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arXiv:2408.06777 · Physical Review A

Density-dependent gauge field with Raman lattices

Xiang-Can Cheng, Zong-Yao Wang, Jinyi Zhang, Shuai Chen, Xiaotian Nie

Published Jan 31, 2025• 3 citations
arXivHTMLPDF

Abstract

The study of the gauge field is an everlasting topic in modern physics. Spin-orbit coupling is a powerful tool in ultracold atomic systems, resulting in an artificial gauge field that can be easily manipulated and observed in a tabletop environment. Combining optical Raman lattices and atom-atom interactions, the artificial gauge field can be made density dependent. In this work we propose a straightforward way to engineer a one-dimensional density-dependent gauge field in a Bose-Hubbard model in spin-orbit-coupled Raman lattices. We study the model from two perspectives: few-body quantum-walk dynamics and the many-body ground state. From the first perspective, we show that large spin-flipped tunneling can lead to a deep two-body bound state. From the second perspective, mean-field and density-matrix renormalization-group calculations consistently reveal three different phases, i.e., the Mott insulator phase, the superfluid phase, and the magnetic superfluid phase. Finally, we discuss the experimental protocol with Raman lattices based on existing experimental platforms.

DOI
10.1103/physreva.111.013319

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The study of the gauge field is an everlasting topic in modern physics. Spin-orbit coupling is a powerful tool in ultracold atomic systems, resulting in an artificial gauge field that can be easily manipulated and observed in a tabletop environment. Combining optical Raman lattices and atom-atom interactions, the artificial gauge field can be made density dependent. In this work we propose a straightforward way to engineer a one-dimensional density-dependent gauge field in a Bose-Hubbard model in spin-orbit-coupled Raman lattices. We study the model from two perspectives: few-body quantum-walk dynamics and the many-body ground state. From the first perspective, we show that large spin-flipped tunneling can lead to a deep two-body bound state. From the second perspective, mean-field and density-matrix renormalization-group calculations consistently reveal three different phases, i.e., the Mott insulator phase, the superfluid phase, and the magnetic superfluid phase. Finally, we discuss the experimental protocol with Raman lattices based on existing experimental platforms.
We propose an experimentally feasible method to generate a one-dimensional optical lattice potential in an ultracold Bose gas system that depends on the transverse momentum of the atoms. The optical lattice is induced by the artificial gauge potential generated by a periodically driven multilaser Raman process. We study the many-body Bose-Hubbard model in an effective 1D case and show that the superfluid--Mott-insulator transition can be controlled via tuning the transverse momentum of the atomic gas. Such a feature enables us to control the phase of the quantum gas in the longitudinal direction by changing its transverse motional state. We examine our prediction via a strong-coupling expansion to an effective 1D Bose-Hubbard model and a quantum Monte Carlo calculation and discuss possible applications.
We propose an experimentally feasible method to generate a one-dimensional optical lattice potential in an ultracold Bose gas system that depends on the transverse momentum of the atoms. The optical lattice is induced by the artificial gauge potential generated by a periodically driven multi-laser Raman process, which depends on the transverse momentum of the atoms. We study the many-body Bose-Hubbard model in an effective 1D case and show that the superfluid--Mott-insulator transition can be controlled via tuning the transverse momentum of the atomic gas. We examined our prediction via a strong-coupling expansion to an effective 1D Bose-Hubbard model and a quantum Monte Carlo calculation, and discuss possible applications of our system.
Ultracold atoms have emerged as an indispensable setting to study quantum many-body systems. Recent experimental and theoretical work has explored the curious phases and novel properties of Bose-Einstein Condensate with optical lattices, and Bose-Einstein Condensate with light-induced artificial spin-orbit coupling. In this thesis, we report our research on these two types of boson systems. In the first topic, in contrast with calculations of bosons in optical lattices that focus on the tight-binding regime, we note that the single-particle states of bosons in a periodic potential generally satisfy the Mathieu equation, and have developed a formalism for studying bosons in an optical lattice using the Mathieu equation. Moreover, based on this formalism, we have proposed a self-consistent scheme for describing interacting bosons in an optical lattice using Hartree Fock approximation. We apply this scheme to quantify the effects of inter-atomic interactions on the properties of bosons in an optical lattice, as exhibited in the comparison between observables of non-interacting and interacting systems, such as the superfluid transition temperature and momentum distribution as probed in time-of-flight expansion. In the second topic, the phases of a Bose-Einstein condensate with light-induced spin-orbit coupling are studied within the mean-field approximation. We obtain the phase diagram at fixed chemical potential and at fixed density for bosons with spin-orbit coupling, finding a regime of phase separation and a regime in which the bosons condensed into a mixed phase. We determine how this phase diagram evolves as a function of the atom interaction parameters and as a function of the strength of light-atom coupling. The mixed phase is found to be stable for sufficiently small light-atom coupling. Specifically, we show that the structure of the phase diagram at fixed chemical potential suggests an unusual density dependence for the mixed phase in a harmonic trapping potential, in which the density of one spin increases with increasing radius, suggesting a unique experimental signature of this state. The collective Bogoliubov sound mode is shown to also provide a signature of the mixed phase, vanishing as the boundary to the regime of phase separation is approached. Together, in these two topics we address the need to enhance the understanding of the unconventional physical properties of Bose-Einstein Condensate in a controlled electromagnetic environment (optical lattices, Raman lasers, etc.), and provide predictions for possible experimental findings.
We consider theoretically ultracold interacting bosonic atoms confined to quasi-one-dimensional ladder structures formed by optical lattices and coupled to the field of an optical cavity. The atoms can collect a spatial phase imprint during a cavity-assisted tunneling along a rung via Raman transitions employing a cavity mode and a transverse running wave pump beam. By adiabatic elimination of the cavity field we obtain an effective Hamiltonian for the bosonic atoms, with a self-consistency condition. Using the numerical density-matrix renormalization-group method, we obtain a rich steady-state diagram of self-organized steady states. Transitions between superfluid to Mott-insulating states occur, on top of which we can have Meissner, vortex liquid, and vortex lattice phases. Also a state that explicitly breaks the symmetry between the two legs of the ladder, namely, the biased-ladder phase, is dynamically stabilized. We investigate the influence that a trapping potential has on the stability of the self-organized phases.
Cold atoms with laser-induced spin-orbit (SO) interactions provide promising platforms to explore novel quantum physics, in particular the exotic topological phases, beyond natural conditions of solids. The past several years have witnessed important progresses in both theory and experiment in the study of SO coupling and novel quantum states for ultracold atoms. Here we review the physics of the SO coupled quantum gases, focusing on the latest theoretical and experimental progresses of realizing SO couplings beyond one-dimension (1D), and the further investigation of novel topological quantum phases in such systems, including the topological insulating phases and topological superfluids. A pedagogical introduction to the SO coupling for ultracold atoms and topological quantum phases is presented. We show that the so-called optical Raman lattice schemes, which combine the creation of the conventional optical lattice and Raman lattice with topological stability, can provide minimal methods with high experimental feasibility to realize 1D to 3D SO couplings. The optical Raman lattices exhibit novel intrinsic symmetries, which enable the natural realization of topological phases belonging to different symmetry classes, with the topology being detectable through minimal measurement strategies. We introduce how the non-Abelian Majorana modes emerge in the SO coupled superfluid phases which can be topologically nontrivial or trivial, for which a few fundamental theorems are presented and discussed. The experimental schemes for achieving non-Abelian superfluid phases are given. Finally, we point out the future important issues in this rapidly growing research field.
We study the many-body phases of bosonic atoms with NNN internal states confined to a one-dimensional (1D) optical lattice under the influence of a synthetic magnetic field and strong repulsive interactions. The NNN internal states of the atoms are coupled via Raman transitions creating the synthetic magnetic field in the space of internal spin states corresponding to recent experimental realizations. We focus on the case of strong SU(N)\text{SU}(N)SU(N) invariant local density-density interactions in which each site of the 1D lattice is at most singly occupied, and strong Raman coupling, in distinction to previous work which has focused on the weak Raman coupling case. This allows us to keep only a single state per site and derive a low-energy effective spin-1/21/21/2 model. The effective model contains first-order nearest-neighbor tunneling terms, second-order nearest-neighbor interactions, and correlated next-nearest-neighbor tunneling terms. By adjusting the flux $\ensuremath{\phi}$, one can tune the relative importance of first-order and second-order terms in the effective Hamiltonian. In particular, first-order terms can be set to zero, realizing a model with dominant second-order terms. We show that the resulting competition between density-dependent tunneling and repulsive density-density interaction leads to an interesting phase diagram including a phase with long-range pair-superfluid correlations. The method can be straightforwardly extended to higher dimensions and lattices of arbitrary geometry, including geometrically frustrated lattices where the interplay of frustration, interactions, and kinetic terms is expected to lead to even richer physics.