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arXiv:1805.05165 · Physical Review Letters

Adiabatic Passage through Chaos

Amit Dey, Doron Cohen, Amichay Vardi

Published Dec 21, 2018• 20 citations
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Abstract

We study the process of nonlinear stimulated Raman adiabatic passage within a classical mean-field framework. Depending on the sign of interaction, the breakdown of adiabaticity in the interacting nonintegrable system is not related to bifurcations in the energy landscape, but rather to the emergence of quasistochastic motion that drains the followed quasistationary state. Consequently, faster sweep rate, rather than quasistatic variation of parameters, is better for adiabaticity.

DOI
10.1103/physrevlett.121.250405

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We study the process of nonlinear stimulated Raman adiabatic passage within a classical mean-field framework. Depending on the sign of interaction, the breakdown of adiabaticity in the interacting nonintegrable system is not related to bifurcations in the energy landscape, but rather to the emergence of quasistochastic motion that drains the followed quasistationary state. Consequently, faster sweep rate, rather than quasistatic variation of parameters, is better for adiabaticity.
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We study the effect of interactions on the conversion of atomic-to-molecular Bose-Einstein condensates via stimulated Raman adiabatic passage. Both energetic instability during avoided crossings and dynamical instability during chaotic intervals limit adiabaticity and impose low sweep-rate boundaries on the efficiency of the process. For the diabatic traverse of avoided crossings, we find a reciprocal power-law dependence of the final unconverted population on sweep rate. For the traverse of chaos, we find a sharp low-rate boundary determined by the dynamical instability parameters. The interplay of these two mechanisms determines which instability controls the failure of molecular production. A judicious choice of sweep parameters is hence required to restore the process efficiency.
Adiabatic passage in systems of interacting bosons is substantially affected by interactions and interparticle entanglement. We consider stimulated raman-adiabatic-passage-like schemes in Bose-Hubbard chains that exhibit low-dimensional chaos (a three-site chain) and high-dimensional chaos (more than three sites). The dynamics that is generated by a transfer protocol exhibits striking classical and quantum chaos fingerprints that are manifested in the mean-field classical treatment, in the truncated Wigner semiclassical treatment, and in the full many-body quantum simulations.
Nonlinear stimulated Raman adiabatic passage (STIRAP) is a fascinating physical process that dynamically explores chaotic and nonchaotic phases. In a recent paper [A. Dey and M. Kulkarni, Phys. Rev. Res. 2, 042004(R) (2020)], such a phenomenon is realized in a cavity-QED platform. There, the emergence of chaos and its impact on STIRAP efficiency are mainly demonstrated in the semiclassical limit. In the present paper we treat the problem in a fully quantum many-body framework. With the aim of extracting quantum signatures of a classically chaotic system, it is shown that an out-of-time-ordered correlator (OTOC) measure precisely captures chaotic and nonchaotic features of the system. The prediction by OTOC is in precise matching with classical chaos quantified by Lyapunov exponent analysis. Furthermore, it is shown that the quantum route corresponding to the semiclassical followed state encounters a dip in single-particle purity within the chaotic phase, depicting a consequence of chaos. A dynamics through the chaotic phase is associated with spreading of the many-body quantum state and an irreversible increase in the number of participating adiabatic eigenstates.
We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.
We study the exact dynamics underlying stimulated Raman adiabatic passage (STIRAP) for a particle in a multilevel anharmonic system (the infinite square well) driven by two sequential laser pulses, each with constant carrier frequency. In phase space regions where the laser pulses create chaos, the particle can be transferred coherently into energy states different from those predicted by traditional STIRAP. It appears that a transition to chaos can provide an additional tool to control the outcome of STIRAP.