Stability of current-carrying states in hard-core bosons with long-range hopping on a square lattice

Abstract

We investigate the stability of current-carrying states with quasi-momentum $K$ in the Bose-condensed phase of the hard-core Bose-Hubbard model on a square lattice, where particles transfer between two sites separated by distance $r$ with hopping amplitude decaying algebraically with $r$ as $\propto r^{-\alpha }$. Using a mean-field theory, we analyze the excitation spectrum and determine the critical quasi-momenta associated with Landau and dynamical instabilities. We find that the long-range hopping suppresses the critical quasi-momenta and makes them vanish at $\alpha =3$. Near $\alpha =3$, we show that the critical quasi-momentum $K_{\mathrm{c}}$ for the dynamical instability exhibits the scaling behavior $K_{\mathrm{c}}\propto {\Delta }^{1+\Delta }$ with $\Delta =\alpha -3$, where the scaling exponent explicitly depends on $\Delta$, as a consequence of the long-range nature of the hopping.

arXiv commentRevised to match the published version. 10 pages, 7 figures

References in corpus (49)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Cold bosonic atoms in optical lattices
• Vortex formation in a stirred Bose-Einstein condensate
• Observation of entanglement propagation in a quantum many-body system
• Josephson Junction Arrays with Bose-Einstein Condensates
• Non-local propagation of correlations in long-range interacting quantum systems
• Experimental realization of a symmetry protected topological phase of interacting bosons with Rydberg atoms
• Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link
• Evidence for a critical velocity in a Bose-Einstein condensed gas
• Quantum phases in an optical lattice
• Landau and Dynamical Instabilities of the Superflow of Bose-Einstein Condensates in Optical Lattices
• Driving phase slips in a superfluid atom circuit with a rotating weak link
• Superfluid and Dissipative Dynamics of a Bose-Einstein Condensate in a Periodic Optical Potential
• A quantum information processor with trapped ions
• Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates
• Observation of dynamical instability for a Bose-Einstein condensate in a moving 1D optical lattice
• Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Strongly inhibited transport of a 1D Bose gas in a lattice
• Superfluid behaviour of a two-dimensional Bose gas
• Continuous Symmetry Breaking in a Two-dimensional Rydberg Array
• Absence of spontaneous magnetic order at non-zero temperature in one- and two-dimensional Heisenberg and XY systems with long-range interactions
• Phase diagram for a Bose-Einstein condensate moving in an optical lattice
• Scalable spin squeezing in a dipolar Rydberg atom array
• Glassy behavior in a binary atomic mixture
• Anomalous Behavior of Spin Systems with Dipolar Interactions
• Bose-Einstein condensates in 1D optical lattices: compressibility, Bloch bands and elementary excitations
• Unstable regimes for a Bose-Einstein condensate in an optical lattice
• Local optical control of the resonant dipole-dipole interaction between Rydberg atoms
• Decay of a superfluid currents in a moving system of strongly interacting bosons
• Analytical and numerical study of hardcore bosons in two dimensions
• Superfluid-insulator transition in a moving system of interacting bosons
• Phase-slip induced dissipation in an atomic Bose-Hubbard system
• Superfluid fraction in an interacting spatially modulated Bose-Einstein condensate
• Engineering Large Stark Shifts for Control of Individual Clock State Qubits
• Two-Dimensional Dynamics of Ultracold Atoms in Optical Lattices
• Enhancing a Many-body Dipolar Rydberg Tweezer Array with Arbitrary Local Controls
• Landau damping: instability mechanism of superfluid Bose gases moving in optical lattices
• $BKT$ transitions in classical and quantum long-range systems
• Generalized Higgs mechanism in long-range interacting quantum systems
• Critical velocity of flowing supersolids of dipolar Bose gases in optical lattices
• Spectroscopy of elementary excitations from quench dynamics in a dipolar XY Rydberg simulator
• Dynamical properties of quantum many-body systems with long range interactions
• Velocity-dependent quantum phase slips in 1D atomic superfluids
• Instability of a superfluid Bose gas induced by a locked thermal gas in an optical lattice
• Detecting the superfluid critical momentum of Bose gases in optical lattices through dipole oscillations
• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices
• Scale-invariant phase transition of disordered bosons in one dimension
• Surface criticality in the mixed-field Ising model with sign-inverted next-nearest-neighbor interaction