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Chinese Physics Letters

Observation of Two-Dimensional Mott Insulator and π-Superfluid Quantum Phase Transition in Shaking Optical Lattice

Jingxin Sun, Pengju Zhao, Zhongshu Hu, Shengjie Jin, Ren Liao, Xiong-Jun Liu, Xuzong Chen

Published Aug 1, 2023• 3 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/40/8/083701

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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.
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.
Quantum phase transition of ultracold atomic gas is one of the core contents in the study of quantum correlational many-body systems. In this paper, two-dimensional (2D) optical lattices are generated by a single fold retroreflected laser beam, and this scheme is used to experimentally design and implement the 2D optical lattice of double wells suitable for isolating and manipulating an array of individual pairs of atoms and predict a topological semimetal in the high orbital bands in this 2D lattice. Two types of optical lattice structures are produced by controlling the laser polarization. One type is the usual 2D optical lattice, which is formed by two independent one-dimensional(1D) optical lattices in two directions and named in-plane lattice, and the other type is the lattice that is formed by the interference between two one-dimensional optical lattices in two directions and called out-plane lattice. When 87Rb BEC (Bose-Einstein condensation) is loaded into the 2D optical lattice, the quantum phase transition between superfluid state and Mott insulator state is observed by controlling the tunneling and in-site interaction. And the phase transition from superfluid state to Mott insulator is judged by observing whether there are interferential lattice points in momentum space. The lattice depths of two cases can be calibrated by Kapitza-Dirac scattering in the ultracold atomic experiment through the time-of-flight absorption imaging. In the in-plane optical lattice, some incorrect points appear in the 45° direction, because the linear polarization degree of beam is impure after being reflected by mirrors and two direction of beam are not completely orthogonal to each other. It is obvious that the two cases have different phase transition points, which is due mainly to the difference in structure. For the in-plane lattice, there are two independent 1D optical lattices, and for the out-plane lattice, the two direction beams mutually interfere with each other, therefore, two optical lattices are not independent of each other. The atoms come back to BEC by reducing the potentials of optical lattice to zero; the temperature of system is slightly higher, because of the jitter of the light lattice. The different behaviors of quantum phase transition are analyzed for two types of optical lattices. This work will provide a platform for the future study of large spin system and strong correlation physics in optical lattices.
Motivated by the recent realization of the strongly correlated driven many-body system showing tunable continuous to the discontinuous quantum phase transition betweenMott insulator (MI) and superfluid with staggered phase (π-SF), we study the two-band extended Bose Hubbard model using the density matrix renormalization group with mean-field (CMFT+DMRG) method in one spatial dimension. In this model, the inter-band coupling and effective detuning energy are related to the resonant shaking frequency and amplitude. We calculate the superfluid order parameters and density of bosons in lower and upper bands to identify the underlining MI and π-SF phases. The bosons transfer from the lower band (ground state) to the upper band (first excited state) when the resonant shaking frequency is increased. For small shaking amplitude, the transfer of bosons is sudden giving rise to discontinuous MI to π-SF transition. For the case of large shaking amplitudes. the boson transferscontinuouslyreflect a continuous MI to π-SF transition. We compare our results with the earlier work.
We study the quantum phase transition between superfluid and Mott-insulator states for ultracold bosons with two internal states forming two bands of an optical lattice. The two atomic states are resonantly coupled by a coherent field enclosed in a single cavity mode, which mediates transitions between the two bosonic particle modes via absorption or emission of cavity photons. As nonlocal atomic coherence can build up via photon assisted tunneling, this coupling shifts the transition to the Mott-insulator phase toward deeper lattice potentials and stronger on-site interaction. Varying the intra and interband on-site interactions leads to several different atomic phase configurations. There are even parameter regions, where a mean-field approach predicts concurrence of a Mott-insulator state in one band and a superfluid in the other band.
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.