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Physical Review A

Stimulated Raman adiabatic passage from atomic to molecular Bose-Einstein condensates: Feedback laser-detuning control and suppression of dynamical instability

Jing Cheng, Shensheng Han, YiJing Yan

Published Mar 30, 2006• 17 citations
Publisher

Abstract

We present a feedback control scheme that designs time-dependent laser-detuning frequency to suppress possible dynamical instability in coupled free-quasibound-bound atom-molecule condensate systems. The proposed adaptive frequency chirp with feedback is shown to be highly robust and very efficient in the passage from an atomic to a stable molecular Bose-Einstein condensate.

DOI
10.1103/physreva.73.035601

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We present a feedback control scheme that designs time-dependent laser-detuning frequency to suppress possible dynamical instability in coupled free-quasibound-bound atom-molecule condensate systems. The proposed adaptive frequency chirp with feedback is shown to be highly robust and very efficient in the passage from an atomic to a stable molecular Bose-Einstein condensate.
Summary form only given. Coherent conversion of an atomic to a molecular Bose-Einstein condensate (BEC) is a first step towards 'superchemistry', which is the atom optics analog of frequency conversion in nonlinear optics. A number of studies of this have shown that direct conversion via Raman photo-association appears feasible, based on stimulated free-bound and bound-bound transitions in the presence of two laser fields E/sup (1)/=E/sub 0//sup (1)/ cos(/spl omega//sup (1)/t) and E/sup (2)/=E/sub 0//sup (2)/ cos(/spl omega//sup (2)/t). Here pairs of atoms from the two-atom continuum are transferred-via an excited bound molecular state-to a bound molecular state of lower energy. Raman photo-association allows coupling to a single molecular state, which can be selected by the Raman laser frequencies /spl omega//sup (1)/ and /spl omega//sup (2)/. However, practical calculations using available lasers and transitions indicate that coherent transfer is often limited by spontaneous emission from the intermediate molecular excited electronic state. A possible route towards minimizing losses and decoherence from spontaneous emission is to use the stimulated Raman adiabatic passage (STIRAP) method (Drummond et al, Phys. Rev. Lett. vol. 81, p. 3055, 1998) in which a counter-intuitive pulse sequence is used where the first input pulse couples the molecular levels, even when there are no molecules present.
The process of stimulated Raman adiabatic passage (STIRAP) provides a possible route for the generation of a coherent molecular Bose-Einstein condensate (BEC) from an atomic BEC. We analyze this process in a three-dimensional mean-field theory, including atom-atom interactions and nonresonant intermediate levels. We find that the process is feasible, but at larger Rabi frequencies than anticipated from a crude single-mode lossless analysis, due to two-photon dephasing caused by the atomic interactions. We then identify optimal strategies in STIRAP allowing one to maintain high conversion efficiencies with smaller Rabi frequencies and under experimentally less demanding conditions.
Robust stimulated Raman exact passages are requisite for controlling nonlinear quantum systems, with wide applications, ranging from ultracold molecules to nonlinear optics to superchemistry. Inspired by shortcuts to adiabaticity, we propose the fast-forward scaling of stimulated Raman adiabatic processes with nonlinearity involved, describing the transfer from an atomic Bose-Einstein condensate to a molecular one by controllable external fields. The fidelity and robustness of atom-molecule conversion are shown to surpass those of conventional adiabatic passages, assisted by the fast-forward driving field. Finally, our results are extended to fractional stimulated Raman adiabatic processes for the coherent superposition of atomic and molecular states.
We study the dynamics of the atomic and molecular Bose-Einstein condensates (BECs) of 87Rb^{87}\text{R}\text{b}87Rb in a spherically symmetric trap coupled by stimulated Raman photoassociation process. Considering the higher order nonlinearity in the atom-atom interaction we analyze the dynamics of the system using coupled modified Gross-Pitaevskii (MGP) equations and compare it with mean-field coupled Gross-Pitaevskii (GP) dynamics. Considerable differences in the dynamics are obtained in these two approaches at large scattering length, i.e., for large values of peak-gas parameter ${x}_{pk}\ensuremath{\ge}{10}^{\ensuremath{-}3}$. We show how the dynamics of the coupled system is affected when the atom-molecule and molecule-molecule interactions are considered together with the atom-atom interaction and also when the strengths of these three interactions are increased. The effect of detuning on the efficiency of conversion of atomic fractions into molecules is demonstrated and the feasibility of maximum molecular BEC formation by varying the Raman detuning parameter at different values of time is explored. Thus by varying the Raman detuning and the scattering length for atom-atom interaction one can control the dynamics of the coupled atomic-molecular BEC system. We have also solved coupled Gross-Pitaevskii equations for atomic to molecular condensate formation through magnetic Feshbach resonance in a BEC of 85Rb^{85}\text{R}\text{b}85Rb. We found similar features for oscillations between atomic and molecular condensates noted in previous theoretical study and obtained fairly good agreement with the evolution of total atomic condensate observed experimentally.
We analyze coherent two-color photoassociation of a Bose-Einstein condensate, focusing on stimulated Raman adiabatic passage (STIRAP) in free-bound-bound transitions from atoms to molecules. This problem raises an interest because STIRAP has been predicted to be absent in the nondegenerate case [Javanainen and Mackie, Phys. Rev. A 58, R789 (1998)]. Nevertheless, we find that Bose stimulation enhances the free-bound dipole matrix element for an atomic condensate, and photoassociative STIRAP turns out to be a viable mechanism for converting an atomic condensate to a molecular condensate with near-unit efficiency.
We generalize the idea of chainwise stimulated Raman adiabatic passage (STIRAP) [Kuznetsova et al., Phys. Rev. A 78, 021402(R) (2008)] to a photoassociation-based chainwise atom-molecule system, with the goal of directly converting two-species atomic Bose-Einstein condensates (BEC) into a ground polar molecular BEC. We pay particular attention to the intermediate Raman laser fields, a control knob inaccessible to the usual three-level model. We find that an appropriate exploration of both the intermediate laser fields and the stability property of the atom-molecule STIRAP can greatly reduce the power demand on the photoassociation laser, a key concern for STIRAPs starting from free atoms due to the small Franck-Condon factor in the free-bound transition.