Quantum phase-estimation protocols can provide a measuring method of phase shift with precision superior to the standard quantum limit (SQL) due to the application of a nonclassical state of light. A squeezed vacuum state, whose variance in one quadrature is lower than the corresponding SQL, has been pointed out as a sensitive resource for quantum phase estimation and the estimation accuracy is directly influenced by the properties of the squeezed state. Here we analyze in detail the influence of the purity and squeezing level of the squeezed state on the accuracy of quantum phase estimation. The maximum precision that can be achieved for a squeezed thermal state is evaluated, and the experimental results are in agreement with the theoretical analyses. It is also found that the width of the phase-estimation interval $\mathrm{\ensuremath{\Delta}}\ensuremath{\theta}$ beyond SQL is correlated with the purity of the squeezed state.
Quantum phase-estimation protocols can provide a measuring method of phase shift with precision superior to the standard quantum limit (SQL) due to the application of a nonclassical state of light. A squeezed vacuum state, whose variance in one quadrature is lower than the corresponding SQL, has been pointed out as a sensitive resource for quantum phase estimation and the estimation accuracy is directly influenced by the properties of the squeezed state. Here we analyze in detail the influence of the purity and squeezing level of the squeezed state on the accuracy of quantum phase estimation. The maximum precision that can be achieved for a squeezed thermal state is evaluated, and the experimental results are in agreement with the theoretical analyses. It is also found that the width of the phase-estimation interval \ensuremathΔ\ensuremathθ beyond SQL is correlated with the purity of the squeezed state.
Abstract We present a theoretical study on the generation and nonclassical properties of hybrid squeezed states (HSS), a class of engineered quantum states with enhanced quantum features. Using a modified beam splitter-Kerr medium scheme, we construct superpositions of squeezed vacuum and two-photon-added squeezed states, providing a flexible framework to generate and control hybrid quantum states. Nonclassicality is analysed via Mandel's Q parameter, photon number distributions, probability distribution functions, and Wigner functions, revealing sub-Poissonian statistics, oscillatory photon distributions, and significant Wigner negativity. Phase-sensitivity analysis within a Mach-Zehnder interferometric framework demonstrates that HSS outperform conventional squeezed and photon-added squeezed states, achieving measurement precisions that exceed the standard quantum limit and approach the Heisenberg limit under optimal parameters. These results establish hybrid squeezed states as a powerful resource for quantum metrology, communication, and optical interferometry.
Squeezed light has lower quantum noise in amplitude or phase than the quantum noise limit (QNL) of classical light. This enables enhancing sensitivity -- quantified by the signal-to-noise ratio (SNR) -- to beyond the QNL in optical techniques such as spectroscopy, gravitational wave detection, magnetometry and imaging. Precision -- the variance of repeated estimates -- has also been enhanced beyond the QNL using squeezed vacuum to estimate optical phase and transmission. However, demonstrations have been limited to femtowatts of probe power. Here we demonstrate simultaneous precision and sensitivity beyond the QNL for estimating modulated transmission using a squeezed amplitude probe of 0.2 mW average (25 W peak) power. This corresponds to 8 orders of magnitude above the power limitations of previous sub-QNL precision measurements. Our theory and experiment show precision enhancement scales with the amount of squeezing and increases with the resolution bandwidth of detection. We conclude that quantum enhanced precision in estimating a modulated transmission increases when observing dynamics at ∼ kHz and above. This opens the way to performing measurements that compete with the optical powers of current classical techniques, but have superior precision and sensitivity beyond the classical limit.
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.
Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of [ 0 , π / 2 ) . Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from [ 0 , π ) , where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology.
We consider an optical interferometer with coherent light in one input and a squeezed vacuum in another. Such an interferometer is known to beat the standard quantum limit of sensitivity to the difference of phase shifts in its arms. We find the ultimate limit of precision for such an interferometer by calculating the quantum Fisher information of the mixed quantum state in one of the interferometer's outputs about the difference phase. We show that, in the vicinity of the black fringe, this information is asymptotically close to the quantum Fisher information about this phase for the two-mode readout. We conclude that the single-mode readout is optimal for phase estimation in squeezing-enhanced interferometry and allows for the Heisenberg scaling of precision. We also show that the optimal local measurement in the vicinity of the black fringe consists of amplifying the output field in a phase-sensitive way and measuring its photon number.
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.