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Journal of Physics B Atomic Molecular and Optical Physics

Second-order coherence of light fields with a beam splitter

Jin Xiong, Nanrun Zhou, Guihua Zeng

Published Nov 21, 2005• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/38/23/011

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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.
The familiar input-output relations for an optical beam splitter are generalized to allow for linear absorption by the medium forming the mirror. Beam-splitter losses generally affect the noise levels detectable in experiments involving nonclassical light. When employed to investigate two-photon interference effects, a lossy beam splitter can lead to apparent nonlinear absorption, which, in the most extreme case, leads to either both or neither of the photons being absorbed. The degree of second-order coherence of antibunched light can be maintained on transmission through the beam splitter but any amplitude squeezing in the incident light is degraded.
The Copenhagen interpretation, in which the core concepts are Heisenberg's uncertainty principle and nonlocal EPR correlation, has been long discussed. Second-order anticorrelation in a beam splitter represents the origin of these phenomena and cannot be achieved classically. Here, the anticorrelation of nonclassicality in a beam splitter is interpreted using the concept of coherence. Unlike the common understanding of photons having a particle nature, anticorrelation is rooted in the wave nature of coherence optics, described by coherence optics, wherein quantum superposition between two input fields plays a key role. This interpretation may pose fundamental questions about the nature of nonclassicality and pave a road to coherence-based quantum information.
We investigate the photon statistics at the outputs of a four-port beam splitter, when a strong coherent field is incident on one input port and various other fields enter at the second inner port. Some non-classical interference effects are encountered. In particular, there is a large difference between the cases when a one photon field enters at input port 2 and when a field in a coherent state with an average of one photon enters at port 2. In the former case the probability P(m) of the difference m between the detected photons at output ports 3 and 4 has a minimum at m = 0 whenever the quantum efficiency exceeds one third. As the quantum efficiency falls from one to zero, the form of the probability distribution P(m/1) changes drastically.
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.