Experiments on the nonequilibrium dynamics of an isolated Bose-Einstein condensate (BEC) in a magnetic double-well trap exhibit a puzzling divergence: While some show dissipation-free Josephson oscillations, others find strong damping. Such damping in isolated BECs cannot be understood on the level of the coherent Gross-Pitaevskii dynamics. Using the Keldysh functional-integral formalism, we describe the time-dependent system dynamics by means of a multimode BEC coupled to fluctuations (single-particle excitations) beyond the Gross-Pitaevskii saddle point. We find that the Josephson oscillations excite an excess of fluctuations when the effective Josephson frequency ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{J}$ is in resonance with the effective fluctuation energy ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{m}$, where both ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{J}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{m}$ are strongly renormalized with respect to their noninteracting values. By evaluating and using the model parameters for the respective experiments, we describe quantitatively the presence or absence of damping.Experiments on the nonequilibrium dynamics of an isolated Bose-Einstein condensate (BEC) in a magnetic double-well trap exhibit a puzzling divergence: While some show dissipation-free Josephson oscillations, others find strong damping. Such damping in isolated BECs cannot be understood on the level of the coherent Gross-Pitaevskii dynamics. Using the Keldysh functional-integral formalism, we describe the time-dependent system dynamics by means of a multimode BEC coupled to fluctuations (single-particle excitations) beyond the Gross-Pitaevskii saddle point. We find that the Josephson oscillations excite an excess of fluctuations when the effective Josephson frequency ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{J}$ is in resonance with the effective fluctuation energy ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{m}$, where both ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{J}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{m}$ are strongly renormalized with respect to their noninteracting values. By evaluating and using the model parameters for the respective experiments, we describe quantitatively the presence or absence of damping.

arXiv:1806.00376Physical Review AAug 24, 201813 citations

Beyond-mean-field effects in dynamics of BEC in the double-well potential

F. Kh. Abdullaev, R. M. Galimzyanov, Akbar M. Shermakhmatov

arXiv:2406.08895The European Physical Journal DSep 1, 20246 citations

Phase-space mixing in dynamically unstable, integrable few-mode quantum systems

Ranchu Mathew, Eite Tiesinga

Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA), focus on the role of motion near separatrices, and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as $O(1/lnN)$ , where $N$ is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady-state value is a damped oscillation. The damping is Gaussian in time with a time scale of $O[{(lnN)}^{2}]$ . We also give the quantitative dependence of the steady-state value and the damping time on the system parameters. Our results are confirmed with numerical TWA simulations.Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA), focus on the role of motion near separatrices, and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as $O(1/lnN)$, where $N$ is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady-state value is a damped oscillation. The damping is Gaussian in time with a time scale of $O[{(lnN)}^{2}]$. We also give the quantitative dependence of the steady-state value and the damping time on the system parameters. Our results are confirmed with numerical TWA simulations.

arXiv:1705.01702Physical Review AJul 5, 201713 citations

Dipolar BEC in a double-well potential

Muhammad Asaduzzaman, D. Blume

Bulletin of the American Physical SocietyMay 20, 20090 citations

Nonlinear dynamics from quantum mechanics for a BEC in a two-well potential

Juha Javanainen

Bulletin of the American Physical SocietyMay 29, 20100 citations

Effect of decoherence on the dynamics of Bose-Einstein condensates in a double-well potential

Wei-Wei Wang, Libin Fu, X. X. Yi

We study the dynamics of a Bose-Einstein condensate in a double-well potential in the mean-field approximation. Decoherence effects are considered by analyzing the couplings of the condensate to the environment. Two kinds of coupling are taken into account. With the first kind of coupling dominating, decoherence can enhance self-trapping by increasing the damping of the oscillations in the dynamics, while decoherence from the second kind of condensate-environment coupling leads to spoiling of the quantum tunneling and self-trapping.We study the dynamics of a Bose-Einstein condensate in a double-well potential in the mean-field approximation. Decoherence effects are considered by analyzing the couplings of the condensate to the environment. Two kinds of coupling are taken into account. With the first kind of coupling dominating, decoherence can enhance self-trapping by increasing the damping of the oscillations in the dynamics, while decoherence from the second kind of condensate-environment coupling leads to spoiling of the quantum tunneling and self-trapping.

arXiv:0704.3823Physical Review AApr 23, 200743 citations

O(1/lnN)

, where

N

is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady-state value is a damped oscillation. The damping is Gaussian in time with a time scale of

O[{(lnN)}^{2}]

. We also give the quantitative dependence of the steady-state value and the damping time on the system parameters. Our results are confirmed with numerical TWA simulations.