Nonclassical fields in a linear directional coupler

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Abstract
In the present paper, we discuss the photon statistics of nonclassical fields in a linear directional coupler. We study the photon distributions at the output ports of the coupler for number-state inputs, as well as for arbitrary-state inputs. In particular, we show that when a number state enters one port of the coupler and the vacuum enters the other port, an SU(2) coherent state is generated at the output ports. If the same number state enters both ports of the coupler, the probability of finding an odd number of photons at either of the output ports vanishes for a particular choice of the coupler length. We show that if a number state enters port 1 and a strong coherent field enters port 2, the coupler can serve as a generator of displaced number states (in fact, in this case the coupler behaves essentially as a homodyne detector). We show that the coupler is equivalent to an imperfect photon detector with efficiency governed by the coupler parameters. We study the effect of dissipative losses within the coupler as well as the effect of scattering coupling in the coupler. The latter leads to equalization of the energy in each guide. We show that in the presence of scattering coupling, the coupler behaves neither like an imperfect photon detector nor a homodyne detector.

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