Photoassociative Frequency Shift in a Quantum Degenerate Gas

We observe a light-induced frequency shift in single-photon photoassociative spectra of magnetically trapped, quantum degenerate Li. The shift is a manifestation of the coupling between the threshold continuum scattering states and discrete bound levels in the excited-state molecular potential induced by the photoassociation laser. The frequency shift is observed to be linear in the laser intensity with a measured proportionality constant that is in good agreement with theoretical predictions. The frequency shift has important implications for a scheme to alter the interactions between atoms in a Bose-Einstein condensate using photoassociation resonances. PACS numbers: 03.75.Fi, 32.80.Pj, 34.50.-s Typeset using REVTEX 1 Photoassociative spectroscopy of trapped atomic gases has been used to measure interatomic interaction potentials with ultra-high sensitivity [1]. Although most photoassociation experiments with trapped atoms have been performed at temperatures near 1 mK, sub-μK temperatures can be achieved using evaporative cooling. This is the temperature regime that recent experiments on Bose-Einstein condensation (BEC) [2–4] have been conducted. There are several important improvements to photoassociative spectroscopy that are realized with a quantum degenerate gas. Since the energy spread of atoms with temperatures under 1 μK is less than 20 kHz, spectroscopic precision can be increased to unprecedented levels. Furthermore, it was recently pointed out that the rate of photoassociation increases with increasing phase space density, nλD, where n is the atomic density and λD is the thermal de Broglie wavelength [5]. Finally, at sub-μK temperatures the spatial extent of the trapped gas can be very small, enabling tighter focusing of the photoassociation laser beam and, therefore, higher light intensities. We have exploited these enhancements to investigate the effect of light intensity on single-photon photoassociation spectra of a magnetically trapped, evaporatively cooled gas of Li. In particular, we have measured a spectral shift proportional to the light intensity [5–8]. This shift is relevant to proposed schemes for utilizing photoassociation to alter the interactions between atoms in a Bose-Einstein condensate [6,7] and for producing ultracold, trapped molecules [5,9–19]. The apparatus used in this experiment, which has been used to produce BEC of Li, has been described previously [20]. Permanent magnets establish an Ioffe-Pritchard type trap with a depth of 10 mK and a bias field of 1004 G at the trap center. Approximately 5× 10 atoms in the F = 2, mF = 2 hyperfine sublevel of Li are directly loaded into the trap from a laser-slowed atomic beam using three-dimensional optical molasses. Following loading, the laser beams are extinguished and the atoms are evaporatively cooled using a microwave field to selectively spin-flip, and thereby remove the hottest atoms. The final temperatures are between 400 and 650 nK, corresponding to between 3× 10 and 1× 10 atoms. Under these conditions, the gas is quantum degenerate, although the fraction of atoms in the condensate is small due to attractive interactions in lithium [21]. 2 Following evaporation, a photoassociation laser beam of frequency ω1, and intensity I, is passed through the trapped atoms. A schematic representation of the relevant molecular potentials and energy levels is shown in Fig. 1. A vibrationally and electronically excited molecule may form when ω1 is tuned to resonance between the continuum level of two colliding atoms and a bound level in the excited-state molecular potential. The excited molecule may spontaneously decay, most probably into a pair of hot atoms or possibly into a ground-state molecule, resulting in a detectable reduction of trapped atoms. The trapped cloud is probed in situ using the phase contrast imaging technique described in Ref. [20] in order to determine the number of remaining atoms N . Since photoassociation removes a significant number of atoms, only one image may be obtained per evaporative cooling cycle. Therefore, to build up a resonance curve, the entire cycle is repeated many times for different values of ω1. The photoassociation light is derived from a low-power (∼10 mW), grating-stabilized, external cavity diode laser. The laser is side-locked to a 3 GHz free-spectral-range (FSR) scannable Fabry-Perot cavity in order to reduce acoustical jitter to an RMS amplitude of ∼1 MHz as measured with an optical spectrum analyzer. A 750 MHz FSR scanning etalon is used to measure the relative frequency separation between the diode laser and another laser which is locked to the 2S1/2 − 2P3/2 atomic resonance. Slow feedback to the 3 GHz cavity maintains this frequency separation to within ∼3 MHz. An ∼8 mW beam from the diode laser is injected into a tapered optical amplifier, providing up to 300 mW of output power at the injected frequency. An acousto-optic modulator and a mechanical shutter are used to chop the amplified beam on and off. The beam is subsequently coupled into a single-mode optical fiber, reducing pointing jitter and intensity variation across the beam profile. The output of the fiber, limited to 70 mW, is focussed at the position of the atoms to a 1/e intensity radius that ranges between 60 and 120 μm. The laser beam waist is always larger than the 1/e density radius of the atoms of ∼40 μm. The photoassociation laser beam is directed nearly parallel to the laser beam used for imaging the atom cloud, which allows for the imaging optics to be used to ensure spatial overlap of the photoassociation laser beam 3 with the atom cloud. The laser frequency ω1 is tuned to near resonance with the v = 69 vibrational level of the excited molecular potential. Since the binding energy of this level, 854 GHz, is much larger than either the 10 GHz fine-structure splitting of the 2P atomic state or any hyperfine interaction, the total electronic spin S decouples from both the electronic orbital angular momentum L and the total nuclear spin I. In this case, the light field only couples to L, and S and I do not change during the photoassociation transition. Therefore, the selection rules for the total spin G = S + I, and its projection MG, are ∆G = 0 and ∆MG = 0 [22], and there is no first-order Zeeman shift in the transition energy. Since both the ground state and excited molecular potentials are Σ states, corresponding to zero projection of L onto the internuclear axis, there is no change in the projection of L, and the transition dipole is oriented along the trap magnetic field bias direction (0,0,1). Geometric constraints, however, require the photoassociation laser beam to propagate along the (1,1,1) direction, so that only 2/3 of the light intensity can be polarized along the transition dipole. In this paper, the reported intensities correspond to those actually measured. Figure 2 shows several resonance curves corresponding to different values of I. The data points are normalized to background images obtained without the photoassociation pulse to account for drift in trap loading conditions. The data clearly demonstrate that the resonance is red-shifted with increasing I. As the intensity is varied the photoassociation pulse time is adjusted to maintain a relatively large and constant signal size. The resonance spectral widths are observed to be between 20 and 30 MHz. The natural linewidth for a long-range vibrational level, such as v = 69, is ∼2Γa [23], where Γa = 2π × 5.9 MHz is the natural linewidth of the atomic 2P excited state of Li. There are several other mechanisms which contribute to the broadening of the observed lineshapes. The relatively large depth of signal leads to a saturation broadening, which is the case even for low I since the pulse duration is extended to maintain a relatively constant signal size. Additionally, inhomogeneous broadening caused by the variation of laser intensity across the spatial extent of the atom cloud is expected to contribute as much as 10 MHz to the width for the largest