Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

Abstract

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Layered chaos in mean-field and quantum many-body dynamics

“…This system consists of a Bose-Einstein condensate (BEC) under periodic driving that breaks generalized parity and time-reversal symmetries (see Fig. 1) [19][20][21]. The ratchet effect, or directionally biased motion, is induced by these symmetry violations [22][23][24] and manifests in the particle current [19,20].…”

“…The ratchet effect, or directionally biased motion, is induced by these symmetry violations [22][23][24] and manifests in the particle current [19,20]. For near resonant driving this results in two regular dynamical regimes, Rabi oscillations for weak particle interaction and self-trapping for strong interactions, with a chaotic regime for intermediate couplings [19][20][21]. This system can be treated in the many-body framework of the Bose-Hubbard model with a time-dependent potential, or, alternatively, in a time-independent truncated Floquet model [19][20][21].…”

“…For near resonant driving this results in two regular dynamical regimes, Rabi oscillations for weak particle interaction and self-trapping for strong interactions, with a chaotic regime for intermediate couplings [19][20][21]. This system can be treated in the many-body framework of the Bose-Hubbard model with a time-dependent potential, or, alternatively, in a time-independent truncated Floquet model [19][20][21]. In either case, a well-defined mean-field limit gives rise to nonlinear dynamics.…”

“…We show agreement between the attractor dimension for both mean-field models. Moreover, we identify four distinct regions of interaction strengths that produce chaotic dynamics, contrasting its identification in the spectral statistics and quantum many-body dynamics [21]. We shall point out, however, that the performed analysis of the dimension of the strange attractor and the correlation dimension of the system are meaningful only if the system is characterized with a nonzero [14][15][16][17][18] generates the effect of driving by two counterpropagating waves in one spatial dimension [19].…”

Open source matrix product states: exact diagonalization and other entanglement-accurate methods revisited in quantum systems

“…Starting with a certain number of predefined rules for the Hamiltonian, sophisticated models can be represented as well as with hand-built ED codes, but at a much lower cost, avoiding development overhead. A preliminary version of this library was used for the momentum-space study of the Bose-Hubbard model in [28]. We envision that open systems will profit from this approach enormously in the future to provide a variety of different Lindblad channels.With these motivations in mind, we present three kinds of algorithms retaining the complete Hilbert space and their efficient implementations for closed systems.…”