Formation of ultracold ⁷Li⁸⁵Rb molecules in the lowest triplet electronic state by photoassociation and their detection by ionization spectroscopy

Ultracold molecules are a source of great interest and a focus of active research due to their promise in areas of research such as novel quantum phase transitions,¹ ultracold chemistry,^2–4 tests of fundamental forces,^5–7 and others. A subset of these ultracold molecules is heteronuclear diatomic alkali molecules that possess a permanent electric dipole moment in the ground electronic state. This attribute is of great interest in using ultracold molecules for quantum computation applications,^8,9 where controlling dipole-dipole interactions is a key to using molecules as qubits.

One common method of creating ultracold molecules is photoassociation (PA). PA creates molecules in an electronically excited state, which quickly decay to high-lying vibrational levels of the lowest singlet (ground) and triplet electronic states. Transferring these molecules to the most deeply bound rovibrational ground-state levels, however, requires transfer pathways that may involve additional excitation steps to states that have a better wave function overlap with the rovibronic ground state.^10,11

Our choice of molecule, ⁷Li⁸⁵Rb, has a large electric dipole moment (∼4.1 debye¹²) in the rovibrational ground state. Experimentally, LiRb is one of the least well-known heteronuclear alkali molecules that can be created in ultracold traps. Very recently, however, studies of two groups have started to shed light on this molecule through spectra in hot vapors,^13–15 as well as, for the first time, PA spectroscopy using trap-loss measurements.^16,17 Especially exciting is the high rate of photoassociation of this molecule, as reported in Refs. 16 and 17. These studies have been guided by the results of several ab initio calculations.^18–20 

In this paper, we report the formation of ultracold ⁷Li⁸⁵Rb molecules in the lowest triplet state, a³Σ⁺, and perform preliminary spectroscopic studies of ultracold ⁷Li⁸⁵Rb molecules using ionization detection. In the process, we have discovered new PA resonances that were not seen in earlier trap-loss spectra. In addition, we also measure resonantly enhanced multiphoton ionization (REMPI) spectra and identify vibrational levels of the following previously unobserved electronic states: 3³Π (v_Π′ = 0–10), 4³Σ⁺ (v_Σ′ = 0–5), and a³Σ⁺ (v″ = 7–13). We compare our observations with ab initio calculations¹⁹ and semi-empirical potentials¹³ and show good agreement between theory and experiment. These initial spectroscopic investigations shed new light on its structure and are important steps toward finding transition pathways to transfer ultracold LiRb molecules into the most deeply bound rotational, vibrational, and electronic (rovibronic) ground state levels.

The paper is organized as follows: In Sec. II, we describe our experimental setup and detection scheme. We discuss PA spectroscopy in Sec. III, the REMPI spectra and their analysis in Sec. IV, the estimation of molecule formation rate in Sec. V, and we conclude in Sec. VI.

In this section, we briefly describe the experimental parameters of our measurements. A more complete description can be found in Ref. 21. We generate a sample of cold LiRb molecules by photoassociating ⁷Li atoms and ⁸⁵Rb atoms in a dual species magneto-optical trap (MOT). We show this PA step in Fig. 1(a), in which we display a diagram of the relevant potential energy curves (PECs) for LiRb.¹⁹ The long-range PECs to which we photoassociate ultracold LiRb molecules are shown in Fig. 1(b). The excited state molecules decay spontaneously to the lowest triplet state, from which we ionize them using REMPI. Vibrational levels of the 3³Π and 4³Σ⁺ electronic states enhance the ionization signal when the ionizing laser is resonant with a transition from the a³Σ⁺ state. The sensitivity of this ionization scheme allows us to detect PA resonances that were unobservable through trap-loss spectroscopy, and the REMPI spectra allow us to determine energy levels of the ground and excited electronic states of the LiRb molecule that have not previously been observed.

We cool and trap atomic ⁷Li and ⁸⁵Rb in a dual species MOT, with atom number N and density n for Li and Rb as N_Li ∼ 5 × 10⁷, n_Li ∼ 5 × 10⁹ cm⁻³ and N_Rb ∼ 1 × 10⁸, n_Rb ∼ 4 × 10⁹ cm⁻³. We use a dark spot Rb MOT to reduce collisional losses in the trap,²¹ leaving most of the trapped ⁸⁵Rb atoms in the F = 2 ground hyperfine level. We monitor the MOT operation and the overlap of the Li and Rb atomic clouds with a pair of CCD cameras. We photoassociate LiRb molecules using the 795 nm output of a Coherent 899 cw Ti:Sapphire (PA) laser, whose output power is typically between 300 and 350 mW and whose collimated beam diameter is ∼0.85 mm. The frequency of the Ti:S laser beam is locked to a temperature stabilized external Fabry-Perot cavity, reducing the laser linewidth to ∼1 MHz. We monitor the PA laser frequency with a Bristol 621 A wavemeter (accuracy ∼60 MHz). The excited state molecules created through PA spontaneously decay to weakly bound vibrational levels of the a³Σ⁺ state, from which we ionize them using the output of a Spectra-Physics PDL-2 pulsed dye laser, pumped by the second harmonic of a Q-switched Nd:YAG (∼7 ns pulse width, 10 Hz repetition rate). The PDL-2 output has a linewidth of ∼0.3 cm⁻¹. We use rhodamine 590 dye in the dye laser. For ionizing the molecules, we typically use a pulse energy of 2-3 mJ and a laser beam diameter of ∼4 mm at the MOT. For REMPI spectroscopy, we fix the Ti:S laser frequency on a chosen PA resonance and monitor the frequency drift by recording the heterodyne beat signal between part of the Ti:S output and a frequency comb (with a 250 MHz frequency difference between comb teeth). The linewidth of the beat signal is ∼2 MHz. During normal operation, the beat signal may drift by ∼5 MHz over a period of 30-45 min, which is the typical length of time required to collect a single data set. This drift is less than the typical linewidth of our PA resonances (∼10 s of MHz) and does not significantly affect our REMPI spectra.

Atomic and molecular ions created by the PDL pulses are accelerated towards a microchannel plate (MCP) detector assembly by a set of three field plates. We bias the MCP at a potential difference of −1.8 kV. Each ion strike registers as a sharp (∼5 ns) current spike, and we record these events to count the number of ions detected for each ionizing pulse. We use time-of-flight (TOF) mass spectrometry to resolve atomic and molecular ions and to count only LiRb⁺ ions. Our maximum count rate is ∼2 LiRb⁺ ions per laser pulse. For PA spectra, we fix the dye laser wavelength and scan the PA laser frequency, whereas for REMPI spectroscopy, we fix the PA laser frequency and tune the output wavelength of the PDL. We control the Nd:YAG firing sequence, tune the dye laser wavelength and Ti:S laser frequency, and record the LiRb⁺ ion counts using a laboratory computer.

We acquire PA spectra by scanning the PA laser in discrete ∼20 MHz frequency steps below the ⁷Li 2s²S_1/2 + ⁸⁵Rb 5p ²P_1/2 asymptote. See Fig. 1(b) for the long-range PECs in this energy range. All the PA line positions Δ_PA in this section are measured relative to the ⁸⁵Rb (5s, F = 2)–⁸⁵Rb (5p_1/2, F = 2) transition at v_1/2 = 377 108.946 GHz. We show the newly observed PA resonances in Fig. 2. As in our trap-loss measurements,^16,17 we observe and assign resonances to all three electronic states [2(0⁺), 2(0⁻), and 2(1)] asymptotic to this level. For Δ_PA ∼ 8 GHz or less, the PA laser disrupts the Rb MOT operation, rendering PA resonances unobservable in this range. As with trap-loss spectroscopy,^16,17 we only observe one rotational level for most of the PA resonances and assign these as J = 1. We include the REMPI wavelengths used to acquire these spectra in Fig. 2.

In our previous trap-loss spectroscopy work, we observed PA levels u_PA = 2–4 of 2(0⁺) and u_PA = 3–5 of 2(0⁻) and 2(1) (We use u_PA to label the vibrational level of the PA state, where u_PA = 1 indicates the first PA level below the dissociation limit). In addition, we now also find lines for u_PA = 5 of 2(0⁺); u_PA = 8, 9, and 11 of 2(0⁻); and u_PA = 6, 7, and 10 of 2(1), visible only through ion detection. We include in Fig. 2 the PA resonances that we observed only using the REMPI detection scheme, but note that for peaks that appear in both detection schemes, the line positions in trap-loss spectra are in excellent agreement (within ∼40 MHz, consistent with the linewidth of the resonances) with the line positions that we now observe through ion detection. We also observe similar hyperfine structure in both sets of spectra. We have normalized all signals in Fig. 2 to the 2(1) u_PA = 5 PA REMPI line strength.

As done in our previous reports,^16,17 we base electronic state assignments of the PA levels on the structure of the PA resonances. The hyperfine energy, E_hfs, scales as E_hfs ∼ Ω/J(J + 1),²³ where Ω is the projection of the total angular momentum, excluding nuclear spin, on the internuclear axis. Hence, Ω = 0 lines have no internal structure to first order, but Ω ≥ 1 lines show hyperfine structure. In Fig. 2, we show the sets of peaks assigned to each of the three electronic states.

In Table I, we list the observed PA lines for the J = 1 line of each vibrational level. Through earlier trap-loss measurements, we identified PA lines up to u_PA = 4 for 2(0⁺), and u_PA = 5 for 2(0⁻) and 2(1).¹⁷ With the more sensitive ionization detection method, we identify an additional seven PA levels, as listed below the dashed lines in Table I, with a binding energy of up to Δ_PA ∼ − 62 cm⁻¹ (∼1862 GHz below the ⁷Li 2s ²S_1/2 + ⁸⁵Rb 5p ²P_1/2 asymptote. One additional weak PA resonance ∼218 GHz below the ⁷Li 2s ²S_1/2 + ⁸⁵Rb 5p ²P_1/2 resonance that was unobserved with earlier trap-loss spectroscopy is also shown in the supplementary material²⁴). We use some of these newly discovered PA lines to record REMPI spectroscopy of ground and excited electronic states (Sec. IV).

In Ref. 17, we derived the C₆ dispersion coefficients of the PA states by fitting the binding energy of the three vibrational levels observed for each electronic series through trap-loss spectra to the Le-Roy Bernstein formula²⁵ for a long range potential described by a single C₆/R⁶ term. It becomes of interest now to re-compute C₆ using our extended data sets for each of these series. We find that the potential is well characterized by C₆/R⁶ over these extended energy ranges. The revised values of C₆ are in good agreement with the original values (C₆ = 10 120 (450) for the 2(0⁺), 12 410 (180) for the 2(0⁻), and 13 130 (330) for the 2(1) electronic states).

We note that we searched for, but were unable to observe, the PA resonances that are missing in Table I, such as u_PA = 6, 7, and 10 of the 2(0⁻) state and u_PA = 8 and 9 of the 2(1) state. Similarly, we were unable to observe more deeply bound PA levels than those shown in Table I.

As mentioned earlier, the electronic ground state molecules formed by spontaneous decay of photoassociated molecules can be ionized via two-photon absorption using the output pulses of the PDL, when the frequency of this laser is one-photon resonant with a transition between a populated ground state, with vibrational level v″ and an excited intermediate state, with vibrational level v′. We show a schematic representation of this REMPI process in Fig. 1. The REMPI spectra allow us to identify the energies of the lowest triplet a³Σ⁺ state and the intermediate 3³Π and 4³Σ⁺ states.

We acquire the spectra presented in this section by fixing the PA laser frequency at one of the three different PA resonances: u_PA = 5, 9, and 11, all belonging to the 2(0⁻) electronic state and tuning the output frequency of the PDL in discrete ∼0.3 cm⁻¹ steps. We record spectra for u_PA = 5 and 11 for PDL frequencies between 17 280 cm⁻¹ and 18 050 cm⁻¹ (wavelengths ∼578.7 and 554.0 nm, respectively) and between 17 589 cm⁻¹ (∼568.5 nm) and 17 821 cm⁻¹ (∼561.1 nm) for u_PA = 9. From one-photon electric-dipole selection rules for transitions valid for Hund’s case c [ΔΩ = 0, ±1 except 0^±↮0^∓], molecules from the 2(0⁻) state decay to 1(0⁻) and 1(1) ground states, which correlate to the a³Σ⁺ state. For the stated PDL wavelength range, LiRb molecules ionize through intermediate electronic states that are asymptotic to the Li(2s) + Rb(4d_j) states (j = 3/2 and 5/2). In the experimental line assignments presented below, we estimate the uncertainty in the transition energies to be ∼0.5 cm⁻¹, mainly due to the PDL linewidth and shot-to-shot fluctuations of the laser frequency.

In Fig. 3(a), we show the complete REMPI spectrum between 17 280 and 18 050 cm⁻¹, recorded with the PA laser fixed at the 2(0⁻) u_PA = 11. As we will show in this section, the frequencies of these spectral lines, as well as those of similar spectra that we recorded with the PA laser fixed at the u_PA = 5 or u_PA = 9 lines of the 2(0⁻) state, allow us to identify the relative energies of several vibrational levels of the lowest triplet a³Σ⁺ state, the excited 3³Π state, and the excited 4³Σ⁺ state.

The REMPI spectra reveal structure on three different energy scales. On the largest scale, we observe recurring features spaced by ∼70 cm⁻¹, as are clearly seen in the total spectrum of Fig. 3(a). In Fig. 3(b), we show a section of the REMPI spectrum between 17 725 and 17 825 cm⁻¹ to highlight some of the identified peaks and the distinct features seen in the spectra (the complete labeled spectra are available in the supplementary material²⁴). In this figure, these features are seen as a grouping of three peaks around 17 740 cm⁻¹ and around 17 810 cm⁻¹. We assign these features separated by ∼70 cm⁻¹ as the progression of 3³Π_Ω vibrational levels $v Π ′$⁠, where we include the spin-orbit component of this state as a subscript: 3³Π_Ω.

Each $v Π ′$ line also has a characteristic triplet substructure, with adjacent “teeth” within each triplet regularly spaced by ∼3 cm⁻¹. We observe that each tooth within a triplet shows almost equal signal strength. This is seen in each of the three sets of u_PA REMPI spectra. We assign these triplets—from lowest to highest frequency—as the Ω = 0, 1, and 2 spin-orbit components of 3³Π, as we have indicated on just one of these triplets near 17 775 cm⁻¹ in Fig. 3(b).

Finally, comparing the overlayed REMPI spectra of u_PA = 5, 9, and 11 reveals several different a³Σ⁺ vibrational levels v″. This is the progression with increasing spacing of the triplet set of peaks as we go towards higher frequency. Transitions from high-lying vibrational levels v″ near the dissociation limit appear stronger than transitions from more deeply bound (lower v″) levels.

Having identified line positions and features corresponding to 3³Π_Ωv_Π′←a³Σ⁺v″ transitions, we now present details of vibrational level assignment of the 3³Π_Ω states.

In order to assign the line positions to vibrational levels of an excited electronic state, we make use of the results of the ab initio calculations of LiRb PECs by Korek et al.,¹⁹ which include spin-orbit interaction. We employ the potential curve of the a³Σ⁺ state calculated by Ivanova et al.¹³ for calculations of the energy spacing between vibrational levels v″ of the ground state and LEVEL 8.0²⁶ to calculate electronic state vibrational levels and Franck-Condon factors (FCFs).

The ab initio potentials with spin-orbit interactions show numerous avoided crossings. For these adiabatic potentials, we assume separation of nuclear and electronic motion based on the Born-Oppenheimer approximation, which gives rise to avoided crossings between electronic states of the same symmetry. However, the relativistic wavefunctions in the vicinity of these avoided crossings change rapidly and result in non-adiabatic effects.²⁷ Hence, we modify the ab initio PECs asymptotic to Li(2s) + Rb(4d_j) and Li(2s) + Rb(6s) by using diabatic crossings and recalculating the PECs. We show the modified diabatic PECs in Fig. 4(a), where we highlight the relevant 3³Π and 4³Σ⁺ potentials.

The 3³Π state consists of four spin-orbit components: Ω = 0⁻, 0⁺, 1, and 2. From LEVEL 8.0 calculations of the diabatic PECs, we calculate and show the spin-orbit components in Fig. 4. At the equilibrium internuclear separation R_e ∼ 5.6 Å, the calculated energy splittings ΔE_Ω between the various Ω components are unequal. Our REMPI spectra, however, reveal a slightly different picture: we observe only three out of four spin-orbit components, and the spacing ΔE_Ω between the components of the triplet structures appears to be nearly equal. While we use the diabatic PECs from Korek et al.¹⁹ to aid our assignment of the spin-orbit components (see Figure 3(b)), the qualitative differences between calculated and observed levels make these assignments tentative. We hope that our measurements will motivate development of an improved model for the 3³Π state. We note that degeneracy of the 0⁺ and 0⁻ components, as well as roughly equal spacing between Ω = 0 and 1, and Ω = 1 and 2 has also been observed in REMPI spectroscopy performed in KRb.²⁸ 

Next, we assign the vibrational levels v_Π′ by comparing calculated vibrational levels and spacing with our experimental results. We tentatively assign v_Π′ starting with 0 because in our REMPI spectra, we do not observe resonances at frequencies below ∼17 323 cm⁻¹. While this could be due to diminishing Franck-Condon factors or the limited tuning range of the rhodamine 590 dye (or both), assigning these lowest observed lines as v_Π′ = 0 is supported by the ∼89.4 cm⁻¹ energy spacing between the lowest vibrational state of the 3³Π_Ω=0 and 4³Σ⁺ states, in good agreement with the ∼85.5 cm⁻¹ spacing predicted in the theoretical PECs of Ref. 19. (We discuss the assignment of the 4³Σ⁺ vibrational levels in Sec. IV E.)

We also use the calculated vibrational spacings ΔG_th of Ref. 19 to aid in assigning the vibrational levels of the 3³Π state. We show these data in Fig. 5, in which the open red circles show the calculated level spacings, and the black closed dots show the experiment spacings. We observe very good agreement between theory and experiment for these data.

We assign a³Σ⁺v″ levels by examining line positions in the u_PA = 5, 9, and 11 REMPI spectra and comparing our observations with the vibrational level spacing ΔG_v″+1/2 calculated from the analytic a³Σ⁺ PEC of Ivanova et al.¹³ Experimental ΔG_v″+1/2 most closely match calculated ΔG_v″+1/2 for v″ = 7–13. In Table II, we compare the calculated vibrational energy spacing ΔG_v″+1/2 with experiment. Entries in the column titled ΔG_v″+1/2 (Expt.) are the average of the observed vibrational spacing for all three 3³Π_Ω spin-orbit components, which we derive from the present spectra. Although the agreement is very good, one should accept these assignments as tentative, since the PEC of Ref. 13 is based on a very limited set of spectral lines.

We observe (Fig. 3(b)) that transitions from v″ = 13, 12, and 11 are strongest when the PA levels used are u_PA = 5, 9, and 11, respectively, i.e., spontaneous decay from more deeply bound PA resonances leads to population in more deeply bound vibrational levels of the a³Σ⁺ state. This strongly suggests the underlying reason for the different line strengths to be the varying wavefunction overlap between the u_PA levels and v″. The strength of these u_PA–v″ transitions, in part, can be qualitatively explained by FCF for decay from the initial PA vibrational levels to the ground triplet state v″. We calculate the FCFs from u_PA = 5, 9, and 11 to a³Σ⁺v″ using the 2(0⁻) ab initio potential from Korek et al. and the a³Σ⁺ potential from Ivanova et al. and show these in Fig. 6. We see that the FCFs for deeper PA levels are larger for more deeply bound ground state vibrational levels, in qualitative agreement with our observations. The calculated FCFs differ in detail from our observations, however, in the distribution of v″ populated through each PA resonance. With the PA laser fixed on u_PA = 5, we primarily populate v″ = 13, 9, and 7 of the ground state; u_PA = 9 populates v″ = 12 and 8; and u_PA = 11 populates v″ = 11, 10, 8, and 7. For the v″ = 13-11 vibrational levels of the a³Σ⁺ state, the agreement with the calculated FCFs is reasonable. For the v″ = 7-10 vibrational levels, however, the theoretical predictions for the transitions from the PA levels do not agree with the experimental observations of the REMPI spectra. Several factors could play a role in such disagreement: the accuracy of the excited state, the presence of avoided crossings among different excited states, and the ionization probability. The excited state used for the FCF calculation is based on fully ab initio calculations, and taking into account the sensitivity of the wave function to small changes in the interaction, a difference between calculations and experiment would be expected. Our calculations are based on a single channel approach, where the excited states are assumed to be uncoupled. This approximation is less accurate if the excited states show interaction among them through the existence of avoided crossings. Finally, we analyze the effect of the ionization probability, since deeper bound states show higher ionization probability than shallow ones. This would explain qualitatively why deeper vibrational levels of the a³Σ⁺ state show more intense REMPI lines than is predicted from FCFs calculation. It is worth mentioning that similar disagreement between calculations and experiment has been observed in other REMPI spectra.^26,28 Revisiting the excited state PECs with the help of experimental data might help to improve theoretical calculations, which in turn may lead to a more accurate calculation of the FCFs.

Additional observations from our spectra are as follows: (i) the 3³Πv_Π′←a³Σ⁺ (v″ = 7) features are weaker than the above mentioned transitions for all three spectra, likely due to only minimal decay to this vibrational level from any of the PA resonances used in our measurements; and (ii) many v″ = 10 transitions are partially obscured by the overlap with stronger v″ = 11 lines. These transitions are most clearly seen in the 17 440–17 600 cm⁻¹ range and labeled in Figure S5(b) in the supplementary material.²⁴ 

In addition to the 3³Π_Ω vibrational levels, we also observe and assign v_Σ′ = 0–5 vibrational levels of the 4³Σ⁺ state. The 4³Σ⁺ diabatic PEC is shown as the blue curve in Fig. 4(a). Unlike the triplet structure originating from spin-orbit splitting of the 3³Π state, we do not observe separate Ω = 0⁻ and 1 components for 4³Σ⁺. This may be due to the small spin-orbit splitting for this state, calculated to be less than 1 cm⁻¹ at the equilibrium internuclear spacing R_e ∼ 5.4 Å. We compare the calculated 4³Σ⁺ vibrational spacing with experiment graphically in Fig. 7.

We recalculate the v″–v_Π′ transition energies with reference to the Li(2s) + Rb(5s) asymptote for each spin-orbit component Ω = 0, 1, and 2 of the 3³Π and 4³Σ⁺ states and present these data in Table III. The calculated energies¹⁹ of these states fall approximately 62-66 cm⁻¹ lower than the observed energies, indicating that the depth of the ab initio potential energy well is too large by this amount. This seems a very reasonable agreement with experiment.

We have fit the 3³Π and 4³Σ⁺ electronic state energies presented in Table IV to

where T_e is the term value, ω_e is the vibrational constant, and ω_ex_e is the anharmonicity, in order to determine the best values for each of these constants. The term values are referenced to the Li(2s) + Rb (5s) asymptote, and, for comparison, we also list theoretical values from Refs. 19 and 20 when available. We note good agreement between our measured values and the theory values in most cases, with the exception of the anharmonicity of the 3³Π states, for which the theory value is five times greater than the measured value.

Before we conclude, we present an estimate of the number of triplet ground state molecules available for REMPI ionization. In earlier trap-loss studies,¹⁷ we observed an excited state molecule formation rate, R_PA, of ∼10⁷ s⁻¹ for resonances near the ⁷Li 2s ²S_1/2 + ⁸⁵Rb 5p ²P_1/2 asymptote. Here, we use ionization data for the 2(0⁻) u_PA = 5 level to estimate R_PA. The following calculation based on Ref. 29 takes into account the molecular creation rate by PA, ionization, and detection efficiencies that will be relevant to ionization detection of ground state molecules as well.

The number of ions detected per ionization pulse, N_ion, depends on (i) N_a, the number of ground (triplet) state molecules in a particular vibrational state (for example, v″ = 12), (ii) the probability, p_ion, of ionizing molecules per ion pulse, and (iii) the detection efficiency e_d. In other words,

For the 2(0⁻) u_PA = 11 level, we record a strong ion signal N_ion ∼ 2 ions/pulse. The ionization probability is calculated as

where σ is the photoionization cross section, and since there is no available data for LiRb in the literature, we estimate it as the same order of magnitude as Rb₂ ∼ 10⁻²² m².²⁹ With pulse energy E ∼ 3 mJ, ionizing laser wavelength λ = 565 nm and the pulsed-laser beam diameter, 2ω = 4 mm, we obtain from Eq. (3)p_ion ∼ 6.5 × 10⁻². Estimating the detection efficiency e_d is difficult, as it is related to the MCP detector efficiency and also the probability that an ion generated by the ionization laser strikes the MCP. Here, we estimate e_d between 0.1 and 0.8. Using the values for p_ion and e_d along with N_ion, we calculate from Eq. (2), an estimate for the number of molecules in the a³Σ⁺ state: N_a ∼ 40–300/pulse. Note: From this, it is possible to estimate the number of a³Σ⁺ state molecules formed per second. Since molecules are not trapped, they drift out of the ionization region in ∼10 ms, while the ionizing laser pulse arrives only once every 100 ms allowing only ∼10% of molecules to be detected. The number of a³Σ⁺ state molecules formed in 100 ms is thus ∼10 N_a, i.e., the a³Σ⁺ state molecule formation rate is ∼4 × 10³–3 × 10⁴ s⁻¹, relatively high and consistent with our previous expectations.^16,17

Solving the rate equation for the number of a³Σ⁺ state molecules, a relation between the photoassociation rate R_PA and the number of those molecules is found,²⁹ 

where t is the time between REMPI laser pulses (0.1 s) and τ is the transit time of the molecules in the ionizing beam volume, i.e., the time that molecules reside in the REMPI beam, and hence, the limiting time for the creation of a³Σ⁺ state molecules that can be ionized. For a 4 mm beam diameter and molecules with kinetic energy ∼1 mK, τ ∼ 10 ms. The PA level, 2(0⁻) u_PA = 5, could decay to many different vibrational levels of the lowest triplet state a³Σ⁺. Nevertheless in Fig. 6, we notice that this decay is mainly to the v″ = 12 level. In Eq. (4), FCF stands for the FCF for decay from the PA level to the v″ = 12 level of a³Σ⁺. In this case, FCF = 0.2. The FCF is calculated from ab initio LiRb PECs¹⁹ using LEVEL 8.0.²⁶ Substituting the FCF, transit time τ, and N_a into Eq. (4), we calculate the excited state molecule formation rate to be R_PA = 2 × 10⁴–2 × 10⁵ s⁻¹. Within the uncertainty in the photoionization cross section σ and detector efficiency e_d, this estimate leads to a photoassociation rate higher than other molecular species, for instance, Rb₂,²⁹ consistent with the extremely high R_PA observed in trap-loss measurements.¹⁶ 

We have discussed the formation of ultracold ⁷Li⁸⁵Rb molecules in the lowest triplet state using PA followed by spontaneous emission and presented preliminary REMPI spectra to probe the high-lying vibrational levels of the lowest triplet state and excited electronic states. Using ionization detection, we have discovered new PA resonances with binding energies up to ∼62 cm⁻¹. Next, we have recorded REMPI spectra by fixing the PA laser at three different resonances, the u_PA = 5, 9, and 11 vibrational lines of the 2(0⁻) electronic state, and identified transitions 3³Π (v_Π′ = 0–10)←a³Σ⁺ (v″ = 7–13). Furthermore, we have also labeled lines corresponding to 4³Σ⁺ (v_Σ′ = 0–5)←a³Σ⁺ (v″ = 7–13) transitions. Overall, we have identified ∼94% of the lines experimentally observed in our REMPI spectra and derived the spectroscopic constants for these newly observed electronic states. At this point, we do not have sufficient information to explain the origin of the unassigned lines. They may be connected with one of several other electronic states—besides the two we have studied—that may be accessible by our REMPI laser, as seen in Fig. 3(a). Further investigation in this direction may be warranted. Nevertheless, these initial investigations of the a³Σ⁺, 3³Π, and 4³Σ⁺ electronic states of the ⁷Li⁸⁵Rb system are a reasonable starting point for our ongoing work on identifying suitable transition pathways to transfer short-lived ultracold molecules into stable, deeply bound-molecules.

We gratefully acknowledge support for early stages of this project from the NSF (No. CCF-0829918), an equipment grant from the ARO (No. W911NF-10-1-0243), and university support through the Purdue OVPR AMO incentive grant. The work of J.P.R. was supported by the Department of Energy, Office of Science, under Award No. DE-SC0010545.