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arXiv:cond-mat/0401219 · Physical Review A

High-light-intensity photoassociation in a Bose-Einstein condensate

Thomas Gasenzer

Published Aug 26, 2004• 16 citations
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Abstract

We investigate theoretically the molecular yield in photoassociation of Bose-Einstein condensed sodium atoms for light intensities of the order of and above those applied in a recent experiment. Our results show that the rate at which ground-state molecules may be formed saturates at high light intensities whereas the loss rate of condensate atoms does not. This is caused by the opposing roles of the short- and long-range pair correlations present near resonance under the influence of the laser and is crucial for the development of efficient photoassociation procedures in a condensate.

DOI
10.1103/physreva.70.021603

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We investigate theoretically the molecular yield in photoassociation of Bose-Einstein condensed sodium atoms for light intensities of the order of and above those applied in a recent experiment. Our results show that the rate at which ground-state molecules may be formed saturates at high light intensities whereas the loss rate of condensate atoms does not. This is caused by the opposing roles of the short- and long-range pair correlations present near resonance under the influence of the laser and is crucial for the development of efficient photoassociation procedures in a condensate.
We form ultracold Na2{\mathrm{Na}}_{2}Na2​ molecules by single-photon photoassociation of a Bose-Einstein condensate, measuring the photoassociation rate, linewidth, and light shift of the J=1J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1J=1, v=135v\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}135v=135 vibrational level of the ${A}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ molecular state. The photoassociation rate constant increases linearly with intensity, even where it is predicted that many-body effects might limit the rate. Our observations are in good agreement with a two-body theory having no free parameters.
A dynamical many-body theory of single color photoassociation in a Bose-Einstein condensate is presented. The theory describes the time evolution of a condensed atomic ensemble under the influence of an arbitrarily varying near-resonant laser pulse, which strongly modifies the binary scattering properties. In particular, when considering situations with rapid variations and high light intensities the approach described in this article leads, in a consistent way, beyond standard mean-field techniques. This allows one to address the question of limits to the photoassociation rate due to many-body effects which has caused extensive discussions in the recent past. Both the possible loss rate of condensate atoms and the amount of stable ground-state molecules achievable within a certain time are found to be stronger limited than according to mean-field theory. By systematically treating the dynamics of the connected Green's function for pair correlations the resonantly driven population of the excited molecular state as well as scattering into the continuum of noncondensed atomic states are taken into account. A detailed analysis of the low-energy stationary scattering properties of two atoms modified by the near resonant photoassociation laser, in particular of the dressed state spectrum of the relative motion prepares for the analysis of the many-body dynamics. The consequences of the finite lifetime of the resonantly coupled bound state are discussed in the two-body as well as in the many-body context. Extending the two body description to scattering in a tight trap reveals the modifications to the near resonant adiabatic dressed levels caused by the decay of the excited molecular state.
We consider two-color heteronuclear photoassociation of a dual-species Bose-Einstein condensate into a Bose-Einstein condensate of dipolar molecules in the J=1J=1J=1 vibronic ground state, where a free-ground laser couples atoms directly to the ground state and a free-bound laser couples the atoms to an electronically excited state. This problem raises an interest because heteronuclear photoassociation from atoms to near-ground-state molecules is limited by the small size of the target state. Nevertheless, the addition of the electronically excited state creates a second pathway for creating molecules in the vibronic ground state, leading to quantum interference between direct photoassociation and photoassociation via the excited molecular state, as well as a dispersivelike shift of the free-ground resonance position. Using LiNa as an example, these results are shown to depend on the detuning and intensity of the free-bound laser, as well as the semiclassical size of both molecular states. Whereas strong enhancement enables saturation of the free-ground transition, coherent conversion from a two-species condensate of atoms to a condensate of dipolar molecules in the vibronic ground state is only possible for a limited range of free-bound detunings near resonance.
The rate of photoassociation (PA) determines how quickly molecules form from atoms illuminated by a resonant laser pulse. Knowledge of limits of this molecular formation rate provide a fundamental component on the maximum rate that a tightly bound ground state molecular Bose-Einstein condensate (BEC) could be formed using a two-photon transition. This molecular synthesis represents the beginning of a new era of ultracold quantum chemistry. The available Feshbach resonance in this system is an indispensable tool to increase the molecular formation rate due to PA in the anticipation of revealing these fundamental rate limits. While the rate saturates in a thermal gas, no evidence of saturation has yet been observed in a BEC. A loss of atoms due to a PA pulse tuned to the v " = 83 excited state molecular vibrational level provides the measurement of the PA rate. The rate varies by several orders of magnitude either by tuning the magnetic field near a Feshbach resonance or by adjusting the PA intensity. We measure the PA rate at magnetic fields between 550-900 Gauss in a BEC and a thermal gas, which is near the Feshbach resonance at 736 Gauss. The rapidly changing rate near the Feshbach resonance reflects the overlap between the ground state and the excited state wavefunctions. We present the first quantitative measurement of the PA rate near a Feshbach resonance. We measure the magnetic field dependence of the molecular resonance position near the Feshbach resonance. We introduce the first observation of a positive energy shift associated with photoassociation. The measured energy shift asymptotically diverges as it approaches the Feshbach resonance and agrees qualitatively with described theory at all magnetic fields. We observe intensity dependent saturation in the PA rate in a thermal gas and the measurements qualitatively agree with a unitarity limited rate. The first conclusive evidence for a suppression of the PA rate occurs for intensities above the saturation intensity. We report the first observed saturation of the PA rate in a BEC. Three separate theories present possible mechanisms for the observed saturation.
In this paper we formulate the time-dependent many-body theory of photoassociation in an atomic Bose-Einstein condensate with realistic interatomic interactions, using and comparing two approximations: the first-order cumulant approximation [Phys. Rev. A 65, 033601 (2002)], and the reduced pair wave approximation [Phys. Rev. A 68, 033612 (2003)]. The two approximations differ only by the way a pair of condensate atoms is influenced by the mean field at short interatomic separations. In both cases we identify two different regimes of photoassociation: the adiabatic regime and the coherent regime. The threshold for the so-called ``rogue dissociation'' [Phys. Rev. Lett. 88, 090403 (2002)] (where the Gross-Pitaevski\ifmmode \breve{\imath}\else \u{\i}\fi{} model breaks down) is found to be different in each regime, shedding new light on the experiment of McKenzie et al. [Phys. Rev. Lett. 88, 120403 (2002)]. Comparing numerical solutions for the two approximations with the Gross-Pitaevski\ifmmode \breve{\imath}\else \u{\i}\fi{} predictions, we find two different effects: reduction of the photoassociation rate at short times, and creation of correlated pairs of atoms when the laser intensity is switched on rapidly. We also observe effects on the symmetry of the photoassociation line shapes, giving the possibility to experimentally distinguish between the two approximations.
We study coherent photoassociation, phenomena analogous to coherent optical transients in few-level systems, which may take place in photoassociation of an atomic Bose-Einstein condensate but not in a nondegenerate gas. We develop a second-quantized Hamiltonian to describe photoassociation, and apply the Hamiltonian both in the momentum representation and in the position representation (field theory). The solution of the two-mode problem, including only one mode each for the atomic and molecular condensates, displays analogs of Rabi oscillations and rapid adiabatic passage. A classical version of the field theory for atoms and molecules is used to demonstrate that, in the presence of photoassociating light, a joint atom-molecule condensate is unstable against the growth of density fluctuations. Experimental complications, including spontaneous emission and unwanted ``rogue'' photodissociation from a photoassociated molecule, are analyzed. A two-color Raman scheme is studied as a method to set up an effective two-mode scheme with reduced spontaneous-emission losses. We discuss photoassociation rates and photoassociation Rabi frequencies for high-lying vibrational states in alkali dimers both on the basis of molecular-structure calculations, and by comparing with an experiment [Wynar et al., Science 287, 1016 (2000)].