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Parametric resonance in Bose-Einstein condensates with periodic modulation of attractive interaction

William B. Cairncross, Axel Pelster

The European Physical Journal DMay 1, 201425 citations

Parametric Quantum Resonances for Bose–Einstein Condensates

P. G. Kevrekidis, A. R. Bishop, Kim Ø. Rasmussen

arXiv:cond-mat/0005024Journal of Low Temperature PhysicsAug 1, 200011 citations

Parametric Resonance in Bose-Einstein Condensates

William B. Cairncross, Axel Pelster

We demonstrate parametric resonance in Bose-Einstein condensates (BECs) with attractive two-body interaction in a harmonic trap under parametric excitation by periodic modulation of the s-wave scattering length. We obtain nonlinear equations of motion for the widths of the condensate using a Gaussian variational ansatz for the Gross-Pitaevskii condensate wave function. We conduct both linear and nonlinear stability analyses for the equations of motion and find qualitative agreement, thus concluding that the stability of two equilibrium widths of a BEC might be inverted by parametric excitation.We demonstrate parametric resonance in Bose-Einstein condensates (BECs) with attractive two-body interaction in a harmonic trap under parametric excitation by periodic modulation of the s-wave scattering length. We obtain nonlinear equations of motion for the widths of the condensate using a Gaussian variational ansatz for the Gross-Pitaevskii condensate wave function. We conduct both linear and nonlinear stability analyses for the equations of motion and find qualitative agreement, thus concluding that the stability of two equilibrium widths of a BEC might be inverted by parametric excitation.

arXiv:1209.3148Sep 14, 20122 citations

Parametrically excited ‘scars’ in Bose–Einstein condensates

Nadav Y. Katz, Oded Agam

Parametric excitation of a Bose–Einstein condensate (BEC) can be realized by periodically changing the interaction strength between the atoms. Above some threshold strength, this excitation modulates the condensate density. We show that, when the condensate is trapped in a potential well of irregular shape, density waves can be strongly concentrated ('scarred') along the shortest periodic orbits of a classical particle moving within the confining potential. While single-particle wave functions of systems whose classical counterpart is chaotic may exhibit rich scarring patterns, in BEC we show that nonlinear effects select mainly those scars that are locally described by stripes. Typically, these are the scars associated with self-retracing periodic orbits that do not cross themselves in real space. Dephasing enhances this behavior by reducing the nonlocal effect of interference.Parametric excitation of a Bose–Einstein condensate (BEC) can be realized by periodically changing the interaction strength between the atoms. Above some threshold strength, this excitation modulates the condensate density. We show that, when the condensate is trapped in a potential well of irregular shape, density waves can be strongly concentrated ('scarred') along the shortest periodic orbits of a classical particle moving within the confining potential. While single-particle wave functions of systems whose classical counterpart is chaotic may exhibit rich scarring patterns, in BEC we show that nonlinear effects select mainly those scars that are locally described by stripes. Typically, these are the scars associated with self-retracing periodic orbits that do not cross themselves in real space. Dephasing enhances this behavior by reducing the nonlocal effect of interference.

arXiv:0903.0968New Journal of PhysicsJul 21, 20107 citations

Excitations of Atomic Bose--Einstein Condensates

Mark Edwards

APSNov 1, 19960 citations

Parametric excitation of a Bose-Einstein condensate in a one-dimensional optical lattice

Meret Krämer, C. Tozzo, F. Dalfovo

We study the response of a Bose-Einstein condensate to a periodic modulation of the depth of an optical lattice. Using Gross-Pitaevskii theory, we show that a modulation at frequency $\ensuremath{\Omega}$ drives the parametric excitation of Bogoliubov modes with frequency $\ensuremath{\Omega}∕2$. The ensuing nonlinear dynamics leads to a rapid broadening of the momentum distribution and a consequent large increase of the condensate size after free expansion. We show that this process does not require the presence of a large condensate depletion. Our results reproduce the main features of the spectrum measured in the superfluid phase by St\"oferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].We study the response of a Bose-Einstein condensate to a periodic modulation of the depth of an optical lattice. Using Gross-Pitaevskii theory, we show that a modulation at frequency $\ensuremath{\Omega}$ drives the parametric excitation of Bogoliubov modes with frequency $\ensuremath{\Omega}∕2$. The ensuing nonlinear dynamics leads to a rapid broadening of the momentum distribution and a consequent large increase of the condensate size after free expansion. We show that this process does not require the presence of a large condensate depletion. Our results reproduce the main features of the spectrum measured in the superfluid phase by St\"oferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].

arXiv:cond-mat/0410122Physical Review AJun 27, 200567 citations

Parametric excitation of a Bose-Einstein condensate with modulated interactions

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