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Journal of Contemporary Physics (Armenian Academy of Sciences)

Refractive index of two-level gas in quantized field of counterpropagating waves

G. A. Muradyan, B. V. Balasanyan

Published Oct 27, 2008• 0 citations
Publisher

Abstract

An expression for the refractive index of a gas of two-level atoms in the quantized single-mode field of counterpropagating waves is calculated. It is shown that in the limit of large numbers of photons the result reproduces the quasiclassical result in only the case of standing wave where intensities of both waves are equal. Explanation of this “strange” situation where the abilities of quantum field theory turn to be more restricted than those of classical theory is given.

DOI
10.3103/s1068337208060042

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An expression for the refractive index of a gas of two-level atoms in the quantized single-mode field of counterpropagating waves is calculated. It is shown that in the limit of large numbers of photons the result reproduces the quasiclassical result in only the case of standing wave where intensities of both waves are equal. Explanation of this “strange” situation where the abilities of quantum field theory turn to be more restricted than those of classical theory is given.
This paper describes new theoretical results and calculations concerning the recently introduced index of refraction of a gas for atomic waves. More precisely, the motion of the atoms of the gas is taken into account and the equation describing the Doppler and Fizeau effects is introduced. The case where the atoms of the wave and the gas have spin 1/2 is also discussed and the rotatory power and circular dichroism of an optically pumped gas is calculated. Finally, the index of the rare gases for sodium waves is calculated. The results show how important it is to take into account glory scattering and Doppler averaging to make a meaningful comparison with experiments. The index appears to be very sensitive to the precise value of the quantum parameter B = 2μDeσ2 (in atomic unit). Using the available interaction potential curves, we obtained a reasonably good agreement between the measurements and the corresponding calculated values. However, some experimental results appear difficult to explain with the best available interaction potentials.
Coherent scattering of a two-level atom in the field of a quantized standing wave of a micromaser is considered under conditions of initial quantum correlation between the atom and the field. Such a correlation can be produced by a broadband parametric source. The interaction leading to scattering of the atom from the nonuniform field occurs in the dispersion limit or in the wing of the absorption line of the atom. Apart from the quantized field, the atom simultaneously interacts with two classical counterpropagating waves with different frequencies, which are acting in the plane perpendicular to the atom’s propagation velocity and to the wavevector of the standing wave. Joint action of the quantized field and two classical waves induces effective two-photon and Raman resonance interaction on the working transition. The effective Hamiltonian of the interaction is derived using the unitary transformation method developed for a moving atom. A strong effect is detected, which makes it possible to distinguish the correlated initial state of the atom and the field in the scattering of atom from the state of independent systems. For all three waves, scattering is not observed when systems with quantum correlation are prepared using a high-intensity parametric source. Conversely, when the atom interacts only with the nonuniform field of the standing wave, scattering is not observed in the case of the initial factorized state.
The propagation of quantum field interacting with a single two-level atom has been studied. Using the Gaussian quantum mode functions, we calculate evolution of the quantum state that includes atomic and field variable. We demonstrated the phase and group velocities of the single photon propagation that can be of great importance for long quantum communications. The results can be used for controlling quantum field propagation, and for design of optical elements such as a quantum prism and a quantum lens.
We investigate possible stationary states of a system consisting of a motionless atom in the resonant field of quantized isofrequency counterpropagating waves. Spontaneous relaxation is ignored. In the initial state (in the absence of an interaction), the photon subsystem has definite numbers of photons in each wave. We obtain analytic expressions for the energy spectrum and wave functions of this system. In particular, we show that the system can be in a stationary state only when the average numbers of photons in the counterpropagating waves are equal. We estimate the time it takes a system with an arbitrary initial number of photons in the counterpropagating waves to make a transition to a stationary state with equal numbers of photons in the waves.
Classically, the refractive index of a medium is due to a response on said medium from an electromagnetic field. It has been shown that a single two-level atom interacting with a single photon undergoes dispersion. The following extends that analyses to a three-level system interacting with two photons. Analysis of the system is completed both numerically for all photonic field modes, and analytically for an adiabatic solution of a single field mode. The findings are not only interesting for understanding additional physical phenomena due to the increased complexity of a three-level, two-photon system, but are also necessary for advancing applications such as quantum communications, quantum computation, and quantum information.
The refractive index of a system is often viewed as the collective response of a medium to an electromagnetic field. Nevertheless, even if targeted at a single atom, the incoming light undergoes the dispersion. By studying the propagation of a single photon interacting with a two-level atom, we examine the dispersion behavior, calculate the phase and group velocity of the photon wave packet, and further analyze the dispersion experienced by the photon. These findings are critical for advancing long-distance quantum communications.