Fourier transform spectroscopy of a spin-orbit coupled Bose gas
Ian B. Spielman, Erin Marshall, Dimitry Trypogeorgos, Ana Vald�Curiel
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 systems Hamiltonian 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 transform of the measured evolution. In addition, by periodically modulating the Hamiltonian we tune the spin- orbit coupling strength, and use our spectroscopy technique to confirm the predicted spectrum. The frequency resolution of our method is only limited 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.