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Physica Scripta

Revealing discontinuous and continuous quantum phase transitions in shaken optical lattices

Sheshgiri S. Shettigar, Bhargav K. Alavani, Ramesh V. Pai

Published Aug 27, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ad7424

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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.
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.
Abstract In this work, we explore the influence of shaking parameters on the single-particle excitation spectra of bosonic atoms confined in a one-dimensional shaken optical lattice. Using mean-field theory to solve the two-band Bose–Hubbard model, we obtain a phase diagram that qualitatively aligns with experimental observations. We employ the Random Phase Approximation (RPA) based on mean-field states to examine excitation spectra across different phases during the phase transitions. Notably, the gapless superfluid (SF) and π -SF phases exhibit roton-maxon excitations, whereas the gapped Mott insulator (MI) phase can manifest as a direct or indirect band-gap MI. These calculations provide detailed insights into how excitations evolve across different phases and how spectral weights areredistributed during the transitions.
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.
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.
The extended effective multiorbital Bose–Hubbard-type Hamiltonian which takes into account higher Bloch bands is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation to current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean-field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid–Mott insulator transition and the absorption spectroscopy, that is, the energy absorption rate when the lattice depth is periodically modulated.
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.