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:1905.02668 · Physical review. E

Dissipative Bose-Josephson junction coupled to bosonic baths

Sudip Sinha, Subhasis Sinha

Published Sep 10, 2019• 11 citations
arXivHTMLPDF

Abstract

We investigate the effect of dissipation in a Bose-Josephson junction (BJJ) coupled to baths of bosons at its two sites. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within a Holstein-Primakoff approximation, which exhibits vanishing of the energy gap and enhanced quantum fluctuations at the critical point. We study the dynamics of BJJ using a time-dependent variational method and analyze stability of different types of steady states. As a special case we study in detail the phase space dynamics of BJJ coupled to a single mode, which reveals diffusive and incoherent behavior with increasing coupling to the bath mode. The dynamical steady states corresponding to the π oscillation and self-trapped state become unstable when their oscillation frequencies are in resonance with the bath modes. We study the Josephson dynamics in the presence of an Ohmic bath with Gaussian noise to incorporate the thermal fluctuations and obtain the Josephson oscillation frequency and damping analytically. We also observe the transition to the symmetry-broken state for strong coupling as well as decay of π oscillation and a self-trapped state to the ground state due to dissipation. Variation of the phase fluctuation with temperature of the bath shows similar behavior as observed in experiment. Finally we discuss the experimental setup to study the observable effects of dissipation in BJJ.

DOI
10.1103/physreve.100.032115

Related papers

Generalized Spin-Boson model and its application to dissipative Bose-Josephson Junction

Sudip Sinha, Supervisor Dr. Subhasis Sinha

We investigate the effect of dissipation in a Bose Josephson junction (BJJ) coupled to bath of bosons at two sites as an application of the generalized spin-boson model. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within Holstein-Primakoff approximation, which exhibits vanishing of energy gap and enhanced quantum fluctuations at the critical coupling. We study the dynamics of BJJ using time-dependent variational method and analyze stability of different types of steady states. As a special case, we study in details the phase space dynamics of BJJ coupled to a single-mode, which reveals diffusive and incoherent behaviour with increasing coupling to the bath mode. The dynamical steady states corresponding to the Pi-oscillation and self-trapped state become unstable in the region where their oscillation frequencies are in resonance with the bath modes. We investigate the time evolution of number imbalance and relative phase in presence of Ohmic bath with Gaussian noise to incorporate thermal fluctuations. Apart from the damping of Josephson oscillations and transition to symmetry broken state for strong coupling, we observe the decay of Pi-oscillation and self-trapped state to the ground state as a result of dissipation. Variation of phase fluctuation with temperature of the bath shows similar behaviour as observed in the experiments.

•May 1, 2019•0 citations

Phase diffusion and fluctuations in a dissipative Bose-Josephson junction

Abhik Kumar Saha, Deb Shankar Ray, Bimalendu Deb

We analyze the phase diffusion, quantum fluctuations and their spectral features of a one-dimensional Bose-Josephson junction (BJJ) nonlinearly coupled to a bosonic heat bath. The phase diffusion is considered by taking into account of random modulations of the BJJ modes causing a phase loss of initial coherence between the ground and excited states, whereby the frequency modulation is incorporated in the system-reservoir Hamiltonian by an interaction term linear in bath operators but nonlinear in system (BJJ) operators. We examine the dependence of the phase diffusion coefficient on the on-site interaction and temperature in the zero- and π-phase modes and demonstrate its phase transition-like behavior between the Josephson oscillation and the macroscopic quantum self-trapping (MQST) regimes in the π-phase mode. Based on the thermal canonical Wigner distribution, which is the equilibrium solution of the associated quantum Langevin equation for phase, coherence factor is calculated to study phase diffusion for the zero- and π-phase modes. We investigate the quantum fluctuations of the relative phase and population imbalance in terms of fluctuation spectra which capture an interesting shift in Josephson frequency induced by frequency fluctuation due to nonlinear system-reservoir coupling, as well as the on-site interaction-induced splitting in the weak dissipative regime.

arXiv:2211.07229•Physical review. E•Mar 31, 2023•6 citations

Chaos and Quantum Scars in Bose-Josephson Junction Coupled to a Bosonic Mode

Sudip Sinha, Subhasis Sinha

We consider a model describing Bose-Josephson junction (BJJ) coupled to a single bosonic mode exhibiting quantum phase transition (QPT). Onset of chaos above QPT is observed from semiclassical dynamics as well from spectral statistics. Based on entanglement entropy, we analyze the ergodic behavior of eigenstates with increasing energy density which also reveals the influence of dynamical steady state known as π-mode on it. We identify the imprint of unstable π-oscillation as many body quantum scar (MBQS), which leads to the deviation from ergodicity and quantify the degree of scarring. Persistence of phase coherence in nonequilibrium dynamics of such initial state corresponding to the π-mode is an observable signature of MBQS which has relevance in experiments on BJJ.

arXiv:1912.06593•Physical Review Letters•Sep 23, 2020•43 citations

Dynamical phase transitions in a two-species bosonic Josephson junction

Jing Tian, Jun Liu, Haibo Qiu +1 more

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.

Frontiers of Physics•Jul 11, 2017•3 citations

Measure synchronization in a two-species bosonic Josephson junction

Jing Tian, Haibo Qiu, Guanfang Wang +2 more

Measure synchronization (MS) in a two-species bosonic Josephson junction (BJJ) is studied based on semiclassical theory. Six different scenarios for MS, including two in the Josephson oscillation regime (the zero-phase mode) and four in the self-trapping regime (the π-phase mode), are clearly shown. Systematic investigations of the common features behind these different scenarios are performed. We show that the average energies of the two species merge at the MS transition point. The scaling of the power law near the MS transition is verified and the critical exponent is 1/2 for all of the different scenarios for MS. We also illustrate MS in a three-dimensional phase space; from this illustration, more detailed information on the dynamical process can be obtained. In particular, by analyzing the Poincaré sections with changing interspecies interactions, we find that the two-species BJJ exhibits separatrix crossing behavior at the MS transition point and such behavior depicts the general mechanism behind the different scenarios for the MS transitions. The new critical behavior found in a two-species BJJ is expected to be found in real systems of atomic Bose gases.

arXiv:1312.2850•Physical Review E•Sep 6, 2013•32 citations

Quantum dynamics and macroscopic quantum tunnelling of two weakly coupled condensates

René John Kerkdyk, Subhasis Sinha

We study the quantum dynamics of a Bose Josephson junction(BJJ) made up of two coupled Bose-Einstein condensates. Apart from the usual ac Josephson oscillations, two different dynamical states of BJJ can be observed by tuning the inter-particle interaction strength, which are known as '$π$-oscillation' with relative phase $π$ between the condensates and 'macroscopic self-trapped' (MST) state with finite number imbalance. By choosing appropiate intial state we study above dynamical branches quantum mechanically and compare with classical dynamics. The stability region of the '$π$-oscillation' is separated from that of 'MST' state at a critical coupling strength. Also a significant change in the energy spectrum takes place above the critical coupling strength, and pairs of (quasi)-degenerate excited states appear. The original model of BJJ can be mapped on to a simple Hamiltonian describing quantum particle in an 'effective potential' with an effective Planck constant. Different dynamical states and degenerate excited states in the energy spectrum can be understood in this 'effective potential' approach. Also possible novel quantum phenomena like 'macroscopic quantum tunneling'(MQT) become evident from the simple picture of 'effective potential'. We study decay of metastable '$π$-oscillation' by MQT through potential barrier. The doubly degenerate excited states in the energy spectrum are associated with the classically degenerate MST states with equal and opposite number imbalance. We calculate the energy splitting between these quasi-degenerate excited states due to MQT of the condensate between classically degenerate MST states.

arXiv:1209.5204•Journal of Physics B Atomic Molecular and Optical Physics•Sep 5, 2013•5 citations
We investigate the effect of dissipation in a Bose-Josephson junction (BJJ) coupled to baths of bosons at its two sites. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within a Holstein-Primakoff approximation, which exhibits vanishing of the energy gap and enhanced quantum fluctuations at the critical point. We study the dynamics of BJJ using a time-dependent variational method and analyze stability of different types of steady states. As a special case we study in detail the phase space dynamics of BJJ coupled to a single mode, which reveals diffusive and incoherent behavior with increasing coupling to the bath mode. The dynamical steady states corresponding to the π oscillation and self-trapped state become unstable when their oscillation frequencies are in resonance with the bath modes. We study the Josephson dynamics in the presence of an Ohmic bath with Gaussian noise to incorporate the thermal fluctuations and obtain the Josephson oscillation frequency and damping analytically. We also observe the transition to the symmetry-broken state for strong coupling as well as decay of π oscillation and a self-trapped state to the ground state due to dissipation. Variation of the phase fluctuation with temperature of the bath shows similar behavior as observed in experiment. Finally we discuss the experimental setup to study the observable effects of dissipation in BJJ.
We investigate the effect of dissipation in a Bose Josephson junction (BJJ) coupled to bath of bosons at two sites as an application of the generalized spin-boson model. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within Holstein-Primakoff approximation, which exhibits vanishing of energy gap and enhanced quantum fluctuations at the critical coupling. We study the dynamics of BJJ using time-dependent variational method and analyze stability of different types of steady states. As a special case, we study in details the phase space dynamics of BJJ coupled to a single-mode, which reveals diffusive and incoherent behaviour with increasing coupling to the bath mode. The dynamical steady states corresponding to the Pi-oscillation and self-trapped state become unstable in the region where their oscillation frequencies are in resonance with the bath modes. We investigate the time evolution of number imbalance and relative phase in presence of Ohmic bath with Gaussian noise to incorporate thermal fluctuations. Apart from the damping of Josephson oscillations and transition to symmetry broken state for strong coupling, we observe the decay of Pi-oscillation and self-trapped state to the ground state as a result of dissipation. Variation of phase fluctuation with temperature of the bath shows similar behaviour as observed in the experiments.
We analyze the phase diffusion, quantum fluctuations and their spectral features of a one-dimensional Bose-Josephson junction (BJJ) nonlinearly coupled to a bosonic heat bath. The phase diffusion is considered by taking into account of random modulations of the BJJ modes causing a phase loss of initial coherence between the ground and excited states, whereby the frequency modulation is incorporated in the system-reservoir Hamiltonian by an interaction term linear in bath operators but nonlinear in system (BJJ) operators. We examine the dependence of the phase diffusion coefficient on the on-site interaction and temperature in the zero- and π-phase modes and demonstrate its phase transition-like behavior between the Josephson oscillation and the macroscopic quantum self-trapping (MQST) regimes in the π-phase mode. Based on the thermal canonical Wigner distribution, which is the equilibrium solution of the associated quantum Langevin equation for phase, coherence factor is calculated to study phase diffusion for the zero- and π-phase modes. We investigate the quantum fluctuations of the relative phase and population imbalance in terms of fluctuation spectra which capture an interesting shift in Josephson frequency induced by frequency fluctuation due to nonlinear system-reservoir coupling, as well as the on-site interaction-induced splitting in the weak dissipative regime.
We consider a model describing Bose-Josephson junction (BJJ) coupled to a single bosonic mode exhibiting quantum phase transition (QPT). Onset of chaos above QPT is observed from semiclassical dynamics as well from spectral statistics. Based on entanglement entropy, we analyze the ergodic behavior of eigenstates with increasing energy density which also reveals the influence of dynamical steady state known as π-mode on it. We identify the imprint of unstable π-oscillation as many body quantum scar (MBQS), which leads to the deviation from ergodicity and quantify the degree of scarring. Persistence of phase coherence in nonequilibrium dynamics of such initial state corresponding to the π-mode is an observable signature of MBQS which has relevance in experiments on BJJ.
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.
Measure synchronization (MS) in a two-species bosonic Josephson junction (BJJ) is studied based on semiclassical theory. Six different scenarios for MS, including two in the Josephson oscillation regime (the zero-phase mode) and four in the self-trapping regime (the π-phase mode), are clearly shown. Systematic investigations of the common features behind these different scenarios are performed. We show that the average energies of the two species merge at the MS transition point. The scaling of the power law near the MS transition is verified and the critical exponent is 1/2 for all of the different scenarios for MS. We also illustrate MS in a three-dimensional phase space; from this illustration, more detailed information on the dynamical process can be obtained. In particular, by analyzing the Poincaré sections with changing interspecies interactions, we find that the two-species BJJ exhibits separatrix crossing behavior at the MS transition point and such behavior depicts the general mechanism behind the different scenarios for the MS transitions. The new critical behavior found in a two-species BJJ is expected to be found in real systems of atomic Bose gases.
We study the quantum dynamics of a Bose Josephson junction(BJJ) made up of two coupled Bose-Einstein condensates. Apart from the usual ac Josephson oscillations, two different dynamical states of BJJ can be observed by tuning the inter-particle interaction strength, which are known as 'πππ-oscillation' with relative phase πππ between the condensates and 'macroscopic self-trapped' (MST) state with finite number imbalance. By choosing appropiate intial state we study above dynamical branches quantum mechanically and compare with classical dynamics. The stability region of the 'πππ-oscillation' is separated from that of 'MST' state at a critical coupling strength. Also a significant change in the energy spectrum takes place above the critical coupling strength, and pairs of (quasi)-degenerate excited states appear. The original model of BJJ can be mapped on to a simple Hamiltonian describing quantum particle in an 'effective potential' with an effective Planck constant. Different dynamical states and degenerate excited states in the energy spectrum can be understood in this 'effective potential' approach. Also possible novel quantum phenomena like 'macroscopic quantum tunneling'(MQT) become evident from the simple picture of 'effective potential'. We study decay of metastable 'πππ-oscillation' by MQT through potential barrier. The doubly degenerate excited states in the energy spectrum are associated with the classically degenerate MST states with equal and opposite number imbalance. We calculate the energy splitting between these quasi-degenerate excited states due to MQT of the condensate between classically degenerate MST states.