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Journal of Physics Communications

Lattice and quintic nonlinearity induced stripe phase in Bose–Einstein condensate under non-inertial and inertial motion

Priyam Das

Published Apr 27, 2018• 1 citation
Publisher

Abstract

We consider a parametrically forced Bose–Einstein condensate in the combined presence of an optical lattice and harmonic oscillator potential in the mean field approach. A spatial symmetry broken Bose-condensed phase in non-inertial and inertial frame yields a stripe phase in the presence of both cubic and quintic nonlinearities. We show that the existence of such stripe phase solely depends on the interplay between the quintic nonlinearity and the lattice potential. Furthermore, we observe that a time-dependent harmonic oscillator frequency destroys such stripe ordering. A linear stability analysis of the obtained solution is performed and we found that the solution is stable. In order to gain a better understanding of the underlying physics, we compute the energy, showing nonlinear compression of the condensate in some parameter domain.

DOI
10.1088/2399-6528/aac0e7

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We consider a parametrically forced Bose–Einstein condensate in the combined presence of an optical lattice and harmonic oscillator potential in the mean field approach. A spatial symmetry broken Bose-condensed phase in non-inertial and inertial frame yields a stripe phase in the presence of both cubic and quintic nonlinearities. We show that the existence of such stripe phase solely depends on the interplay between the quintic nonlinearity and the lattice potential. Furthermore, we observe that a time-dependent harmonic oscillator frequency destroys such stripe ordering. A linear stability analysis of the obtained solution is performed and we found that the solution is stable. In order to gain a better understanding of the underlying physics, we compute the energy, showing nonlinear compression of the condensate in some parameter domain.
We consider a parametrically forced Bose-Einstein condensate in the combined presence of an optical lattice and harmonic oscillator potential in the mean field approach. A spatial symmetry broken Bose-condensed phase in non-inertial and inertial frame yields a stripe phase in the presence of both cubic and quintic nonlinearities. We show that existence of such stripe phase solely depends on the interplay between the quintic nonlinearity and lattice potential. Furthermore, we observe that a time-dependent harmonic oscillator frequency destroys such stripe ordering. A linear stability analysis of the obtained solution is performed and we found that the solution is stable. In order to gain a better understanding of the underlying physics, we compute the energy, showing nonlinear compression of the condensate in some parameter domain.
In a one-dimensional shallow optical lattice, in the presence of both cubic and quintic nonlinearity, a superfluid density wave is identified in a Bose-Einstein condensate. Interestingly, it ceases to exist when only one of these interactions is operative. We predict the loss of superfluidity through a classical dynamical phase transition, where modulational instability leads to the loss of phase coherence. In a certain parameter domain, the competition between lattice potential and the interactions is shown to give rise to a stripe phase, where atoms are confined in finite domains. In a pure two-body case, apart from the known superfluid and insulating phases, a density wave insulating phase is found to exist, possessing two frequency modulations commensurate with the lattice potential.
In a one-dimensional shallow optical lattice, in the presence of both cubic and quintic nonlinearity, a superfluid density wave is identified in a Bose-Einstein condensate. Interestingly, it ceases to exist when only one of these interactions is operative. We predict the loss of superfluidity through a classical dynamical phase transition, where modulational instability leads to the loss of phase coherence. In a certain parameter domain, the competition between lattice potential and the interactions is shown to give rise to a stripe phase, where atoms are confined in finite domains. In a pure two-body case, apart from the known superfluid and insulating phases, a density wave insulating phase is found to exist, possessing two frequency modulations commensurate with the lattice potential.
We study Bose–Einstein condensate in the combined presence of time modulated optical lattice and harmonic trap in the mean-field approach. Through the self-similar method, we show the existence of sinusoidal lattice modes in this inhomogeneous system, commensurate with the lattice potential. A significant advantage of this system is wide tunability of the parameters through chirp management. The combined effect of the interaction, harmonic trap and lattice potential leads to the generation of nonlinear resonances, exactly where the matter wave changes its direction. When the harmonic trap is switched off, the BEC undergoes a nonlinear compression for the static optical lattice potential. For better understanding of chirp management and the nature of the sinusoidal excitation, we investigate the energy spectrum of the condensate, which clearly reveals the generation of nonlinear resonances in the appropriate regime. We have also identified a classical dynamical phase transition occurring in the system, where loss of superfluidity takes the superfluid phase to an insulating state.
The stability and collective excitations of binary Bose–Einstein condensates with cubic and quintic nonlinearities in variable anharmonic optical lattices are investigated. By using the variational approach, the influences of the quintic nonlinearities and the shape of the external potential on the stability are discussed in details. It is found that the quintic intraspecies and interspecies interatomic interactions profoundly affect the stability criterion and collective excitations of the system. The shape dependent potential form that characterizes the optical lattice deeply alters the stability regions. Direct numerical simulations of the mean-field coupled Gross–Pitaevskii equation describing the system agree well with the analytical predictions.
We study superfluid (SF) states of strongly interacting Bose-Bose mixtures with equal mass and intracomponent interaction in optical lattices both in the presence and absence of a barrier potential. We show that the SF order parameters obey the two-component nonlinear Schr\"odinger equation (NLSE) with not only cubic but also quintic nonlinearity in the vicinity of the first-order transitions to the Mott insulators with even fillings. In the case of no barrier potential, we analyze solitary-wave solutions of the cubic-quintic NLSE. When the SF state changes from a ground state to a metastable one, a standard dark solitary wave turns into a bubblelike dark solitary wave, which has a nonvanishing density dip and no $\ensuremath{\pi}$-phase kink even in the case of a standing solitary wave. It is shown that the former and latter solitary waves are dynamically unstable against an out-of-phase fluctuation and an in-phase fluctuation, respectively, and the dynamical instabilities are weakened when one approaches the transition point. We find that the size and the inertial mass of the solitary waves diverge at the first-order transition point. We suggest that the divergence of the inertial mass may be detected through measurement of the relation between the velocity and the phase jump of the solitary wave. In the presence of a barrier potential, we reveal that when the barrier strength exceeds a certain critical value, the SF state that was metastable without the barrier is destabilized towards complete disjunction of the SF. The presence of the critical barrier strength indicates that the strong barrier potential qualitatively changes the criticality near the metastability limit of the SF state. We derive critical behaviors of the density, the compressibility, and the critical current near the metastability limit induced by the barrier. It is also found that the relation between the supercurrent and the phase jump across the barrier exhibits a peculiar behavior, owing to the nontopological nature of the bubblelike solitary wave.