Spinor BECs are powerful tools for studying fundamental quantum mechanical light-matter interactions and quantum information technologies. Because BECs are easily controllable with external electric, magnetic, and optical fields, they provide a rich playground for creating and studying analogs of phenomena first described in solid state physics, particle physics, and even condensed matter physics. In order to completely characterize the dynamics of such systems, one needs access to the spatial distributions of both the populations and the relative phases of the internal magnetic spin states of the BEC.
Conventional imaging techniques are destructive and only give information about the population distributions. Here, we propose two new methods to access the relative ground state phase of a spin-1 BEC. In the first method, a two-photon Raman process acts as an optical waveplate for atoms, which, when combined with standard Stern-Gerlach absorption imaging techniques, gives access to the analogous Stokes parameters—and hence the relative ground state phases—of the BEC. The relative Rabi frequencies and relative geometric phase of the optical beams determine the retardance and angle of the phase plate. The second method is non-destructive and approaches the problem from the opposite direction. We treat the atoms as a waveplate that alters the polarization of light propagating through it. The optical polarization determines which internal electronic states of the atom are coupled by the light, which results in an accumulated phase that depends on the light frequency. The phase rotates the light polarization, which when measured with standard polarimetry techniques, reveals both the populations and relative phases of the states.
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Imaging Stokes Parameters of Spinor BECs
JT Schultz, A Hansen, N Bigelow
Conference on Coherence and Quantum Optics, M6 (2013)
This work has been supported by The National Science Foundation (NSF), The Army Research Office (ARO) of the United States Army Research Laboratory (ARL), The Defense Advanced Research Projects Agency (DARPA) of The United States Department of Defense (DOD), and the NASA-JPL Physical Science Research Program Cold Atom Laboratory (CAL).