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Journal of the Korean Physical Society

Adding a single photon to a coherent state

Seokhyun Jang, Kisik Kim

Published Apr 1, 2014• 2 citations
Publisher

Abstract

We investigate the connection between the particle nature of light and its nonclassical character. When we can associate a precise number of photons, in some sense, to a particular state of light, the state possesses a full particle nature. We show that whenever a complete particle nature emerges in the state of light, the corresponding nonclassical measure becomes unity, and the state becomes maximally nonclassical.

DOI
10.3938/jkps.64.1230

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We investigate the connection between the particle nature of light and its nonclassical character. When we can associate a precise number of photons, in some sense, to a particular state of light, the state possesses a full particle nature. We show that whenever a complete particle nature emerges in the state of light, the corresponding nonclassical measure becomes unity, and the state becomes maximally nonclassical.
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.
When a single quantum of electromagnetic field excitation is added to the same spatiotemporal mode of a coherent state, a new field state is generated that exhibits intermediate properties between those of the two parents. Such a single-photon-added coherent state is obtained by the action of the photon creation operator on a coherent state and can thus be regarded as the result of the most elementary excitation process of a classical light field. Here we present and describe in depth the experimental realization of such states and their complete analysis by means of a novel ultrafast, time-domain, quantum homodyne tomography technique clearly revealing their nonclassical character.
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.
Single-photon-added coherent states are the result of the most elementary amplification process of classical light fields by a single quantum of excitation. Being intermediate between a single-photon Fock state (fully quantum-mechanical) and a coherent (classical) one, these states offer the opportunity to closely follow the smooth transition between the particle-like and the wavelike behavior of light. We report the experimental generation of single-photon-added coherent states and their complete characterization by quantum tomography. Besides visualizing the evolution of the quantum-to-classical transition, these states allow one to witness the gradual change from the spontaneous to the stimulated regimes of light emission.
“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.