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Single shot measurement theory of phase contrast imaging of Bose-Einstein condensates

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Abstract

Phase Contrast Imaging (PCI) is a non-destructive method of probing the state of Bose-Einstein Condensates (BECs). In a PCI measurement, an off-resonant laser beam is illuminated on a BEC and a homodyne measurement is performed on the light which passes through the BEC. The interaction between laser beam and the atomic BEC encodes information about the atomic BEC on the phase-shift accumulated by laser beam. Past theories of PCI measurement have focused on continuous measurement, and treat the problem by deriving a master equation which causes an effective measurement induced decoherence. This allows for calculation of the backaction on the BEC, but not the information that is gained by the measurement. We introduce a simple theory to capture the physics of PCI measurement, which allows quantifying the information-disturbance trade-off, and works in the single shot regime. We show a universal scaling law for the information-disturbance trade-off that is valid for a wide range of particle numbers in the BEC.

© 2014 Optical Society of America

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