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arXiv:1903.11664 · Physical Review A

Quantum-induced birefringence in nonlinear optical materials

V. A. De Lorenci, Lawrence H. Ford

Published Jul 12, 2019• 0 citations
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Abstract

The influence of quantum fluctuations of the electromagnetic field on the propagation of a polarized light wave in a nonlinear dielectric is investigated. It is shown that in some cases the fluctuations couple to the optical nonlinearities of the medium and make its refractive index dependent on the polarization of the propagating wave. As a consequence, two light waves propagating in the same direction but with different polarizations will have different speeds, so there will be a Kerr-effect birefringence induced by quantum fluctuations. We consider the case of the electromagnetic field in a squeezed vacuum state, where there are regions where the mean squared electric field can be negative and the birefringence effect has the opposite sign to the Kerr effect in classical physics. We give some estimates for the magnitude of these effects, and discuss their possible observability.

DOI
10.1103/physreva.100.013819

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The influence of quantum fluctuations of the electromagnetic field on the propagation of a polarized light wave in a nonlinear dielectric is investigated. It is shown that in some cases the fluctuations couple to the optical nonlinearities of the medium and make its refractive index dependent on the polarization of the propagating wave. As a consequence, two light waves propagating in the same direction but with different polarizations will have different speeds, so there will be a Kerr-effect birefringence induced by quantum fluctuations. We consider the case of the electromagnetic field in a squeezed vacuum state, where there are regions where the mean squared electric field can be negative and the birefringence effect has the opposite sign to the Kerr effect in classical physics. We give some estimates for the magnitude of these effects, and discuss their possible observability.
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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.
The standard process for the production of strongly squeezed states of light is optical parametric amplification (OPA) below threshold in dielectric media such as LiNbO3 or periodically poled KTP. Here, we present a graphical description of squeezed light generation via OPA. It visualizes 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 secondorder nonlinearity, respectively. Our pictures visualize the phase dependent amplification and deamplification of quantum uncertainties and give the phase relations between all propagating electro-magnetic 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 higherorder effects of the non-linear dielectric polarization such as four-wave mixing and the optical Kerr effect.
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In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.