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Physical Review A

Dynamical stabilization of a superfluid motion in the presence of an ac force

L. Morales-Molina, E. Arévalo

Published Sep 29, 2017• 2 citations
Publisher

Abstract

We study the superfluid behavior motion of interacting particles in a periodic potential subject to an external ac force. We observe a dynamical stabilization of the superfluid motion in the presence of ac forces around the boundary of the Brillouin zone. We analyze relevant nonlinear Floquet-Bloch states within the mean field approximation that display loops in the energy spectrum. In particular, we investigate with some detail the transport properties of these states at the edge of the Brillouin zone, showing the existence of a nonvanishing motion of particles. These findings are corroborated by a nonlinear generalization of the Hellmann-Feynman expression for the group velocity. Our results shed new light on the observation of stable persistent motion of particles in periodic potentials.

DOI
10.1103/physreva.96.033637

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We study the superfluid behavior motion of interacting particles in a periodic potential subject to an external ac force. We observe a dynamical stabilization of the superfluid motion in the presence of ac forces around the boundary of the Brillouin zone. We analyze relevant nonlinear Floquet-Bloch states within the mean field approximation that display loops in the energy spectrum. In particular, we investigate with some detail the transport properties of these states at the edge of the Brillouin zone, showing the existence of a nonvanishing motion of particles. These findings are corroborated by a nonlinear generalization of the Hellmann-Feynman expression for the group velocity. Our results shed new light on the observation of stable persistent motion of particles in periodic potentials.
Superflow of a Bose–Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results of the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau–Zener tunnelling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making a transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.
The Bloch states of Bose-Einstein condensates (BECs) in pure nonlinear lattices (NLs) are dynamically unstable so that they cannot show superfluidity. We overcome this problem by finding that the two-component BECs in NLs can be stabilized by coherent linear coupling. Furthermore, in the limit of strong coherent coupling, the lowest Bloch band in the whole Brillouin zone can be dynamically stable. We also find a hysteretic behavior with looplike structure in the Bloch band resembling the so-called ``swallowtail'' loop. The dynamical stabilization and the looplike band structure can be realized in experiments by current technology. Our results are obtained from a discrete model, and major results are also confirmed by a continuum model.
We study theoretically the superfluidity and stability of a Bose-Einstein condensate (BEC) whose interatomic scattering length is periodically modulated with optical Feshbach resonance. Our numerical study finds that the properties of this periodic BEC are strongly influenced by the modulation strength. When the modulation strength is small, only the Bloch waves close to the Brillouin zone edge suffer both Landau and dynamical instabilities. When the modulation strength is strong enough, all Bloch waves become dynamically unstable. In other words, the periodic BEC loses its superfluidity completely.
We study multiple-period Bloch states of a Bose-Einstein condensate with spatially periodic interatomic interaction. Solving the Gross-Pitaevskii equation for the continuum model, and also using a simplified discrete version of it, we investigate the energy-band structures and the corresponding stability properties. We observe an ``attraction-induced dynamical stability'' mechanism caused by the localization of the density distribution in the attractive domains of the system and the isolation of these higher-density regions. This makes the superfluid stable near the zone boundary and also enhances the stability of higher-periodic states if the nonlinear interaction strength is sufficiently high.
We investigate the band structure of a Bose-Einstein condensate in a one-dimensional periodic potential by calculating stationary solutions of the Gross-Pitaevskii equation, which have the form of Bloch waves. We demonstrate that loops (``swallow tails'') in the band structure occur both at the Brillouin zone boundary and at the center of the zone, and they are therefore a generic feature. A physical interpretation of the swallow tails in terms of periodic solitons is given. The linear stability of the solutions is investigated as a function of the strength of the mean-field interaction, the magnitude of the periodic potential, and the wave vector of the condensate. The regions of energetic and dynamical stability are identified by considering the behavior of the Gross-Pitaevskii energy functional for small deviations of the condensate wave function from a stationary state. It is also shown how for long-wavelength disturbances the stability criteria may be obtained within a hydrodynamic approach.
We experimentally study the dynamics of weakly interacting Bose-Einstein condensates of cesium atoms in a 1D optical lattice with a periodic driving force. After a sudden start of the driving, we observe the formation of stable wave packets at the center of the first Brillouin zone (BZ) in momentum space, and we interpret these as Floquet solitons in periodically driven systems. The wave packets become unstable when we add a trapping potential along the lattice direction, leading to a redistribution of atoms within the BZ. The concept of a negative effective mass and the resulting changes to the interaction strength and effective trapping potential are used to explain the stability and the time evolution of the wave packets. We expect that similar states of matter waves exist for discrete breathers and other types of lattice solitons in periodically driven systems.