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arXiv:2307.16479 · Physical Review A

Sub-shot-noise interferometry with two-mode quantum states

Quentin Marolleau, Charlie Leprince, Victor Gondret, Denis Boiron, Christoph Ira Westbrook

Published Feb 2, 2024• 2 citations
arXivHTMLPDF

Abstract

We study the feasibility of sub-shot-noise interferometry with imperfect detectors, starting from twin Fock states and two-mode squeezed vacuum states. We derive analytical expressions for the corresponding phase uncertainty. We find that one can achieve phase shift measurements below the standard quantum limit, as long as the losses are smaller than a given threshold, and that the measured phase is close enough to an optimal value. We provide our analytical formulas in a python package, accessible online.

DOI
10.1103/physreva.109.023701

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We study the feasibility of sub-shot-noise interferometry with imperfect detectors, starting from twin Fock states and two-mode squeezed vacuum states. We derive analytical expressions for the corresponding phase uncertainty. We find that one can achieve phase shift measurements below the standard quantum limit, as long as the losses are smaller than a given threshold, and that the measured phase is close enough to an optimal value. We provide our analytical formulas in a python package, accessible online.
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We present in this paper a new scheme for optical interferometry. We utilize coherent-beam-stimulated two-mode squeezed light, which interacts with a phase shifter and is then squeezed again before detection. Our theoretical device has the potential to reach far below the shot-noise limit in phase sensitivity. This new proposal avoids the pitfalls of other setups, such as difficulty in creating the required resource. Furthermore, our scheme requires no complicated detection protocol, relying instead only on simple intensity measurement. Also, bright, coherent sources 'boost' squeezed light, creating a very sensitive device. This hybrid scheme relies on no unknown components and can be constructed with current technology. In this paper, we present our analysis of this relatively straightforward device, using the operator propagation method. We derive the phase sensitivity and provide a simple numerical example of the power of our new proposal. Sensitivity to unknown phase shifts scales as a shot-noise-limited Mach–Zehnder interferometer, multiplied by a sub-Heisenberg contribution from the squeezed light.
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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 Δ θ ∝ 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 θ , 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.