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Acta Physica Polonica A

Optical Tomogram of Number State Filtered Coherent States

J. Merlin, A. Basherrudin Mahmud Ahmed

Published May 1, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.141.516

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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.
We have examined both single and entangled two-mode multiphoton coherent states and shown how the ‘Janus-faced’ properties between two partner states are mirrored in appropriate tomograms. Entropic squeezing, quadrature squeezing and higher-order squeezing properties for a wide range of nonclassical states are estimated directly from tomograms. We have demonstrated how squeezing properties of two-mode entangled states produced at the output port of a quantum beamsplitter are sensitive to the relative phase between the reflected and transmitted fields. This feature allows for the possibility of tuning the relative phase to enhance squeezing properties of the state. Finally, we have examined the manner in which decoherence affects squeezing and the changes in the optical tomogram of the state due to interaction with the environment.
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.
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.
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.
The ability to tailor photon-number statistics is central to the generation and control of nonclassical states of light. Here, we investigate how Fock-state filtering of squeezed coherent states can be used to engineer their photon statistics. We consider the selective removal of the m=0m=0m=0 and m=1m=1m=1 Fock components and show that this process can enhance the sub-Poissonian character of the field, depending on the coherent amplitude. We then analyze the evolution of these engineered states in a thermal environment. Although all states eventually relax toward thermal statistics, the signatures of the filtering process may persist over a significant part of the evolution, while the purity of the filtered states is rapidly degraded by incoherent population redistribution. Our results illustrate both the potential and the limitations of photon-number engineering in realistic, dissipative settings.
We theoretically study the optical tomograms of maximally entangled states generated at the output modes of a beam splitter. We consider even and odd coherent states in one of the input modes and vacuum state in the other input mode of the beam splitter. 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. Two distinct types of optical tomograms are observed in any one of the output modes of the beam splitter based on the quadrature measurement in the other output mode if the output modes are entangled. The different features shown by the optical tomograms are verified by investigating the photon-number statistics of the corresponding state. We analyze the effect of decoherence on the optical tomograms of the entangled states.