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arXiv:2605.03746 · The European Physical Journal Plus

Tomogram-based quantifiers of nonclassicality dynamics in Kerr and cubic media

K. M. Athira, M. J. Neethu, M. Rohith

quant-phSubmitted May 4, 2026• Announced May 5, 2026• 0 citations
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Abstract

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 $Q$-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.

Journal reference
The European Physical Journal Plus, 141, 527, (2026)
DOI
10.1140/epjp/s13360-026-07775-6
Comments
32 pages, 20 figures

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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.
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By analyzing the optical tomogram of a linear superposition of coherent states, we show that distinctive signatures of the macroscopic superposition states are displayed directly in the optical tomograms of the states. We also study the effect of decoherence on the optical tomograms of the macroscopic superposition states. Since the wave packet fractional revivals are associated with the generation of macroscopic superposition states, these signatures help in visualizing the revivals and fractional revivals occurring in a nonlinear medium directly in the optical tomogram of the time-evolved state. We found that the optical tomogram of the time-evolved state at the instants of fractional revivals show structures with sinusoidal strands. Using a class of initial superposed wave packets evolving in the Kerr-like medium, we further show that the condition for the occurrence of fractional revival phenomenon depends on the number of wave packets composing the initial superposition state. In the case of a two-mode electromagnetic field, we investigate the entanglement of the state directly using the optical tomogram. We have shown that the signatures of entanglement can be observed directly in the single-mode optical tomogram of the state without reconstructing the density matrix of the system. We also analyze the effect of decoherence on the optical tomograms of the entangled states. Further, we examine the optical tomograms of the entangled states generated using a beam splitter with a Kerr medium placed into one of its input modes. We have found the signatures of entanglement in the optical tomogram for the entangled states generated at the instants of two- and three-subpacket fractional revival times.
Abstract Several nonclassical effects displayed by wave packets governed by nonlinear Hamiltonians can be identified and assessed directly from tomograms without attempting to reconstruct the Wigner function or the density matrix explicitly. We have demonstrated this for both single-mode and bipartite systems. We have shown that a wide spectrum of effects such as the revival phenomena, quadrature squeezing, and Hong–Mandel and Hillery type higher-order squeezing in a generic single-mode system and the double-well Bose–Einstein condensate (BEC) can be obtained from appropriate tomograms in a straightforward manner. We have examined the manner in which decoherence affects the nature of the state of a generic single-mode system at specific instants during temporal evolution. We have investigated entropic squeezing of the subsystem state of a bipartite system as it evolves in time, solely from tomograms. The procedures that we have demonstrated can be readily adapted to multimode systems. Further, for the double-well BEC we have identified an indicator of entanglement between subsystems that can be obtained directly from the tomogram. This mirrors the qualitative behavior of the subsystem von Neumann entropy and the subsystem linear entropy.
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.
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.
The optical tomogram of the number state filtered coherent states is studied comprehensively.The superposition of coherent state and number state is reflected in the optical tomogram via quantum interference.The qualitative signatures of the nonclassicality are captured as rapid oscillations in the optical tomogram of number state filtered coherent states.Entropic squeezing is estimated directly from the optical tomogram through the Shannon information entropy.The effects of the non-unit quantum efficiency of the photodetectors on the optical tomogram and the entropic squeezing are observed.Finally, two decoherence models, namely phase damping and amplitude damping models, are employed to assess the degradation of the nonclassical features in the optical tomogram.