Elements of Vortex-Dipole Dynamics in a Nonuniform Bose–Einstein Condensate

Sakhel, Roger R.; Sakhel, Asaad R.

doi:10.1007/s10909-016-1636-3

Cited by 7 publications

(4 citation statements)

References 75 publications

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“…here, α z is inverse harmonic oscillator length = 1/a ⊥ . Quasi 2D harmonic oscillator energy turned out to be, nz,nr,m = (2n r + |m| + 1)hω ⊥ + 1/2hω z (9) to study the LLL approximation we set n r = 0 for which single particle angular momentum takes the values m ≥ 0 and the choice for n r = 0, 1 corresponds to m = ±1, ±2.. termed as the beyond LLL approximation in the above Eq. ( 8).…”

Section: The Single Particle Energy Spectrummentioning

confidence: 99%

“…The achievement of Bose-Einstein condensates (BECs) in harmonically trapped atomic vapours has stimulated explosively growing interest in the system of interacting bosons [2][3][4][5][6][7][8][9][10][11] and for the parabolic trap is studied for contact potentia.. Theoretical studies in quasi-two dimensions are mainly focused on the rotating properties and vortex structure in BEC.…”

Section: Introductionmentioning

confidence: 99%

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Vortices in rotating Bose gas interacting via finite range Gaussian potential in a quasi-two-dimensional harmonic trap

Hamid¹,

Ahsan²

2022

Preprint

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A system of harmonically trapped N=16 spin-0 bosons confined in quasi-2D symmetricalx − y plane interacting via a finite range repulsive Gaussian potential is studied under an externally impressed rotation to an over all angular velocity Ω about the z−axis. The exact diagonalization (ED) of n × n many-body Hamiltonian matrix in a given subspace of quantized total angular momentum 0 ≤ L z ≤ 4N is performed using Davidson algorithm.For N = 16and L z = 32, the dimensionality of the Hilbert space turns out to be n = 384559.With increase in the interaction range in the Gaussian potential, the active Fock space size gets reduced and hence computation becomes more feasible compared to the zero-range δfunction potential. Following this idea, we considered the interaction-range parameter σ = 0.30, 0.50 and 0.75 to study the finite-range effects on the many-body ground state. The trap velocity Ω being the Langrange multiplier associated with the angular momentum L z for the rotating systems, the L z −Ω phase diagram (or stability line) is drawn which determines the critical angular velocities, Ω c i , i =, 0, 1, 2.., at which, for a given angular momentum L z , the system goes through a quantum phase transition. Further with increase in interaction range σ, the quantum mechanical coherence extends over more and more particles in the system resulting in an enhanced stability of the i th vortical state with angular momentum L z (Ω c i ) leading to a delayed onset of the the next vortical state L z Ω c i+1 at a higher value of the next critical angular velocity Ω c i+1 . There is an increase in the critical angular velocity (Ω c i , i = 1, 2, 3 • • •) and in the largest condensate fraction λ 1 , calculated using single particle reduced density matrix(SPRDM) eigen-values with increase in the interaction range σ. We calculated the von-Neumann quantum entropy (S 1 ), degree of condensation (C d ) and the conditional probability density (CPDs). There is no significant change in von-Neumann entropy S 1 and the degree of condensation C d in slow-rotating gas in the region 0 ≤ L z ≤ (L z = N ). However, for higher angular momentum, L z ≥ 2N , with increase in interaction range σ, small variations in S 1 and C d are observed. We plot the isosurface CPDs

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Section: The Single Particle Energy Spectrummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vortices in rotating Bose gas interacting via finite range Gaussian potential in a quasi-two-dimensional harmonic trap

Hamid¹,

Ahsan²

2022

Preprint

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“…The motion of a vortex depends on the flow pattern of its nearby vortices [70]. This means that the vortices are usually aware of each other [71]. When the two VDs reach their minimum distance, the antivortex 2 is closer to the vortex 3 than the antivortex 4, thus the effect of the antivortex 2 on the vortex 3 plays a major role.…”

Section: Oblique Collision Dynamics Of Two Vortex Dipolesmentioning

confidence: 99%

Oblique collisions and catching-up phenomena of vortex dipoles in a uniform Bose–Einstein condensate

2019

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We investigate the collisional dynamics of two vortex dipoles in a uniform two-dimensional Bose-Einstein condensate. It is found that the dynamics are deeply related to the moving directions and sizes of the initial vortex dipoles. For the oblique collisions of two vortex dipoles with the same size, we find that the vortices in the two initial vortex dipoles recombine into two new vortex dipoles which scatter in the opposite directions. For the catching-up processes of two vortex dipoles with different size, we find that the faster vortex dipole speeds up and passes through the slower vortex dipole. If the size of the vortex dipoles are small, we also observe vortex annihilation and vortex resurrection. The corresponding parameter ranges of different collisional dynamics are discussed.

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“…As far as the methods for studying the dynamics of BECs is concerned, this has until just recently, been frequently undertaken by the mean-field time-dependent Gross-Pitaevskii equation (TDGPE) (see e.g. [8,[37][38][39][40][41][42][43][44]). And although the use of this equation is widely spread and prevalent in its conventional form, being essentially a powerful method, its validity requires all particles to occupy a single lowest energy state.…”

Section: Introductionmentioning

confidence: 99%

Unpredictable condensate–depletion dynamics in one-dimensional power-law traps

Sakhel¹,

Sakhel²

2022

J. Phys.: Condens. Matter

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The dynamic depletion of a trapped one-dimensional Bose-Einstein condensate (BEC) that is driven by laser stirring is numerically explored using beyond mean-field methods. For this purpose, the multi-configurational time-dependent Hartree method for bosons (MCTDHB) [Alon \ea, Phys. Rev. A {\bf 77}, 033613 (2008)] is applied. In order to induce the depletion, the BEC is excited by a negative Gaussian potential (dimple) whose depth is modulated with time. The BEC is examined in various trapping geometries, with different interactions, and the condensate depletion is recorded as a function of time. A general power--law trap is considered that can be experimentally generated and shaped by the holographic methods of Bruce \ea\ [Bruce \ea, Phys. Rev. A {\bf 84}, 053410 (2011)]. The chief goal is to explore the interplay between trapping geometry and interactions in defining the depletion dynamics. It is chiefly found, that the details of these depletion dynamics are unpredictable and determined by a combination of the principle dimple depth, trap, and interactions. One significant feature of this work is that quite a number of plateaus is reached in the aforementioned dynamics.

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Elements of Vortex-Dipole Dynamics in a Nonuniform Bose–Einstein Condensate

Cited by 7 publications

References 75 publications

Vortices in rotating Bose gas interacting via finite range Gaussian potential in a quasi-two-dimensional harmonic trap

Vortices in rotating Bose gas interacting via finite range Gaussian potential in a quasi-two-dimensional harmonic trap

Oblique collisions and catching-up phenomena of vortex dipoles in a uniform Bose–Einstein condensate

Unpredictable condensate–depletion dynamics in one-dimensional power-law traps

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