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Quantum Optics Journal of the European Optical Society Part B

Role of the higher optical Kerr nonlinearities in self-squeezing of light

R. Tanaś, S. Kielich

Published Feb 1, 1990• 19 citations
Publisher

Abstract

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.

DOI
10.1088/0954-8998/2/1/003

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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.
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The systematic theory of the formation of the short light pulses in the squeezed state during the propagation in a medium with inertial Kerr nonlinearity is developed. The algebra of time-dependent Bose-operators is elaborated and the normal-ordering theorem for them is formulated. It is established that the spectral region where the quadrature fluctuations are weaker than the shot-noise, depends on both the relaxation time of the nonlinearity and the magnitude of the nonlinear phase shift. It is also shown that the frequency at which suppression of the fluctuation is greatest can be controlled by adjusting the phase of the initial coherent light pulse. The spectral correlation function of photons is introduced and photon antibunching is found.
The standard process for the production of strongly squeezed states of light is degenerate optical parametric amplification (OPA) below threshold in nonlinear dielectric media such as LiNbO3 or periodically poled potassium titanyl phosphate (KTP). Here, we present a graphical description of squeezed-light generation via OPA, visualizing the interaction between the nonlinear dielectric polarization of the medium and the electromagnetic quantum field. We explicitly focus on the transfer from the field's ground state to a squeezed vacuum state and from a coherent state to a bright squeezed state by the medium's second-order nonlinearity, respectively. Our pictures illustrate the phase-dependent amplification and deamplification of quantum uncertainties and give the phase relations between all propagating electromagnetic fields as well as the internally induced dielectric polarizations. The graphical description can also be used to describe the generation of nonclassical states of light via higher-order effects of the nonlinear dielectric polarization such as four-wave mixing and the optical Kerr effect.
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.
Under the assumption of strong (classical) pump condition, the coherent light interacting with a medium of second-order nonlinearity gives rise to a model represented by a quadratic Hamiltonian. By exploiting this model, we obtain the squeezing and the higher-order squeezing of the input coherent light. These phenomena are found to depend on the classical intensity but do not depend on the number of photons present in the input coherent radiation field. For the same physical model, it is found that the photons are bunched in the input vacuum field provided that two-photon processes dominate over one-photon processes. Depending on the suitable choice of phases and interaction time, we show both photon bunching and photon antibunching phenomena for the vacuum field and for the field with a large number of photons as well. The results obtained in this paper are completely analytical in nature and provide a feeling for the physical situation in an explicit manner.