For the one-dimensional Bose-Hubbard theoretical model of condensed matter,the quantum phase transition process of the superfluid-Mott insulation state in the one-dimensional Bose-Hubbard model is realized by continuously changing the depth of the optical lattice well and preparing the temperature of the quantum gas.Through the ultra-cold atomic Time of Flight(TOF) imaging method,the interference pattern of the momentum space of the quantum gas in the diffusion process is analyzed,and the change data of the superfluid component and the Mott insulation state component in the quantum phase transition process are obtained.Experimental results show that the quantum gas in the optical lattice can simulate the one-dimensional Bose-Hubbard theoretical model.
For the one-dimensional Bose-Hubbard theoretical model of condensed matter,the quantum phase transition process of the superfluid-Mott insulation state in the one-dimensional Bose-Hubbard model is realized by continuously changing the depth of the optical lattice well and preparing the temperature of the quantum gas.Through the ultra-cold atomic Time of Flight(TOF) imaging method,the interference pattern of the momentum space of the quantum gas in the diffusion process is analyzed,and the change data of the superfluid component and the Mott insulation state component in the quantum phase transition process are obtained.Experimental results show that the quantum gas in the optical lattice can simulate the one-dimensional Bose-Hubbard theoretical model.
We discuss the superfluid (SF) to Mott-insulator transition of cold atoms in optical lattices recently observed by Greiner et al (2002 Nature 415 39). The fundamental properties of both phases and their experimental signatures are discussed carefully, including the limitations of the standard Gutzwiller approximation. It is shown that in a one-dimensional dilute Bose-gas with a strong transverse confinement (Tonks-gas), even an arbitrary weak optical lattice is able to induce a Mott-like state with crystalline order, provided the dimensionless interaction parameter is larger than a critical value of order one. The SF–insulator transition of the Bose–Hubbard model in this case continuously evolves into a transition of the commensurate–incommensurate type with decreasing strength of the external optical lattice.
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.
Ultracold bosonic gases in optical lattices are strongly correlated quantum systems similar to solids. The strong correlation between the electrons in a solid on the one hand, and the bosonic atoms in optical lattice on the other, exhibit various quantum phenomena like insulation, conductivity, localization of electrons and atoms, respectively. Controlled by the intensity of the lattice laser, the ultracold bosonic gas can be transferred from a regime with superfluid character for shallow lattices into a regime of strong correlations, the Mott insulator. As an additional external parameter besides the lattice depth, one can generate spatial inhomogeneities by superimposing an additional standing wave (so-called two-color superlattices), which gives rise to localization effects or the formation of a Bose-glass phase. In the present work, numerical simulations are employed in order to investigate characteristic signatures of the quantum phases in the low-energy excitation spectrum of one-dimensional systems. We simulate temporal small amplitude modulations of the optical lattice in analogy to experiments, and evaluate the response of the system from the time-evolved initial state. The lattice systems are described in the framework of the Bose-Hubbard model. For the evaluation of the time-evolved state, we employ several numerical methods. We analyze systems of small size (6 particles on 6 sites) using an exact time-evolution by integration of the time-dependent Schrödinger equation. The formulation of an importance truncation scheme enables us to retain only the relevant components of the model space in the strongly correlated regime and, thus, allows for the investigation of systems with 10 particles on 10 sites using exact time-evolution. Based on this method, we present results of the Mott-insulating regime as well as for the Bose-glass phase. Furthermore, we employ particle-hole methods, which allow for the treatment of systems with experimental lattice sizes and particle numbers. Starting from the equation of motion method we adapt the Tamm-Dancoff approximation as well as the random-phase approximation for the occupation number representation of the Bose-Hubbard model. We present results of simulations of up to 50 particles on 50 sites and discuss the impact of the lattice depth on the low-energy excitations (U-resonance). Moreover, the impact of a two-color superlattice and the variation of its amplitude is investigated.
We study the dynamics of phase transitions in the one-dimensional Bose-Hubbard model. To drive the system from a Mott insulator to a superfluid phase, we change the tunneling frequency at a finite rate. We investigate the buildup of correlations during fast and slow transitions using variational wave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, and numerical simulations. We show that time-dependent correlations satisfy characteristic scaling relations that can be measured in optical lattices filled with cold atoms.
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.
We discuss the superfluid to Mott insulator transition of an atomic Bose gas in an optical lattice with high filling factors. We show that in this multiband situation, the long-wavelength physics is described by a single-band Bose-Hubbard model. We determine the many-body renormalization of the tunneling and interaction parameters in the effective Bose-Hubbard Hamiltonian, and consider the resulting model at nonzero temperatures. We show that, in particular, for a one- or two-dimensional optical lattice, the Mott-insulator phase is more difficult to realize than anticipated previously.