A Dynamical Phase Transition of Binary Species BECs Mixtures in a Double Well Potential

Tian, Jing; Qiu, Haibo

doi:10.1007/s10773-016-3164-y

Cited by 4 publications

(4 citation statements)

References 18 publications

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“…Additionally, the adaptation of such optimal control methodologies to low-dimensional truncated Galerkin dynamics is a technique that could find significant potential for further applications. Some possibilities include multi-component and spinor condensates [18] where few-mode approximations have proven useful [11,40,42]. Moreover, extending such control strategies beyond the mean-field framework and into the realm of many-body effects [27,31], is of particular interest in its own right; for a review of the latter, see, e.g., the recent preprint of [29].…”

Section: Discussionmentioning

confidence: 99%

“…Some more mathematical examples include the analysis of the double-well bifurcation structure [3,14], the low-dimensional representation of the associated dynamical problem (and its fidelity) [23,26], and the effect of changing the nonlinear exponent on the bifurcation [22,35]. Among the many more physical examples are the interactions of multiple dispersive (e.g., atomic) species [11,40,42], incorporating beyond-mean-field (i.e., manybody) effects [27,31], and the effect of larger spatial dimension (and possibly four wells) [43], among others.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential

Adriazola¹,

Goodman²

2022

Preprint

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We pose the problem of transferring a Bose-Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the timedependent form of the potential. We derive a reduced dynamical system using a Galerkin truncation onto a finite set of eigenfunctions and find that including three modes suffices to effectively control the full dynamics, described by the Gross-Pitaevskii model of BEC. The functional form of the control is reduced to finite dimensions by using a Galerkin-type method called the chopped random basis (CRAB) method, which is then optimized by a genetic algorithm called differential evolution (DE). Finally, we discuss the the extent to which the reduction-based optimal control strategy can be refined by means of including more modes in the Galerkin reduction.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential

Adriazola¹,

Goodman²

2022

Preprint

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“…Here, â † j (â j ) and b † j ( bj ) are the creation (annihilation) operators of the species a and b respectively that residing in the jth well, j = L, R. The parameters t a and t b describe the coupling (tunneling) between two wells, g a(b) and g ab stand for intraspecies and interspecies interaction strength respectively, which is explicitly given by: [38]. Here A αβ is the s-wave scattering length between atoms, m αβ is the reduced mass, where we denote g α = g αα and α, β = a, b.…”

Section: The Modelmentioning

confidence: 99%

Binary mixture of Bose-Einstein condensates in a double-well potential: Berry phase and two-mode entanglement

Günay

2020

Phys. Rev. A

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A binary mixtures of Bose-Einstein condensate (BEC) structures exhibit an incredible richness in terms of holding different kinds of phases. Depending on the ratio of the inter-and intra-atomic interactions, the transition from mixed to separated phase, which is also known as the miscibilityimmiscibility transition, has been reported in different setups and by different groups. Here, we describe such type of quantum phase transition (QPT) in an effective Hamiltonian approach, by applying Holstein-Primakoff transformation in the limit of large number of particles. We demonstrate that non-trivial geometric phase near the critical coupling is present, which confirms the connection between Berry phase and QPT. We also show that, by using the spin form of Hillery & Zubairy criterion, a two mode entanglement accompanies this transition in the limit of large, but not infinite number of particles. APPENDIXHere we show the derivations of Eqs. (29) and (30). By inserting displaced operators defined in Eq. (12) into the

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“…These include the dynamics of spin-orbit-coupled condensates [3][4][5], the existence of nonlinear steady state [6], the cross structure of the level [7,8], the nonlinear Landau-Zener tunneling [9], and the the nonlinear Josephson oscillation [10,11]. Most recently, the tunneling probabilities of few bosons [12], the nonequilibrium dynamical ion transfer [13], the asymmetric many-body loss [14], the dynamical phase transition of binary species BECs [15], Interaction blockade [16]and the interaction-modulated tunneling dynamics [17] have also been explored, respectively.…”

Section: Introductionmentioning

confidence: 99%

Dynamical phase transition of two-component Bose–Einstein condensate with nonlinear tunneling in an optomechanical cavity-mediated double-well system

Tan

et al. 2018

J. Phys. B: At. Mol. Opt. Phys.

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We investigate the dynamical phase transition of two-component Bose-Einstein condensate with nonlinear tunneling, which is trapped inside a double-well and dispersively coupled to a single mode of a high-finesse optical cavity with one moving end mirror driven by a single mode standing field. The nonlinear tunneling interaction leads to an increase of stability points and riches the phase diagram of the system. It is shown that the appearance of the moving end mirror speeds up the tunneling of Bose-Einstein condensates, which makes population difference between two wells and regulates the number of the stability points of the system.

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A Dynamical Phase Transition of Binary Species BECs Mixtures in a Double Well Potential

Cited by 4 publications

References 18 publications

Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential

Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential

Binary mixture of Bose-Einstein condensates in a double-well potential: Berry phase and two-mode entanglement

Dynamical phase transition of two-component Bose–Einstein condensate with nonlinear tunneling in an optomechanical cavity-mediated double-well system

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