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.
Highlights
Cold-atom systems offer the possibility of engineering single-particle dispersions that are analogs to those present in condensed matter systems, thereby creating exotic atomic ‘materials’, with interaction-dominated or topologically non-trivial band structures [1, 2]
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
The properties of such materials depend on their underlying band structure, and a multitude of techniques have been developed for measuring the single particle dispersion relation
Summary
Cold-atom systems offer the possibility of engineering single-particle dispersions that are analogs to those present in condensed matter systems, thereby creating exotic atomic ‘materials’, with interaction-dominated or topologically non-trivial band structures [1, 2]. 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. 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.
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