Stabilization of matter wave solitons in weakly coupled atomic condensates

Radha, R.; Vinayagam, P. S.

doi:10.1016/j.physleta.2012.01.029

Cited by 8 publications

(7 citation statements)

References 33 publications

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“…For condensates in a time independent harmonic trap, λ(t) = λ 0 (a constant), Equation (11) yields γ(t) = γ 0 exp (λ 0 t), where γ 0 is an arbitrary constant. Considering a vacuum seed solution, i.e., q 1 (x, t) = q 2 (x, t) = 0, and employing gauge transformation approach [39][40][41][42], we obtain…”

Section: The Model and Lax Pairmentioning

confidence: 99%

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Bright soliton dynamics in spin orbit-Rabi coupled Bose-Einstein condensates

Vinayagam

Radha²,

Bhuvaneswari

et al. 2017

Communications in Nonlinear Science and Numerical Simulation

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We investigate the dynamics of a spin-orbit (SO) coupled BECs in a time dependent harmonic trap and show the dynamical system to be completely integrable by constructing the Lax pair. We then employ gauge transformation approach to witness the rapid oscillations of the condensates for a relatively smaller value of SO coupling in a time independent harmonic trap compared to their counterparts in a transient trap. Keeping track of the evolution of the condensates in a transient trap during its transition from confining to expulsive trap, we notice that they collapse in the expulsive trap. We further show that one can manipulate the scattering length through Feshbach resonance to stretch the lifetime of the confining trap and revive the condensate. Considering a SO coupled state as the initial state, the numerical simulation indicates that the reinforcement of Rabi coupling on SO coupled BECs generates the striped phase of the bright solitons and does not impact the stability of the condensates despite destroying the integrability of the dynamical system.

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Section: The Model and Lax Pairmentioning

confidence: 99%

“…Considering a vacuum seed solution, i.e., q 1 (x, t) = q 2 (x, t) = 0, and employing gauge transformation approach [39][40][41][42], we obtain…”

Section: The Model and Lax Pairmentioning

confidence: 99%

Bright soliton dynamics in spin orbit-Rabi coupled Bose-Einstein condensates

Vinayagam

Radha²,

Bhuvaneswari

et al. 2017

Communications in Nonlinear Science and Numerical Simulation

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“…where γ(t) is the strength of the FWM terms, and λ 2 (t) is the strength of the anti-trapping (expulsive) potential. These potentials occur in various physical contexts, such as the interaction of optical and matter-wave solitons with barriers [32]- [35], and splitting of wave packets in interferometers [36].…”

Section: The Modelmentioning

confidence: 99%

Persistent bright solitons in sign-indefinite coupled nonlinear Schrödinger equations with a time-dependent harmonic trap

Radha¹,

Vinayagam²,

Sudharsan³

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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We introduce a model based on a system of coupled nonlinear Schrödinger (NLS) equations with opposite signs in front of the kinetic and gradient terms in the two equations. It also includes time-dependent nonlinearity coefficients and a parabolic expulsive potential. By means of a gauge transformation, we demonstrate that, with a special choice of the time dependence of the trap, the system gives rise to persistent solitons. Exact single-and two-soliton analytical solutions and their stability are corroborated by numerical simulations. In particular, the exact solutions exhibit inelastic collisions between solitons.

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“…Equations (109) have also been investigated for ν(t) = 0 [66,67] and the dynamics of vector BECs has been analyzed. The explicit forms of one soliton solution of equations (109) can be written as [74] ψ…”

Section: A Impact Of Weak Time Dependent Rabi Couplingmentioning

confidence: 99%

“…The fact that the trap frequency Γ(t) varies exponentially with the time dependent coupling coefficient ν(t) (see equation (9) in Ref. [74]) indicates that the density of the bright solitons or the condensates could build up in a very shot span of time. This means that the dynamical system could enter into the domain of instability very quickly.…”

Section: A Impact Of Weak Time Dependent Rabi Couplingmentioning

confidence: 99%

An Analytical Window into the World of Ultracold Atoms

Radha¹,

Vinayagam²

2015

Preprint

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In this paper, we review the recent developments which had taken place in the domain of quasi one dimensional Bose-Einstein Condensates (BECs) from the viewpoint of integrability. To start with, we consider the dynamics of scalar BECs in a time independent harmonic trap and observe that the scattering length can be suitably manipulated either to compress the bright solitons to attain peak matter wave density without causing their explosion or to broaden the width of the condensates without diluting them. When the harmonic trap frequency becomes time dependent, we notice that one can stabilize the condensates in the confining domain while the density of the condensates continue to increase in the expulsive region. We also observe that the trap frequency and the temporal scattering length can be manoeuvred to generate matter wave interference patterns indicating the coherent nature of the atoms in the condensates. We also notice that a small repulsive three body interaction when reinforced with attractive binary interaction can extend the region of stability of the condensates in the quasi-one dimensional regime.On the other hand, the investigation of two component BECs in a time dependent harmonic trap suggests that it is possible to switch matter wave energy from one mode to the other confirming the fact that vector BECs are long lived compared to scalar BECs. The Feshbach resonance management of vector BECs indicates that the two component BECs in a time dependent harmonic trap are more stable compared to the condensates in a time independent trap. The introduction of weak (linear) time dependent Rabi coupling rapidly compresses the bright solitons which however can be again stabilized through Feshbach resonance or by finetuning the Rabi coupling while the spatial coupling of vector BECs introduces a phase difference between the condensates which subsequently can be exploited to generate interference pattern in the bright or dark solitons.

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Stabilization of matter wave solitons in weakly coupled atomic condensates

Cited by 8 publications

References 33 publications

Bright soliton dynamics in spin orbit-Rabi coupled Bose-Einstein condensates

Bright soliton dynamics in spin orbit-Rabi coupled Bose-Einstein condensates

Persistent bright solitons in sign-indefinite coupled nonlinear Schrödinger equations with a time-dependent harmonic trap

An Analytical Window into the World of Ultracold Atoms

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