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Physics Letters A

Squeezing in higher order nonlinear optical processes

Mark S. Hillery, Muhammad Suhail Zubairy, K. Wódkiewicz

Published Jul 1, 1984• 24 citations
Publisher
DOI
10.1016/0375-9601(84)90120-8

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Squeezing of the electromagnetic field is a purely quantum mechanical phenomenon and this quantum effect is expected to manifest itself in optical processes in which the nonlinear response of the system to the radiation field plays an important role. It has generated a great deal of interest in view of the possibility of reducing the noise of an optical signal below the vacuum limit i.e. zero-point oscillations. In this paper the concept of nth-order amplitude squeezing is introduced in the fundamental mode in four- and six-wave mixing processes as a generalization of the higher-order squeezing under short-time approximation based on a fully quantum mechanical approach. It established the coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators. The condition for occurrence of nth-order squeezing is obtained from which higher-order squeezing upto n=3 are studied. Dependence of squeezing on photon number is also established. The conditions for obtaining maximum and minimum squeezing are obtained. The method of present investigation can be applied to any higher-order non-linear optical processes and the technique can also be extended for studying squeezing in any N-photon process in general. Further, nth-order squeezing of radiation in N-photon process can also be investigated. The results obtained may help in selecting a suitable process to generate optimum squeezing in the radiation field.

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Interaction of squeezed states with nonlinear optical systems

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The concept of squeezing, which generally implies that one quadrature component of an optical field has measured fluctuations below the vacuum limit, is generalized to higher moments of even order. Higher-order squeezing is encountered in many of the nonlinear processes that generate second-order squeezing. It is shown that the field produced in degenerate parametric downconversion is squeezed to all even orders and is intrinsically squeezed to orders 2,6,10…. Higher-order squeezing also shows up in second harmonic generation and in resonance fluorescence from an atom. However, in those cases there is no intrinsic squeezing beyond the second order, although a strong second-order squeezing effect is manifest in the higher-order moments of the field.
Squeezing of radiation is a purely quantum mechanical phenomenon which has no classical counterpart. This quantum effect is expected to manifest itself in optical processes in which the nonlinear response of the system to the radiation field plays an important role. The concept of squeezing started in mid 1980s. Since then there has been an enormous upsurge of interest in this field owing to its low noise property. In the present paper various aspects of squeezing of radiation are studied and possible means of generation of squeezed light in which the quantum fluctuations are reduced below shot noise limit are investigated. The amplitude of the electric field of a mode of an electromagnetic field is always associated with quantum mechanical fluctuations. Squeezing states are characterised by reduced quantum fluctuations in one quadrature component of the field at the expense of increased fluctuations in the other noncommuting component. A fully quantum mechanical approach is followed. In the present paper we intend to review different aspects of squeezing and higher order squeezing in higher order Raman processes as well as in multiwave mixing processes. A comparative study between different processes are made which will pave a way for easier generation of squeezed light.
Squeezing of the electromagnetic field is a purely quantum mechanical phenomenon and this quantum effect is expected to manifest itself in optical processes in which the nonlinear response of the system to the radiation field plays an important role. It has generated a great deal of interest in view of the possibility of reducing the noise of an optical signal below the vacuum limit i.e. zero-point oscillations. In this paper the concept of nth-order amplitude squeezing is introduced in the fundamental mode in four- and six-wave mixing processes as a generalization of the higher-order squeezing under short-time approximation based on a fully quantum mechanical approach. It established the coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators. The condition for occurrence of nth-order squeezing is obtained from which higher-order squeezing upto n=3 are studied. Dependence of squeezing on photon number is also established. The conditions for obtaining maximum and minimum squeezing are obtained. The method of present investigation can be applied to any higher-order non-linear optical processes and the technique can also be extended for studying squeezing in any N-photon process in general. Further, nth-order squeezing of radiation in N-photon process can also be investigated. The results obtained may help in selecting a suitable process to generate optimum squeezing in the radiation field.