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arXiv:1111.2175 · Physical Review A

Kelvin-Helmholtz instability in two-component Bose gases on a lattice

Emil Lundh, J.-P. Martikainen

Published Feb 23, 2012• 12 citations
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Abstract

We explore the stability of the interface between two phase-separated Bose gases in relative motion on a lattice. Gross-Pitaevskii-Bogoliubov theory and the Gutzwiller ansatz are employed to study the short- and long-time stability properties. The underlying lattice introduces effects of discreteness, broken spatial symmetry, and strong correlations, all three of which are seen to have considerable qualitative effects on the Kelvin-Helmholtz instability. Discreteness is found to stabilize low flow velocities because of the finite energy associated with displacing the interface. Broken spatial symmetry introduces a dependence not only on the relative flow velocity but also on the absolute velocities. Strong correlations close to a Mott transition will stop the Kelvin-Helmholtz instability from affecting the bulk density and creating turbulence; instead, the instability will excite vortices with Mott-insulator-filled cores.

DOI
10.1103/physreva.85.023628

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We explore the stability of the interface between two phase-separated Bose gases in relative motion on a lattice. Gross-Pitaevskii-Bogoliubov theory and the Gutzwiller ansatz are employed to study the short- and long-time stability properties. The underlying lattice introduces effects of discreteness, broken spatial symmetry, and strong correlations, all three of which are seen to have considerable qualitative effects on the Kelvin-Helmholtz instability. Discreteness is found to stabilize low flow velocities because of the finite energy associated with displacing the interface. Broken spatial symmetry introduces a dependence not only on the relative flow velocity but also on the absolute velocities. Strong correlations close to a Mott transition will stop the Kelvin-Helmholtz instability from affecting the bulk density and creating turbulence; instead, the instability will excite vortices with Mott-insulator-filled cores.
A superfluid flow beyond a critical momentum in an optical lattice decays drastically by the interplay between nonlinearity due to the interparticle interactions in Bose-Einstein condensate and periodicity of the lattice; this instability is called dynamical instability. The complex density modulational profiles after the condensate becomes unstable observed experimentally is not completely understood, while the dynamical instability has been studied theoretically and experimentally. In this paper, we analyze the density modulation of condensates as a precursor of the dynamical instability in the two-dimensional Bose-Hubbard model. Our analysis has clarified the unexplored properties of the density modulations associated with the dynamical instability at low filling and in a wide range of interactions, while the previous works have analyzed the density modulation on the basis of Gross-Pitaevskii equation under the specific condition that one-dimensional optical lattice is very shallow and the filling is very large. The numerical simulations based on the dynamical Gutzwiller approximation elucidate that the principal mode of density modulation highly depends on interaction strength U and the momentum acceleration rate. We briefly discuss these features with the stability phase diagram calculated on the basis of the Bogoliubov theory.
The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.
Dynamical instabilities at the interface between two Bose-Einstein condensates that are moving relative to each other are investigated using mean-field and Bogoliubov analyses. Kelvin-Helmholtz instability is dominant when the interface thickness is much smaller than the wavelength of the unstable interface mode, whereas the counter-superflow instability becomes dominant in the opposite case. These instabilities emerge not only in an immiscible system but also in a miscible system where an interface is produced by external potential. Dynamics caused by these instabilities are numerically demonstrated in rotating trapped condensates.
We study the stability of superflow of Bose gases in optical lattices by analyzing the Bose-Hubbard model within the Gutzwiller mean-field approximation. We calculate the excitation spectra of the homogeneous Bose-Hubbard model at unit filling to determine the critical momenta for the Landau and dynamical instabilities. These two critical momenta are shown to approach each other when the on-site interaction increases towards the Mott transition point. In order to make a direct connection with realistic experiments, we next take into account a parabolic trapping potential and compute the real-time dynamics of dipole oscillations induced by suddenly displacing the trap center. We consider the following two cases: standard soft-core bosons, whose interparticle interactions include the on-site one only; and hard-core bosons with long-range dipole-dipole interactions. For both cases, we show that the dipole oscillation is significantly damped when the maximum local momentum exceeds a certain threshold, which quantitatively agrees with the critical momentum for the dynamical instability in the homogeneous system. In the case of dipolar hard-core bosons, the dynamical instability of dipole oscillations leads to the formation of checkerboard density waves in the superfluid phase near the boundary to the supersolid phase.
We investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean-field theory as well as bosonic dynamical mean-field theory. We find that the interplay of strong interspecies repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.