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The European Physical Journal D

Quantum-jump approach to dipole dephasing: Application to inversionless amplification

J. Mompart, R. Corbalán

Published Jan 1, 1999• 3 citations
Publisher

Abstract

We present a model for simulating atomic dipole dephasing within the Monte-Carlo wave function formalism which leads to the same results as the standard density-matrix formalism. In this model dipole dephasing processes are accounted by quantum-jumps into one of the atomic energy eigenstates. This fact allows us to obtain analytical expressions for the effects of elastic collisions on the various physical processes responsible for amplification without population inversion in a cascade three-level atomic configuration.

DOI
10.1007/pl00021600

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We present a model for simulating atomic dipole dephasing within the Monte-Carlo wave function formalism which leads to the same results as the standard density-matrix formalism. In this model dipole dephasing processes are accounted by quantum-jumps into one of the atomic energy eigenstates. This fact allows us to obtain analytical expressions for the effects of elastic collisions on the various physical processes responsible for amplification without population inversion in a cascade three-level atomic configuration.
Several recent studies have shown that the time evolution of an atom submitted to coherent laser fields and to dissipative processes, such as spontaneous emission of photons or excitation by a broadband incoherent field, can be considered to consist of a sequence of coherent evolution periods separated by quantum jumps occurring at random times. A general statistical analysis of this random sequence is presented for the case in which the number of relevant atomic states is finite and the delay functions giving the distribution of the time intervals between two successive jumps can easily be calculated. These general considerations are then applied to a simple model recently proposed for demonstrating the possibility of amplification without inversion of populations. We show how the quantum-jump approach allows one to calculate the respective contributions of the various physical processes responsible for the amplification or the attenuation of the probe field and to get new insights into the relevant physical mechanisms.
We review amplification and lasing without inversion (AWI and LWI) in homogeneously broadened closed three-level systems in the framework of both density-matrix and quantum- jump formalisms. With the density-matrix formalism: (1) we study the nature of quantum interference in these systems; (2) determine analytically the conditions for AWI and locate the position of maxima and minima in the probe absorption spectrum; and (3) study various regimes of lasing, namely, continuous wave, self-pulsing and giant pulse lasing. Within the quantum-jump formalism we calculate the relative probabilities of the various physical processes responsible for probe field amplification and absorption.
We review amplification and lasing without inversion (AWI and LWI) in homogeneously broadened closed three-level systems in the framework of both density-matrix and quantum- jump formalisms. With the density-matrix formalism: (1) we study the nature of quantum interference in these systems; (2) determine analytically the conditions for AWI and locate the position of maxima and minima in the probe absorption spectrum; and (3) study various regimes of lasing, namely, continuous wave, self-pulsing and giant pulse lasing. Within the quantum-jump formalism we calculate the relative probabilities of the various physical processes responsible for probe field amplification and absorption.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
In this chapter a quantum mechanical treatment of atomic response to the fields of an electromagnetic wave is presented. Absorption and emission of energy by atoms involves transition between their quantized energy levels driven by an interaction Hamiltonian. Schrodinger equation is used to derive the equations of motion for the density matrix of the atom, which is better suited to include the effects of mechanisms other than the interaction Hamiltonian – collisions, level decays, level shifts, etc. that also affect the state of the atom. Using the density matrix equation of motion and focusing on two atomic levels, induced dipole moment for a single two-level atom and polarization and susceptibility for a collection of two-level atoms, including the effects of level decays, and collisions, are calculated. Equations of motion for level populations are also derived. These expressions naturally predict stimulated emission as well as absorption. Expressed in terms of spontaneous emission rate they confirm the validity of equations derived in Chapter 5 using the dipole oscillator model of atomic response. The limit in which quantum mechanical equations for atomic response reduce to the classical dipole oscillator equations is also discussed.
This thesis is concerned with the amplification of coherent radiation from an active medium under conditions which require no population inversion between the energy levels. Gain without population inversion may be obtained by creating a sufficiently strong correlation between pairs of atomic states, usually with the help of external sources of resonant electromagnetic radiation. Our main objective is to investigate two possible selections for the active medium: a three level atom in a lambda configuration and a Raman-driven four level model. For both we identify the conditions that lead to inversionless laser action, we calculate the small signal gain and investigate the physical mechanisms which are responsible for the emergence of gain. While the ultimate cause of the gain is quantum interference, we propose attractive alternative pictures based on the dressed states of the coupled atom-driving field systems. We address the important practical issue of the effect of atomic motion and related Doppler broadening on the inversionless gain profile and we also analyze the transient response of each laser model with the help of the appropriate Maxwell-Bloch equations. Finally we develop a fully quantum mechanical description of the lambda model and find that the radiated field can display unique quantum features which manifest themselves with sub-Poissonian photon fluctuations.