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arXiv:2608.22668 · Brazilian Journal of Physics

Fock-state filtering of squeezed states: enhanced nonclassicality and effects of a thermal bath

João Pedro Gonzalez de Oliveira, A. Vidiella-Barranco

quant-phphysics.opticsSubmitted Aug 24, 2026• Announced Aug 25, 2026• 0 citations• Revised Aug 28, 2026 (v2)
v1 · Aug 24, 2026v2 · Aug 28, 2026
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Abstract

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 $m=0$ and $m=1$ 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.

Comments
Accepted for publication in the Brazilian Journal of Physics Collection in honor of Prof. Amir O. Caldeira, "Frontiers in Quantum Mechanics and the 45 Years of the Caldeira-Leggett Model"

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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.
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Number state filtering in coherent states leads to sub-Poissonian photon statistics. These states are more suitable for phase estimation when compared with the coherent states. Nonclassicality of these states is quantified in terms of the negativity of the Wigner function and the entanglement potential. Filtering of the vacuum from a coherent state is almost like the photon-addition. However, filtering makes the state more resilient against dissipation than photon-addition. Vacuum state filtered coherent states perform better than the photon-added coherent states for a two-way quantum key distribution protocol. A scheme to generate these states in multi-photon atom-field interaction is presented.
Abstract The effect of two quantum state engineering processes that can be used to burn a hole at vacuum in the photon number distribution of quantum states of radiation field is compared using various witnesses of lower‐ and higher‐order nonclassicality as well as a measure of nonclassicality. Specifically, the modification in nonclassical properties due to vacuum state filtration and a single photon addition on an even coherent state, binomial state, and Kerr state are investigated using the criteria of lower‐ and higher‐order antibunching, squeezing, and sub‐Poissonian photon statistics. Further, the amount of nonclassicality present in these engineered quantum states having enormous applications in continuous variable quantum communication is quantified and analyzed by using an linear entropy‐based entanglement potential. It is observed that all the quantum states studied here are highly nonclassical, and the hole‐burning processes can introduce/enhance nonclassical features. However, it is not true in general. A hole at vacuum implies a maximally nonclassical state (as far as Lee's nonclassical depth is concerned), but a particular process of hole burning at vacuum does not ensure the existence of any particular nonclassical feature. Specifically, lower‐ and higher‐order squeezing are not observed for photon‐added and vacuum filtered even coherent states.
A possible way of generating nonclassical states of light is via the truncation of a given state in the Fock basis. In recent work, we presented an alternative scheme for such quantum scissors [ Phys. Rev. A 104 , 033715 ( 2021 ) PLRAAN 1050-2947 10.1103/PhysRevA.104.033715 ], employing a nondegenerate parametric amplifier, a beam splitter, and photodetectors. An advantage of this setup is that it does not require the generation of Fock states beforehand, as in previous proposals. Here we extend this treatment to mixed input states. We show the possibilities of generating truncated states with either a maximum Fock number N or states having a minimum Fock number N . We discuss two specific examples of states to be truncated: (i) the thermal state and (ii) the phase-diffused coherent state. In either case, the generated field states can present sub-Poissonian statistics as well as non-Gaussian character. These nonclassical properties can be adjusted by changing the parameters of the scissors, e.g., the amplifier strength and the beam-splitter transmittance.
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