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Communications in Theoretical Physics

Effects of Quantum Correction on Dynamical Phase Transition in a Single Species Bosonic Josephson Junction

Jing Tian, Haibo Qiu

Published Aug 1, 2013• 2 citations
Publisher

Abstract

In this paper, by employing Bogliubov backreaction method, we investigate quantum correction effects on dynamical phase transition in a single species bosonic Josephson junction induced by increasing nonlinear interaction. Compared with mean field theory results, we find that the transition point is shifted. The dynamical phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point of the mean field theory.

DOI
10.1088/0253-6102/60/2/05

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In this paper, by employing Bogliubov backreaction method, we investigate quantum correction effects on dynamical phase transition in a single species bosonic Josephson junction induced by increasing nonlinear interaction. Compared with mean field theory results, we find that the transition point is shifted. The dynamical phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point of the mean field theory.
We investigate dynamical phase transitions that are induced by interspecies interaction in a two-species bosonic Josephson junctions (BJJ), based on semi-classical theory. In zero-phase mode, similar to the case of a single-species BJJ, we observe the well-known dynamical phase transition from Josephson oscillation to self-trapping, which can be induced by both enhanced repulsive and attractive interspecies interactions. In π phase mode, dynamical phase transitions are even more interesting and counter-intuitive. We characterize a dynamical phase transition with the merging of two separate phase space domains into one, which is induced by increasing repulsive interspecies interaction. On the other hand, we find that by increasing attractive interspecies interaction, a phase separation of two formally overlapped phase space domains will occur. At last, we reveal that these intriguing dynamical phase transitions are caused by different kinds of bifurcations.
An atomic Josephson junction realized with dipolar bosons in a double-well potential can be described by an extended Bose-Hubbard model in which dipolar interactions generate an effective on-site interaction and nearest-neighbor pair tunneling. Using mean-field theory and exact diagonalization, we investigate how this correlated process affects zero-temperature equilibrium and dynamical properties of the system. In equilibrium, we show that pair tunneling induces ground-state parity modulations and significantly reshapes the phase diagram, producing qualitative changes in the quantum phase transitions toward NOON and phase-NOON states, as well as quantitative shifts of the critical points. Out of equilibrium, we demonstrate that it modifies the conditions for macroscopic quantum self-trapping, and assess its impact by comparing mean-field and fully quantum evolution, including the emergence of dynamical quantum phase transitions.
In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the discrete self-trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote special attention to the critical regime which reduces to the dynamical bifurcation point in the thermodynamic limit of infinite bosonic population. Specifically, we highlight an anomalous scaling in the population imbalance between the two wells of the trapping potential, as well as in two quantities borrowed from quantum information theory, i.e., the entropy of entanglement and the ground-state fidelity. Our analysis is not limited to the zero-temperature case, but considers thermal effects as well.
We study Hilbert-space localization of the many-body dynamics due to ergodicity breaking and analyze this effect in terms of the entanglement entropy and the entanglement spectrum. We find a transition from a regime driven by quantum tunneling to a regime that is dominated by boson-boson interaction, where the latter exhibits ergodicity breaking. Properties of this transition are captured by observation time averaging, which effectively suppresses the large dynamical entanglement fluctuations near the critical point. We employ this approach to the experimentally available bosonic Josephson junction. In this example, the transition from a tunneling regime to Hilbert-space localization reveals clear signatures in the entanglement entropy and entanglement spectrum. Interestingly, the transition point is reduced by quantum effects in comparison to the well-known result of the mean-field approximation in the form of self-trapping. This indicates that quantum fluctuations reduce the classical self-trapping. Different scaling with respect to the number of bosons, NNN, is found in the tunneling and the localization regime: While the entanglement entropy grows logarithmically with NNN in the tunneling regime, it increases linearly in the localized regime. Our results indicate that entanglement provides a concept for a sensitive diagnosis for the transition from a quantum tunneling regime to Hilbert-space localization.
We investigate the nonlinear self-trapping phenomenon of a Bose-Einstein condensate (BEC) in a symmetric double well, emphasizing its underlying dynamical phase transition. As the nonlinear parameter characterizing the interaction between the degenerate atoms increases, the BEC becomes self-trapped, manifesting an asymmetric distribution of the atomic density profile. The essence of this phenomenon is revealed to be a continuous phase transition and the underlying critical behavior is studied analytically and found to follow a logarithmic scaling law. We then go beyond the mean-field treatment and extend our treatment to discuss the effect of many-body quantum fluctuations on the transition. It is found that the transition point is shifted and the scaling law is broken. In particular, the quantum phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point. The underlying physics is revealed.
We study the Josephson junction made of a one-dimensional ultradilute quantum liquid in a double-well potential. We analyze the dynamics as a function of the interaction strength and compare the results to the standard bosonic Josephson junction. It is found that the beyond-mean-field effects alter the dynamics, particularly in the regime, where the beyond-mean-field corrections dominate over the residual mean-field interaction. In that case, we observe nonlinear dynamics describing localization revivals instead of regular Josephson oscillations. In the regime where the ultradilute quantum liquids perform the regular Josephson oscillations, their frequency is also significantly changed in comparison with the regular Josephson junction. These results provide experimental characteristics of the ultradilute quantum liquids that contrast with the Josephson oscillations of a regular Bose-Einstein condensate.