Direct Space Quantum Optics: Light Propagation in a Nonlinear Medium

Izo I. Abram, E. Cohen

Starting with the canonical quantization procedure for the electromagnetic field inside an effective (linear or nonlinear) medium, we present a direct-space formulation of the theory of quantum optics. This approach does not use the conventional modal decomposition of the field, but relies on the electromagnetic momentum operator defined in terms of local electric- and magnetic-field operators. The momentum operator contains all the information on the spatial characteristics of the field, and can describe the translation of a short light pulse in a nonlinear medium, without a modal analysis of the pulse. Propagation is described through an operatorial wave equation that relates the temporal evolution of an electromagnetic pulse to its spatial progression. Through this equation, the direct-space approach to quantum optics can treat traveling-wave nonlinear-optical phenomena and, at the same time, account for their quantum statistics. The theory is applied to squeezed-light generation by the parametric down-conversion of a short laser pulse, as an illustration.

高志 近藤

L. Deng, Chengjie Zhu, E. W. Hagley +1 more

We discuss nonlinear optical processes in the presence of quantum gases. We show that, in contrast to a normal gas, where the medium ``passively'' participates in nonlinear optical processes, quantum gases ``actively'' interact with the wave mixing process by enforcing the properties arising from condensed matter physics on the generation and propagation of new light fields. This manifestation of condensed matter physics leads to intriguing suppression and enhancement effects in directional wave generation and propagation processes that have no counterpart in a normal gas. This opens a new chapter on light-matter-wave mixing and scattering: nonlinear optics with quantum gases.

Kazuhiko Misawa

Darrick E. Chang, Vladan Vuletić, Mikhail D. Lukin

Izo I. Abram

Classical optics describes quite successfully the propagation of laser light, both in free-space and inside a transparent medium. On the other hand, neither classical optics nor the conventional formulation of quantum optics can address adequately the propagation of nonclassical light. Nonclassical states of light are usually described by second-quantization operators acting onto the vacuum state of the radiation field, and the corresponding expectation values of the electric and magnetic fields are often zero. Clearly, the description of propagation of nonclassical light requires a direct quantum mechanical treatment of the spatial progression of the field operators. This chapter outlines the main features of propagative quantum optics, and examines more particularly the treatment of propagation through a linear (refractive) medium, and across a refractive interface. In order to facilitate the discussion of the physical ideas, a plane-wave propagation geometry, which greatly simplifies the mathematical treatment, is used.