited state molecules decay to the ground state and population in X¹Σ⁺(v=0) accumulates. The experimentally determined PECs are from [16–19], shown with exaggerated vibrational level positions.

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Consider the effect of OP light with a broad spectral distribution to the red of 978.62nm. This wavelength couples X¹Σ⁺(v=0) → A–b complex (N=1), N=1 being the lowest vibrational level of the Ω=0 component of the b³Π, and consequently the lowest vibrational level in the excited state manifold. The A–b complex is a heavily mixed system of electronic states, therefore the effective vibrational levels are perturbed and numbered using index N. For this spectral distribution, the OP light would not be energetic enough to drive population from X¹Σ⁺(v=0) forming a dark state, yet it will pump population out of X¹Σ⁺(v ≥1).

To check the viability of this approach and to determine a suitable spectral bandwidth, we estimate the transition rates from X¹Σ⁺ → Ω=0 components of the A–b complex to provide insight into the expected OP behavior. Note, there are 87 singlet ground state vibrational levels; however, transition dipole moments were available only for X¹Σ⁺(v=0–65) from [25]. We choose a 985nm spectral component based on the known initial vibrational distribution, and this wavelength corresponds to the strongest calculated transition moments from deeply bound singlet ground states. We note that the 985nm component addresses population throughout the singlet and triplet ground states. However, in order to more efficiently drive the higher lying vibrational levels, we include a 1206nm spectral component. This wavelength selection is a compromise based on the availability of laser diodes and wavelengths closer to 1255nm would access more efficient pumping pathways. We calculate transition rates based on the readily available diode lasers assuming a flat-top spectral intensity profile spanning 979–991nm at 300 mW and 1203–1209nm at 1.5 W focused to 1mm in diameter. We conclude that a sufficient range of singlet ground state vibrational levels may be coupled via optical pumping by this experimentally feasible laser system. Of course, increasing the spectral width would couple even more levels thereby increasing the transfer efficiency to X¹Σ⁺(v=0).

We create the broadband OP light by overlapping the output of four 2W 980nm multi-mode diode lasers [26], each tuned to a slightly different wavelength, and a 2.5W 1206nm broad area diode laser [27]. These free-running diodes are temperature stabilized, however there is no active wavelength stabilization. Also, there is no 4-f line shaping with a mask as in [5] and these diodes are simply temperature tuned for wavelength selection. As shown in Figs. 2(a) and 2(b), the OP light has a spectral component centered at 985nm with ∼10nm width and another component centered at 1206nm with a ∼5nm width, respectively. The solid vertical line in Fig. 2(a) indicates the wavelength coupling X¹Σ⁺(v=0) → A–b complex (N=1). The OP light is to the red of this transition satisfying the requirement for the formation of a dark state.

 

Fig. 2 Relative intensities of the OP diodes. (a) Combined spectral profile of the four 980nm diodes. Vertical line indicates the transition wavelength to drive population out of X¹Σ⁺(v=0). (b) The 1206nm diode spectral profile.

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4. Results and discussion

With this choice of OP light, we observe significant transfer to X¹Σ⁺(v=0), determined by comparing REMPI spectra [15, 21], assigned with PDS, taken with and without OP. To locate detection lines for measuring the populated vibrational levels we utilize both a 2 and a 3 photon REMPI procedure which cover a range of 800–812nm, 840–870nm, and 535–545nm. The 3 photon REMPI utilizes the A–b complex for the first transition and these wavelengths are calibrated to select atomic lines. Figure 3(a) shows the detected vibrational states in the initial distribution with labels for the deepest states, X¹Σ⁺(v=4–6,19). The REMPI range here is selected because it contains one of the detection lines for the vibrational ground state. The state assignments in Fig. 3 are as described in [21] and known with high certainty due to the well known excited state assignments also from experimental data [18]. After vibrational OP, Fig. 3(b) shows the final distribution. Only the lowest three states, X¹Σ⁺(v=0–2), are populated while other vibrational levels are completely or mostly depopulated. From prior work [21] we know that another X¹Σ⁺(v=0) REMPI detection line exists in the 535–545nm range and our OP results were confirmed using such a 535–545nm REMPI scan.

 

Fig. 3 Three photon REMPI scans revealing populated vibrational levels in the singlet ground state. (a) Initial distribution of vibrational levels with X¹Σ⁺(v=4–6,19) labeled. (b) Final distribution after the sample is optically pumped. X¹Σ⁺(v=0–2) are populated. Vibrational assignments are experimentally confirmed using pulsed depletion spectroscopy [21]. The wavelength is calibrated against known atomic transitions to within 0.2 cm⁻¹.

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OP experiments are conducted using combinations of the 985nm and 1206nm spectral components to investigate how initial vibrational states are being pumped to (v=0). The 1206nm spectral component alone does not significantly populate X¹Σ⁺(v=0); however, it does increase population in other deeply bound singlet ground states. The 985nm spectral component saturates population driven into X¹Σ⁺(v=0) as a function of OP intensity, and when the two spectral components are combined, the transfer rate to X¹Σ⁺(v=0) is nearly doubled. This increase arises from the 1206nm spectral component transferring population into vibrational states that are accessible with the 985nm component and driven to X¹Σ⁺(v=0). These results confirm the presence of higher lying vibrational levels in the initial distribution.

When the OP is optimized, we observe 50 NaCs ions the X¹Σ⁺(v=0) detection channel per REMPI pulse. At this rate, however, we approach saturation of the standard CEM, meaning that the rate of ion bombardment is nearing the max output pulse rate, and actual production rates may be higher than those detected. A conservative estimate for the transfer rate into X¹Σ⁺(v=0) is ∼1×10⁵ molecules/s from the initial rovibrational distribution created by the 32 GHz PA resonance. This is estimated by considering the detected ions per REMPI pulse, the detector efficiency, a geometric factor describing the ratio of detected molecules to those outside of the ionizer pulse region, and the 10 Hz experimental repetition rate. We also find accumulation in X¹Σ⁺(v=1, 2) with 45 ions per REMPI pulse, consistent with the relative spectral intensities of the diodes illustrated in Fig. 2 and the calculated transition rates.

Due to the non-uniformity of the OP spectral intensity in Fig. 2, one might infer that there would be inaccessible ground vibrational states creating pockets of dark and quasi-dark vibrational states where population would persist in the singlet ground state. A dark state is a state that does not couple to the excited state and a quasi-dark state is one that is coupled but still retains population. Quasi-dark states might be the result of a lack of intensity to drive transitions or the rate of excitation is less than the decay rate into that state. In the REMPI spectra, however, we find only a few quasi-dark states with population not completely depleted starting from X¹Σ⁺(v=1,2,8,13,15,19), and we see no evidence of a true dark state other than X¹Σ⁺(v=0) when the two spectral component OP light is used. We observe depletion in the triplet ground state for a³Σ⁺(v=12), verifying that here the triplet ground state is not a dark state. The formation and assignment of this vibrational state is discussed in [20]. From calculated transition energies provided by [25], we know that the OP light will drive transitions throughout the triplet ground state to the Ω=0–2 components of the b³Π.

Here, we measure the initial rotational distribution by performing cw depletion spectroscopy on the sample. Figure 4(a) presents the initial rotational distribution created by the 960 GHz PA resonance that is part of the (4)Ω=1 progression; it creates the same ground state rotational distribution as the 32 GHz PA resonance. This PA line is used here because the scan has the best signal to noise ratio. By using the X¹Σ⁺(v=4) → A–b complex (N=70) transition, we find that PA through J=1 in the excited state, populates J=0,1,2 in the singlet ground state as shown by the solid line in Fig. 4(a). The assignments were made by comparing line positions to calculated values from [25]. Selecting the PA state is a crucial step when constructing the initial distribution and higher rotational states may be populated depending on the PA channel selected. The dotted line in Fig. 4(a) illustrates J=1,3 being populated via PA through J=2 in the excited state.

 

Fig. 4 Ground state rotational levels are labeled using cw depletion and transitions are known from [25]. Dashed areas indicate range of noise in the signal. (a) Initial ground state rotational population distribution. Solid (dotted) line shows population created by (4)Ω=1 PA resonance at 960 GHz through J=1 (J=2). Note both the R and P transitions are shown out of J=1 in the ground state. (b) Final rotational population distribution by optically pumping the initial distribution created by the J=1 PA resonance at 32 GHz. X¹Σ⁺(v=0, J=0) is populated (scan is vertically shifted 1200 units). The J=1 arrow is grayed indicating uncertainty of population in this state. The frequency is calibrated with a wavemeter known to within 0.3 GHz.

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For each transition during OP, the rotational state selection rule is ΔJ=±1 and we expect a spread in rotational states as OP drives population into X¹Σ⁺(v=0). Figure 4(b) illustrates the rotational states that are populated within X¹Σ⁺(v=0) by driving transitions between X¹Σ⁺(v=0) → A–b complex(N=77). From this depletion scan, we determine that the final rotational distribution populates J_final=0–4 and a significant fraction is in X¹Σ⁺(v=0, J=2).

The ΔΛ=0 Hönl-London (HL) factors describing the branching ratios for the X¹Σ⁺ → A¹Σ⁺ rotational transitions are used in a monte carlo simulation to model the cw depletion spectroscopy results. We use an initial rotational state distribution of J_initial=0–2 and alter the rotational state weighted by the HL factors for two thousand molecules and a specified number of cycles. Each cycle consists of the excitation and decay transitions. This model predicts the final population distribution for 1–6 cycles is centered at J_final=2 with population ranging from J_final=0–6 as depicted in Fig. 5. When modeling 3–8 cycles, we find the rotational population disperses over ΔJ_final=0–10 with a majority in states J_final=2,4,6 which is contrary to the observed spectrum. Therefore, we infer the molecules do not undergo many transitions before populating X¹Σ⁺(v=0, J=2) due to the FC overlap of the ground and excited states.

 

Fig. 5 Results of a monte-carlo simulation of an initial rotational distribution (striped) driven between 1 and 6 cycles (black) or 3 and 8 cycles (gray) weighted by the Hönl-London factors for ΔΛ=0 transitions. The final rotational distribution for 1–6 cycles (black) closely resembles experimental results.

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The rotational state modeling predicts a small number of cycles in the experiment; therefore, we estimate the number of vibrational cooling cycles using a separate monte carlo simulation. It models the optical pumping assuming a flat-top OP spectral profile covering 979–991nm and 1203–1209nm. The simulation utilizes the transitions accessible with the OP spectrum, and the excitation and decay transitions are determined using the vibrational state branching ratios between the A–b complex and the singlet and triplet ground states provided by [25]. From this simulation, we predict that 20% of a uniform initial population distribution covering X¹Σ⁺(v=4–65) is driven to X¹Σ⁺(v=0) in 6 cycles (12 transitions) or less. These results are consistent with the observed rotational state dispersion, as well as with our estimated formation rates, highlighting the optical pumping efficiency obtained using the A–b complex.

5. Applications to other heteronuclear species

Luminorefrigeration may be generalized to any system where the lowest excited electronic states are well matched with the ground electronic state. We note that KCs, LiCs, and RbCs have PECs similar to NaCs for the ground state and A–b complex. For example, we calculate FC factors for the experimentally determined singlet ground state [28] and deperturbed A¹Σ⁺ and b³Π states [29] using LEVEL [22] for the KCs molecule. The calculated FC map indicates reasonable overlap, and favorable transition moments [30] suggest similar OP results may be obtained with appropriate laser diode selection for ∼988–1000 nm coverage.

6. Conclusion

To conclude, we demonstrate a simple method to enhance production of ultracold, rovibrational singlet ground state molecules. This is the first application of vibrational optical pumping in a heteronuclear, highly polar sample with an experimentally verified rotational distribution. Broadband cw light drives the initial population distribution from the singlet ground state to the A¹Σ⁺–b³Π complex in a series of absorption and spontaneous emission cycles and population accumulates in X¹Σ⁺(v=0) at an estimated rate of ∼1×10⁵ molecules/s, populating X¹Σ⁺(v=0, J=0–4). A cw approach has low risk of multiphoton excitation and minimal rotational state dispersion and the efficiency is limited only by the bandwidth of the OP laser system.

In the future, we plan to increase population in X¹Σ⁺(v=0, J=0) via rotational optical pumping. We are currently exploring the unique properties of the lowest vibrational levels in the A¹Σ⁺–b³Π complex which will facilitate the transfer of X¹Σ⁺(v=0, J=2) → X¹Σ⁺(v=0, J=0).