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arXiv:1705.05609 · Optica

Deterministic phase measurements exhibiting super-sensitivity and super-resolution

Clemens Schäfermeier, Miroslav Ježek, Lars S. Madsen, Tobias Gehring, Ulrik L. Andersen

Published Jan 16, 2018• 39 citations
arXivHTMLPDF

Abstract

Phase super-sensitivity is obtained when the sensitivity in a phase measurement goes beyond the quantum shot noise limit, whereas super-resolution is obtained when the interference fringes in an interferometer are narrower than half the input wavelength. Here we show experimentally that these two features can be simultaneously achieved using a relatively simple setup based on Gaussian states and homodyne measurement. Using 430 photons shared between a coherent- and a squeezed vacuum state, we demonstrate a 22-fold improvement in the phase resolution while we observe a 1.7-fold improvement in the sensitivity. In contrast to previous demonstrations of super-resolution and super-sensitivity, this approach is fully deterministic.

DOI
10.1364/optica.5.000060

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Phase super-sensitivity is obtained when the sensitivity in a phase measurement goes beyond the quantum shot noise limit, whereas super-resolution is obtained when the interference fringes in an interferometer are narrower than half the input wavelength. Here we show experimentally that these two features can be simultaneously achieved using a relatively simple setup based on Gaussian states and homodyne measurement. Using 430 photons shared between a coherent- and a squeezed vacuum state, we demonstrate a 22-fold improvement in the phase resolution while we observe a 1.7-fold improvement in the sensitivity. In contrast to previous demonstrations of super-resolution and super-sensitivity, this approach is fully deterministic.
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.
Interference of light fields plays an important role in various high-precision measurement schemes. It has been shown that superresolving phase measurements beyond the standard coherent state limit can be obtained either by using maximally entangled multiparticle states of light or using complex detection approaches. Here we show that superresolving phase measurements at the shot noise limit can be achieved without resorting to nonclassical optical states or to low-efficiency detection processes. Using robust coherent states of light, high-efficiency homodyne detection, and a deterministic binarization processing technique, we show a narrowing of the interference fringes that scales with 1/√[N] where N is the mean number of photons of the coherent state. Experimentally we demonstrate a 12-fold narrowing at the shot noise limit.
The modern scientific method is critically dependent on precision measurements of physical parameters. A classic example is the measurement of the optical phase enabled by optical interferometry, where the error on the measured phase is conventionally bounded by the so-called Heisenberg limit. To achieve phase estimation at the Heisenberg limit, it has been common to consider protocols based on highly complex N00N states of light. However, despite decades of research and several experimental explorations, there has been no demonstration of deterministic phase estimation with N00N states reaching the Heisenberg limit or even surpassing the shot noise limit. Here we use a deterministic phase estimation scheme based on a source of Gaussian squeezed vacuum states and high-efficiency homodyne detection to obtain phase estimates with an extreme sensitivity that significantly surpasses the shot noise limit and even beats the conventional Heisenberg limit as well as the performance of a pure N00N state protocol. Using a high-efficiency setup with a total loss of about 11%, we achieve a Fisher information of 15.8(6) rad^{-2} per photon-a significant increase in performance compared to state of the art and beyond an ideal six photon N00N state scheme. This work represents an important achievement in quantum metrology, and it opens the door to future quantum sensing technologies for the interrogation of light-sensitive biological systems.
Interference metrology is a method for achieving high precision detection by phase estimation. The phase sensitivity of a traditional interferometer is subject to the standard quantum limit, while its resolution is constrained by the Rayleigh diffraction limit. The resolution and sensitivity of phase measurement can be enhanced by using quantum metrology. We propose a quantum interference metrology scheme using the entangled squeezed vacuum state, which is obtained using the magic beam splitter, expressed as | ψ ⟩ = ( | ξ ⟩ | 0 ⟩ + | 0 ⟩ | ξ ⟩ ) / 2 + 2 / cosh ⁡ r , such as the N00N state. We derive the phase sensitivity and the resolution of the system with Z detection, project detection, and parity detection. By simulation and analysis, we determine that parity detection is an optimal detection method, which can break through the Rayleigh diffraction limit and the standard quantum limit.
Classically, the resolution of optical measurements is limited by the Rayleigh limit and their sensitivity by the shot noise limit. However, non-classical measurements can surpass these limits. Measuring the photon number parity using a photon-number resolving detector, super resolved phase measurements up to 144 better than the Rayleigh limit are presented, with coherent states of up to 4,200 photons on average. An additional measurement that can be implemented with standard single-photon detectors is proposed and demonstrated. With this scheme, super resolution at the shot noise limit is demonstrated with coherent states of up to 200 photons on average.