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arXiv:quant-ph/0104119 · Solvay Conference on Physics

STIMULATED EMISSION WITH NON-EQUILIBRIUM STATE OF RADIATION

Luigi Accardi, Kentaro Imafuku, С. В. Козырев

Published Aug 1, 2003• 2 citations
arXivHTMLPDF

Abstract

The stimulated emission from an atom interacting with radiation in non-equilibrium state is considered. The stochastic limit, applied to the non-relativistic Hamiltonian describing the interaction, shows that the state of atoms, driven by some non-equilibrium state of the field approaches a stationary state which can continuously emit photon, unlike the case with an equilibrium state.

DOI
10.1142/9789812704634_0009

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The stimulated emission from an atom interacting with radiation in non-equilibrium state is considered. The stochastic limit, applied to the non-relativistic Hamiltonian describing the interaction, shows that the state of atoms, driven by some non-equilibrium state of the field approaches a stationary state which can continuously emit photon, unlike the case with an equilibrium state.
The stochastic limit of quantum theory suggests a new, constructive, approach to nonequilibrium phenomena. We illustrate this approach when considering the interaction of 3-level system with a quantum field in a nonequilibrium state. We describe a class of states of the quantum field for which a stationary state drives the system to an inversely populated state. We find that the quotient of the population of the energy levels in the simplest case is described by the double Einstein formula which involves products of two Einstein emission/absorption factors. Emission and absorption of radiation by 3-level atom in nonequilibrium stationary state is described.
Radiation can change the energy state of matter via three optical processes: spontaneous emission, absorption and stimulated emission. In spontaneous emission, an excited atomic or molecular state decays to a lower energy state with the emission of a photon of energy equal to the difference in the quantum state energies. Photon absorption is the reverse process, with a photon causing excitation from a lower to an excited quantum state. Stimulated emission was first proposed by Einstein in a paper published in 1917. He attempted to balance spontaneous emission and photon absorption, but could not get the correct balance without the postulated process of stimulated emission (see Section 4.2). With stimulated emission, an excited quantum state is stimulated to decay to a lower quantum state by an impinging photon. The existing photon survives with another identical photon being created (so that energy is conserved). The rates at which radiative transitions occur can be calculated using quantum mechanics. The time-dependent Schrodinger equation is used with the system wavefunction comprising time-varying linear combinations of the two wavefunctions for the lower and upper quantum states. In semi-classical treatments, an atom is treated quantum mechanically with the radiation field treated classically. There is a perturbation in energy associated with, say, the electric field of the radiation interacting with the electric dipole of the atom, though other interactions can be significant if the electric dipole interaction energy is small. In absorption, for example, a differential equation representing the change in ‘weighting’ of the wavefunction from the lower to upper state is obtained. A ‘time constant’ for the speed of change represents the rate of the radiative process. We examine the quantum mechanical nature of radiation absorption in Section 10.1 before discussing (Section 10.3) another important parameter arising with radiative transitions between discrete bound quantum states: the lineshape function. Quantum Theory of the Atom–Radiation Interaction An expression for the Einstein B-coefficient for photo-absorption is derived using quantum mechanics in this section. Einstein determined the detailed balance relationship between the rates of spontaneous emission, photo-absorption and stimulated emission when light interacts with an atom by considering an atomic system of two energy levels which are in equilibrium with a black-body radiation field. We use a semi-classical treatment where the atom is treated quantum mechanically and the radiation field is treated as a classical oscillating electric field.
We have considered the induced processes that occur in a driven two-level atom, where a laser photon is absorbed and emitted by the ground and by the excited states of the atom, respectively. In the low-intensity limit of the laser field, the induced spectra arising when a laser photon is absorbed by the ground state of the atom consist of two peaks describing induced-absorption and stimulated-emission processes, respectively, where the former prevails over the latter. Asymmetry of the spectral lines occurs at off-resonance and its extent depends on the detuning of the laser field. The physical, process where a laser photon is emitted by the excited state is the reverse of that arising from the absorption of a laser photon by the ground state of the atom. The former differs from the latter in that the emission of a laser photon by the excited state occurs in the low-frequency regime and that the stimulated-emission process prevails over that of the induced absorption. In this case, amplification of ultrashort pulses is likely to occur without the need of population inversion between the optical transitions. The computed spectra are graphically presented and discussed.
Using a tight binding approach, the Green's function for radiation fields ( R F ) in a resonator is calculated by considering that they are interacting with a vacuum field in an external environment outside the resonator. The general formulas for the rates of the spontaneous and stimulated emission from an atom in an excited state are given, of which the latter is evaluated for an initial state with only one photon. The emission rate is obtained for an arbitrary ratio between the wavelength of R F and the cavity length. The stimulated emission is also controllable by changing an initial one-photon state and an atomic position.