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Optica Acta International Journal of Optics

On the Possibility of Almost Complete Self-squeezing of Strong Electromagnetic Fields

R. Tanaś, S. Kielich

Published Jan 1, 1984• 33 citations
Publisher

Abstract

The propagation of quantized electromagnetic fields through optically isotropic media with cubic optical nonlinearity is considered. Analytical solutions are presented in closed form showing that the light field can emerge from the medium in a squeezed quantum state. A detailed numerical analysis of the results is performed and presented graphically. Over 90 per cent of the squeezing permitted by quantum-mechanical theory is achieved in this way. The dependence of the squeezing effect on the polarization state of the field and the nonlinear molecular parameters is also discussed.

DOI
10.1080/713821396

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The propagation of quantized electromagnetic fields through optically isotropic media with cubic optical nonlinearity is considered. Analytical solutions are presented in closed form showing that the light field can emerge from the medium in a squeezed quantum state. A detailed numerical analysis of the results is performed and presented graphically. Over 90 per cent of the squeezing permitted by quantum-mechanical theory is achieved in this way. The dependence of the squeezing effect on the polarization state of the field and the nonlinear molecular parameters is also discussed.
In this chapter we review a number of quantum features of optical fields associated with propagation of intense light through nonlinear, isotropic media. We begin with the classical description of field propagation, introducing the nonlinear polarization of the medium which enters as the source term into the approximate field equations obtained from the Maxwell equations in the slowly varying amplitude approximation. This establishes the classical background for further quantum considerations. Next, we quantize the field and construct the effective Hamiltonian from which we get equations of motion for the quantum fields. We discuss a number of quantum effects such as photon antibunching, squeezing, the formation of Schrodinger cats and kittens, changes in field polarization due to the quantum nature of the field, as well as the quantum description of the field phase. The characteristic feature of quantum evolution — the periodicity — is strongly affected by dissipation. We give exact analytical formulae describing the quantum evolution of the field, including dissipation. We have collected results illustrating various aspects of quantum evolution and we believe that this review, although far from complete, will be a useful source of information on the subject.
The part played by higher-order optical nonlinearities in self-squeezing of intense light propagating in a nonlinear Kerr medium is discussed. An analytical formula for the normally ordered variances of the field is derived under the assumption that the nonlinearity parameters of the medium are small and the number of photons is very great. The saddle-point approach is used to evaluate the sums over large numbers of photons. The analytical formula is illustrated graphically for several sets of nonlinearity coefficients. It is shown that, for large numbers of photons, the higher-order contributions are substantial and can modify the magnitude of squeezing as well as the range of the parameters over which squeezing can be observed.
It is shown that generation of quadrature-squeezed states of a vector electromagnetic field in which quantum fluctuations in one of the quadrature components are smaller than in the coherent state can occur in cubically nonlinear media (birefringent fibers) with efficient energy transfer between the polarization modes of the field. It is shown that for certain distributions of the initial total power between modes, light with suppressed quantum fluctuations in both polarization modes of the vector field is formed at the fiber exit. The optimal conditions for obtaining quadrature-squeezed light are determined. New analytical expressions are obtained for the degree of squeezing in the two polarization modes in the case when there is no energy transfer between the polarization components of the field propagating in the fiber (eigenmodes of two-wave mixing).
We consider quantum-mechanically partially polarized light propagating through a Kerr-like medium. Using the usual form of the induced polarization P=A(E\ensuremath{\cdot}E∗{\mathrm{E}}^{\mathrm{*}}E∗)E+B(E\ensuremath{\cdot}E)E∗{\mathrm{E})\mathrm{E}}^{\mathrm{*}}E)E∗, the theory is formulated in terms of an effective Hamiltonian which is quartic in terms of the operators for two orthogonally polarized modes. Exact solutions in closed form for the Heisenberg equations of motion are obtained. These solutions are used to evaluate the physical behavior of various observables as the field propagates through a nonlinear medium. We also present explicit results for the time evolution of the input coherent and Fock states of the field. We show the generation of states that are macroscopic superposition of coherent states. We also find that if the input field is completely polarized, then due to quantum effects the output field becomes partially polarized. This is in contrast to the classical prediction and can have an important bearing on questions like topological phases of light propagating through a nonlinear medium. Numerical results for the energy in each mode, the correlation between two modes, and the higher-order correlations are presented. The input photon statistics is found to make a considerable difference in the dynamics.
A brief review of theoretical studies of the quantum state of polarization of light exhibiting the level of fluctuations in at least one of the Stokes parameters which is below the quantum noise limit is presented. Two approaches to generation of polarization-squeezed state of light are analyzed in detail: by propagating coherent radiation in a cubic nonlinear medium and by mixing radiation of two orthogonally polarized quadrature-squeezed modes. The degree of polarization of light is discussed. Other areas of quantum polarization optics, in particular, entanglement of quantum Stokes parameters and quantum polarization tomography, are also discussed.