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arXiv:2411.07793

Nonclassicality and sub-Planck structures of photon subtracted compass states

Das, Amit, Sobhan Kumar Sounda

Published Nov 12, 2024• 0 citations
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Abstract

We discuss the nonclassical properties of photon subtracted compass states (PSCS). Nonclassical behavior is studied using various parameters like the Wigner function, squeezing, and photon statistical parameters like Mandels Q function, secondorder correlation function, Agarwal Tara $A_3$ criterion, and photon number distribution. Further analysis is being done to investigate the subPlanck structures in the Wigner functions of these PSCS. We also show that the photon subtraction causes the loss of sensitivity due to displacement of the states in phase space.

DOI
10.48550/arxiv.2411.07793

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We discuss the nonclassical properties of photon subtracted compass states (PSCS). Nonclassical behavior is studied using various parameters like the Wigner function, squeezing, and photon statistical parameters like Mandels Q function, secondorder correlation function, Agarwal Tara A3A_3A3​ criterion, and photon number distribution. Further analysis is being done to investigate the subPlanck structures in the Wigner functions of these PSCS. We also show that the photon subtraction causes the loss of sensitivity due to displacement of the states in phase space.
We investigate the nonclassical properties of the photon-added-then-subtracted coherent squeezed state(PASCSS) via the sub-Poissonian statistics,the photon-number distribution,and the negativity of the Wigner function.It is found that the PASSCS is a superposition state of D(β)S(ζ)|0>,D(β)S(ζ)|1>,and D(β)S(ζ)|2>.We find that the Mandel Q parameter,the photon-number distribution,and the negative volume of the Wigner function of the PASCSS are all periodic functions of the compound φ-θ/2 with a period π involved with squeezing and displacement parameters.
The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale $\ensuremath{\hbar}$, which are crucial in determining the sensitivity of these states to phase-space displacements. In the present work we introduce compasslike states that may have connection to the contemporary experiments, which are obtained by either adding photons to or subtracting photons from the superposition of two squeezed-vacuum states. We show that when a significant quantity of photons is added (or subtracted), the Wigner functions of these states are shown to have phase-space structures of an area that is substantially smaller than the Planck scale. In addition, these states exhibit sensitivity to displacements that is much higher than the standard quantum limit. Finally, we show that both the size of the sub-Planck structures and the sensitivity of our states are strongly influenced by the average photon number, with the photon-addition case having a higher average photon number leading to the smaller sub-Planck structures and, consequently, being more sensitive to displacement than the photon-subtraction case. Our states offer unprecedented resolution to the external perturbations, making them suitable for quantum sensing applications.
We investigate the nonclassical properties of the photon-added-then-subtracted coherent squeezed state (PASCSS) via the sub-Poissonian statistics, the photon-number distribution, and the negativity of the Wigner function. It is found that the PASCSS is a superposition state of D (β) S (ζ)|0〉, D (β) S (ζ)|1〉, and D (β) S (ζ)|2〉. We find that the Mandel Q parameter, the photon-number distribution, and the negative volume of the Wigner function of the PASCSS are all periodic functions of the compound φ − θ/2 with a period π involved with squeezing and displacement parameters.
We discuss nonclassical properties of single-photon subtracted squeezed vacuum states in terms of the sub-Poissonian statistics and the negativity of the Wigner function. We derive a compact expression for the Wigner function from which we find the region of phase space where Wigner function is negative. We find an upper bound on the squeezing parameter for the state to exhibit sub-Poissonian statistics. We then study the effect of decoherence on the single-photon subtracted squeezed states. We present results for two different models of decoherence, viz. amplitude decay model and the phase diffusion model. In each case we give analytical results for the time evolution of the state. We discuss the loss of nonclassicality as a result of decoherence. We show through the study of their phase-space properties how these states decay to vacuum due to the decay of photons. We show that phase damping leads to very slow decoherence, slower than the photon-number decay.
We introduce the photon-subtracted squeezed coherent state (PSSCS), which is theoretically constructed by repeatedly subtracting photons from the squeezed coherent state (SCS) with squeezing parameter r and displacement amplitude α=|α|eiφ. Employing the normal ordering form of density operator of the SCS, we study the nonclassicality of the PSSCS by analyzing Mandel’s Q-parameter, quadratures squeezing, photon-number distribution (PND), and Wigner function (WF). We find that the PND in a PSSCS is a periodic function of φ with a period π and exhibits more remarkable oscillations than that of a SCS in the case of strong squeezing. The partial negative region of the WF is sensitive to r and |α|. The fidelity between PSSCS and SCS is analyzed, which manifests that larger photon subtraction number may result in lower fidelity. By virtue of the thermal entangled state representation the decoherence of the PSSCS in thermal environment is studied through the time evolution of the WF. The negative volume of the WF gradually diminishes with the increase of evolution time and thermal photon number, respectively. The study of the PSSCS shows that generating new photon-number-controllable nonclassical states from a weak coherent light may be realized by subtracting suitable photons from a SCS.
Abstract Nonclassical properties of photon added and subtracted displaced Fock states are studied using various witnesses of lower‐ and higher‐order nonclassicality. Compact analytic expressions are obtained for the nonclassicality witnesses. Using those expressions, it is established that these states and the states that can be obtained as their limiting cases (except coherent states) are highly nonclassical as they show the existence of lower‐ and higher‐order antibunching and sub‐Poissonian photon statistics, in addition to the nonclassical features revealed through the Mandel parameter, zeros of Q function, Klyshko's criterion, and Agarwal–Tara criterion. Further, some comparison between the nonclassicality of photon added and subtracted displaced Fock states have been performed using witnesses of nonclassicality. This has established that between the two types of non‐Gaussianity inducing operations (i.e., photon addition and subtraction) used here, photon addition influences the nonclassical properties more strongly. Further, optical designs for the generation of photon added and subtracted displaced Fock states from squeezed vacuum state have also been proposed.