Spontaneous Emission of an Atom Near an Oscillating Mirror

Abstract

We investigate the spontaneous emission of one atom placed near an oscillating reflecting plate. We consider the atom modeled as a two-level system, interacting with the quantum electromagnetic field in the vacuum state, in the presence of the oscillating mirror. We suppose that the plate oscillates adiabatically, so that the time-dependence of the interaction Hamiltonian is entirely enclosed in the time-dependent mode functions, satisfying the boundary conditions at the plate surface, at any given time. Using time-dependent perturbation theory, we evaluate the transition rate to the ground-state of the atom, and show that it depends on the time-dependent atom-plate distance. We also show that the presence of the oscillating mirror significantly affects the physical features of the spontaneous emission of the atom, in particular the spectrum of the emitted radiation. Specifically, we find the appearance of two symmetric lateral peaks in the spectrum, not present in the case of a static mirror, due to the modulated environment. The two lateral peaks are separated from the central peak by the modulation frequency, and we discuss the possibility to observe them with actual experimental techniques of dynamical mirrors and atomic trapping. Our results indicate that a dynamical (i.e. time-modulated) environment can give new possibilities to control and manipulate also other radiative processes of two or more atoms or molecules nearby, for example their cooperative decay or the resonant energy transfer. I. INTRODUCTIONRecent advances in quantum optics techniques and atomic physics have opened new perspectives for cavity quantum electrodynamics and solid state physics, making possible engineering systems with a tunable atom-photon coupling. Nowadays, the possibility to tailor and control radiative processes through suitable environments is of crucial importance in many different areas, ranging from condensed matter physics to quantum optics and quantum information theory [1,2].One of the most fundamental quantum processes is the spontaneous emission of radiation by atoms [3]. Purcell in 1946 first suggested that spontaneous emission is not an unvarying property of the atoms, but it can be controlled (enhanced or inhibited) through the environment [4]. Physical properties of spontaneously emitted radiation depend strongly on the environment where the atom is placed: modifying the photon density of states and vacuum field fluctuations allows to change the spontaneous emission rate [5,6]. Many physical systems have been explored in the literature to investigate this important process. These include, for example, atoms in cavities or waveguides [5,[7][8][9][10], quantum dots in photonic crystals or in a medium with a photonic band gap [11][12][13], and quantum emitters in metamaterials [14]. Spontaneous decay of excited atoms in the presence of a driving laser field has been also investigated [15]. Many experiments showing modifications of spontaneous emission of atoms in external environments (a single mirror, optical cavit...

Fifty Years of the Dynamical Casimir Effect

“…A possibility of exciting the Rydberg atoms passing near the boundary with oscillating parameters ("oscillating effective mirror") was studied in [419]. The influence of the oscillating boundary on the spontaneous emission rate of an atom placed nearby this boundary was considered in [420,421]. The influence of the DCE on the fidelity of the quantum state transfer between two qubits in the ultrastrong coupling regime was studied in [405].…”

Motion induced excitation and radiation from an atom facing a mirror

“…It is worth to remark that in both situations (parallel o perpendicular motions), if the atom's center of mass oscillates harmonically with a frequency Ω cm < Ω, the spectrum of the emitted photons will have three different frequencies ω = Ω, Ω ± Ω cm . A similar phenomenon occurs for an atom in front of an oscillating mirror [6,7], in the adiabatic approximation. Only two frequencies would be present in the spectrum when Ω cm > Ω.…”

“…Introducing the explicit form of the Dirichlet propagator above into (7), and using an entirely analogous approach to the one of [10] we obtain, after some algebra:…”

“…Another interesting line of research, closely related to the present paper, focusses on single atoms near a mirror, and in relative motion to it. For example, for a two level atom in its excited state, an oscillating mirror induces modifications in the decay probability and in the spectrum of the emitted photons [6,7]. Oscillating atoms near a perfect mirror have been considered in a number of situations, most of them using simplifying assumptions, either about the direction of the emitted photons [8,9] or considering a scalar rather than the EM field [10].…”

Collective spontaneous emission of two entangled atoms near an oscillating mirror

“…Recent investigations have shown that the presence of a dynamical environment can give additional possibilities (not present in the case of a static environment) to manipulate and control radiative properties of atoms or molecules coupled to a quantum field. For example the spontaneous emission of an excited atom located near a perfectly reflecting plate that oscillates adiabatically has been recently discussed [29,30], and it has been shown that the motion of the mirror significantly affects the atomic decay rate, as well as the spectrum of the emitted radiation, exhibiting the presence of two lateral and almost symmetrical peaks, not present in the case of a static boundary [29]. Similar results were also obtained in the case of an excited atom embedded in a dynamical photonic crystal, when its transition frequency is close to the photonic band edge of the photonic crystal [31].…”