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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Relative Particle Nature and Nonclassicality of Light

Sung-Guk Shin, Jaewoo Noh, Kisik Kim

Published Jan 1, 2007• 0 citations
Publisher

Abstract

We consider the n photon added pure state constructed from a certain reference state of light. It is shown that the realizable n photon added pure states can be obtained only when the coherent state is taken as the reference state. These n photon added pure states are then identical to the displaced number states and they are as nonclassical as the conventional number states according to the criterion based on the quasi-probability distributions. The maximum nonclassicality possessed by the n photon added pure states is discussed in terms of relative particle nature which is distinguished from the absolute particle character of the conventional number states.

DOI
10.1364/cqo.2007.cmi9

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We consider the n photon added pure state constructed from a certain reference state of light. It is shown that the realizable n photon added pure states can be obtained only when the coherent state is taken as the reference state. These n photon added pure states are then identical to the displaced number states and they are as nonclassical as the conventional number states according to the criterion based on the quasi-probability distributions. The maximum nonclassicality possessed by the n photon added pure states is discussed in terms of relative particle nature which is distinguished from the absolute particle character of the conventional number states.
“The word ‘classical’ means only one thing in science: it's wrong!” We have previously emphasized the fact that all states of light are quantum mechanical and are thus nonclassical, deriving some quantum features from the discreteness of the photons. Of course, in practice, the nonclassical features of light are difficult to observe. (We shall use “quantum mechanical” and “nonclassical” more or less interchangeably here.) Already we have discussed what must certainly be the most nonclassical of all nonclassical states of light – the single-photon state. Yet, as we shall see, it is possible to have nonclassical states involving a very large number of photons. But we need a criterion for nonclassicality. Recall that in Chapter 5 we discussed such a criterion in terms of the quasi-probability distribution known as the P function, P (α). States for which P (α) is positive everywhere or no more singular than a delta function, are classical whereas those for which P (α) is negative or more singular than a delta function are nonclassical. We have shown, in fact, that P (α) for a coherent state is a delta function, and Hillery has shown that all other pure states of the field will have functions P (α) that are negative in some regions of phase space and are more singular than a delta. It is evident that the variety of possible nonclassical states of the field is quite large.
By the use of nonclassical depth as a criterion for nonclassicality, we show that states generated by first adding (subtracting) multiphotons to an arbitrary state and then subtracting (adding) multiphotons from the resulting state is certainly nonclassical if the addition number of photons is equal to or larger than the subtraction number. The explicit expressions of nonclassical depth are found for both the single-photon-subtracted Gaussian state and the photon-added-then-subtracted thermal state. Based on the expressions, we show that the nonclassicality of the initial Gaussian state can be enhanced by the photon subtraction process. We also notice that the photon-added-then-subtracted thermal state is nonclassical if the initial thermal mean photon number is not zero, and the nonclassicality increases monotonously as the initial thermal mean photon number increases.
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.
In this paper, we construct the m-photon-added and m-photon-subtracted coherent states on a sphere. These states are shown to satisfy the usual conditions of continuity in the label, normalizability, and the resolution of identity. The preparation of the constructed states, as the states of the radiation field, is considered. We examine and analyze the nonclassical properties of these states, including the photon mean number, Mandel parameter, and quadrature squeezing. We find that these states are sub-Poissonian in nature, whereas the degree of squeezing is reduced (enhanced) by increasing m for the photon-added (photon-subtracted) coherent states on a sphere. The results also exhibit that the curvature of the sphere contributes to the enhancement of nonclassical behavior of the photon-added and photon-subtracted coherent states on the sphere.
We introduce marginal states of light which are barely classical and hence lie on the boundary between classical and nonclassical states. A marginal state may be obtained as an output of a beam splitter with vanishingly small transmission coefficient and a very intense nonclassical light as an input. We also point out that any marginal state can be made to be maximally nonclassical by adding a single photon. The close relation between nonclassicality and the particle nature of light is addressed.