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arXiv:1802.10050 · Journal of Physics B Atomic Molecular and Optical Physics

Homodyne nonclassical area as a nonclassicality indicator

M. Rohith, Suresh Kannan, C. Sudheesh

Published Jan 26, 2023• 4 citations
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Abstract

Abstract We propose a legitimate and easily computable nonclassicality indicator for the states of the electromagnetic field based on the standard deviation in the measurement of the homodyne rotated quadrature operator. The proposed nonclassicality indicator is the nonclassical area projected by the optical tomogram of the quantum state of light on the optical tomographic plane. If the nonclassical area projected by the optical tomogram of a quantum state is greater than zero, the state is nonclassical, and the area is zero for the pure classical state. It is also noted that the nonclassical area of a quantum state increases with an increase in the strength of nonclassicality-inducing operations on the state, such as squeezing, photon addition, etc. We have tested the validity of the nonclassical area measure by calculating the same for certain well-known nonclassical states, and found that essential features of the nonclassicality shown by the states are captured in the nonclassical area. We also show that the nonclassical area is robust against environment-induced decoherence of the states. The nonclassical area projected by the optical tomogram of a quantum state of light is experimentally tractable using the balanced homodyne detection of the quadrature operator of the field, avoiding the reconstruction of the density matrix or the quasiprobability distribution of the state.

DOI
10.1088/1361-6455/acb678

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Abstract We propose a legitimate and easily computable nonclassicality indicator for the states of the electromagnetic field based on the standard deviation in the measurement of the homodyne rotated quadrature operator. The proposed nonclassicality indicator is the nonclassical area projected by the optical tomogram of the quantum state of light on the optical tomographic plane. If the nonclassical area projected by the optical tomogram of a quantum state is greater than zero, the state is nonclassical, and the area is zero for the pure classical state. It is also noted that the nonclassical area of a quantum state increases with an increase in the strength of nonclassicality-inducing operations on the state, such as squeezing, photon addition, etc. We have tested the validity of the nonclassical area measure by calculating the same for certain well-known nonclassical states, and found that essential features of the nonclassicality shown by the states are captured in the nonclassical area. We also show that the nonclassical area is robust against environment-induced decoherence of the states. The nonclassical area projected by the optical tomogram of a quantum state of light is experimentally tractable using the balanced homodyne detection of the quadrature operator of the field, avoiding the reconstruction of the density matrix or the quasiprobability distribution of the state.
A legitimate and easily computable measure of nonclassicality for the pure state of the single-mode electromagnetic field based on the standard deviation in the measurement of the homodyne rotated quadrature operator is proposed. The proposed quantity is an effective nonclassical area projected by the optical tomogram of the quantum state of light on to the optical tomographic plane. It is found that if the nonclassical area projected by the optical tomogram of a pure single-mode quantum state is greater than zero the state is strictly a nonclassical state and it is zero for the classical state. Nonclassical area spanned by the optical tomogram of nonclassical states of light such as Fock states, squeezed states, photon-added coherent states, and even and odd coherent states, have been evaluated theoretically. Nonclassical area projected by the optical tomogram of a quantum state of light may be experimentally tractable using the balanced homodyne detection of the quadrature operator of the field avoiding the reconstruction of density matrix or the quasiprobability distribution of the state.
We propose a convenient and easily computable nonclassicality quantifier for bosonic field states based on the Wigner-Yanase skew information. The proposed nonclassicality quantifier is reflected by the quantum interaction between the maximum phase angle of the homodyne rotated quadrature operator and the bosonic field states. If the value of the nonclassical quantifier is greater than one-half, the state is nonclassical, and the quantifier is one-half for the pure classical. It is worth mentioning that an increase in the strength of nonclassicality inducing operations, such as squeezing and photon addition, leads to an enhancement of the nonclassicality in the quantum state. By computing some well-known nonclassical states and summarizing their existence features, we have confirmed the validity of our proposed nonclassicality quantifier. We have shown that in a range of values of the nonclassicality of the Gaussian state, revealing the sufficiency of the quantifier. We also compare it with two common nonclassical quantifiers to illustrate its advantages.
The reliable quantification of nonclassicality in quantum states under realistic decoherence remains a central challenge in advancing quantum technologies. Conventional quantifiers such as Wigner negativity, Mandel's QQQ-parameter, nonclassical depth, etc., are often experimentally intractable, non-unique, or insensitive to key quantum signatures. We demonstrate that tomogram-based measures, the homodyne nonclassical area and sum tomographic entropy, offer a robust, experimentally accessible alternative for quantifying nonclassicality dynamics, as they can be directly obtained from optical tomograms via balanced homodyne detection, avoiding density matrix reconstruction and ensuring feasibility. We study coherent, photon-added coherent, and even coherent states evolving in Kerr and cubic nonlinear systems, with environmental effects modelled using the Lindblad master equation under amplitude and phase damping. The homodyne nonclassical area, which quantifies the excess quadrature variance beyond that of a coherent state, tracks both the onset and decay of nonclassicality, clearly identifying fractional revivals, wave packet splitting, and macroscopic superpositions. We find that amplitude damping drives a rapid monotonic decay toward the vacuum, while phase damping allows partial revival features to survive longer. Complementing this, the sum tomographic entropy derived from conjugate-quadrature tomograms captures higher-order fractional revivals and phase-space interference through persistent entropy minima under weak damping. Our results establish homodyne-based quantifiers as powerful, real-time, and experimentally viable tools for tracking nonclassical dynamics in nonlinear optical media, offering a compelling alternative to conventional, experimentally challenging measures.
Although nonclassical quantum states are important both conceptually and as a resource for quantum technology, it is often difficult to test whether a given quantum system displays nonclassicality. A simple method to certify nonclassicality is introduced, based on easily accessible collective atomic quadrature measurements, without the need of full state tomography. The statistics is analyzed beyond the ground-state noise level by direct sampling of a regularized atomic quadrature quasiprobability. Nonclassicality of a squeezed ensemble of $2\ifmmode\times\else\texttimes\fi{}{10}^{5}$ cesium atoms is demonstrated, with a significance of up to 23 standard deviations.
Scalable methods for detecting and quantifying the nonclassical nature of a quantum state in noisy environments are challenging due to a complex relationship between noise and quantum coherence. In particular, identifying experimentally accessible signatures of synchronization in such regimes remains an open problem. By leveraging promising experimental implementation, we underpin what possible direct measures of nonclassicality are available. This work outlines accessing quantum synchronization (QS) in the steady state of a driven quantum van der Pol oscillator (vdPo) using two distinct figures of merit: (i) the nonclassical area δδδ and (ii) the second-order correlation function g(2)(0)g^{(2)}(0)g(2)(0), both of which are viable in experimental architectures. The nonclassical area quantifier based on homodyne tomography allows us to assess the nonclassical nature of the vdPo state directly from the tomogram without requiring full state reconstruction or Wigner function negativity. Within a well-defined parameter regime of drive strength and detuning, both δδδ and g(2)(0)g^{(2)}(0)g(2)(0) exhibit pronounced signatures of synchronization that complements the phase coherence between the drive and the vdPo. We derive an analytical expression for the steady state density matrix and the corresponding tomogram of the system, valid for arbitrary strengths of the harmonic drive. Analysis of the quantum tomogram uncovers clear phase locking behaviour, enabling the identification of the synchronization region (Arnold tongue) directly in terms of g(2)(0)g^{(2)}(0)g(2)(0) and δδδ. Furthermore, the behaviour of g(2)(0)g^{(2)}(0)g(2)(0) provides a statistical perspective that reinforces the tomographic signatures of QS. By analyzing the interplay between the aforementioned metrics, our findings indicate a scalable and experimentally relevant framework for characterizing QS in the driven vdPo.
Nonclassicality filters provide a universal method to visualize the nonclassicality of arbitrary quantum states of light through negativities of a regularized Glauber-Sudarshan PPP function, also denoted as nonclassicality quasiprobability. Such filters are introduced and analyzed for optimizing the experimental certification of nonclassical effects. An analytic filter is constructed which preserves the full information on the quantum state. For balanced homodyne detection, the number of data points is analyzed to get the negativities of the nonclassicality quasiprobability with high statistical significance. The method is applied to different scenarios, such as phase-randomized squeezed vacuum states, single-photon-added thermal states, and heralded state engineering with array detectors. The generalization to visualize quantum correlations of multimode radiation fields is also considered.