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Title: Sub-shot-noise phase sensitivity with a Bose-Einstein condensate Mach-Zehnder interferometer

Abstract

Bose-Einstein condensates (BEC), with their coherence properties, have attracted wide interest for their possible application to ultraprecise interferometry and ultraweak force sensors. Since condensates, unlike photons, are interacting, they may permit the realization of specific quantum states needed as input of an interferometer to approach the Heisenberg limit, the supposed lower bound to precision phase measurements. To this end, we study the sensitivity to external weak perturbations of a representative matter-wave Mach-Zehnder interferometer whose input are two Bose-Einstein condensates created by splitting a single condensate in two parts. The interferometric phase sensitivity depends on the specific quantum state created with the two condensates, and, therefore, on the time scale of the splitting process. We identify three different regimes, characterized by a phase sensitivity {delta}{theta} scaling with the total number of condensate particles N as (i) the standard quantum limit {delta}{theta}{approx}1/N{sup 1/2} (ii) the sub shot-noise {delta}{theta}{approx}1/N{sup 3/4}, and the (iii) the Heisenberg limit {delta}{theta}{approx}1/N. However, in a realistic dynamical BEC splitting, the 1/N limit requires a long adiabaticity time scale, which is hardly reachable experimentally. On the other hand, the sub-shot-noise sensitivity {delta}{theta}{approx}1/N{sup 3/4} can be reached in a realistic experimental setting. We also show that the 1/N{sup 3/4} scalingmore » is a rigorous upper bound in the limit N{yields}{infinity}, while keeping constant all different parameters of the bosonic Mach-Zehnder interferometer.« less

Authors:
;  [1]; ; ;  [1]
  1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
Publication Date:
OSTI Identifier:
20718784
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 72; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.72.043612; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; BOSE-EINSTEIN CONDENSATION; DISTURBANCES; ENERGY LEVELS; INTERFEROMETRY; MACH-ZEHNDER INTERFEROMETER; NOISE; PHOTONS; SENSITIVITY; VISIBLE RADIATION

Citation Formats

Pezze, L, Smerzi, A, Istituto Nazionale per la Fisica della Materia BEC-CRS and Dipartimento di Fisica, Universita di Trento, I-38050 Povo, Collins, L A, Berman, G P, and Bishop, A R. Sub-shot-noise phase sensitivity with a Bose-Einstein condensate Mach-Zehnder interferometer. United States: N. p., 2005. Web. doi:10.1103/PhysRevA.72.043612.
Pezze, L, Smerzi, A, Istituto Nazionale per la Fisica della Materia BEC-CRS and Dipartimento di Fisica, Universita di Trento, I-38050 Povo, Collins, L A, Berman, G P, & Bishop, A R. Sub-shot-noise phase sensitivity with a Bose-Einstein condensate Mach-Zehnder interferometer. United States. https://doi.org/10.1103/PhysRevA.72.043612
Pezze, L, Smerzi, A, Istituto Nazionale per la Fisica della Materia BEC-CRS and Dipartimento di Fisica, Universita di Trento, I-38050 Povo, Collins, L A, Berman, G P, and Bishop, A R. Sat . "Sub-shot-noise phase sensitivity with a Bose-Einstein condensate Mach-Zehnder interferometer". United States. https://doi.org/10.1103/PhysRevA.72.043612.
@article{osti_20718784,
title = {Sub-shot-noise phase sensitivity with a Bose-Einstein condensate Mach-Zehnder interferometer},
author = {Pezze, L and Smerzi, A and Istituto Nazionale per la Fisica della Materia BEC-CRS and Dipartimento di Fisica, Universita di Trento, I-38050 Povo and Collins, L A and Berman, G P and Bishop, A R},
abstractNote = {Bose-Einstein condensates (BEC), with their coherence properties, have attracted wide interest for their possible application to ultraprecise interferometry and ultraweak force sensors. Since condensates, unlike photons, are interacting, they may permit the realization of specific quantum states needed as input of an interferometer to approach the Heisenberg limit, the supposed lower bound to precision phase measurements. To this end, we study the sensitivity to external weak perturbations of a representative matter-wave Mach-Zehnder interferometer whose input are two Bose-Einstein condensates created by splitting a single condensate in two parts. The interferometric phase sensitivity depends on the specific quantum state created with the two condensates, and, therefore, on the time scale of the splitting process. We identify three different regimes, characterized by a phase sensitivity {delta}{theta} scaling with the total number of condensate particles N as (i) the standard quantum limit {delta}{theta}{approx}1/N{sup 1/2} (ii) the sub shot-noise {delta}{theta}{approx}1/N{sup 3/4}, and the (iii) the Heisenberg limit {delta}{theta}{approx}1/N. However, in a realistic dynamical BEC splitting, the 1/N limit requires a long adiabaticity time scale, which is hardly reachable experimentally. On the other hand, the sub-shot-noise sensitivity {delta}{theta}{approx}1/N{sup 3/4} can be reached in a realistic experimental setting. We also show that the 1/N{sup 3/4} scaling is a rigorous upper bound in the limit N{yields}{infinity}, while keeping constant all different parameters of the bosonic Mach-Zehnder interferometer.},
doi = {10.1103/PhysRevA.72.043612},
url = {https://www.osti.gov/biblio/20718784}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 72,
place = {United States},
year = {2005},
month = {10}
}