Quantum Theory Of Light Propagation Research Articles

Quantum vacuum emission in a nonlinear optical medium illuminated by a strong laser pulse

A strong light pulse propagating in a nonlinear Kerr medium produces a change in the refractive index, which makes light travel at different speeds inside and outside the pulse. By tuning the pulse velocity, an analog black hole horizon can be obtained in a suitable frequency window. In this paper, we develop a quantum theory of light propagation for this system, including the frequency dispersion of the refractive index of the medium by coupling the electromagnetic field to matter polarization fields. In a configuration with a single black hole horizon, the spectrum of spontaneously emitted particles presents some similarities with Hawking radiation. Furthermore, even in horizonless systems spontaneous vacuum emission is still possible due to the dispersive nature of the medium, yet with dramatically different spectral properties.

Optical analog of population trapping in the continuum: Classical and quantum interference effects

A quantum theory of light propagation in two optical channel waveguides tunnelling-coupled to a common continuum of modes (such as those of a slab waveguide) is presented, and classical and quantum interference effects are investigated. For classical light, the photonic system realizes an optical analogue of coherent population trapping in the continuum encountered in atomic physics, where destructive interference between different light leakage channels leads to the appearance of a trapped state embedded in the continuum. For nonclassical light, two-photon interference effects are predicted, such as the tendency of photon pairs to bunch when decaying into the continuum.

Quantum gravitational optics

In quantum theory, the curved spacetime of Einstein's general theory of relativity acts as a dispersive optical medium for the propagation of light. Gravitational rainbows and birefringence replace the classical picture of light rays mapping out the null geodesics of curved spacetime. Even more remarkably, superluminal propagation becomes a real possibility, raising the question of whether it is possible to send signals into the past. In this article, we review recent developments in the quantum theory of light propagation in general relativity and discuss whether superluminal light is compatible with causality.

Canonical quantum theory of light propagation in amplifying media

We introduce a quantum theory for the propagation of light through a dielectric slab which acts as a linear amplifier. We show that the theory is canonical, and that self-consistency imposes a natural constraint on the round-trip gain provided by the medium.

Quantum theory of light propagation III. Counter-propagating waves

In order to reduce our general quantum description of light propagation to the standard one we use a method of introducing new variables of the counter-propagating waves (CPW variables). We discuss the effect of the dispersion for Stokes and anti-Stokes modes for chosen relations among some parameters. If we neglect the dispersion in this nonlinear process, no coupling to the wave going in the opposite direction giving rise to a nonlinear reflection of light can take place in this case. The photon space and time dependent modal annihilation and creation operators and the other corresponding quantities remain always dependent only on one of two new CPW variables. We can employ the approach of the standard propagation and relate space and time simply by the velocity of propagation.

Quantum theory of light propagation I. General theory

We present a particular approach to quantum theory of light propagation in nonlinear medium using space and time dependent modal operators. Spatial and temporal evolutions of this space and time dependent modal operators are given by the Heisenberg-like equation involving the momentum operator and Heisenberg equation, respectively, which can be justified from point of view of quantum electrodynamics. This useful concept can be applied to an arbitrary nonlinear interaction.

Quantum theory of light propagation II. Application to Raman scattering

We present the quantum theory of propagation in Raman scattering of a strong laser field using space and time dependent modal operators governed by the Heisenberg-like equation involving the momentum operator and Heisenberg equation. We adopt the quasidistribution related to anti-normal ordering of boson operators and the generalized superposition of the coherent field and quantum noise. We study the temporal and onedimensional spatial evolution of the photon and phonon statistics, the quadrature variances, as well as the mean integrated intensity of the fields, including the nonclassical ones.

Phase properties of light propagating in a Kerr medium: Stokes parameters versus Pegg-Barnett predictions.

The quantum theory of light propagation in a Kerr medium is applied to describe changes in the polarization state of light. A number of purely quantum effects arising during the propagation are analyzed. Stokes operators and Pegg-Barnett formalism are used to describe the evolution of the polarization ellipse. The predictions of these approaches are compared, showing some striking differences in the quantum regime of small photon numbers.

Dissipation and fluctuation due to foreign-atom collisions: A Langevin-type equation approach.

We present a formal quantum-mechanical treatment of the damping and fluctuations of a generic radiator atom due to collisions with foreign gas atoms. By working in the Heisenberg picture, the fluctuating noise sources are identified with the damping. Under the same approximations as the conventional line-shape broadening theory in the impact (Markov) approximation, the fluctuation-dissipation theorem is satisfied in the form of the conservation of an equal-time commutator for the atomic operators. The implications of this type of approach for the quantum theory of light propagation in an active medium is addressed. Simple cases for two-level and three-level \ensuremath{\Lambda}-type systems are given explicitly.

Quantum Fluctuations in the Stokes Parameters of Light Propagating in a Kerr Medium

Abstract The quantum theory of light propagation in a nonlinear Kerr medium is applied to calculate the Stokes parameters and their variances in the process of light propagation. Exact quantum formulae are derived for the expectation values of the Stokes operators and thus for the azimuth θ and ellipticity η of the beam. The role of quantum fluctuations in light polarization characteristics is discussed. The periodic behaviour of quantum evolution of the light polarization is revealed explicitly. It is shown that the degree of polarization is diminished at early stages of each period of the evolution but then reverts to its initial state of complete polarization at the end of the period. The variances of the Stokes parameters are also periodic and intensity-dependent; however, they never fall below their coherent state values.

Quantum theory of light propagation: Linear medium.

We have developed a quantum-mechanical formalism which permits the treatment of light propagation within the conceptual framework of quantum optics. The formalism rests on the calculation of the momentum operator for the radiation field, and yields directly a description for the spatial progression of the electromagnetic waves. In this paper we give a quantum-mechanical treatment for refraction and reflection by applying our formalism to propagation through a linear dielectric. The fidelity with which this formalism reproduces all results known from classical optics demonstrates its validity.

Quantum Theory of Light Propagation in Amplifying Media

Quantum Theory of Light Propagation in Amplifying Media

Quantum theory of light propagation in a fluctuating laser-active medium

The basic equations are derived which describe the propagation of an electromagnetic field in a fluctuating laser-active medium. The well-known methods of Langevinequations and master-equation for a few discrete modes are generalized to meet also the case of a radiation field with continuous spectrum. The medium is described by two-level atoms which are embedded in a merely passive solid matrix and homogeneously distributed over space. They have an inversion which is kept constant by an externally applied pump. The atomic line may be homogeneously or inhomogeneously broadened. We obtain a complete set of partial differential equations for the field operators with damping terms and fluctuating forces homogeneously distributed over the material. The telegraph equation with a fluctuating force occurs as a special case. After the exact elimination of the atomic variables we obtain a nonlinear field equation for the radiation field alone. By means of a pseudo-Hamiltonian and by a simple one-dimensional example we show that in a certain sense there exists a close formal analogy between the present theory and the theory of an interacting Bose gas. The characteristic differences between the two theories are also discussed. We find, that there occurs a phase transition of the radiation field because above a certain threshold of the pump the photons condense into a single mode and establish an “offdiagonal-long-range order”. The amplitude fluctuations and the phase fluctuations, which restore the broken phase symmetry, are calculated in detail. A new condition for the occurrence of undamped spiking (pulse formation) for a continuum of modes is derived.