Fourier transform spectroscopy of a spin-orbit coupled Bose gas

TL;DR

This paper introduces a Fourier transform spectroscopy method to directly measure band structures in quantum gases, demonstrated on a spin-orbit coupled Bose-Einstein condensate, enabling detailed spectral analysis of quantum states.

Contribution

The authors develop a novel spectroscopy technique that reconstructs band structures from population dynamics, applicable to various quantum systems including optical lattices.

Findings

Successfully measured the dispersion relation of a spin-orbit coupled Bose gas.

Demonstrated tunability of the spin-orbit coupling strength via periodic modulation.

Method's frequency resolution limited only by coherent evolution timescale.

Abstract

We describe a Fourier transform spectroscopy technique for directly measuring band structures, and apply it to a spin-1 spin-orbit coupled Bose-Einstein condensate. In our technique, we suddenly change the Hamiltonian of the system by adding a spin-orbit coupling interaction and measure populations in different spin states during the subsequent unitary evolution. We then reconstruct the spin and momentum resolved spectrum from the peak frequencies of the Fourier transformed populations. In addition, by periodically modulating the Hamiltonian, we tune the spin-orbit coupling strength and use our spectroscopy technique to probe the resulting dispersion relation. The frequency resolution of our method is limited only by the coherent evolution timescale of the Hamiltonian and can otherwise be applied to any system, for example, to measure the band structure of atoms in optical lattice potentials.