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arXiv:quant-ph/0511214 · Physical Review Letters

Time-Reversal and Super-Resolving Phase Measurements

Kevin J. Resch, K. L. Pregnell, Robert Prevedel, Alexei Gilchrist, Geoff J. Pryde, Jeremy L. O’Brien, Andrew G. White

Published May 31, 2007• 265 citations
arXivHTMLPDF

Abstract

We demonstrate phase super-resolution in the absence of entangled states. The key insight is to use the inherent time-reversal symmetry of quantum mechanics: our theory shows that it is possible to measure, as opposed to prepare, entangled states. Our approach is robust, requiring only photons that exhibit classical interference: we experimentally demonstrate high-visibility phase super-resolution with three, four, and six photons using a standard laser and photon counters. Our six-photon experiment demonstrates the best phase super-resolution yet reported with high visibility and resolution.

DOI
10.1103/physrevlett.98.223601

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We demonstrate phase super-resolution in the absence of entangled states. The key insight is to use the inherent time-reversal symmetry of quantum mechanics: our theory shows that it is possible to measure, as opposed to prepare, entangled states. Our approach is robust, requiring only photons that exhibit classical interference: we experimentally demonstrate high-visibility phase super-resolution with three, four, and six photons using a standard laser and photon counters. Our six-photon experiment demonstrates the best phase super-resolution yet reported with high visibility and resolution.
We present two experiments that achieve phase super-resolution at telecommunication wavelengths. One of the experiments is realized in the space domain and the other is realized in the time domain. Both experiments show high visibility and are performed with standard lasers and single-photon detectors. The first experiment uses six-photon coincidences, whereas the latter experiment needs no coincidence measurements, is easy to perform, and achieves, in principle, arbitrarily high phase super-resolution. Here, we demonstrate a 30-fold increase of the resolution. We stress that neither entanglement nor joint detection is needed in these experiments, which demonstrates that neither is necessary to achieve phase super-resolution.
Measurement, whilst being physically fundamental, is also fundamentally physical. Classical interferometric measurements suffer from physical limitations where the shot noise limit forms an upper bound of √n on a phase shift Δφ that can be resolved, with n being the average number of photons detected, making their applicability in modern nanoscale experiments quite restricted. Exotic quantum states such as maximally entangled NOON states (|N0〉A;B+|0N〉A;B)/√2, where N is the number of entangled photons are of particular importance as they have repeatedly been shown to exhibit phase super-resolution. Interesting post selection schemes and time-reversed detection schemes have been investigated for phase estimation using NOON states. These methods are inherently non-deterministic at the preparation or measurement stage and thus do not optimise resources, for instance the number of photons passing through the sample greatly exceeds those used in the measurement.
We observed two-photon phase superresolution in an unbalanced Michelson interferometer with classical Gaussian laser pulses. Our work is a time-reversed version of a two-photon interference experiment using an unbalanced Michelson interferometer. A measured interferogram exhibits two-photon phase superresolution with a high visibility of 97.997.9%\ifmmode\pm\else\textpm\fi{}0.4%97.9. Its coherence length is about 22 times longer than that of the input laser pulses. It is a classical analog to the large difference between the one- and two-photon coherence lengths of entangled photon pairs.
The ultimate sensitivity of optical measurements is a key element of many recent works. Classically, it is mainly limited by the shot noise limit. However, a measurement setup that incorporates quantum mechanical principles can surpass the shot noise limit and reach the Heisenberg limit. Nevertheless, many of those experiments fail to break even the classical shot-noise limit. Following a recent proposal, we present here the results of optical phase measurements with a photon-number resolving detector using coherent states of up to 4200 photons on average. An additional scheme that can be implemented using standard single-photon detectors is also presented, and the results of the two schemes are compared. These measurements present deterministic single-shot sub-wavelength super-resolution up to 288 better than the optical wavelength. The results follow the classically limited sensitivity, up to 86 times better than the wavelength.
Precision measurements are important across all fields of science. In particular, optical phase measurements can be used to measure distance, position, displacement, acceleration, and optical path length. Quantum entanglement enables higher precision than would otherwise be possible. We demonstrated an optical phase measurement with an entangled four-photon interference visibility greater than the threshold to beat the standard quantum limit-the limit attainable without entanglement. These results open the way for new high-precision measurement applications.