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Laser Physics

Frustration of a Bose gas inside an optical lattice

Marco Polini, Rosario Fazio, M. P. Tosi, Jairo Sinova, Allan H. MacDonald

Published Jan 1, 2004• 4 citations
OpenAlex

Abstract

Under suitable conditions, the Hamiltonian of a gas of cold bosonic atoms inside a rotating optical lattice can be mapped onto that of a frustrated Bose-Hubbard model. Here, the role of magnetic frustration is played by the angular frequency of rotation of the lattice. The system can be fully frustrated at experimentally attainable values of the frequency of rotation, and a superlattice of vortices appears in the ground state. This has several implications on observable quantities such as the superfluid density and the momentum distribution function. In the limit of large on-site occupation and in dimensionality D ≥ 2, the system can be mapped into an array of Josephson junctions in a magnetic field.

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Under suitable conditions, the Hamiltonian of a gas of cold bosonic atoms inside a rotating optical lattice can be mapped onto that of a frustrated Bose-Hubbard model. Here, the role of magnetic frustration is played by the angular frequency of rotation of the lattice. The system can be fully frustrated at experimentally attainable values of the frequency of rotation, and a superlattice of vortices appears in the ground state. This has several implications on observable quantities such as the superfluid density and the momentum distribution function. In the limit of large on-site occupation and in dimensionality D ≥ 2, the system can be mapped into an array of Josephson junctions in a magnetic field.
We consider a rotating Bose-Einstein condensate in a square optical lattice in the regime in which the Hamiltonian of the system can be mapped onto a Josephson junction array. In an approximate scheme where the couplings are assumed uniform, the ground state energy is formulated in terms of the vortex configuration. The results are compared with experimental results and also previously reported results for frustrated XY model. We also show that vortex configuration is robust with respect to change of couplings and therefore the results remain valid when we consider more realistic model with non-uniform couplings.
We study the Bose-condensed ground states of bosons in a two-dimensional optical lattice in the presence of frustration due to an effective vector potential, for example, due to lattice rotation. We use a mapping to a large-SSS frustrated magnet to study quantum fluctuations in the condensed state. Quantum effects are introduced by considering a 1/S1/S1/S expansion around the classical ground state. The large-SSS regime should be relevant to systems with many particles per site. As the system approaches the Mott insulating state, the hole density becomes small. Our large-SSS results show that, even when the system is very dilute, the holes remain a (partially) condensed system. Moreover, the superfluid density is comparable to the condensate density. In other words, the large-SSS regime does not display an instability to noncondensed phases. However, for cases with fewer than 1/3 flux quantum per lattice plaquette, we find that the fractional condensate depletion increases as the system approaches the Mott phase, giving rise to the possibility of a noncondensed state before the Mott phase is reached for systems with smaller SSS.
Following a novel experimental arrangement which can rotate a two-dimensional optical lattice at frequencies up to several kilohertz we discuss the ground state of the two-dimensional Bose-Hubbard Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing U(1) quantum rotor approach and the topologically constrained path integral.Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields.We derive an effective quantum action for the Bose-Hubbard model, which enables a non-perturbative treatment of the zero-temperature phase transition in the rotating frame.We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f = 0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice.Performed calculations revealed strong non-monotonical dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.
We investigate the ground state structure of two-dimensional Josephson junction arrays consisting of Bose-Einstein condensates trapped by both a rotating harmonic potential and a corotating deep optical lattice with square symmetry. Monte Carlo simulations of the uniformly frustrated XY model in a wide range of the frustration parameter f reveal that the stable configuration of vortices for a simple fractional number f is a staircase structure, consisting of diagonal chains of vortices with periodic lattice of unit cells.
Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of up to one atom per lattice site. The entry of vortices into the system is characterized by jumps of $2\ensuremath{\pi}$ in the phase winding of the condensate wave function. A lattice of size $L\ifmmode\times\else\texttimes\fi{}L$ can have at most $L\ensuremath{-}1$ quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasiangular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasiangular momentum of the ground state changes.
Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of a ``synthetic'' orbital magnetic field, we study the ``fully frustrated'' Bose-Hubbard model and quantum XY\mathrm{XY}XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group method, we show that these kinetically frustrated boson models admit three phases at integer filling: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable ``chiral Mott insulator'' (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, study a Jastrow variational wave function which captures its correlations, present results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we consider generalizations to a staggered flux Bose-Hubbard model and a two-dimensional (2D) version of the CMI in weakly coupled ladders.