Formation of ultracold polar molecules in the rovibrational ground state
Ultracold LiCs molecules in the absolute ground state X, =0, =0 are formed via a single photo-association step starting from laser-cooled atoms. The selective production of =0, =2 molecules with a 50-fold higher rate is also demonstrated. The rotational and vibrational state of the ground state molecules is determined in a setup combining depletion spectroscopy with resonant-enhanced multi-photon ionization time-of-flight spectroscopy. Using the determined production rate of up to molecules/s, we describe a simple scheme which can provide large samples of externally and internally cold dipolar molecules.
pacs:37.10.Mn, 33.20.-t, 33.80.Rv
A gaseous cloud of translationally ultracold molecules, i.e. well below a temperature of 1 mK, in their rovibrational ground state is the starting point for many intriguing scientific applications, such as the exploration of quantum phases in dipolar gases Micheli et al. (2006); Pupillo et al. (2008), the development of quantum computation techniques Rabl et al. (2006), precision measurements of fundamental constants Zelevinsky et al. (2008), and the investigation and control of ultracold chemical reactions Tscherbul and Krems (2006). A number of experimental approaches are currently being studied to prepare and manipulate ultracold molecules Doyle et al. (2004); Dulieu et al. (2006). Up to now, the formation of ultracold molecules in the lowest vibrational level of the electronic ground state has been demonstrated for ultracold KRb Nikolov et al. (2000), RbCs Sage et al. (2005), and Cs Viteau et al. (2008), in all cases using complex photo-association schemes in an ultracold gas of atoms involving both continuous and pulsed laser fields. In an alternative approach, ultracold gaseous samples of magneto-associated, weakly bound molecules, so-called Feshbach molecules, have recently been transferred into deeply bound vibrational states, yet not the lowest state, by coherent adiabatic passage Winkler et al. (2007); Ospelkaus et al. (2008/06/22/online); Danzl et al. (2008) .
In this work we demonstrate the production of ultracold LiCs molecules in the absolute vibrational and rotational ground state X,=0,=0, by scattering the light of a single narrow-band photo-association (PA) laser off pairs of magneto-optically trapped lithium and cesium atoms. We unambiguously assign the produced quantum state using high resolution, rotationally selective depletion spectroscopy combined with resonance enhanced multi-photon ionization time-of-flight (REMPI-TOF) mass spectrometry. The sequence of the formation and detection steps is schematically shown in Fig. 1.
Cs and Li atoms out of a double species oven are slowed in a Zeeman slower and trapped in an overlapped magneto-optical trap (MOT) for lithium and a forced dark-spot MOT (SPOT) Ketterle et al. (1993) for cesium. We trap 410 cesium atoms and 10 lithium atoms at densities of 310cm and 10cm respectively. Time-of-flight expansion was used to measure a cesium temperature of 250(50)K. Due to the large photon recoil and unresolved hyperfine structure of the excited state, the lithium atoms have a temperature of hundreds of K. In the cesium SPOT, 97% of the atoms are in the lower hyper-fine ground state =3, while in the lithium MOT 80% of the atoms are in the upper hyper-fine state =2. Therefore the atoms collide mainly on the Li(2=2)+Cs(6=3) asymptote. For PA 500mW of light from a Ti:Sa laser are collimated to a waist of 1.0 mm and passed through the center of the trap region, left on continuously during all measurements. For the detection of formed molecules, first all cesium atoms in the trap are quenched to the ground state by blocking the cesium repumper, because two photon ionization of excited cesium atoms would form a strong background signal for the detection of LiCs ions. After 0.6 ms a pulsed dye laser (pulse energy 4 mJ, pulse length 7 ns, bandwidth 2 GHz) ionizes ground state molecules. The laser beam is collimated to a waist of 5 mm and is aligned to pass roughly one beam diameter below the trapped atoms in order to prevent excessive ionization of atoms. The ions are then detected in a high resolution time-of-flight mass spectrometer and are counted in a single-ion counting setup (for details see Ref. Kraft et al. (2006, 2007)). The extraction fields of 47 V/cm are switched on only 0.5 ms before the ionization pulse for 1 ms, so that the PA is performed mainly under field-free conditions. This experimental cycle is repeated at 20 Hz.
We determine the relative collision energy of lithium and cesium atoms by fitting the shape of a narrow, temperature-broadened PA resonance with the model of Ref. Jones et al. (1999). Assuming a natural linewidth of =7 MHz, we deduce a relative collision temperature of 530(80)K, dominated by the temperature of the lithium atoms. This is well below the Li-Cs -wave centrifugal barrier of 1.6 mK derived from the C dispersion coefficient of Ref. Marinescu et al. (1994). Assuming a Boltzmann distribution of collision energies, we expect a -wave contribution on the order of 5% and no contributions from higher partial waves.
For the production of ground state molecules, photo-association is performed via the B state correlated to the Li(2)+Cs(6) asymptote. We identify vibrational levels from =35 just below the asymptote down to =4 and find excellent agreement with the energies calculated from an experimental energy curve for this state Stein et al. (2008).
For the experiments presented in this work we focus on the =4,=1 and =2 levels of the B state which are addressed with PA light of 946.56 nm. Typical PA scans of the corresponding resonances are shown in Fig. 2. Both resonances show substructure which reflects the molecular hyperfine interactions. For PA we always choose the strongest component. It is noteworthy to mention the strongly increased PA rate for the =2 over the =1 resonance by roughly a factor of 20. This is in contrast to ratios 1 observed in our experiment for higher vibrational levels . A full analysis of the observed PA lineshapes will be subject of further studies.
The excited B, =4 molecules decay spontaneously only into the X state Stein et al. (2008). Using the experimental potential curves from Ref. Stein et al. (2008); Staanum et al. (2007) and an ab-initio -dependent dipole moment function foo (a), Einstein coefficients for the spontaneous decay from B,=4 into X levels are calculated. Tab. 1 shows the deduced relative population of the X levels. From these calculations 23% of all excited state molecules are expected to decay into the X,=0 level. We note that nearly all excited =4 molecules are expected to decay into bound molecules, since the sum over all Franck-Condon (FC) factors for decay into the X state is close to unity Drag et al. (2000).
|Rel. pop. [%]||23||1||12||2||3||8||2||1||5||6||2||35||0|
The formation of X molecules is detected by two-photon ionization with typical wavelengths in the range of 575 nm to 600 nm. At these energies, vibrational levels =0-4 of the X state can be ionized via the well known intermediate B state. Fig. 3 shows a REMPI scan together with expected positions for transitions from the X,=0-3 levels to intermediate levels in the B state. Resonances are clearly visible at the expected positions for transitions from X,=0 to intermediate levels B,=13-17. However some of these resonances could also include contributions from higher vibrational states. The intensities required for the ionization of ground state molecules strongly saturate the first resonant bound-bound transitions, therefore the rotational structure of the ground state levels is not resolved.
In order to further identify the internal quantum states of the ultracold ground state molecules we perform depletion spectroscopy of the formed ground state molecules Wang et al. (2007). An additional narrow band laser optically pumps population out of rovibrational levels of the X ground state (Fig. 1). Those levels are coupled to specific rovibrational levels in the B potential from which spontaneous decay leads to higher-lying vibrational levels. The full scheme for the depletion spectroscopy is as follows: with the PA laser locked at a chosen resonance, the REMPI laser is set to selectively ionize one vibrational ground state and a cw dye laser (bandwidth 5 MHz, typically 40mW, =0.7 mm), aligned collinear with the PA light, is scanned. Rotational components of the chosen vibrational level are detected as a reduction of the ion count rate when the narrow cw dye laser is resonant with transitions to excited state levels. The expected positions of the depletion resonances are given by where , the term energy difference between excited and ground state vibrational level, and (), the excited state (ground state) rotational constant, are calculated from experimental potential energy curves Staanum et al. (2007); Stein et al. (2008).
Depletion scans were performed for X,=0 molecules, ionized via the intermediate B,=14 level at an ionization wavelength of 16999.4 cm (marked with a star in Fig. 3). In the scan of Fig. 4 a), the molecules are produced by PA via B,=4,=2 (Fig. 2, right trace). We observe that excitation on the transitions from X,=0,=2 to B,=12,=1-3 reduces the ion count rate down to the background level. Therefore, the ions at this REMPI resonance originate predominantly in the X,=0 level. The spontaneous decay of the B,=4,=2 level occurs only via the Q-branch (=0) leading to the population of only =2 rotational levels, as shown by the rotational assignment in Fig. 4 a) foo (b). From the measured spectrum we derive the excited state rotational constant =3.10(5) GHz in excellent agreement with the calculated value of 3.096 GHz. In combination with the calculated ground state rotational constant one gets =16895.75(2) cm which is also in very good agreement with the expected value of 16895.77 cm. The depletion resonances show a width of about 2 GHz, which can be attributed to hyperfine broadening of the excited states (typically 500 MHz) and strong saturation of the transition. Hyperfine structure of deeply bound ground state levels is expected to be below 1 MHz and is therefore not resolved in the current experiment.
Fig. 4 b) shows a depletion scan for =0 molecules produced via the PA resonance B,=4,=1 (Fig. 2, left trace). With and from the depletion spectrum of Fig. 4 a) and the calculated value for the exact positions of the depletion resonances are known. Using the widths found for the =2 depletion resonances and relative population strengths from Hönl-London-Factors, we fit spectra for different excited state parities to the data in Fig. 4 b). The only free fit parameters are the level of the undepleted ion signal and the depletion depth. The precisely known positions of the depletion resonances make a single excited state parity unlikely and we attribute the observed spectrum to PA via both parity components with equal strength leading to population of X,=0,=0,1 and 2 states foo (c).
For molecules in the absolute ground state X,=0,=0, produced by PA via B,=4,=1, on average 510 LiCs ions are detected per ionization pulse. Since the experiment is running at 20 Hz this yields a detection rate of 0.1 ions/s. Taking into account a geometric overlap factor of 40%, a typical on-resonance ionization probability of 1%, and a detector efficiency of 20% Fraser (2002), this results in a production rate of about 110 molecules/s in the =0,=0 absolute ground state. For molecules in the X,=0,=2 state, produced by PA via B,=4,=2, on average 0.2 LiCs ions per ionization pulse are detected. Following the same argument as above, this results in a production rate of about 510 molecules/s in the ground state level =0, comparable to the rate given in Ref. Sage et al. (2005) for RbCs and roughly a factor 20 smaller than the rate given in Ref. Viteau et al. (2008) for the homonuclear Cs. However, we want to point out that we determine rates for the population of a single vibrational and rotational state, while in the cited references the produced molecules are distributed over a range of rotational states. The translational temperature of the molecules is estimated based on the atomic values and a simple kinematic model to be about 260 K, dominated by the temperature of the heavier cesium; contributions from photon recoil during the single absorption and emission cycle are not significant.
As the presented scheme for the formation of molecules relies on spontaneous decay, it allows the continuous accumulation of molecules in the absolute ground state. Due to the large vibrational level spacing in LiCs accidental re-excitation of formed molecules by the narrow-band PA laser is very unlikely. This accumulative approach is in contrast to schemes involving adiabatic transfer. The molecules produced in the presented setup could be trapped in an electrostatic trap Kleinert et al. (2007). Alternatively, one could start from a mixture of lithium and cesium atoms in an optical dipole trap Mudrich et al. (2002), where typically 10-fold increased densities could lead to a production rate on the order of 510 molecules/s for ground state molecules in =0,=2. On a time scale of seconds, a large part of the trapped atom pairs may therefore be transformed into molecules. In a final step of adiabatic transfer using microwaves at 22.5 and 11.2 GHz, the =2 molecules could be transferred to =0. Excited vibrational states would be constantly removed by inelastic collisions with ultracold atoms, as shown for Cs+Cs Staanum et al. (2006); Zahzam et al. (2006). Sympathetic cooling in the dipole trap Mudrich et al. (2002) may yield molecular samples with temperatures down to the nanokelvin regime. This may open up am efficient route to form stable quantum gases of molecules in their absolute internal ground state.
Acknowledgements.We thank S.D. Kraft and P. Staanum for contributions at the early stage of the experiment. We also thank E. Tiemann and A. Pashov for providing experimental LiCs potentials before publication and, together with J. Hutson, for fruitful discussions. This work is supported by the DFG under WE2661/6-1 in the framework of the Collaborative Research Project QuDipMol within the ESF EUROCORES EuroQUAM program. JD acknowledges partial support of the French-German University. AG is a postdoctoral fellow of the Alexander von Humboldt-Foundation.
- Micheli et al. (2006) A. Micheli et al., Nature Physics 2, 341 (2006).
- Pupillo et al. (2008) G. Pupillo et al., Phys. Rev. Lett. 100, 050402 (2008).
- Rabl et al. (2006) P. Rabl et al., Phys. Rev. Lett. 97, 033003 (2006).
- Zelevinsky et al. (2008) T. Zelevinsky et al., Phys. Rev. Lett. 100, 043201 (2008).
- Tscherbul and Krems (2006) T. V. Tscherbul and R. V. Krems, Phys. Rev. Lett. 97, 083201 (2006).
- Doyle et al. (2004) J. Doyle et al., Eur. Phys. J. D 31, 149 (2004).
- Dulieu et al. (2006) O. Dulieu et al., J. Phys. B 39 (2006), introductory review.
- Nikolov et al. (2000) A. N. Nikolov et al., Phys. Rev. Lett. 84, 246 (2000).
- Sage et al. (2005) J. M. Sage et al., Phys. Rev. Lett. 94, 203001 (2005).
- Viteau et al. (2008) M. Viteau et al., Science 321, 232 (2008).
- Winkler et al. (2007) K. Winkler et al., Phys. Rev. Lett. 98, 043201 (2007).
- Ospelkaus et al. (2008/06/22/online) S. Ospelkaus et al., Nature Physics (2008/06/22/online).
- Danzl et al. (2008) J. G. Danzl et al., Science p. 1159909 (2008).
- Staanum et al. (2007) P. Staanum et al., Phys. Rev. A 75, 042513 (2007).
- Stein et al. (2008) A. Stein et al., Eur. Phys. J. D 48, 177 (2008).
- Korek et al. (2006) M. Korek et al., Can. J. Phys. 84, 959 (2006).
- Ketterle et al. (1993) W. Ketterle et al., Phys. Rev. Lett. 70, 2253 (1993).
- Kraft et al. (2006) S. D. Kraft et al., J. Phys. B 39, S993 (2006).
- Kraft et al. (2007) S. D. Kraft et al., Appl. Phys. B 89, 453 (2007).
- Jones et al. (1999) K. M. Jones et al., Phys. Rev. A 61, 012501 (1999).
- Marinescu et al. (1994) M. Marinescu et al., Phys. Rev. A 49, 982 (1994).
- foo (a) The dipole moment function was calculated as described in Ref. Aymar and Dulieu (2005). The transition dipole moment varies not more than 10 % around an average value of 9.9 Debye over the relevant distances.
- Drag et al. (2000) C. Drag et al., IEEE J. Quantum Electron. 36, 1378 (2000).
- Wang et al. (2007) D. Wang et al., Phys. Rev. A 75, 032511 (2007).
- foo (b) This clearly indicates the excitation of a single parity component of B: for even rotational levels in , the odd parity component decays only via the Q-branch into while the even parity component decays via the P- and R-branch. Odd parity levels of only couple to even partial waves of the scattering continuum. As =2 can not be excited from continuum states with angular momentum =0 via a dipole transition, the excitation can only originate in =2, which suggests the presence of a -wave shape resonance. Note that the doubling of the PA levels is on the order of 1MHz Stein et al. (2008).
- foo (c) The strong -wave contribution to the PA via B,=4,=2 couples also to the negative parity component of B,=4,=1. Decay from this component populates X,=0,=0,2 as observed. The additional population of =1 can be explained by p-wave contributions to the continuum wave function.
- Fraser (2002) G. W. Fraser, Int. J. Mass Spect. 215, 13 (2002).
- Kleinert et al. (2007) J. Kleinert et al., Phys. Rev. Lett. 99, 143002 (2007).
- Mudrich et al. (2002) M. Mudrich et al., Phys. Rev. Lett. 88, 253001 (2002).
- Staanum et al. (2006) P. Staanum et al., Phys. Rev. Lett. 96, 023201 (2006).
- Zahzam et al. (2006) N. Zahzam et al., Phys. Rev. Lett. 96, 023202 (2006).
- Aymar and Dulieu (2005) M. Aymar and O. Dulieu, J. Chem. Phys. 122, 204302 (2005).