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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Binomial mixed state reflected from a grey body

F Egbe, Kang Il Seo, Ching Tsung Lee

Published Dec 1, 1995• 1 citation
Publisher

Abstract

The photon-number distribution for the single-mode radiation, as the result of the number state reflected from a grey body, has been given by Bekenstein and Schiffer. This problem is extended to the case where the incident light is the binomial mixed state. The nonclassical effects of the reflected radiation are studied. The nonclassical depth is determined explicitly. As expected, the nonclassical depth of the state decreases as the absorptivity increases. The critical point in the transition from nonclassical state to classical one is located. It is shown that the state becomes the negative-binomial mixed state at this transition point.

DOI
10.1088/1355-5111/7/6/003

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The photon-number distribution for the single-mode radiation, as the result of the number state reflected from a grey body, has been given by Bekenstein and Schiffer. This problem is extended to the case where the incident light is the binomial mixed state. The nonclassical effects of the reflected radiation are studied. The nonclassical depth is determined explicitly. As expected, the nonclassical depth of the state decreases as the absorptivity increases. The critical point in the transition from nonclassical state to classical one is located. It is shown that the state becomes the negative-binomial mixed state at this transition point.
The photon-number distribution for the gray-body radiation given by Bekenstein and Schiffer [Phys. Rev. Lett. 72, 2512 (1994)] is used to study its nonclassical effects. It is shown that as the absorptivity varies from 0 to 1, the gray-body state changes from an extremely nonclassical state to an extremely classical one. The critical point of this transition is located. It is discovered that the negative binomial state is a special case of the gray-body radiation at the transition point; hence, it is an example of borderline states such as the coherent state. The explicit expressions for the factorial moments, the Q parameter, the P function, and the nonclassical depth of the gray-body state as functions of absorptivity and temperature are derived.
In the recent years, effect of photon addition and subtraction to a quantum state of light is explored for coherent state, thermal state, Schrödinger cat state, Gaussian state and many more. It is reported that the phenomena of photon addition or subtraction significantly affect nonclassical properties of the states of light. Here we wish to study the effect of photon addition and subtraction to the binomial start of radiation on the nonclassical properties of the state. We observed that the depth of nonclassicality increases with photon addition and decreases with photon subtraction in antibunching and squeezing phenomenon. We also report significant changes in photon number distribution and variable with depending parameters.
We introduce the binomial state of the quantized radiation field, which is a state that yields a binomial counting probability distribution. It reduces to the coherent state and to the number state in different limits. The binomal state is quantum mechanical in nature, and we show that it produces light that is antibunched, sub-poissonian, and squeezed for certain parameter ranges. A mixed binomial state is also defined. Particular attention is devoted to the mixed Bernoulli state which is an important special case. The properties of this mixed state indicate that squeezing might be present in individual atomic emissions.
Using the quantum theory of a lossless beam splitter, we determine the joint and marginal photon-number distributions at its output ports, for two arbitrary (not necessarily independent) input fields. The joint probability at the output of the beam splitter turns out to be a Fourier series in the relative phase between the output beams. Photomixing with the number states exhibits no phase sensitivity. An elementary example of phase sensitive dependence in the photon-number domain is obtained with the Bernoulli states, which are a subclass of the binomial states.1 For a joint input Bernoulli state, the probability of detecting one photon (or zero photons) at either output port varies sinusoidally with the relative phase. For independent Bernoulli states incident on the beam splitter, the results differ and depend on whether the input is in a pure or mixed state. Photomixing of other nonclassical states exhibit higher orders of phase-induced modulation of the output photon-number probabilities.