Nonlinear Interactions and Non-classical Light

Abstract

The term non-classical concerns light whose properties cannot be explained by classical electrodynamics and which requires invoking quantum principles to be understood. Its existence is a direct consequence of field quantization; its study is a source of our understanding of many quantum phenomena. Non-classical light also has properties that may be of technological significance. We start this chapter by discussing the definition of non-classical light and basic examples. Then some of the most prominent applications of non-classical light are reviewed. After that, as the principal part of our discourse, we review the most common sources of non-classical light. We will find them surprisingly diverse, including physical systems of various sizes and complexity, ranging from single atoms to optical crystals and to semiconductor lasers. Putting all these dissimilar optical devices in the common perspective we attempt to establish a trend in the field and to foresee the new cross-disciplinary approaches and techniques of generating non-classical light.

Appendix: Is Coherent Light Quantum?

Let us consider the following series of thought experiments. The toolbox we need contains a source of laser light, a beam splitter, two time resolving detectors of high bandwidth, and electronic equipment to analyze the detector signals. In the first experiment (1) measuring the intensity correlations after splitting the laser light with the beam splitter yields a $g^{(2)}(\tau )$ which is independent of time $\tau$. This can be described by a classical model, namely classical light fields without fluctuations—fine. Now the second experiment (2) is to measure the intensity of the laser light as a function of time. The result is a fluctuating detector signal (corresponding to the Poisson statistics of the photons in a quantum language). A classical model can also describe this. This time it is a model in which the classical electric fields fluctuate—this is also fine, but note that the models required are not compatible.

You may not be satisfied and argue that the fluctuation observed in experiment (2) may well come from the detectors themselves contributing noise. This would average out in experiment (1) because the noises introduced by the two detectors are of course not correlated. But suppose the lab next door happens to have amplitude squeezed light, with intensity fluctuations suppressed by 15 dB below the shot noise. Measuring the squeezed light intensity noise you convince yourself easily that the detector does not introduce enough noise to explain experiment (2). Note that this test should convince you even if you have no clue what the squeezed light is.

But you do not want to give up so easily and you say “what if a classically noisy light field enters the second input port, uncorrelated with the laser light but likewise modeled by classical stochastic fluctuations?”. And you are right, this more involved classical model would explain both experiments (1) and (2)—yet there is (3) a third experiment we can do. We can check the intensity of the light arriving at this second input port of the beam splitter and no matter how sensitive the intensity measuring detectors are they will detect no signal. But this is not compatible with a classical model: classical fluctuations always lead to measurable intensity noise.

We conclude by noting that obviously coherent states are non-classical because there is no single classical stochastic model which describes all possible experiments with laser light. But as we have seen it is tedious to go through these arguments, and no simple measure of non-classicality was found so far qualifying a coherent state as non-classical. Nevertheless, the non-classical nature of a coherent state is used in some quantum protocols.

It is interesting to note that there is a much different scenario in which experiments with coherent states cannot be described classically without field quantization, i.e. with semi classical theory. Coherent states lead e.g. to a revival of Rabi oscillations in their interaction with an atom in the Jaynes Cummings model. This effect can only be properly described when properly accounting for the quantization of the electromagnetic field [305, 306]. Thus the hypothesis is that for any pure quantum state it is always possible to find experimental scenarios, which can only be properly described using field quantization. Let us furthermore note that also thermal states, i.e. mixed quantum states, can still be somewhat nonclassical in nature if the classical excess noise is not too much larger than the underlying quantum uncertainty.