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arXiv:2409.00952 · Physical Review Letters

Many-Body Adiabatic Passage: Instability, Chaos, and Quantum Classical Correspondence

Anant Vijay Varma, Amichay Vardi, Doron Cohen

Published Feb 6, 2025• 4 citations
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Abstract

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.

DOI
10.1103/physrevlett.134.053201

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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.
We study the many-body dynamics of stimulated Raman adiabatic passage in the presence of on-site interactions. In the classical mean-field limit, explored in A. Dey et al. [Phys. Rev. Lett. 121, 250405 (2018)], interaction-induced chaos leads to the breakdown of adiabaticity under the quasistatic variation of the parameters, thus producing low-sweep-rate boundaries on efficient population transfer. We show that for the corresponding many-body system, alternative quantum pathways from the initial to the target state open up at even slower sweep rates. These quantum detours avoid the chaotic classical path and hence allow a robust and efficient population transfer.
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.
Abstract This work develops a quantum control application of many-body quantum chaos for ultracold bosonic gases trapped in optical lattices. It is long known how to harness exponential sensitivity to changes in initial conditions for control purposes in classically chaotic systems. In the technique known as targeting, instead of a hindrance to control, the instability becomes a resource. Recently, this classical targeting has been generalized to quantum systems either by periodically countering the inevitable quantum state spreading or by introducing a control Hamiltonian, where both enable localized states to be guided along special chaotic trajectories toward any of a broad variety of desired target states. Only strictly unitary dynamics are involved; i.e. it gives a coherent quantum targeting. In this paper, the introduction of a control Hamiltonian is applied to Bose–Hubbard systems in chaotic dynamical regimes. Properly selected unstable mean field solutions can be followed particularly rapidly to states possessing precise phase relationships and occupancies. In essence, the method generates a quantum simulation technique that can access rather special states. The protocol reduces to a time-dependent control of the chemical potentials, opening up the possibility for application in optical lattice experiments. Explicit applications to custom state preparation and stabilization of quantum many-body scars are presented in one- and two-dimensional lattices (three-dimensional applications are similarly possible).
We consider a quantum many-body system-the Bose-Hubbard system on three sites-which has a classical limit, and which is neither strongly chaotic nor integrable but rather shows a mixture of the two types of behavior. We compare quantum measures of chaos (eigenvalue statistics and eigenvector structure) in the quantum system, with classical measures of chaos (Lyapunov exponents) in the corresponding classical system. As a function of energy and interaction strength, we demonstrate a strong overall correspondence between the two cases. In contrast to both strongly chaotic and integrable systems, the largest Lyapunov exponent is shown to be a multivalued function of energy.
We apply the Bose-Hubbard Hamiltonian to a three-well system and show analytically that coherent transport via adiabatic passage (CTAP) of NNN noninteracting particles across the chain is possible. We investigate the effect of detuning the middle well to recover CTAP when onsite interparticle interactions would otherwise disrupt the transport. The case of small interactions is restated using first-order perturbation theory to develop criteria for adiabaticity that define the regime where CTAP is possible. Within this regime we investigate restricting the Hilbert space to the minimum necessary basis needed to demonstrate CTAP, which dramatically increases the number of particles that can be efficiently considered. Finally, we compare the results of the Bose-Hubbard model to a mean-field three-mode Gross-Pitaevskii analysis for the equivalent system.