An alternative to the quantization of electro-optic feedback
Vlasta Peřinová, A. Lukš, J. Křepelka · Physica Scripta · 2012
A simple feedback system may be based on a beam splitter, a homodyne detection and a modulator. A single-mode treatment leads to violations of the commutation relations for an in-loop mode of the system. The lowering of noise of one quadrature has been labelled 'squashing'. Violations of the commutation relations do not occur when one does not replace the c-number parameter of displacement in the modulator with an operator, even though the latter should be directly proportional to a quadrature measurement behind the beam splitter. This outcome is not a quantum-mechanical expectation value, but a random variable. In this framework, we analyse this system and another one, where the beam-splitter transmittance is modulated through a feedback loop. To predict the squeezing of a quadrature, it is necessary to realize a consistent quantization of the feedback circuit.