Hall response of interacting bosonic atoms in strong gauge fields: from condensed to FQH states

TL;DR

This paper explores how the Hall response of interacting bosonic atoms in strong gauge fields can identify phase transitions from Bose-Einstein condensates to fractional quantum Hall states, using numerical and experimental approaches.

Contribution

It introduces a method to use Hall response measurements to detect phase transitions and characterize ground states in bosonic systems under strong gauge fields.

Findings

Hall response signals phase transitions between different quantum states.

Spectral structure and transition pathways are revealed through response analysis.

Experimental protocol for probing gauge fields and linear response in optical lattices is proposed.

Abstract

Interacting bosonic atoms under strong gauge fields undergo a series of phase transitions that take the cloud from a simple Bose-Einstein condensate all the way to a family of fractional-quantum-Hall-type states [M. Popp, B. Paredes, and J. I. Cirac, Phys. Rev. A 70, 053612 (2004)]. In this work we demonstrate that the Hall response of the atoms can be used to locate the phase transitions and characterize the ground state of the many-body state. Moreover, the same response function reveals within some regions of the parameter space, the structure of the spectrum and the allowed transitions to excited states. We verify numerically these ideas using exact diagonalization for a small number of atoms, and provide an experimental protocol to implement the gauge fields and probe the linear response using a periodically driven optical lattice. Finally, we discuss our theoretical results in relation to recent experiments with condensates in artificial magnetic fields [ L. J. LeBlanc, K. Jimenez-Garcia, R. A. Williams, M. C. Beeler, A. R. Perry, W. D. Phillips, and I. B. Spielman, Proc. Natl. Acad. Sci. USA 109, 10811 (2012)] and we analyze the role played by vortex states in the Hall response.