Relaxation to a Phase-Locked Equilibrium State in a One-Dimensional Bosonic Josephson Junction

Pigneur, Marine; Berrada, Tarik; Bonneau, Marie; Schumm, Thorsten; Demler, Eugene; Schmiedmayer, Jörg

doi:10.1103/physrevlett.120.173601

Cited by 109 publications

(165 citation statements)

References 43 publications

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“…Such collapse of oscillations in the many-body dynamics of p(t) has been reported earlier also [49,50]. For a symmetric double well, such collapse of oscillations has recently been observed [71] in the oscillations of the population imbalance which is directly related to the survival probability, see appendix B.2. This makes a many-body calculation necessary for Λ0.1 for a system of N=1000 bosons.…”

Section: Survival Probabilitysupporting

confidence: 63%

“…x t N 0 , ρ(x, t) being the density of the system at time t. Another common quantity to characterize the density oscillations in experiments is the population imbalance [71] which is defined as = -( ) n t ; N N N L R N L,R being the atom numbers in the left (L) and the right (R) well at time t, respectively. Note that both p(t) and n(t) are closely related and have similar qualitative features as they both characterize the same density oscillations.…”

Section: B2 Physical Quantitiesmentioning

confidence: 99%

“…While p(t) can oscillate about a mean value 0.5 between a maximum 1 and a minimum 0, n(t) can oscillate about a mean-value 0. Also in case of oscillations of n(t), the peak values depend on the experimental set up and can be controlled by varying the vertical shift between the two wells, see [71]. Therefore, the amplitudes of oscillations are different for p(t) and n(t), though the frequencies are in-principle the same as the frequencies depend on the tunneling rate between the two wells.…”

Section: B2 Physical Quantitiesmentioning

confidence: 99%

“…However, a systematic study of the dynamics of a many-particle bosonic system in an asymmetric double well for different interaction regimes using a numerically-exact many-body method is, to the best of our knowledge, yet to be reported. We stress that such study has become necessary in view of mounting experimental evidences that the beyond mean-field physics can actually be observed, for example see [71,72]. A proper many-body method automatically includes all participating bands in the asymmetric double well.…”

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confidence: 99%

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Many-body quantum dynamics of an asymmetric bosonic Josephson junction

Haldar

Alon

2019

New J. Phys.

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The out-of-equilibrium quantum dynamics of an interacting Bose gas trapped in a one-dimensional asymmetric double-well potential is studied by solving the many-body Schrödinger equation numerically accurately. We examine how the gradual loss of symmetry of the confining trap affects the macroscopic quantum tunneling dynamics of the system between the two wells. In an asymmetric double well, the two wells are not equivalent anymore, say, the left well is deeper than the right one. Accordingly, we analyze the dynamics by initially preparing the condensate in both the left and the right wells. The dynamics of the system is characterized by the time evolution of a few physical quantities of increasing many-body complexity, namely, the survival probability, depletion and fragmentation, and the many-particle position and momentum variances. In particular, we have examined the frequencies and amplitudes of the oscillations of the survival probabilities, the time scale for the development of fragmentation and its degree, and the growth and oscillatory behavior of the many-particle position and momentum variances. There is an overall suppression of the oscillations of the survival probabilities in an asymmetric double well, except for resonant values of asymmetry for which the one-body ground state energy in the right well matches with one of the one-body excited states in the left well, thereby resulting in resonantly enhanced tunneling from the right well ground state. Overall, depending on whether the condensate is initially prepared in the left or right well, the repulsive inter-atomic interactions affect the survival probabilities differently. For a sufficiently strong repulsive interaction, the system is found to become fragmented. The degree of fragmentation depends both on the asymmetry of the trap and the initial well in which the condensate is prepared in a non-trivial manner. Furthermore, we show that the phenomenon of resonantly enhanced tunneling can be accompanied by a large degree of fragmentation (depletion) for the strong (weak) interaction. The many-particle position and momentum variances follow the density oscillations of the system in the asymmetric double well and bears prominent signatures of the degree of depletion or fragmentation, depending on the strength of the interactions. These quantities further exhibit a fine structure signifying a breathing-mode oscillation. Finally, a universality of fragmentation for systems made of different numbers of particles but the same interaction parameter is also found and its dependence on the asymmetry is investigated. The phenomenon is robust despite the asymmetry of the junction and admits a macroscopically-large fragmented condensate characterized by a diverging many-particle position variance. This is as far as one can get from the dynamics of the density in the junction.recently. This has opened a whole new research field of strongly correlated systems with potential applications in quantum technology and quantum simulation of condensed-matter problems [...

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Section: Survival Probabilitysupporting

confidence: 63%

Section: B2 Physical Quantitiesmentioning

confidence: 99%

Section: B2 Physical Quantitiesmentioning

confidence: 99%

mentioning

confidence: 99%

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Many-body quantum dynamics of an asymmetric bosonic Josephson junction

Haldar

Alon

2019

New J. Phys.

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“…We see that the distribution function is determined by the expectation value φ(0, t) , set by R(t) via (36), along with quadratic fluctuations α j and β j , determined by the covariance matrix |Q j (t)| 2 . The essential quantities R(t) and Q(t) are obtained by solving the nonlinear, self-consistent system of equations (33). The distribution function (40) can be conveniently sampled: one draws numbers α j and β j from a Gaussian distribution with covariance matrix |Q j (t)| 2 and computes the corresponding values of…”

Section: E Full Distribution Functions and Multipoint Correlation Fumentioning

confidence: 99%

Self-consistent time-dependent harmonic approximation for the sine-Gordon model out of equilibrium

Nieuwkerk¹,

Eßler²

2019

J. Stat. Mech.

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We derive a self-consistent time-dependent harmonic approximation for the quantum sine-Gordon model out of equilibrium and apply the method to the dynamics of tunnel-coupled one-dimensional Bose gases. We determine the time evolution of experimentally relevant observables and in particular derive results for the probability distribution of subsystem phase fluctuations. We investigate the regime of validity of the approximation by applying it to the simpler case of a nonlinear harmonic oscillator, for which numerically exact results are available. We complement our self-consistent harmonic approximation by exact results at the free fermion point of the sine-Gordon model.

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Out-of-horizon correlations following a quench in a relativistic quantum field theory

Kukuljan

Sotiriadis

Takács

2020

J. High Energ. Phys.

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One of the manifestations of relativistic invariance in non-equilibrium quantum field theory is the "horizon effect" a.k.a. light-cone spreading of correlations: starting from an initially short-range correlated state, measurements of two observers at distant space-time points are expected to remain independent until their past light-cones overlap. Surprisingly, we find that in the presence of topological excitations correlations can develop outside of horizon and indeed even between infinitely distant points. We demonstrate this effect for a wide class of global quantum quenches to the sine-Gordon model. We point out that besides the maximum velocity bound implied by relativistic invariance, clustering of initial correlations is required to establish the "horizon effect". We show that quenches in the sine-Gordon model have an interesting property: despite the fact that the initial states have exponentially decaying correlations and cluster in terms of the bosonic fields, they violate the clustering condition for the soliton fields, which is argued to be related to the non-trivial field topology. The nonlinear dynamics governed by the solitons makes the clustering violation manifest also in correlations of the local bosonic fields after the quench.

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Relaxation to a Phase-Locked Equilibrium State in a One-Dimensional Bosonic Josephson Junction

Cited by 109 publications

References 43 publications

Many-body quantum dynamics of an asymmetric bosonic Josephson junction

Many-body quantum dynamics of an asymmetric bosonic Josephson junction

Self-consistent time-dependent harmonic approximation for the sine-Gordon model out of equilibrium

Out-of-horizon correlations following a quench in a relativistic quantum field theory

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