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arXiv:1501.04785 · Physical Review A

Quantum phase transition of bosons in a shaken optical lattice

Jiao Miao, Boyang Liu, Wei Zheng

Published Mar 17, 2015• 11 citations
arXivHTMLPDF

Abstract

Recently, the lattice shaking technique has been used to couple different Bloch bands resonantly. For the one-dimensional (1D) case in which shaking is along only one direction, experimental observation of domain-wall formation has been explained by superfluid Ising transition. Inspired by these, we generalize to a two-dimensional case in which shaking is along two orthogonal directions. Analogous to the 1D case, we find three different phases, the normal superfluid (NSF) phase, the ${D}_{4}$ symmetry-breaking superfluid $({D}_{4}\mathrm{SF})$ phase, and the Mott insulator (MI) phase. Furthermore, we demonstrate that an interaction effect induced by inhomogeneous band mixing can modify the critical shaking amplitude. Unlike in the 1D case, shaking types also can modify the critical shaking amplitude. We also construct a low-energy effective field theory to study the quantum criticality of bosons near the tricritical point of NSF, ${D}_{4}\mathrm{SF}$, and MI phases. Moreover, we find a Bose liquid with anisotropically algebraic order and propose to change a Bose-Einstein condensate into a noncondensed Bose liquid by tuning the shaking amplitude approaching the critical value.

DOI
10.1103/physreva.91.033404

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Recently, the lattice shaking technique has been used to couple different Bloch bands resonantly. For the one-dimensional (1D) case in which shaking is along only one direction, experimental observation of domain-wall formation has been explained by superfluid Ising transition. Inspired by these, we generalize to a two-dimensional case in which shaking is along two orthogonal directions. Analogous to the 1D case, we find three different phases, the normal superfluid (NSF) phase, the D4{D}_{4}D4​ symmetry-breaking superfluid (D4SF)({D}_{4}\mathrm{SF})(D4​SF) phase, and the Mott insulator (MI) phase. Furthermore, we demonstrate that an interaction effect induced by inhomogeneous band mixing can modify the critical shaking amplitude. Unlike in the 1D case, shaking types also can modify the critical shaking amplitude. We also construct a low-energy effective field theory to study the quantum criticality of bosons near the tricritical point of NSF, D4SF{D}_{4}\mathrm{SF}D4​SF, and MI phases. Moreover, we find a Bose liquid with anisotropically algebraic order and propose to change a Bose-Einstein condensate into a noncondensed Bose liquid by tuning the shaking amplitude approaching the critical value.
We study the quantum phase transitions and identify a tricritical point between a normal Bose superfluid, a superfluid that breaks additional Z(2) Ising symmetry, and a Mott insulator in a recent shaken optical lattice experiment. We show that near the transition between normal and Z(2) symmetry breaking superfluids, bosons can condense into a momentum state with high or even locally maximum kinetic energies due to the interaction effect. We present a general low-energy effective field theory that treats both the superfluid transition and the Ising transition in a uniform framework. Using the perturbative renormalization group method, we find that the critical behavior of the quantum phase transition belongs to a universality class different from that of a dilute Bose gas.
We study an extended Bose-Hubbard model with next-nearest-neighbor (NNN) hopping in a shaken optical lattice. We show how mean-field phase diagram evolves with the change of NNN hopping amplitude t2{t}_{2}t2​, which can be easily tuned via shaking amplitude. As t2{t}_{2}t2​ increases, a Z2{Z}_{2}Z2​-symmetry-breaking superfluid (Z2SF)({Z}_{2}\mathrm{SF})(Z2​SF) phase emerges at the bottom of the Mott lobs. The tricritical points between normal superfluid, Z2SF{Z}_{2}\mathrm{SF}Z2​SF, and Mott insulator (MI) phases are identified. We further demonstrate the tricritical point can be tuned to the tip of the Mott lobe, in which case a new critical behavior has been predicted. Within random-phase approximation, excitation spectra in the three phases are obtained, which indicate how the phase transitions occur.
Abstract We perform the cluster mean-field with density matrix renormalization (CMFT+DMRG) calculation on the two-band extended Bose–Hubbard model to uncover the physics behind the discontinuous transitions observed in the one-dimensional shaken optical lattice with hybridized two lowest Bloch bands. We determine the superfluid, Mott insulator, and staggered superfluid phases associated with this model using the appropriate order parameters. We obtained the phase diagrams for two values of shaking amplitudes and illustrated the phases and nature of phase transitions. The transition from Mott insulator and superfluid to staggered superfluid is discontinuous for small shaking amplitudes. We analyse how the shaking frequency controls the effective chemical potential in the model and, consequently, the ground state energy that drives the discontinuous transition. Finally, we compare our results with those of earlier works.
The Mott insulator and superfluid phase transition is one of the most prominent phenomena in ultracold atoms. We report the observation of a novel 2D quantum phase transition between the Mott insulator and π superfluid in a shaking optical lattice. In the deep optical lattice regime, the lowest S band can be tuned to Mott phase, while the higher px,y bands are itinerant for having larger bandwidth. Through a shaking technique coupling the s-orbital to px,y -orbital states, we experimentally observe the transition between the states of the S and px,y bands, leading to a quantum phase transition from two-dimensional s-orbital Mott phase to the px,y -orbital superfluid which condensed at (π, π) momentum. Using the band-mapping method, we also observe the changes of atomic population in different energy bands during the transition, and the experimental results are well consistent with theoretical expectations.
We consider ultracold bosons in a two-dimensional square optical lattice described by the Bose-Hubbard model. In addition, an external time-dependent sinusoidal force is applied to the system, which shakes the lattice along one of the diagonals. The effect of the shaking is to renormalize the nearest-neighbor-hopping coefficients, which can be arbitrarily reduced, can vanish, or can even change sign, depending on the shaking parameter. Therefore, it is necessary to account for higher-order-hopping terms, which are renormalized differently by the shaking, and to introduce anisotropy into the problem. We show that the competition between these different hopping terms leads to finite-momentum condensates with a momentum that may be tuned via the strength of the shaking. We calculate the boundaries between the Mott insulator and the different superfluid phases and present the time-of-flight images expected to be observed experimentally. Our results open up possibilities for the realization of bosonic analogs of the Fulde, Ferrel, Larkin, and Ovchinnikov phase describing inhomogeneous superconductivity.
Observation of 2D Mott insulator and πππ-superfluid quantum phase transition in shaking optical lattice
The Mott insulator and superfluid phase transition is one of the most prominent phenomena in ultracold atoms. In this work, we report the observation of a novel 2D quantum phase transition between Mott insulator and πππ superfluid in a shaking optical lattice. In the deep optical lattice regime, the lowest sss-band can be tuned to Mott phase, while the higher px,yp_{x,y}px,y​ bands are itinerant for having larger bandwidth. Through a shaking technique coupling the sss orbital to px,yp_{x,y}px,y​ orbital states, we experimentally observe the transition between the states of the sss and px,yp_{x,y}px,y​ bands, leading to a quantum phase transition from 2D sss-orbital Mott phase to the px,yp_{x,y}px,y​-orbital superfluid which condensed at (π,π)(π,π)(π,π) momentum.