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Optik

Analytical investigation on interactions among squeezed vacuum and coherent state, coherent vacuum and squeezed state, and among phase squeezed and amplitude squeezed states of light

Saibal Mitra, Sourangshu Mukhopadhyay

Published May 17, 2014• 1 citation
Publisher
DOI
10.1016/j.ijleo.2014.03.013

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The higher order moments and hence the amplitude-squared squeezing of input coherent light coupled to a quantum driven harmonic oscillator with time-dependent mass and frequency (DHTDMF) are investigated. Exact analytical expressions for the purpose of investigating the amplitude-squared squeezing of the input coherent light are exhibited. The squeezing in the normal sense of the input coherent light is independent of the driven term. On the other hand, the higher order (amplitude-squared) squeezing is sensitive to the driven term. In order to realize the flavour of the analytical approach, we give an interesting special case for the DHTDMF having ω(t) = ω(0) = ω, and driven term . It is found that the effects of the driven term are negligible if the oscillator is in the off-resonance situation. The condition of strong input coherent light also ensures the suppression of the effects of driven terms. By using a complete analytical method, we give an approximate analytical form of the relevant equations for investigating the amplitude-squared squeezed states. We carefully examine the special situations when the oscillator is underdamped, overdamped and critically damped (from both directions). The possibility of getting amplitude-squared squeezing of the input vacuum field is also discussed. To provide the feelings of the analytical results and hence the deep realizations of the physical system, we give a few results graphically. The realization of the present model in classical and in quantum mechanical pictures are clearly indicated.
Hofmann and Ono [Phys. Rev. A76, 031806, (2007)] showed that the mixing of coherent light and single-mode squeezed light at a beam splitter gives good approximation results in a superposition of path-entangled photon number states (so-called N00N states), which can be used for phase-shift measurements by coincident detections at the output of an interferometer. They showed that N00N states for arbitrary photon number N could be produced by this procedure. Afek et al. [Science328, 879 (2010)] have implemented the Hofmann–Ono proposal in the laboratory. In this paper, we show that, for a given coherent state amplitude and a given squeezing parameter, the mixing of coherent states and photon-subtracted squeezed vacuum states at the first beam splitter of an interferometer leads to improved phase-shift measurement sensitivity when using the photon-number detection technique on one of the output beams of the device. We also show that the phase-shift measurements will also be super-resolved to a greater degree than is possible by mixing coherent and squeezed vacuum light of the same field parameters.
We study the phase sensitivity of an SU(1,1) interferometer with two input beams in the displaced squeezed vacuum state and the coherent state, respectively. We find that there exists an optimal squeezing fraction of the displaced squeezed vacuum state that optimizes the phase sensitivity. We also examine the effects of some factors, including the loss, mean photon number of the input beams and amplitude gain of the optical parameter amplifiers, on the optimal squeezing fraction so that we can choose the optimal values to enhance the phase sensitivity.