Quantum chaos in a Bose-Hubbard dimer with modulated tunneling

Abstract

In the large-N , classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically evolving state that are correlated with the presence of chaos in the classical limit. We propose the statistical distance between initially similar number distributions as a reliable measure to distinguish regular from chaotic behaviour in the quantum dynamics. Besides being experimentally accessible, number distributions can be efficiently reconstructed numerically from binned phase-space trajectories in a truncated Wigner approximation. Although the evolving Wigner function becomes very irregular in the chaotic regions, the truncated Wigner method is nevertheless able to capture accurately the beyond mean-field dynamics.

Thermalization in a Bose-Hubbard dimer with modulated tunneling

“…Our results build on, and are complementary to, previous studies in Refs. [1,15,22]. Our protocol is realizable experimentally and provides an alternative platform to explore ideas relevant to quantum thermodynamics and the dynamics of quantum information.…”

“…In this paper we demonstrate the use of the fidelity outof-time-order correlator (FOTOC) [1] for studying the manifestation of chaos in a system of ultra-cold bosons in a double-well potential with periodically modulated tunnelling [22]. Our proposal can be immediately realised experimentally and highlights the utility of FOTOC dynamics for characterizing scrambling and thermalisation in Floquet systems.…”

Quantum chaos in a system with high degree of symmetries

“…That is why in the argument of this b 2 function enters ν9−even = ν9−odd = ν/18. Since the dynamics of subspaces 1-8 have the same temporal scale, their individual contributions add coherently to build up the correlation hole and they dominate the second term inside the parenthesis in (19).…”

“…A semiclassical analysis connected with Bloch oscillations was presented in [17]. Recently the out-of-time-order correla-tor and the Lyapunov exponent have been studied in the model [18] and the statistical distance between initially similar number distributions has been proposed as a reliable measure to distinguish regular from chaotic behavior in a Bose-Hubbard dimer [19].…”

Multiparticle Entanglement Dynamics of Quantum Chaos in a Bose-Einstein condensate

“…Atomic Bose-Einstein condensates (BECs) can be trapped in time-dependent potentials having almost arbitrary geometries and are therefore emerging as ideal candidates for the study of quantum chaos in many-body systems [5][6][7][8][9][10]. Several efforts have been devoted to investigate chaotic dynamics in both scalar and spinor BECs, including driven two-mode [11], tilted triple-well [12], kicked ring [13], kicked optical-lattice [14], barrier-height-modulated double-well [15], dissipative double-well [16], dissipative optical-lattice [3], spin-1 [17], spin-2 [18], and coupled spinor atom-molecule BECs [19]. A paradigmatic model to study quantum chaos is the kicked rotor [20,21] which can be realized with trapped BECs [22][23][24][25][26].…”