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Physical Review A

Laser-induced "two-atom" coherence

Munir Hasan Nayfeh, G. Barry Hillard

Published Apr 1, 1984• 5 citations
Publisher

Abstract

Our analysis shows that if an electromagnetic field excites a coherent superposition of states of two different types of atoms, then the results of a collision of those two atoms can be quite different from the usual dephasing that a coherently excited atom suffers upon collision with another atom. We present the concept of "two-atom" coherence as one feature of this interaction where the field of a given wavelength may interact with the system coherently over a wide range of internuclear distances.

DOI
10.1103/physreva.29.1907

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Our analysis shows that if an electromagnetic field excites a coherent superposition of states of two different types of atoms, then the results of a collision of those two atoms can be quite different from the usual dephasing that a coherently excited atom suffers upon collision with another atom. We present the concept of "two-atom" coherence as one feature of this interaction where the field of a given wavelength may interact with the system coherently over a wide range of internuclear distances.
A method for producing electronic-state coherences using either collisionally-aided radiative excitation (or "optical collision") or laser-induced collisional energy transfer (or "radiative collision") is proposed. Two atoms, AAA and ${A}^{\ensuremath{'}}$, collide in the presence of two pulsed-laser fields having frequencies $\ensuremath{\Omega}$ and ${\ensuremath{\Omega}}_{1}$. It is shown that by choosing ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ such that an energy-conserving transition can occur in the composite $A{A}^{\ensuremath{'}}$ system, one can create an electronic-state coherence in the AAA or ${A}^{\ensuremath{'}}$ atoms. The coherence can be produced between states of the same or of opposite parity; if it is between states of opposite parity, coherent emission at frequency ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ may be generated. The relationship of this work to theories of "pressure-induced extra resonances" in four-wave mixing is discussed.
In analogy to Glauber's analysis of optical coherence, we adopt an operational approach to introduce different classes of atomic coherence associated with different types of measurements. For the sake of concreteness we consider specifically fluorescence, nonresonant imaging, and ionization. We introduce definitions of coherence appropriate to them, which we call electronic, density, and field coherence, respectively. We illustrate these concepts in various descriptions of Bose-Einstein condensation, showing that each of these descriptions makes different implicit assumptions on the coherence of the system. We also study the impact of elastic collision on the field and density coherence properties of atom lasers.
The analysis of the phenomenon of refraction of electromagnetic waves at the interface between two media suggests that their velocity when passing from one medium to another changes. This chapter describes the basic principles of amplification and discusses the main features of wave propagation in amplifying media. Amplification occurs due to the induced coherent emission by excited atoms under the influence of the field of the electromagnetic wave. The chapter illustrates the attenuation of waves in an absorbing medium by using the Bouguer’s law. Bouguer’s law holds for a wide range of electromagnetic radiation—from radio waves to X-rays and gamma rays. The chapter discusses the main features of the different types of lasers such as solid-state lasers, gas lasers, dye lasers, and semiconductor lasers. It also includes some exercise problems related to the propagation of electromagnetic waves in amplifying media.
Recent studies of the decoherence induced by the quantum nature of the laser field driving a two-state atom [J. Gea-Banacloche, Phys. Rev. A 65, 022308 (2002); S. J. van Enk and H. J. Kimble, Quantum Inf. Comput. 2, 1 (2002)] have been questioned by Itano [W. M. Itano, Phys. Rev. A 68, 046301 (2003)] and the proposal made that all decoherence is due to spontaneous emission. We analyze the problem within the formalism of cascaded open quantum systems. Our conclusions agree with the Itano proposal. We show that the decoherence, nevertheless, may be divided into two parts---that due to forwards scattering and to scattering out of the laser mode. Previous authors attribute the former to the quantum nature of the laser field.
We show that an arbitrary system described by two dipole moments exhibits coherent superpositions of internal states that can be completely decoupled from the dissipative interactions (responsible for decoherence) and an external driving laser field. These superpositions, known as dark or trapping states, can be completely stable or can coherently interact with the remaining states. We examine the master equation describing the dissipative evolution of the system and identify conditions for population trapping and also classify processes that can transfer the population to these undriven and nondecaying states. It is shown that coherent transfers are possible only if the two systems are nonidentical, that is the transitions have different frequencies and/or decay rates. In particular, we find that the trapping conditions can involve both coherent and dissipative interactions, and depending on the energy level structure of the system, the population can be trapped in a linear superposition of two or more bare states, a dressed state corresponding to an eigenstate of the system plus external fields or, in some cases, in one of the excited states of the system. A comprehensive analysis is presented of the different processes that are responsible for population trapping, and we illustrate these ideas with three examples of two coupled systems: single V- and $\ensuremath{\Lambda}$-type three-level atoms and two nonidentical two-level atoms, which are known to exhibit dark states. We show that the effect of population trapping does not necessarily require decoupling of the antisymmetric superposition from the dissipative interactions. We also find that the vacuum-induced coherent coupling between the systems could be easily observed in $\ensuremath{\Lambda}$-type atoms. Our analysis of the population trapping in two nonidentical atoms shows that the atoms can be driven into a maximally entangled state which is completely decoupled from the dissipative interaction.