Optical Bragg, atom Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices

TL;DR

This paper develops a unified theory for detecting various quantum phases and excitation spectra of ultracold atoms in optical lattices using optical Bragg, atomic Bragg, and cavity QED methods, emphasizing sensitivity to density and valence bond orders.

Contribution

It introduces a systematic approach to detect complex quantum phases, including VBS and CDW-VBS, via three experimental methods, considering realistic conditions like temperature and trapping.

Findings

Detection methods couple to density and valence bond order parameters.

Valence bond order coupling is highly sensitive to superfluid and VBS phases.

Analysis includes effects of finite temperature and harmonic traps.

Abstract

Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases and quantum phase transitions between these phases. However, so far, how to detect these quantum phases and phase transitions effectively remains an outstanding challenge. In this paper, we will develop a systematic and unified theory of using the optical Bragg scattering, atomic Bragg scattering or cavity QED to detect the ground state and the excitation spectrum of many quantum phases of interacting bosons loaded in bipartite and frustrated optical lattices. We show that the two photon Raman transition processes in the three detection methods not only couple to the density order parameter, but also the {\sl valence bond order} parameter due to the hopping of the bosons on the lattice. This valence bond order coupling is very sensitive to any superfluid order or any Valence bond (VB) order in the quantum phases to be probed. These quantum phases include not only the well known superfluid and Mott insulating phases, but also other important phases such as various kinds of charge density waves (CDW), valence bond solids (VBS), CDW-VBS phases with both CDW and VBS orders unique to frustrated lattices, and also various kinds of supersolids. The physical measurable quantities of the three experiments are the light scattering cross sections, the atom scattered clouds and the cavity leaking photons respectively. We analyze respectively the experimental conditions of the three detection methods to probe these various quantum phases and their corresponding excitation spectra. We also address the effects of a finite temperature and a harmonic trap.