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arXiv:1209.4716 · Science

Quantum-Enhanced Optical-Phase Tracking

Hidehiro Yonezawa, Daisuke Nakane, Trevor A. Wheatley, Kohjiro Iwasawa, Shuntaro Takeda, Hajime Arao, Kentaro Ohki, Koji Tsumura, Dominic William Berry, Timothy C. Ralph, Howard M. Wiseman, Elanor H. Huntington, Akira Furusawa

Published Sep 20, 2012• 219 citations
arXivHTMLPDF

Abstract

Tracking a randomly varying optical phase is a key task in metrology, with applications in optical communication. The best precision for optical-phase tracking has until now been limited by the quantum vacuum fluctuations of coherent light. Here, we surpass this coherent-state limit by using a continuous-wave beam in a phase-squeezed quantum state. Unlike in previous squeezing-enhanced metrology, restricted to phases with very small variation, the best tracking precision (for a fixed light intensity) is achieved for a finite degree of squeezing because of Heisenberg's uncertainty principle. By optimizing the squeezing, we track the phase with a mean square error 15 ± 4% below the coherent-state limit.

DOI
10.1126/science.1225258

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Tracking a randomly varying optical phase is a key task in metrology, with applications in optical communication. The best precision for optical-phase tracking has until now been limited by the quantum vacuum fluctuations of coherent light. Here, we surpass this coherent-state limit by using a continuous-wave beam in a phase-squeezed quantum state. Unlike in previous squeezing-enhanced metrology, restricted to phases with very small variation, the best tracking precision (for a fixed light intensity) is achieved for a finite degree of squeezing because of Heisenberg's uncertainty principle. By optimizing the squeezing, we track the phase with a mean square error 15 ± 4% below the coherent-state limit.
We propose a self-guided quantum phase estimation protocol based on a squeezed vacuum state and a stochastic optimization algorithm. Our protocol dynamically aligns the measurement basis with the target phase, eliminating the need for prior knowledge of the squeezing parameter. We demonstrate that this approach successfully tracks the target phase across the entire [0, π) periodicity interval, achieving a measurement precision that surpasses the Standard Quantum Limit and approaches the Heisenberg Limit.
Quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters. Similar to the estimation of a constant phase, there is a standard quantum limit for stochastic phase estimation, which can be obtained with the Mach–Zehnder interferometer and coherent input state. Recently, it has been shown that the stochastic standard quantum limit can be surpassed with nonclassical resources such as squeezed light. However, practical methods to achieve quantum enhancement in the stochastic phase estimation remain largely unexplored. Here we propose a method utilizing the SU(1,1) interferometer and coherent input states to estimate a stochastic optical phase. As an example, we investigate the Ornstein–Uhlenback stochastic phase. We analyze the performance of this method for three key estimation problems: prediction, tracking, and smoothing. The results show significant reduction of the mean square error compared with the Mach–Zehnder interferometer under the same photon number flux inside the interferometers. In particular, we show that the method with the SU(1,1) interferometer can achieve fundamental quantum scaling, achieve stochastic Heisenberg scaling, and surpass the precision of the canonical measurement.
Quantum-enhanced optical phase tracking is a quantum optical technique for tracking and measuring optical phases with high accuracy. It has important applications in laser interferometry, spectral analysis, and optical measurements. In this study, we propose a quantum-enhanced optical phase tracking protocol based on squeezed state optical fields. By using a continuous solid-state laser source with a central wavelength of 1064 nm, combing second harmonic generation, optical parametric oscillator, and PDH (Pound-Drever-Hall) locking technology, we prepare an initial squeezed state with a squeezing level of (8.0±0.2) dB. Through signal modulation technique and demodulation technique, we control the phase of the squeezed state optical field, thereby realizing the quantum-enhanced tracking of optical phases within the range of 0－2π. Compared with classical protocols, this protocol can suppress the noise fluctuations of phase tracking to at least 6.27 dB below the shot noise limit, improving the phase tracking accuracy by more than 76.4%. Because of the high requirements for phase measurement accuracy in applications such as angle estimation, phased array radar, and phased array sonar, this protocol is expected to improve the phase estimation accuracy beyond the shot noise limit. It provides compressed light sources for relevant fields, laying a theoretical and experimental foundation for higher-precision spatial positioning and quantum ranging techniques. The probe is made of amino acids arranged in a linear chain and joined together by peptide bonds between the carboxyl and amino groups of adjacent amino acid residues. The sequence of amino acids in a protein is determined by a gene and encoded in the genetic code. This can happen either before the protein is used in the cell, or as part of control mechanism.
Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is possible when we have very precise knowledge of and control over the model. However, uncertainties in key parameters underlying the system are unavoidable and may impact the quality of the estimate. We show here how quantum optical phase estimation of a squeezed state of light exhibits improvement when using a robust fixed-interval smoother designed with uncertainties explicitly introduced in parameters underlying the phase noise.
According to the Heisenberg uncertainty principle, the precision of any physical quantity measurement is limited by quantum fluctuation in general, which leads to the so-called standard quantum limit (SQL). The SQL can be beaten by using squeezed light, hence enhancing the measurement accuracy. Squeezed light is a typical nonclassical light, it exhibits reduced noise in one quadrature component. Since Caves proposed the scheme of phase measurement enhancement with squeezing, squeezed light has been used to enhance measurement precision in many areas. This review focuses on the following four kinds of precision measurements based on squeezed light: the measurements of relative phase, small lateral displacement and tilt, magnetic field, and clock synchronization. For all of these measurements, vacuum squeezing has been used to enhance measurement precision, while the types of squeezing (squeezing angle, transverse mode, polarization etc.) are different. For phase measurement, quadrature squeezing is injected into the conventionally unused input port of Mach-Zehnder interferometer (MZI) or Michelson interferometer (MI). For displacement or tilt measurement, a vacuum squeezing beam of a special transverse mode is coupled into an intense coherent beam, yielding a spatial-squeezed light whose transverse position or tilt angle noise is lower than that of a classical light beam. Based on the Faraday effect of polarization rotation, the magnetic field can be detected precisely. The precision can be increased further by using the polarization squeezing. The polarization squeezing can be generated by coupling two orthogonal polarized beams together, a coherent beam and a vacuum squeezed beam. Various polarization squeezing can be illustrated on the Poincaré sphere. Finally, in the clock synchronization based on the optical frequency comb, squeezed light can be used to enhance the time measurement precision. A theoretical scheme with multimode squeezing of supermode (a kind of mode describing the frequency mode of a pulse laser beam) is introduced. The squeezing has extensively been applied into the quantum precision measurements such as gravitational wave detection as well as biological measurement and will play a more important role in the near future.