On the Phase-Space Approach to Squeezed Phenomena in Quantum Optics
It is well known that a phase-space description of optical effects associated with the coherent states of the annihilation boson operator: a∣α〉 = α∣α〉 offers a very powerful tool in many quantum optics applications. However, many effects like, for example, reduced quantum fluctuations, squeezed states, optical homodyne and heterodyne detection of light generated by nonlinear optical devices are closely connected with two-photon physics, where the conventional approach based on single-mode boson operators is not very useful. It has been shown1 that this kind of two-photon physics is related to the SU(1,1) Lie group which form a natural generalization of the Heisenberg-Weyl group for the case of two photon effects. Because of this we shall present here a new phase-space approach to the problem of reduced quantum fluctuations and squeezed states, entirely based on the SU(1,1) geometry.
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