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Strongly Interacting Two-component Coupled Bose Gas in a 1D Optical Lattice

Sagarika Basak, Han Pu

Published Jun 1, 2021• 0 citations
OpenAlex

Abstract

Two-component coupled Bose gas in a 1D optical lattice is examined. In addition to the postulated Mott insulator and Superfluid phases, multiple bosonic components manifest spin degrees of freedom. Coupling of the components in the Bose gas within same site and neighboring sites leads to substantial change in the previously observed spin phases revealing fascinating remarkable spin correlations. In the presence of strong interactions it gives rise to unconventional effective ordering of the spins leading to unprecedented spin phases: site-dependent $z\textsf{-}x$ spin configuration with tunable (by hopping parameter) proclivity of spin alignment along $z$. Exact analysis and Variational Monte Carlo (VMC) along with stochastic minimization on Entangled Plaquette State (EPS) bestow a unique and enhanced perspective into the system beyond the scope of mean-field treatment. The physics of complex intra-component tunneling and inter-component coupling and filling factor greater than unity are discussed.

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•Jan 1, 2010•0 citations
Two-component coupled Bose gas in a 1D optical lattice is examined. In addition to the postulated Mott insulator and Superfluid phases, multiple bosonic components manifest spin degrees of freedom. Coupling of the components in the Bose gas within same site and neighboring sites leads to substantial change in the previously observed spin phases revealing fascinating remarkable spin correlations. In the presence of strong interactions it gives rise to unconventional effective ordering of the spins leading to unprecedented spin phases: site-dependent z-xz\textsf{-}xz-x spin configuration with tunable (by hopping parameter) proclivity of spin alignment along zzz. Exact analysis and Variational Monte Carlo (VMC) along with stochastic minimization on Entangled Plaquette State (EPS) bestow a unique and enhanced perspective into the system beyond the scope of mean-field treatment. The physics of complex intra-component tunneling and inter-component coupling and filling factor greater than unity are discussed.
Two-component coupled Bose gas in a 1D optical lattice is examined. In addition to the postulated Mott insulator and superfluid phases, multiple bosonic components manifest spin degrees of freedom. Coupling of the components in the Bose gas leads to substantial changes in the previously observed spin phases, giving rise to a new effective spin Hamiltonian and unraveling remarkable spin correlations. The system in the absence of coupling exhibits ferromagnetic and nonferromagnetic spin phases for on-site intracomponent interaction stronger than intercomponent interaction. Upon introduction of coupling, the phase transition switches from first to second order. For comparable on-site inter- and intracomponent interactions, with coupling, instead of one, two spin phases emerge with a second-order phase transition. Exact diagonalization and variational Monte Carlo with stochastic minimization on the entangled-plaquette state bestow a unique and enhanced perspective on the system beyond the scope of a mean-field treatment.
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.
The Bose-Hubbard model of a twofold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose gas.
Advances in pure optical trapping techniques now allow the creation of degenerate Bose gases with internal degrees of freedom. Systems such as 87Rb,39K^{87}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}^{39}\mathrm{K}87Rb,39K, or 23Na^{23}\mathrm{Na}23Na in the F=1F=1F=1 hyperfine state offer an ideal platform for studying the interplay of superfluidity and quantum magnetism. Motivated by the experimental developments, we study ground-state phases of a two-component Bose gas loaded on an optical lattice. The system is described effectively by the Bose-Hubbard Hamiltonian with on-site and near-neighbor spin-spin interactions. An important feature of our investigation is the inclusion of interconversion (spin-flip) terms between the two species, which has been observed in optical lattice experiments. Using mean-field theory and quantum Monte Carlo simulations, we map out the phase diagram of the system. A rich variety of phases is identified, including antiferromagnetic (AF) Mott insulators and ferromagnetic and AF superfluids.
Interactions between quantum particles can give rise to behaviors greater than the sum of their parts. The low-dimensional cold atomic framework provides a unique platform with exquisite control and enhanced correlations to develop a deeper understanding of such quantum phenomena, with promise for emerging technologies. In this thesis, I study novel quantum many-body physics in spinor gases trapped in optical lattices and develop efficient theoretical tools for such investigations. My work illustrates the central role of spin and charge degrees of freedom for comprehending and manipulating intricate quantum behaviors. With a broad goal of understanding the emergent physics in strongly correlated many-body systems, in Chapter 2, I investigate the two-component coupled Bose gas. An unprecedented phase emerges from the coupling of two components in the nearest-neighbor sites via a resonant two-photon Raman transition. Furthermore, coupling provides a novel tuning knob for the controlled manipulation of spin phases. Probing for behaviors away from the Mott state, the limitations of existing theoretical approaches are exposed. To address this, in Chapter 3, I develop a powerful theoretical framework for the unrestricted study of strongly correlated systems, valid even for large spin systems. This generalized effective spin-chain (GESC) formalism has numerous advantages: elegant mathematical form, computationally efficient parameterization, generalized for arbitrary spin and statistics, and universality: not limited to lattice systems. Importantly, leveraging a spin–charge separated form, it provides a unique vantage into system behaviors originating from quantum fluctuations. Motivated by the immense potential of anyons in cold atomic setups, in Chapter 4, I investigate the combined effect of fractional statistics and the presence of multiple components on their ground state and dynamical properties. This reveals the potential of statistical-phase-induced transition between different system phenomena. The GESC formalism is extended to consider anyons and used to obtain insights into the origin of exchange-phase-dependent and independent behavior. I demonstrate the versatility of the GESC formalism, in Chapter 5, to Bose–Fermi mixtures, beyond one-dimensional systems, and to consider long-range interactions. In doing so, avenues are provided for leveraging the immense utility of this formalism in exploring the novel physics such systems have to offer.
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.