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arXiv:1411.5111 · Physical Review A

Heisenberg-limited metrology with information recycling

Simon A. Haine, Stuart S. Szigeti, Matthias D. Lang, Carlton M. Caves

Published Apr 30, 2015• 30 citations
arXivHTMLPDF

Abstract

Information recycling has been shown to improve the sensitivity of atom interferometers by exploiting atom-light entanglement. In this Rapid Communication, we apply information recycling to an interferometer where the input quantum state has been partially transferred from some donor system. We demonstrate that when the quantum state of this donor system is from a particular class of number-correlated Heisenberg-limited states, information recycling yields a Heisenberg-limited phase measurement. Crucially, this result holds irrespective of the fraction of the quantum state transferred to the interferometer input and also for a general class of number-conserving quantum-state-transfer processes, including ones that destroy the first-order phase coherence between the branches of the interferometer. This result could have significant applications in Heisenberg-limited atom interferometry, where the quantum state is transferred from a Heisenberg-limited photon source, and in optical interferometry where the loss can be monitored.

DOI
10.1103/physreva.91.041802

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Information recycling has been shown to improve the sensitivity of atom interferometers by exploiting atom-light entanglement. In this Rapid Communication, we apply information recycling to an interferometer where the input quantum state has been partially transferred from some donor system. We demonstrate that when the quantum state of this donor system is from a particular class of number-correlated Heisenberg-limited states, information recycling yields a Heisenberg-limited phase measurement. Crucially, this result holds irrespective of the fraction of the quantum state transferred to the interferometer input and also for a general class of number-conserving quantum-state-transfer processes, including ones that destroy the first-order phase coherence between the branches of the interferometer. This result could have significant applications in Heisenberg-limited atom interferometry, where the quantum state is transferred from a Heisenberg-limited photon source, and in optical interferometry where the loss can be monitored.
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We investigate the prospect of enhancing the phase sensitivity of atom interferometers in the Mach-Zehnder configuration with squeezed light. Ultimately, this enhancement is achieved by transferring the quantum state of squeezed light to one or more of the atomic input beams, thereby allowing operation below the standard quantum limit. We analyze in detail three specific schemes that utilize (1) single-mode squeezed optical vacuum (i.e., low-frequency squeezing), (2) two-mode squeezed optical vacuum (i.e., high-frequency squeezing) transferred to both atomic inputs, and (3) two-mode squeezed optical vacuum transferred to a single atomic input. Crucially, our analysis considers incomplete quantum state transfer (QST) between the optical and atomic modes, and the effects of depleting the initially prepared atomic source. Unsurprisingly, incomplete QST degrades the sensitivity in all three schemes. We show that by measuring the transmitted photons and using information recycling [Phys. Rev. Lett. 110, 053002 (2013)], the degrading effects of incomplete QST on the sensitivity can be substantially reduced. In particular, information recycling allows scheme (2) to operate at the Heisenberg limit irrespective of the QST efficiency, even when depletion is significant. Although we concentrate on Bose-condensed atomic systems, our scheme is equally applicable to ultracold thermal vapors.
It has been known for a while that, provided by the Heisenberg Uncertainty Principle, certain types of quantum correlated light should yield a better scaling law than the one with ordinary laser light. Hitherto, however, there is no such device practically used outside laboratories. The fact that quantum correlations are easy to be destroyed under decoherence essentially makes their utilities problematic for real world applications. For the optical interferometers, the most significant decoherence phenomenon is the photon loss. And yet, there has been no real-world device for quantum-enhanced sensing that overcomes the photon loss effects. In order to analyze the photon loss effects the description of the quantum states of light calls for a density matrix formalism, rather than the usual pure state approach. Here we take an example of the input states for the Heisenberg-limited interferometry, namely the optimal state, and show the description of the quantum state of light based on the reduced density matrix.
The feasibility of a Heisenberg-limited phase measurement using a Mach-Zehnder interferometer fed with twin photon correlated light is investigated theoretically. To take advantage of the Heisenberg limit, 1/N1/N1/N, for the phase sensitivity, one wants the number of correlated photons, NNN, to be high. This favors the use of parametric oscillation rather than the weaker but better correlated source given by parametric down-conversion. In real systems, decorrelation arising from photon absorption, mode mismatch, and nonideal detectors must be considered. In this paper we address the problem of detection when correlated photons are used as the input. We study the influence of photon statistics and of imperfect quantum correlation of the input light, and show that it is still possible to break the classical 1/N1/\sqrt{N}1/N​ phase sensitivity limit in nonideal experimental conditions. All the results are valid in the general case of quantum correlated bosons.
The quantum Fisher information and quantum correlation parameters are employed to study the application of nonclassical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state is determined by its intermode correlations (which depends on path entanglement) and intramode correlations (which depends on the photon statistics). In light of these results, we consider the performance of quantum-enhanced optical interferometers. Furthermore, we propose a Heisenberg-limited metrology protocol involving standard elements from passive and active linear optics, for which the quantum Cram\'er-Rao bound is saturated with an intensity measurement. Interestingly, the quantum advantage for this scheme is derived solely from the nonclassical photon statistics of the probe state and does not depend on entanglement. We study the performance of this scheme in the presence of realistic losses and consequently predict a substantial enhancement over the shot-noise limit with current technological capabilities.
Phase measurement using a lossless Mach–Zehnder interferometer with certain entangled N-photon states can lead to a phase sensitivity of the order of 1/N, the Heisenberg limit. However, previously considered output measurement schemes are different for different input states to achieve this limit. We show that it is possible to achieve this limit just by the parity measurement for all the commonly proposed entangled states. Based on the parity measurement scheme, the reductions of the phase sensitivity in the presence of photon loss are examined for the various input states.