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arXiv:1407.7421 · Physical Review A

Orbital-driven melting of a bosonic Mott insulator in a shaken optical lattice

Christoph Sträter, André Eckardt

Published May 4, 2015• 15 citations
arXivHTMLPDF

Abstract

In order to study the interesting interplay between localized and dispersive orbital states in a system of strongly interacting ultracold atoms in an optical lattice, we investigate the possibility to coherently couple the lowest two Bloch bands by means of resonant periodic forcing. For bosons in one dimension we show that a strongly interacting Floquet system can be realized, where at every lattice site two (and only two) near-degenerate orbital states are relevant, whose tunneling matrix elements differ in sign and magnitude. By smoothly tuning both states into resonance, the system is predicted to undergo an orbital-driven Mott-insulator-to-superfluid transition. As a consequence of kinetic frustration, this transition can be either continuous or first order, depending on parameters such as lattice depth and filling.

DOI
10.1103/physreva.91.053602

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In order to study the interesting interplay between localized and dispersive orbital states in a system of strongly interacting ultracold atoms in an optical lattice, we investigate the possibility to coherently couple the lowest two Bloch bands by means of resonant periodic forcing. For bosons in one dimension we show that a strongly interacting Floquet system can be realized, where at every lattice site two (and only two) near-degenerate orbital states are relevant, whose tunneling matrix elements differ in sign and magnitude. By smoothly tuning both states into resonance, the system is predicted to undergo an orbital-driven Mott-insulator-to-superfluid transition. As a consequence of kinetic frustration, this transition can be either continuous or first order, depending on parameters such as lattice depth and filling.
The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.
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.
We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength ppp and a period l=qal=qal=qa, where qqq is an integer and aaa is the lattice spacing. We show that the Schr\"odinger equation for the noninteracting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields qqq energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying ppp for a given qqq. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the ppp and qqq dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several reentrant field-induced SI transitions for any fixed period qqq. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity qqq (q/2)(q/2)(q/2) in real space for odd (even) qqq and suggest experiments to test our theory.
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.
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 investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean-field theory as well as bosonic dynamical mean-field theory. We find that the interplay of strong interspecies repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.