Kumbakonam, India
Kumbakonam, India

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Shin H.J.,Kyung Hee University | Radha R.,Center for Nonlinear Science | Kumar V.R.,Center for Nonlinear Science | Kumar V.R.,CAS Institute of Physics
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2011

In this Letter, we investigate the dynamics of Bose-Einstein Condensates (BECs) with spatially inhomogeneous interaction and generate bright solitons for the condensates by solving the associated mean field description governed by the Gross-Pitaevskii (GP) equation. We then investigate the properties of BECs in an optical lattice and periodic potential. We show that the GP equation in an optical lattice potential is integrable provided the interaction strength between the atoms varies periodically in space. The model discussed in the Letter offers the luxury of choosing the form of the lattice without destroying the integrability. Besides, we have also brought out the possible ramifications of the integrable model in the condensates of quasi-particles. © 2011 Elsevier B.V. All rights reserved.


Balaz A.,University of Belgrade | Paun R.,Horia Hulubei National Institute of Physics and Nuclear Engineering | Nicolin A.I.,Horia Hulubei National Institute of Physics and Nuclear Engineering | Balasubramanian S.,Center for Nonlinear Science | Ramaswamy R.,Center for Nonlinear Science
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2014

We study the emergence of Faraday waves in cigar-shaped collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement. Considering a Gaussian-shaped radially inhomogeneous scattering length, we show through extensive numerical simulations and detailed variational treatment that the spatial period of the emerging Faraday waves increases as the inhomogeneity of the scattering length gets weaker, and that it saturates once the width of the radial inhomogeneity reaches the radial width of the condensate. In the regime of strongly inhomogeneous scattering lengths, the radial profile of the condensate is akin to that of a hollow cylinder, while in the weakly inhomogeneous case the condensate is cigar shaped and has a Thomas-Fermi radial density profile. Finally, we show that when the frequency of the modulation is close to the radial frequency of the trap, the condensate exhibits resonant waves which are accompanied by a clear excitation of collective modes, while for frequencies close to twice that of the radial frequency of the trap, the observed Faraday waves set in forcefully and quickly destabilize condensates with weakly inhomogeneous two-body interactions. © 2014 American Physical Society.


Vinayagam P.S.,Center for Nonlinear Science | Radha R.,Center for Nonlinear Science | Porsezian K.,Pondicherry University
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2013

Using gauge transformation method, we generate rogue waves for the two-component Bose-Einstein condensates (BECs) governed by the symmetric coupled Gross-Pitaevskii (GP) equations and study their dynamics. We also suggest a mechanism to tame the rogue waves either by manipulating the scattering length through Feshbach resonance or the trapping frequency, a phenomenon not witnessed in the domain of BECs, and we believe that these results may have wider ramifications in the management of rogons. © 2013 American Physical Society.


Radha R.,Center for Nonlinear Science | Vinayagam P.S.,Center for Nonlinear Science | Porsezian K.,Pondicherry University
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2013

We reconsider the collisional dynamics of bright solitons in the coupled nonlinear Schrödinger equation. We observe that apart from the intensity redistribution in the interaction of bright solitons, one also witnesses a rotation of the trajectories of bright solitons. The angle of rotation can be varied by suitably manipulating the self-phase-modulation (SPM) or cross-phase-modulation (XPM) parameters. The rotation of the trajectories of the bright solitons arises due to the excess energy that is injected into the dynamical system through SPM or XPM. This extra energy contributes not only to the rotation of the trajectories, but also to the realignment of intensity distribution between the two modes. We also notice that the angular separation between the bright solitons can also be maneuvered suitably. The above results, which exclude quantum superposition for the field vectors, may have wider ramifications in nonlinear optics, Bose-Einstein condensates, and left- and right-handed metamaterials. © 2013 American Physical Society.


Radha R.,Center for Nonlinear Science | Vinayagam P.S.,Center for Nonlinear Science | Porsezian K.,Pondicherry University
Romanian Reports in Physics | Year: 2014

We study the dynamics of spatially coupled Bose-Einstein condensates and generate bright and dark solitons employing gauge transformation approach. We observe that when bright/dark solitons evolve in time, the centre of localization of the wave packet gets shifted to the left. We also notice that the spatial coupling stretches the wave packet which can be used as a mechanism to stabilize the condensates. The impact of spatial coupling is suitably exploited to generate an interference pattern in the collision of bright-bright, dark-dark and dark-bright solitons.


Ramesh Kumar V.,Center for Nonlinear Science | Radha R.,Center for Nonlinear Science | Wadati M.,Tokyo University of Science
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2010

We investigate the coupled Gross-Pitaevskii equation describing the dynamics of two hyperfine states of Bose-Einstein condensates and deduce the integrability condition for the propagation of bright vector solitons. We show how the transient trap and scattering length can be suitably tailored to bring about fascinating collisional dynamics of vector solitons. © 2010 Elsevier B.V. All rights reserved.


Balasubramanian S.,Center for Nonlinear science | Ramaswamy R.,Center for Nonlinear science | Nicolin A.I.,Horia Hulubei National Institute of Physics and Nuclear Engineering
Romanian Reports in Physics | Year: 2013

In this short note, we investigate by variational means the emergence of Faraday waves in cigar-shaped Bose-Einstein condensates with radially inhomoge-neous scattering lengths subject to periodic modulations of the radial confining potential. Our main result is that for weakly inhomogeneous scattering lengths, the Faraday waves follow a dispersion relation identical to that observed in condensates with spatially homogeneous scattering lengths.


Radha R.,Center for Nonlinear Science | Vinayagam P.S.,Center for Nonlinear Science
Romanian Reports in Physics | Year: 2015

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. © 2015, Editura Academiei Romane. All rights reserved.


Radha R.,Center for Nonlinear Science | Vinayagam P.S.,Center for Nonlinear Science
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2012

We investigate the dynamics of a weakly coupled two component Bose-Einstein condensate and generate bright soliton solutions. We observe that when the bright solitons evolve in time, the density of the condensates shoots up suddenly by virtue of weak coupling indicating the onset of instability in the dynamical system. However, this instability can be overcome either through Feshbach resonance by tuning the temporal scattering length or by suitably changing the time dependent coupling coefficient, thereby extending the lifetime of the condensates. © 2012 Elsevier B.V. All rights reserved.


Kumar V.R.,Center for Nonlinear Science | Radha R.,Center for Nonlinear Science | Wadati M.,Tokyo University of Science
Journal of the Physical Society of Japan | Year: 2010

We introduce a phase imprint into the macroscopic order parameter governing the dynamics of Bose-Einstein condensates with attractive two-body interactions described by a cubic Gross-Pitaevskii (GP) equation and then engineer the imprinted phase suitably to generate the modified GP equation. The modified GP equation describes the dynamics of condensates with both two-(attractive) and three-body (attractive and repulsive) interactions in an expulsive harmonic trap. Employing gauge transformation approach, we then construct bright solitons of the modified GP equation. We observe that the attractive three-body interactions introduce an additional nontrivial phase in the matter wave solitons arising due to attractive two-body interactions without changing their density while the repulsive three-body interactions enormously increase the density of the condensates without causing any change in the phase of the solitons originating from attractive two-body interactions. © 2010 The Physical Society of Japan.

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