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arXiv:1801.08959 · Physical Review A

Stabilization of nonlinear lattices: A route to superfluidity and hysteresis

Gentaro Watanabe A, Yongping Zhang

Published Jul 24, 2018• 5 citations
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Abstract

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.

DOI
10.1103/physreva.98.013625

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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.
Bose-Einstein condensates (BECs) in periodic potentials generate interesting physics on the instabilities of Bloch states. The lowest-energy Bloch states of BECs in pure nonlinear lattices are dynamically and Landau unstable, which breaks down BEC superfluidity. In this paper we propose to use an out-of-phase linear lattice to stabilize them. The stabilization mechanism is revealed by the averaged interaction. We further incorporate a constant interaction into BECs with mixed nonlinear and linear lattices and reveal its effect on the instabilities of Bloch states in the lowest band.
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.
We calculate the band structure of ultracold atoms located inside a laser-driven optical cavity. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (noncavity) optical lattices. However, in our case the nonlinearity derives from the cavity back-action rather than from direct interatomic interactions. We find both bi- and tristable regimes associated with the lowest band, and show that the multistability we observe can be analyzed in terms of swallowtail catastrophes. Dynamic and energetic stability of the mean-field solutions is also discussed, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the atomic band structure has important implications for proposals concerning Bloch oscillations of atoms inside optical cavities [Peden et al., Phys. Rev. A 80, 043803 (2009); Prasanna Venkatesh et al., Phys. Rev. A 80, 063834 (2009)].
Recently spin-orbit (SO)-coupled superfluids in free space or harmonic traps have been extensively studied, motivated by the recent experimental realization of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics of SO-coupled BEC in optical lattices has been largely unexplored. In this paper, we show that in a suitable parameter region the lowest Bloch state forms an isolated flat band in a one-dimensional SO-coupled optical lattice, which thus provides an experimentally feasible platform for exploring the recently celebrated topological flatband physics in lattice systems. We show that the flat band is preserved even with the mean-field interaction in BEC. We investigate the superfluidity of the BEC in SO-coupled lattices through dynamical and Landau stability analysis, and show that the BEC is stable on the whole flat band.
All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one dimensional lattice of impurities are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the nonlinear Schr\odinger, or Gross-Pitaevskii, equation for both repulsive and attractive condensates. The appearance of swallowtails in the bands is examined and interpreted in terms of the condensates superfluid properties. The nonlinear stability properties of the Bloch states are described and the stable regions of the bands and swallowtails are mapped out. We find that the Kronig-Penney potential has the same properties as a sinusoidal potential; Bose-Einstein condensates are trapped in sinusoidal optical lattices. The Kronig-Penney potential has the advantage of being analytically tractable, unlike the sinusoidal potential, and, therefore, serves as a good model for experimental phenomena.
Bloch band and stabilities of Bloch waves of superfluid Fermi gases in one-dimensional (1D) periodic optical lattices are discussed. Within the hydrodynamical theory and the two-mode approximation, the Bloch band structure, the energetic and dynamical instabilities of Bloch waves at the first Brilliouin zone are presented. The results show that, when the atom density is beyond a critical value, a loop structure in the Bloch band at the zone edge is developed along the BEC-BCS crossover. The Bloch band structure and the stabilities of Bloch waves are modified dramatically when the system crosses from the BEC side to the BCS side, and they can be adjusted to the required characteristics by changing the atom's interaction (with the Feshbach resonance technique), the atom density, and the lattice parameters. The analytical expressions of the critical atom density for exciting the loop structure and maintaining the stabilities of Bloch waves are obtained.