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

Year: 2012

Authors: Chwedenczuk J., Hyllus P., Piazza F., Smerzi A.

Autors Affiliation: Faculty of Physics, University of Warsaw, ul. Hoza 69, 00-681 Warsaw, Poland; Department of Theoretical Physics, University of the Basque Country UPV/EHU, PO Box 644, E-48080 Bilbao, Spain; Physik Department, Technische Universitat Munchen, 85747 Garching, Germany; INO-CNR and LENS, 50125 Firenze, Italy; INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy

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.

Journal/Review: NEW JOURNAL OF PHYSICS

Volume: 14      Pages from: 93001-1  to: 93001-19

More Information: We gratefully acknowledge discussions with Julian Grond and Aurelien Perrin. We thank Baltazar Brukalski for preparing figure 1. JCh acknowledges the Foundation for Polish Science International TEAM Program cofinanced by the EU European Regional Development Fund, and support from the National Science Center. PH acknowledges support from the ERC Starting Grant GEDENTQOPT and CHIST-ERA QUASAR. FP acknowledges support from the Alexander Von Humboldt Foundation. AS acknowledges support from the EU-STREP Project QIBEC.
KeyWords: Quantum; States; Entanglement; Spectroscopy; Limit
DOI: 10.1088/1367-2630/14/9/093001

Citations: 18
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