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arXiv:1807.00015 · Physical Review Research

Floquet-induced superfluidity with periodically modulated interactions of two-species hardcore bosons in a one-dimensional optical lattice

Tao Wang, Shijie Hu, Sebastian Eggert, Michael Fleischhauer, Axel Pelster, Xue‐Feng Zhang

Published Mar 6, 2020• 13 citations
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Abstract

The authors show that a novel paring state between two bosonic species is possible, where the density of one species induces a gauge phase of the other species. To achieve this `gauge dressed superfluid two experimental proposals are suggested, where two hyperfine states of interacting bosons are time-periodically driven in a one-dimensional optical lattice.

DOI
10.1103/physrevresearch.2.013275

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The authors show that a novel paring state between two bosonic species is possible, where the density of one species induces a gauge phase of the other species. To achieve this `gauge dressed superfluid two experimental proposals are suggested, where two hyperfine states of interacting bosons are time-periodically driven in a one-dimensional optical lattice.
Following a proposed scheme for realizing the time-periodically modulated Rabi frequency in experiments, we suggest density-dependent hoppings of two-species hardcore bosons in a one-dimensional optical lattice. Distinct from the previous work [Phys. Rev. Res. 2, 013275 (2020)], we study effects in the first resonance region. In the effective Hamiltonian, the intraspecies hopping occurs only if the density discrepancy of the other species on these sites is zero, while the interspecies one is allowed once the relevant density discrepancy becomes nonzero. At integer-1 filling, the quantum phase diagram of the effective Hamiltonian is determined by the perturbation analysis together with numerical calculations. We find that in the limit of dominant J1{J}_{1}J1​, the system becomes a double-degenerate dimerized state spontaneously breaking the translation symmetry. The interplay of J0,J1{J}_{0}, {J}_{1}J0​,J1​, and the fixed U‾=1\overline{U}=1U=1 leads to three BKT transition lines and a tricritical BKT point. Exact transition lines are obtained by the level spectroscopic technique. Besides, general physical properties, including the charge gap, neutral gap, superfluid density, and dimerization strength, are investigated as well.
We propose a scenario to create a topological superfluid in a periodically driven two-dimensional square optical lattice. We study the phase diagram of a spin-orbit coupled sss-wave pairing superfluid in a periodically driven two-dimensional square optical lattice. We find that a phase transition from a trivial superfluid to a topological superfluid occurs when the potentials of the optical lattices are periodically changed. The topological phase is called the Floquet topological superfluid and can host Majorana fermions.
We suggest to view ultracold atoms in a time-periodically shifted optical lattice as a 'dressed matter wave', analogous to a dressed atom in an electromagnetic field. A possible effect lending support to this concept is a transition of ultracold bosonic atoms from a superfluid to a Mott-insulating state in response to appropriate "dressing" achieved through time-periodic lattice modulation. In order to observe this effect in a laboratory experiment, one has to identify conditions allowing for effectively adiabatic motion of a many-body Floquet state.
Advances in experimental atomic systems have given us access to highly tunable quantum systems, and to an unprecedented range of observables of these systems. One fundamental system that has been made accessible in this way is a gas of bosons trapped in a periodic potential. We present here a several studies of the many-body physics of bosons in optical lattices. We discuss the ferromagnetic effects of a single vacancy in a two-species gas on a lattice. We present a derivation of the superfluid density, the order parameter for the superfluid state, and discuss the mathematical subtleties of calculating it. Finally, we calculate the dynamics of bosonic lattice systems, in the presence of inelastic light scattering used as a density measurement, and during a ramp of the interaction strength from the Mott to the superfluid phase.
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.
It is well known that the supersolid form of matter can arise in a single species of cold bosonic atoms in an optical lattice due to long range interactions. We present a scenario where a supersolid is induced in one of the components of a mixture of two species bosonic atoms where there is no long range interactions. We study a system of normal and hardcore boson mixture with only the former possessing long range interactions. We consider three cases: the first where the total density is commensurate and the other two where they are incommensurate . By suitable choices of the densities and the interaction strengths of the atoms, we predict that the charge density wave and the supersolid orders can be induced in the hardcore species as a result of the competing interatomic interactions.