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Sub-shot-noise interferometry from measurements of the one-body density (Articolo in rivista)

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Sub-shot-noise interferometry from measurements of the one-body density (Articolo in rivista) (literal)

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Chwedenczuk J. [ 1 ] ; Hyllus P. [ 2 ] ; Piazza F. [ 3 ] ; Smerzi A. [ 4,5,6,7 ] (2012)
Sub-shot-noise interferometry from measurements of the one-body density
in New journal of physics
(literal)

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Chwedenczuk J. [ 1 ] ; Hyllus P. [ 2 ] ; Piazza F. [ 3 ] ; Smerzi A. [ 4,5,6,7 ] (literal)

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[ 1 ] Univ Warsaw, Fac Phys, PL-00681 Warsaw, Poland [ 2 ] Univ Basque Country UPV EHU, Dept Theoret Phys, E-48080 Bilbao, Spain [ 3 ] Tech Univ Munich, Dept Phys, D-85747 Garching, Germany [ 4 ] INO CNR, I-50125 Florence, Italy [ 5 ] LENS, I-50125 Florence, Italy [ 6 ] INO CNR BEC Ctr, I-38123 Povo, Italy [ 7 ] Univ Trent, Dipartimento Fis, I-38123 Povo, Italy (literal)

Titolo

Sub-shot-noise interferometry from measurements of the one-body density (literal)

Abstract

We derive the asymptotic maximum-likelihood phase estimation uncertainty for any interferometric protocol where the positions of the probe particles are measured to infer the phase, but where correlations between the particles are not accessible. First, we apply our formula to the estimation of the phase acquired in the Mach-Zehnder interferometer and recover the well-known momentum formula for the phase sensitivity. Then, we apply our results to interferometers with two spatially separated modes, which could be implemented with a Bose-Einstein condensate trapped in a double-well potential. We show that in a simple protocol which estimates the phase from an interference pattern, a sub-shot-noise phase uncertainty of up to Delta theta proportional to N-2/3 can be achieved. One important property of this estimation protocol is that its sensitivity does not depend on the value of the phase theta, contrary to the sensitivity given by the momentum formula for the Mach-Zehnder transformation. Finally, we study the experimental implementation of the above protocol in detail, by numerically simulating the full statistics as well as by considering the main sources of detection noise, and argue that the shot-noise limit could be surpassed with current technology. (literal)

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