2005/08/29 by Luca Pezzè, L. Pezze', L. A. Collins A. Smerzi +4 · 2 citations
Computer Science · Physics and Astronomy · #Bose–Einstein condensate #Coherence (philosophical gambling strategy) #Cold Atom Physics and Bose-Einstein Condensates #Heisenberg limit #Interferometry #Mach–Zehnder interferometer #Matter wave #Mechanical and Optical Resonators #Optics #Phase (matter) #Physics #Quantum #Quantum Information and Cryptography #Quantum computer #Quantum limit #Quantum mechanics #Quantum network #Realization (probability) #Scaling #Sensitivity (control systems) #Shot noise #Statistics #cond-mat.other
paper · pdf · doi:10.1103/physreva.72.043612
4 figures
arxiv created 2005/08/29 · openalex publication_date 2005/10/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \ensuremathΔ\ensuremathθ scaling with the total number of condensate particles N as (i) the standard quantum limit \ensuremathΔ\ensuremathθ\ensuremath∼1∕N1∕2, (ii) the sub shot-noise \ensuremathΔ\ensuremathθ\ensuremath∼1∕N3∕4, and the (iii) the Heisenberg limit \ensuremathΔ\ensuremathθ\ensuremath∼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 \ensuremathΔ\ensuremathθ\ensuremath∼1∕N3∕4 can be reached in a realistic experimental setting. We also show that the 1∕N3∕4 scaling is a rigorous upper bound in the limit N\ensuremath→\ensuremath∞, while keeping constant all different parameters of the bosonic Mach-Zehnder interferometer.