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arXiv:1211.3570

Quantum-Dense Metrology

S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller‐Ebhardt, K. Danzmann, Roman Schnabel

Published Nov 15, 2012• 0 citations
arXivHTMLPDF

Abstract

Quantum metrology utilizes entanglement for improving the sensitivity of measurements. Up to now the focus has been on the measurement of just one out of two non-commuting observables. Here we demonstrate a laser interferometer that provides information about two non-commuting observables, with uncertainties below that of the meter's quantum ground state. Our experiment is a proof-of-principle of quantum dense metrology, and uses the additional information to distinguish between the actual phase signal and a parasitic signal due to scattered and frequency shifted photons. Our approach can be readily applied to improve squeezed-light enhanced gravitational-wave detectors at non-quantum noise limited detection frequencies in terms of a sub shot-noise veto-channel.

DOI
10.48550/arxiv.1211.3570

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Quantum metrology utilizes entanglement for improving the sensitivity of measurements. Up to now the focus has been on the measurement of just one out of two non-commuting observables. Here we demonstrate a laser interferometer that provides information about two non-commuting observables, with uncertainties below that of the meter's quantum ground state. Our experiment is a proof-of-principle of quantum dense metrology, and uses the additional information to distinguish between the actual phase signal and a parasitic signal due to scattered and frequency shifted photons. Our approach can be readily applied to improve squeezed-light enhanced gravitational-wave detectors at non-quantum noise limited detection frequencies in terms of a sub shot-noise veto-channel.
Quantum-dense metrology constitutes a special case of quantum metrology in which two orthogonal phase space projections of a signal are simultaneously sensed beyond the shot-noise limit. Previously, it was shown that the additional sensing channel that is provided by quantum-dense metrology contains information that can be used to identify and to discard corrupted segments from the measurement data. Here, we propose and demonstrate a new method in which this information is used for improving the sensitivity without discarding any measurement segments. Our measurement reached sub-shot-noise performance, although initially strong classical noise polluted the data. The new method has high potential for improving the noise spectral density of gravitational-wave detectors at signal frequencies of high astrophysical relevance.
Quantum metrology enables us to estimate optical phase shifts beyond the shot noise limit. Applications include quantum-enhanced biological measurement [1], microscopy [2] and gravitational wave detection[3]. For two-mode N-photon system, the NOON state can achieve the highest possible phase sensitivity where multi-photon coherence between two states significantly contributes to improving the phase sensitivity. Another alternative approach to improve the phase sensitivity by use of squeezed states. Squeezing is usually characterized by reducing the quantum noise of desired observable at the expense of increasing the quantum noise for its non-commute partner. Because shot-noise limits the phase sensitivity of any classical states, the reduced quantum noise can be used for improving the phase sensitivity. Here we experimentally study the phase sensitivity of an optical spin-squeezed state by using linear optics. We generated the optical spin-squeezed state using one photon subtraction from a down converted photon source. To implement the sub-shot noise measurement, we used multiplexed photon number resolving detectors so that we can reconstruct the photon number statistics of the state. In the talk, we will analyse the generated state in terms of both squeezing and phase sensitivity by using Fisher information.
Quantum dense metrology (QDM) performs high-precision measurements by a two-mode entangled state created by an optical parametric amplifier (PA), where one mode is a meter beam and the other is a reference beam. In practical applications, the photon losses of meter beam are unavoidable, resulting in a degradation of the sensitivity. Here, we employ coherent feedback that feeds the reference beam back into the PA by a beam splitter to enhance the sensitivity in a lossy environment. The results show that the sensitivity is enhanced significantly by adjusting the splitting ratio of the beam splitter. This method may find its potential applications in QDM. Furthermore, such a strategy that two non-commuting observables are simultaneous measurements could provide a new way to individually control the noise-induced random drift in phase or amplitude of the light field, which would be significant for stabilizing the system and long-term precision measurement.
It is well known that classical states of light exhibit shot noise, characteristic of independent or uncorrelated particles. For phase estimation problems, this leads to a shot-noise limited uncertainty of 1/sqrt[N], where N is the number of particles detected. It is also well known that the shot-noise limit is not fundamental: squeezed states and entangled states can be used for sub-shot-noise phase measurements. The uncertainty principle sets a fundamental limit of 1/N, known as the "Heisenberg" limit. We have recently demonstrated a method, using parametric downconversion and post-selection, to generate entangled "NOON" states suitable for sub-shot-noise phase measurements [M.W. Mitchell et al, Nature 429, 161 (2004)]. We generated a three-photon NOON state and demonstrated three-fold improvement in phase resolution with this state. The relationship between phase resolution and phase uncertainty depends on prior information about the phase being estimated. As in the case of phase measurements with squeezed states, extra precision in one dimension is gained at the cost of reduced precision in other dimensions. Only when prior information is incorporated can entangled-state metrology be applied to beat the shot-noise limit. We illustrate this relationship and discuss adaptive strategies for phase estimation and the possibility of reaching the Heisenberg limit.
Quantum noise limited interferometry for subhertz phase measurement is of essence in precision metrology applications, such as gravitational wave detection. However, suppression of subhertz classical noises below the shot-noise level is very challenging in practice. Two-frequency interferometry has been previously proposed to avoid low-frequency noises and may be useful for squeezing-enhanced high-precision phase measurement. Here we experimentally demonstrate a subhertz interferometer at the standard quantum noise (shot-noise) limit, by use of dual-frequency coherent probe light at the input and phase-sensitive heterodyne detection to measure the output interfered light. When the interferometer is locked at a dark fringe, the noise floor of the phase variance in the interferometer reaches the shot-noise level down to Fourier frequencies below 1 Hz. This work should pave a way for a realization of subhertz interferometry beyond the shot-noise limit.
Quantum metrology enables estimation of optical phase shifts with precision beyond the shot-noise limit. One way to exceed this limit is to use squeezed states, where the quantum noise of one observable is reduced at the expense of increased quantum noise for its complementary partner. Because shot-noise limits the phase sensitivity of all classical states, reduced noise in the average value for the observable being measured allows for improved phase sensitivity. However, additional phase sensitivity can be achieved using phase estimation strategies that account for the full distribution of measurement outcomes. Here we experimentally investigate a model of optical spin-squeezing, which uses post-selection and photon subtraction from the state generated using a parametric downconversion photon source, and we investigate the phase sensitivity of this model. The Fisher information for all photon-number outcomes shows it is possible to obtain a quantum advantage of 1.58 compared to the shot-noise value for five-photon events, even though due to experimental imperfection, the average noise for the relevant spin-observable does not achieve sub-shot-noise precision. Our demonstration implies improved performance of spin squeezing for applications to quantum metrology.