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Journal of the Korean Physical Society

Variation of nonclassical states of light

Kisik Kim

Published Jan 1, 2018• 1 citation
Publisher

Abstract

We consider a beam splitter as an optical device to generate a class of nonclassical states out of a nonclassical input state. On sending a nonclassical light toward one input port and the vacuum to the other, one can generally obtain the two output lights which are less nonclassical than the input state. We also consider the limit, in which the input intensity grows indefinitely and the trasmission coefficient vanishes such that their product becomes finite, to find various states of light lying between nonclassical and classical states.

DOI
10.3938/jkps.72.192

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We consider a beam splitter as an optical device to generate a class of nonclassical states out of a nonclassical input state. On sending a nonclassical light toward one input port and the vacuum to the other, one can generally obtain the two output lights which are less nonclassical than the input state. We also consider the limit, in which the input intensity grows indefinitely and the trasmission coefficient vanishes such that their product becomes finite, to find various states of light lying between nonclassical and classical states.
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.
Abstract Beam splitters are routinely used for generating entanglement. Their entangling properties have been studied extensively, with nonclassicality of the input states a prerequisite for entanglement at the output. Here we quantify the amount of entanglement generated by weakly-reflecting beam splitters, and look for nonclassical states that are not entangled by general beam splitters. We extend the known class of results to mixed and non-Gaussian states, finding that inputting highly nonclassical combinations of unpolarized states that are squeezed and displaced onto a beam splitter can still yield separable output states. This is important in light of the challenge of characterizing mixed state entanglement. We further identify a parallel between SU(2) unpolarized states and the two-mode vacuum. Our result is crucial for understanding the generation of modal entanglement by beam splitters.
A beam splitter is a simple, readily available device which can act to entangle output optical fields. We show that a necessary condition for the fields at the output of the beam splitter to be entangled is that the pure input states exhibit nonclassical behavior. We generalize this proof for arbitrary (pure or impure) Gaussian input states. Specifically, nonclassicality of the input Gaussian fields is a necessary condition for entanglement of the field modes with the help of a beam splitter. We conjecture that this is a general property of beam splitters: Nonclassicality of the inputs is a necessary condition for entangling fields in a beam splitter.
The second-order coherence of optical fields at output ports of a beam splitter is investigated. The properties of the second-order coherence are not only strongly dependent on the input states but also quite involved with the nature of the beam splitter. When parameters of both the input states and the beam splitter are chosen appropriately, the fields at the output ports will exhibit quantum behaviour. Between the two output modes, there stands mode–mode correlation which can even be anticorrelation. Some nonclassical properties, such as the photon antibunching effect of the input fields, may be destroyed by the beam splitter.
From the explicit form of the probability amplitude for two cascade-placed beam splitters (with one squeezed state input and two coherent state inputs), we calculated the probability amplitude of the output beam as a function of the transmittance of the two beam splitters and the amplitude and the relative phase of the three input states. At a certain condition, the output beam had no vacuum and was in a highly nonclassical state that contained more than one photon. Armed with explicit probability amplitude for two beam splitters and two coherent states, the squeezed vacuum state might be a very useful tool for generating highly nonclassical light.