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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Spontaneous-emission feedback in a three-level quantum system: A case of conflict between semi-classical and quantum theories of radiation

Guy Oliver, Osman Atabek

Published Mar 1, 1973• 1 citation
Publisher
DOI
10.1007/bf02738642

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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 investigated the spontaneous emission of a giant atom coupled with a semi-infinite waveguide. Our model considers the giant atom a two-level system coupled to the semi-infinite waveguide at two points. Based on the Hamiltonian in real space, the first-order delay-differential equation for the atomic excitation amplitude is obtained using the Schrödinger equation. Furthermore, the dynamics of spontaneous emission controlled by quantum coherent feedback due to the semi-infinite waveguide in the non-Markov regime are discussed in two cases, with the coupling strengths between the giant atom and the semi-infinite waveguide at the two coupling points being identical in one case and having a phase difference in the other case. The spontaneous emission exhibits partial decay due to multiple excitations from the quantum feedback and two-point coupling. When the coupling strengths are identical, the decay of the atomic excitation can be either increased or inhibited substantially, even forming a steady state, due to the self-interference due to the two-point coupling. The quantum coherent feedback can either further increase the decay of the excited state or maintain the steady state formed by self-interference. Moreover, a new steady state can be built due to quantum coherent feedback, which cannot exist in the self-interference system. The decay rates can also be increased or decreased by manipulating the phase difference between the coupling strengths at the two coupling points. It can destroy the steady state formed by self-interference or build a steady state based on the chosen phase difference. One can leverage quantum coherent feedback to manipulate the steady state value of the population of the excited states by adjusting the phase difference. The dissipation can increase the decay rates of the excited states. Furthermore, it also destroys steady states. Our results may find applications in developing quantum devices such as quantum memory based on giant atom-waveguide systems.
Semi-classical calculation of an oscillating dipole induced in a two-level atom indicates that spherical radiation from the dipole under coherent interaction, i.e., Rayleigh scattering, has a power level comparable to that of spontaneous emission resulting from an incoherent process. Whereas spontaneous emission is nearly isotropic and has random polarization generally, Rayleigh scattering is strongly anisotropic and polarized in association with incident light. In the case where Rabi frequency is much larger than frequency detuning and spontaneous emission rate, while the power of spontaneous emission varies with time at the Rabi frequency, the power of Rayleigh scattering oscillates at twice the Rabi frequency. Moreover, the radiation pressure force acting on an atom due to Rayleigh scattering exceeds that caused by spontaneous emission when frequency detuning is large.