Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1309.0784 · Physical Review A

Dynamics of entanglement in a dissipative Bose-Hubbard dimer

Tadeusz Pudlik, Holger Hennig, Dirk Witthaut, David K Campbell

Published Dec 4, 2013• 25 citations
arXivHTMLPDF

Abstract

We study the connection between the semiclassical phase space of the Bose-Hubbard dimer and inherently quantum phenomena in this model, such as entanglement and dissipation-induced coherence. Near the semiclassical self-trapping fixed points, the dynamics of Einstein-Podolski-Rosen (EPR) entanglement and condensate fraction consists of beats among just three eigenstates. Since persistent EPR entangled states arise only in the neighborhood of these fixed points, our analysis explains essentially all of the entanglement dynamics in the system. We derive accurate analytical approximations by expanding about the strong-coupling limit; surprisingly, their realm of validity is nearly the entire parameter space for which the self-trapping fixed points exist. Finally, we show significant enhancement of entanglement can be produced by applying localized dissipation.

DOI
10.1103/physreva.88.063606

Related papers

The open Bose-Hubbard dimer

Tadeusz Pudlik

This dissertation discusses a number of theoretical models of coupled bosonic modes, all closely related to the Bose-Hubbard dimer. In studying these models, we will repeatedly return to two unifying themes: the classical structure underlying quantum dynamics and the impact of weakly coupling a system to an environment. Or, more succinctly, semiclassical methods and open quantum systems. \n \nOur primary motivation for studying models such as the Bose-Hubbard is their relevance to ongoing ultracold atom experiments. We review these experiments, derive the Bose-Hubbard model in their context and briefly discuss its limitations in the first half of Chapter 1. In its second half, we review the theory of open quantum systems and the master equation description of the dissipative Bose-Hubbard model. This opening chapter constitutes a survey of existing results, rather than original work. \n \nIn Chapter 2, we turn to the mean-field limit of the Bose-Hubbard model. After reviewing the striking localization phenomena predicted by the mean-field (and confirmed by experiment), we identify the first corrections to this picture for the dimer. The most interesting of these is the dynamical tunneling between the self-trapping points of the mean-field. We derive an accurate analytical expression for the tunneling rate using semiclassical techniques. \n \nWe continue studying the dynamics near the self-trapping fixed points in Chapter 3, focusing on corrections to the mean-field that arise at larger nonlinearities and on shorter time scales than dynamical tunneling. We study the impact of dissipation on coherence and entanglement near the fixed points, and explain it in terms of the structure of the classical phase space. \n \nThe last chapter of the dissertation is also devoted to a dissipative bosonic dimer model, but one arising in a very different physical context. Abandoning optical lattices, we consider the problem of formulating a quantum model of operation of the cylindrical anode magnetron, a vacuum tube crossed-field microwave amplifier. We derive an effective dissipative dimer model and study its relationship to the classical description. Our dimer model is a first step towards the analysis of solid-state analogs of such devices.

•Jan 1, 2016•0 citations

Self-Trapping and Liouvillian Spectral Transitions in a Dissipative Bose-Hubbard Dimer

Subhendu Saha, Raka Dasgupta

We study the self-trapping transition in dissipative double wells using mean-field theory and exact diagonalization. We find that, similar to the conventional interaction-driven transition from oscillatory dynamics to self-trapping, dissipation alone can also induce self-trapping-like localization in one well. The resulting state, although transient and decaying, persists for a substantial time. At the mean-field level, the interaction- and dissipation-driven transitions are discontinuous and continuous, respectively. When interaction and dissipation both are present, their interplay produces three dynamical regimes: (i) at weak interaction, increasing dissipation drives a transition from oscillations to self-trapping; (ii) at moderate interaction, self-trapping at weak dissipation, oscillatory dynamics at intermediate dissipation, and re-entrant self-trapping at strong dissipation; and (iii) at strong interaction, self-trapping persists but is weakened by dissipation. We connect the transition with the Liouvillian spectrum. It is observed that purely dissipation-driven transition coincides with an exceptional point in the spectra, and a peak in the Liouvillian gap, marking the onset of the quantum-Zeno regime. In the presence of interactions, however, the onset of the Zeno regime is shifted to dissipation strengths larger than that required for the self-trapping transition.

arXiv:2610.25222•Oct 18, 2026•0 citations

Self-trapping mechanisms in the dynamics of three coupled Bose-Einstein condensates

Roberto Franzosi, Vittorio Penna

We formulate the dynamics of three coupled Bose-Einstein condensates within a semiclassical scenario based on the standard boson coherent states. We compare such a picture with that of K. Nemoto et al. [Phys. Rev. A 63, 013604 (2001)] and show how our approach entails a simple formulation of the dimeric regime therein studied. This allows us to recognize the parameters that govern the bifurcation mechanism causing self-trapping, and paves the way to the construction of analytic solutions.

arXiv:cond-mat/0103460•Physical Review A•Dec 4, 2001•60 citations

Driven Bose-Hubbard dimer under nonlocal dissipation: A bistable time crystal

Cristóbal Lledó, Th. K. Mavrogordatos, Marzena Hanna Szymańska

We investigate the critical behavior of the open coherently-driven Bose-Hubbard dimer under nonlocal dissipation. A conserved quantity arises from the nonlocal nature of the dissipation, rendering the dimer multistable. In the weak-coupling semiclassical limit, the displayed criticality takes the form of amplitude bistability and breaking of spatial and temporal symmetries. A period-bistable time crystal is formed, consisting of Josephson-like oscillations. Mean-field dynamics and quantum trajectories complement the spectral analysis of the Liouvillian in the approach to the semiclassical limit.

arXiv:1901.04438•Physical review. B./Physical review. B•Aug 16, 2019•64 citations

Optically bistable driven-dissipative Bose-Hubbard dimer: Gutzwiller approaches and entanglement

Wim Casteels, Michiel Wouters

We examine theoretically the driven-dissipative Bose-Hubbard dimer in the optical bistable regime. Various approximation schemes based on a Gutzwiller mean-field decoupling are applied and compared. Depending on the system parameters, we show that a decoupling with respect to the real space or to the reciprocal space can be more accurate. The Gutzwiller decoupling is applied both at the level of the density matrix and for the wave function during a quantum trajectory simulation. The latter is shown to be a more accurate approximation. A Gaussian approximation for the nonhomogeneous antibonding mode is also explored. We also show that entanglement in this system is witnessed by squeezing in reciprocal space.

arXiv:1702.02444•Physical Review A•Apr 21, 2017•29 citations

Entanglement and entropy production in coupled single-mode Bose-Einstein condensates

Izabella Lovas, József Fortágh, Eugene Demler +1 more

We investigate the time evolution of the entanglement entropy of coupled single-mode Bose-Einstein condensates in a double-well potential at $T=0$ temperature by combining numerical results with analytical approximations. We find that the coherent oscillations of the condensates result in entropy oscillations on the top of a linear entropy generation at short time scales. Due to dephasing, the entropy eventually saturates to a stationary value, in spite of the lack of equilibration. We show that this long-time limit of the entropy reflects the semiclassical dynamics of the system, revealing the self-trapping phase transition of the condensates at large interaction strength by a sudden entropy jump. We compare the stationary limit of the entropy to the prediction of a classical microcanonical ensemble and find surprisingly good agreement in spite of the nonequilibrium state of the system. Our predictions should be experimentally observable on a Bose-Einstein condensate in a double-well potential or on a two-component condensate with interstate coupling.

arXiv:1706.04571•Physical Review A•Aug 17, 2017•7 citations
We study the connection between the semiclassical phase space of the Bose-Hubbard dimer and inherently quantum phenomena in this model, such as entanglement and dissipation-induced coherence. Near the semiclassical self-trapping fixed points, the dynamics of Einstein-Podolski-Rosen (EPR) entanglement and condensate fraction consists of beats among just three eigenstates. Since persistent EPR entangled states arise only in the neighborhood of these fixed points, our analysis explains essentially all of the entanglement dynamics in the system. We derive accurate analytical approximations by expanding about the strong-coupling limit; surprisingly, their realm of validity is nearly the entire parameter space for which the self-trapping fixed points exist. Finally, we show significant enhancement of entanglement can be produced by applying localized dissipation.
This dissertation discusses a number of theoretical models of coupled bosonic modes, all closely related to the Bose-Hubbard dimer. In studying these models, we will repeatedly return to two unifying themes: the classical structure underlying quantum dynamics and the impact of weakly coupling a system to an environment. Or, more succinctly, semiclassical methods and open quantum systems. \n \nOur primary motivation for studying models such as the Bose-Hubbard is their relevance to ongoing ultracold atom experiments. We review these experiments, derive the Bose-Hubbard model in their context and briefly discuss its limitations in the first half of Chapter 1. In its second half, we review the theory of open quantum systems and the master equation description of the dissipative Bose-Hubbard model. This opening chapter constitutes a survey of existing results, rather than original work. \n \nIn Chapter 2, we turn to the mean-field limit of the Bose-Hubbard model. After reviewing the striking localization phenomena predicted by the mean-field (and confirmed by experiment), we identify the first corrections to this picture for the dimer. The most interesting of these is the dynamical tunneling between the self-trapping points of the mean-field. We derive an accurate analytical expression for the tunneling rate using semiclassical techniques. \n \nWe continue studying the dynamics near the self-trapping fixed points in Chapter 3, focusing on corrections to the mean-field that arise at larger nonlinearities and on shorter time scales than dynamical tunneling. We study the impact of dissipation on coherence and entanglement near the fixed points, and explain it in terms of the structure of the classical phase space. \n \nThe last chapter of the dissertation is also devoted to a dissipative bosonic dimer model, but one arising in a very different physical context. Abandoning optical lattices, we consider the problem of formulating a quantum model of operation of the cylindrical anode magnetron, a vacuum tube crossed-field microwave amplifier. We derive an effective dissipative dimer model and study its relationship to the classical description. Our dimer model is a first step towards the analysis of solid-state analogs of such devices.
We study the self-trapping transition in dissipative double wells using mean-field theory and exact diagonalization. We find that, similar to the conventional interaction-driven transition from oscillatory dynamics to self-trapping, dissipation alone can also induce self-trapping-like localization in one well. The resulting state, although transient and decaying, persists for a substantial time. At the mean-field level, the interaction- and dissipation-driven transitions are discontinuous and continuous, respectively. When interaction and dissipation both are present, their interplay produces three dynamical regimes: (i) at weak interaction, increasing dissipation drives a transition from oscillations to self-trapping; (ii) at moderate interaction, self-trapping at weak dissipation, oscillatory dynamics at intermediate dissipation, and re-entrant self-trapping at strong dissipation; and (iii) at strong interaction, self-trapping persists but is weakened by dissipation. We connect the transition with the Liouvillian spectrum. It is observed that purely dissipation-driven transition coincides with an exceptional point in the spectra, and a peak in the Liouvillian gap, marking the onset of the quantum-Zeno regime. In the presence of interactions, however, the onset of the Zeno regime is shifted to dissipation strengths larger than that required for the self-trapping transition.
We investigate the critical behavior of the open coherently-driven Bose-Hubbard dimer under nonlocal dissipation. A conserved quantity arises from the nonlocal nature of the dissipation, rendering the dimer multistable. In the weak-coupling semiclassical limit, the displayed criticality takes the form of amplitude bistability and breaking of spatial and temporal symmetries. A period-bistable time crystal is formed, consisting of Josephson-like oscillations. Mean-field dynamics and quantum trajectories complement the spectral analysis of the Liouvillian in the approach to the semiclassical limit.
We examine theoretically the driven-dissipative Bose-Hubbard dimer in the optical bistable regime. Various approximation schemes based on a Gutzwiller mean-field decoupling are applied and compared. Depending on the system parameters, we show that a decoupling with respect to the real space or to the reciprocal space can be more accurate. The Gutzwiller decoupling is applied both at the level of the density matrix and for the wave function during a quantum trajectory simulation. The latter is shown to be a more accurate approximation. A Gaussian approximation for the nonhomogeneous antibonding mode is also explored. We also show that entanglement in this system is witnessed by squeezing in reciprocal space.
We investigate the time evolution of the entanglement entropy of coupled single-mode Bose-Einstein condensates in a double-well potential at T=0T=0T=0 temperature by combining numerical results with analytical approximations. We find that the coherent oscillations of the condensates result in entropy oscillations on the top of a linear entropy generation at short time scales. Due to dephasing, the entropy eventually saturates to a stationary value, in spite of the lack of equilibration. We show that this long-time limit of the entropy reflects the semiclassical dynamics of the system, revealing the self-trapping phase transition of the condensates at large interaction strength by a sudden entropy jump. We compare the stationary limit of the entropy to the prediction of a classical microcanonical ensemble and find surprisingly good agreement in spite of the nonequilibrium state of the system. Our predictions should be experimentally observable on a Bose-Einstein condensate in a double-well potential or on a two-component condensate with interstate coupling.