Symmetry breaking and self-trapping of a dipolar Bose-Einstein condensate in a double-well potential

Xiong, Bo; Gong, Jiangbin; Pu, Han; Bao, Weizhu; Li, Baowen

doi:10.1103/physreva.79.013626

Cited by 83 publications

(90 citation statements)

References 41 publications

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“…The occurrence of quantized vortices is a hallmark of the superfluid nature of BECs. In addition, condensation of bosonic atoms and molecules with significant dipole moments whose interaction is both nonlocal and anisotropic has recently been achieved experimentally in trapped 52 Cr and 164 Dy gases [1,22,27,32,33,36,48].…”

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confidence: 99%

A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

Bao¹,

Marahrens²,

Tang³

et al. 2013

SIAM J. Sci. Comput.

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Abstract. We propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating Bose-Einstein condensates (BECs) in a rotational frame with or without longrange dipole-dipole interaction (DDI). We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with an angular momentum rotation term and/or long-range DDI, state the twodimensional (2D) GPE obtained from the 3D GPE via dimension reduction under anisotropic external potential, and review some dynamical laws related to the 2D and 3D GPEs. By introducing a rotating Lagrangian coordinate system, the original GPEs are reformulated to GPEs without the angular momentum rotation, which is replaced by a time-dependent potential in the new coordinate system. We then cast the conserved quantities and dynamical laws in the new rotating Lagrangian coordinates. Based on the new formulation of the GPE for rotating BECs in the rotating Lagrangian coordinates, a time-splitting spectral method is presented for computing the dynamics of rotating BECs. The new numerical method is explicit, simple to implement, unconditionally stable, and very efficient in computation. It is spectral-order accurate in space and second-order accurate in time and conserves the mass on the discrete level. We compare our method with some representative methods in the literature to demonstrate its efficiency and accuracy. In addition, the numerical method is applied to test the dynamical laws of rotating BECs such as the dynamics of condensate width, angular momentum expectation, and center of mass, and to investigate numerically the dynamics and interaction of quantized vortex lattices in rotating BECs without or with the long-range DDI. 1. Introduction. Bose-Einstein condensation (BEC), first observed in 1995 [4,18,23], has provided a platform to study the macroscopic quantum world. Later, with the observation of quantized vortices [2,19,34,35,37,39,50], rotating BECs have been extensively studied in the laboratory. The occurrence of quantized vortices is a hallmark of the superfluid nature of BECs. In addition, condensation of bosonic atoms and molecules with significant dipole moments whose interaction is both nonlocal and anisotropic has recently been achieved experimentally in trapped 52 Cr and 164 Dy gases [1,22,27,32,33,36,48].At temperatures T much smaller than the critical temperature T c , the properties of BEC in a rotating frame with long-range dipole-dipole interaction (DDI) are well

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confidence: 99%

A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

Bao¹,

Marahrens²,

Tang³

et al. 2013

SIAM J. Sci. Comput.

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“…The BEC in double-well potential trap have got much attention because of its richness in physics [10][11][12][13][14]. This motivated the study of the BEC trapped in rotating double-well potential [15].…”

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Pinning of hidden vortices in Bose-Einstein condensates

2014

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We study the vortex dynamics and vortex pinning effect in Bose-Einstein condensate in a rotating double-well trap potential and co-rotating optical lattice. We show that, in agreement with the experiment, the vortex number do not diverge when the rotational frequency Ω → 1 if the trap potential is of anisotropic double-well type. The critical rotational frequency as obtained from numerical simulations agrees very well with the value √ l/l for l = 4 which supports the conjecture that surface modes with angular momentum l = 4 are excited when the rotating condensate is trapped in double-well potential. The vortex lattice structure in a rotating triple-well trap potential and its pinning shows very interesting features. We show the existence and pinning of a new type of hidden vortices whose phase profile is similar to that of the visible vortices.

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“…In nonlinear systems, because additional nonlinearity always give rise to the effect of SSB, phase transition and SSB are also important issues and attract great attention. Among many kinds of nonlinear systems, double-well potential (DWP) or dual-core system is the most essential model employed to study the phase transition and SSB of the nonlinear states [2][3][4][5][6][7][8][9]. In DWP system, the important process relating to the phase transition and SSB is symmetric breaking bifurcation (SBB), which determines the process of symmetric states transiting to the asymmetric ones [10][11][12][13][14][15][16][17].…”

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Switch between the Types of the Symmetry Breaking Bifurcation in Optically Induced Photorefractive Rotational Double-Well Potential

Chen

Luo

et al. 2013

J. Phys. Soc. Jpn.

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We study the possibility of switching the types of symmetry breaking bifurcation (SBB) in the cylinder shell waveguide with helical double-well potential along propagation direction. This model is described by the one-dimensional nonlinear Schrödinger (NLS) equation. The symmetry-and antisymmetry-breakings can be caused by increasing the applied voltage onto the waveguide in the self-focusing and -defocusing cases, respectively. In the self-focusing case, the type of SBB can be switched from supercritical to subcritical. While in the self-defocusing case, the type of SBB can not be switched because only one type of SBB is found. PACS numbers: 42.65.Tg; 47.20.Ky; 05.45.Yv; 42.65.Hw Phase transition is a fundamental topic in many branches of physics. Spontaneous symmetric breaking (SSB), which is the transition from the symmetric ground state (GS) to that which does not follow the symmetry of the potential, always plays an important role in inducing the transition [1]. In nonlinear systems, because additional nonlinearity always give rise to the effect of SSB, phase transition and SSB are also important issues and attract great attention. Among many kinds of nonlinear systems, double-well potential (DWP) or dual-core system is the most essential model employed to study the phase transition and SSB of the nonlinear states [2][3][4][5][6][7][8][9]. In DWP system, the important process relating to the phase transition and SSB is symmetric breaking bifurcation (SBB), which determines the process of symmetric states transiting to the asymmetric ones [10][11][12][13][14][15][16][17]. There are two kinds of SBB, subcritical and super critical, which are tantamount to the phase transition of the first and second kind respectively. The former kind of SBB, subcritical type, features branches of the asymmetric states going at first backward after the bifurcation point then turning forward. While the latter one, the supercritical type, features the asymmetric branches going immediately to the forward direction after the bifurcation point. Different settings with different environments may possibly lead to different types of SBB. An interesting problem is the possibility to control the type of the SBB, and thus to switch between the respective phase transitions of the two kinds. About this problem, it has been reported that the addition of a periodic potential (optical lattice) acting in the unconfined direction changes the character of the SBB from sub-to supercritical [7]. Recently, it is also reported that the periodical modulation of the linearcoupling constant, which is induced by the electromagnetically induced transparency (EIT) via the double-Λ system, can change the SBB from sub-to supercritical with the increase of the total power of the probe beams [17].Very recently, a setting with rotational (alias helical) DWP potential in a cylinder shell waveguide was performed [18], which reported that the rotating speed of the potential could also induce the symmetry breaking of the nonlinear modes. It is well known that r...

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Symmetry breaking and self-trapping of a dipolar Bose-Einstein condensate in a double-well potential

Cited by 83 publications

References 41 publications

A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

Pinning of hidden vortices in Bose-Einstein condensates

Switch between the Types of the Symmetry Breaking Bifurcation in Optically Induced Photorefractive Rotational Double-Well Potential

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