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Photon number states

A. M. Fox

Published Apr 27, 2006• 0 citations
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Abstract

Abstract In the previous three chapters we have studied several different ways in which the quantum states of light can be classified. In Chapter 5 we looked at the photon statistics and classified the light as being sub-Poissonian, Poissonian, or super-Poissonian. Then in Chapter 6 we studied the second-order correlation function, and classified the light as antibunched, coherent or bunched. Finally, in Chapter 7 we studied coherent states and several forms of squeezed light.

DOI
10.1093/oso/9780198566724.003.0008

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Abstract In the previous three chapters we have studied several different ways in which the quantum states of light can be classified. In Chapter 5 we looked at the photon statistics and classified the light as being sub-Poissonian, Poissonian, or super-Poissonian. Then in Chapter 6 we studied the second-order correlation function, and classified the light as antibunched, coherent or bunched. Finally, in Chapter 7 we studied coherent states and several forms of squeezed light.
Abstract The task of quantum optics is to study the consequences of considering a beam of light as a stream of photons rather than as a classical wave. It turns out that the differences are rather subtle, and we have to look quite hard to see significant departures from the predictions of the classical theories. In this chapter we shall approach the subject from the perspective of the statistical properties of the photon stream. We shall study the three different types of photon statistics that can occur, namely: Poissonian, super-Poissonian, and sub-Poissonian.
Abstract In the preceding two chapters we have explored the consequences of quantizing the energy of a light beam in terms of the number of photons. This enabled us to classify light according to either the photon statistics or the second-order correlation function. In this chapter we shall consider the effects of quantizing the electric and magnetic fields that comprise the light. We shall make use of our knowledge of the quantum harmonic oscillator, and adopt a predominantly intuitive approach, leaving the rigorous mathematics to the next chapter.
Canonical coherent states of a quantum harmonic oscillator have been generalized by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight function. Superpositions of these states are considered in the present scenario as a generalization of the optical Schrödinger cat states. The Fock space is assumed to be canonical or finite-dimensional. The photon number distribution of these generalized Schrödinger cat states departs from the Poisson statistics in various ways for high photon numbers. For small nonvanishing values of the label, the photon number distribution is sub-Poissonian (nonclassical) or super-Poissonian, according to the interference properties. In fact, the sub- or super-Poissonian statistics is determined by the interplay between the relative phase and a critical value of the phase. The photon number distribution is uniquely sub-Poissonian for large values of the label.
After developing the concept of displaced squeezed vacuum states in the nonunitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values † k a a in general form.Then we consider the displacement of the squeezed vacuum states and calculate their photon statistics and their quasiprobabilities.The expectation values of the displaced states are related to the expectation values of the undisplaced states and are calculated for some simplest cases which are sufficient to discuss their categorization as sub-Poissonian and super-Poissonian statistics.A large set of these states do not belong to sub-or to super-Poissonian states but are also not Poissonian states.We illustrate in examples their photon distributions.This shows that the notions of sub-and of super-Poissonian statistics and their use for the definition of nonclassicality of states are problematic.In Appendix A we present the most important relations for ( ) 1,1 SU treatment of squeezing and the disentanglement of their operators.Some initial members of sequences of expectation values for squeezed vacuum states are collected in Appendix E.
Abstract We report on a step-by-step-series of experiments from statistical optics with classical light to undergraduate quantum optics with single-photon states, particularly suitable to paving an introductory way to quantum phenomena. We build up a progressive process analysing temporal variations of the irradiance of light discerned by measuring the value of the non-delayed second-order correlation function g (2) ( τ = 0). We demonstrate how Poisson distributed photoelectron counts from constant irradiance ( g (2) (0) = 1) can be used to calibrate the apparatus. Measurements with harmonically modulated irradiance of Poissonian light give an introduction to g (2) (0) correlation analysis. After these introductory steps, we demonstrate photon bunching with (pseudo-) thermal light ( g (2) (0) ≈ 2), and finally show quantum antibunching of photons in Fock states ( g (2) (0) ≈ 0). All measurements are in excellent agreement with the theoretical predictions.