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arXiv:2006.14678 · Physical Review A

Asymptotic population imbalance of an ultracold bosonic ensemble in a driven double well

Jie Chen, Aritra K. Mukhopadhyay, Peter Schmelcher

Published Sep 1, 2020• 5 citations
arXivHTMLPDF

Abstract

We demonstrate that an ultracold many-body bosonic ensemble confined in a one-dimensional double-well potential exhibits a population imbalance between the two wells at large timescales, when the depth of the wells is modulated by a time-dependent driving force. The specific form of the driving force is shown to break spatial parity and time-reversal symmetries, which leads to such an asymptotic population imbalance (API). The value of the API can be flexibly controlled by changing the phase of the driving force and the total number of particles. While the API is highly sensitive to the initial state in the few-particle regime, this dependence on the initial state is lost as we approach the classical limit of large particle numbers. We perform a Floquet analysis in the few-particle regime and an analysis based on a driven classical nonrigid pendulum in the many-particle regime. Although the obtained API values in the many-particle regime agree very well with those obtained in the classical limit, we show that there exists a significant disagreement in the corresponding real-time population imbalance due to quantum correlations.

DOI
10.1103/physreva.102.033302

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Journal of Physics Conference Series•Oct 1, 2019•0 citations
We demonstrate that an ultracold many-body bosonic ensemble confined in a one-dimensional double-well potential exhibits a population imbalance between the two wells at large timescales, when the depth of the wells is modulated by a time-dependent driving force. The specific form of the driving force is shown to break spatial parity and time-reversal symmetries, which leads to such an asymptotic population imbalance (API). The value of the API can be flexibly controlled by changing the phase of the driving force and the total number of particles. While the API is highly sensitive to the initial state in the few-particle regime, this dependence on the initial state is lost as we approach the classical limit of large particle numbers. We perform a Floquet analysis in the few-particle regime and an analysis based on a driven classical nonrigid pendulum in the many-particle regime. Although the obtained API values in the many-particle regime agree very well with those obtained in the classical limit, we show that there exists a significant disagreement in the corresponding real-time population imbalance due to quantum correlations.
We demonstrate that an ultracold many-body bosonic ensemble confined in a one-dimensional double-well potential can exhibit chaotic dynamics due to the presence of a single impurity. The nonequilibrium dynamics is triggered by a quench of the impurity-Bose interaction and is illustrated via the evolution of the population imbalance for the bosons between the two wells. While the increase of the postquench interaction strength always facilitates the irregular motion for the bosonic population imbalance, it becomes regular again when the impurity is initially populated in the highly excited states. Such an integrability to chaos (ITC) transition is fully captured by the transient dynamics of the corresponding linear entanglement entropy, whose infinite-time-averaged value additionally characterizes the edge of the chaos and implies the existence of an effective Bose-Bose attraction induced by the impurity. To elucidate the physical origin for the observed ITC transition, we perform a detailed spectral analysis for the mixture with respect to both the energy spectrum as well as the eigenstates. Specifically, two distinguished spectral behaviors upon a variation of the interspecies interaction strength are observed. While the avoided level crossings take place in the low-energy spectrum, the energy levels in the high-energy spectrum possess a bandlike structure and are equidistant within each band. This leads to a significant delocalization of the low-lying eigenvectors, which, in turn, accounts for the chaotic nature of the bosonic dynamics. By contrast, those highly excited states bear a high resemblance to the noninteracting integrable basis, which explains the recovery of the integrability for the bosonic species. Finally, we discuss the induced Bose-Bose attraction as well as its impact on the bosonic dynamics.
We investigate the nonlinear dynamics of a Bose-Einstein condensate trapped in a double-well potential of a one-dimensional lattice, where the interatomic interactions are periodically modulated in time. In the typical case of a symmetric double-well, we observe collective particle emission under resonant driving, where the excitation regimes are explicitly constrained by the interplay between the drive strength and the hopping amplitude. By introducing a depth asymmetry between the wells, we find that moderate bias specifically enhances the emission rate, while large asymmetry suppresses it. The particle jets can be further controlled by modulating the hopping amplitudes, where the emission is weakened for finite hopping imbalances. These results outline the roles of asymmetry and external driving in precisely manipulating quantum many-body transport, and may offer insights into the design of atomtronic devices.
We revisit the dynamics of a Bose-Einstein condensate in a double-well potential, from the regime of Josephson plasma oscillations to the self-trapping regime, by means of the Bogoliubov quasiparticle projection method. For a very small imbalance between the left and right wells only the lowest Bogoliubov mode is significantly occupied. In this regime the system performs plasma oscillations at the corresponding frequency, and the evolution of the condensate is characterized by a periodic transfer of population between the ground and the first excited state. As the initial imbalance is increased, more excited modes---though initially not macroscopically occupied---get coupled during the evolution of the system. Since their population also varies with time, the frequency spectrum of the imbalance turns out to be still peaked around a single frequency, which is continuously shifted towards lower values. The nonlinear mixing between Bogoliubov modes eventually drives the system into the the self-trapping regime, when the population of the ground state can be transferred completely to the excited states at some time during the evolution. For simplicity, here we consider a one-dimensional setup, but the results are expected to hold also in higher dimensions.
We investigate the excitation properties of finite ultracold bosonic systems in a one-dimensional harmonic trap with a time-dependent interaction strength. The driving of the interatomic coupling induces excitations of the relative motion exclusively with specific and controllable contributions of momentarily excited many-body states. Mechanisms for selective excitation to few-body analogs of collective modes and acceleration occur in the vicinity of resonances. Via the few-body spectrum and a Floquet analysis, we study the excitation mechanisms and the corresponding impact of the driving frequency and strength as well as the initial correlation of the bosonic state. The fundamental case of two atoms is analyzed in detail and forms a key ingredient for the bottom-up understanding of cases with higher atom numbers, thereby examining finite-size corrections to macroscopic collective modes of oscillation.
Abstract We study the tunneling dynamics of N = 10 one-dimensional interacting bosons confined in a temporally driven double well potential that imitates a quantum seesaw and how we can manipulate these dynamics by changing the drive of the seesaw potential. We emulate the seesaw with a driven double well potential and consider two driving protocols: an harmonic constant-frequency drive and a chirped drive with linearly increasing frequency. We consider the time-dependent many-body Schrödinger equation of a repulsively interacting quasi-one-dimensional few-boson system. We solve it by using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) as implemented in the MCTDH-X software. For an harmonic drive and at small values of the driving amplitude, the dynamics of the particles become very slow rendering a stationary-like state. In a phase-space picture the population imbalance between the wells follows a trajectory which is restricted to a comparatively small region of space. For an harmonic drive at intermediate amplitudes, the dynamics become periodic in nature, implying that the bosons populate each of wells periodically. At comparatively large amplitudes of the harmonic drive, the dynamics show features of chaos in phase-space representation. For the chirped drive with a driving frequency increasing linearly in time, the imbalance of the atoms in the seesaw, however, has a temporal evolution that is faster for certain frequency ranges. The tunneling dynamics in such cases, for small amplitudes, show the appearance of quasi-periodicity with simultaneously present slow and fast oscillations. Increasing the amplitude of the chirped drive, we observe that the dynamics, although being periodic, become severely damped in their amplitude. Our study establishes that by tuning the temporal evolution of the quantum seesaw, a precise control of tunneling dynamics of the correlated bosons can be achieved. Since harmonic driving and chirp frequency modulation of the seesaw are experimentally achievable, our simulations can be experimentally realized in laboratories dealing with cold atomic gases.