Spontaneous emission spectra of two initially excited closely spaced identical atoms are very sensitive to the strength and the direction of the applied magnetic field. We consider the relevant schemes that ensure the determination of the mutual spatial orientation of the atoms and the distance between them by entirely optical means. A corresponding theoretical description is given accounting for the dipole-dipole interaction between the two atoms in the presence of a magnetic field and for polarizations of the quantum field interacting with magnetic sublevels of the two-atom system.
Spontaneous emission spectra of two initially excited closely spaced identical atoms are very sensitive to the strength and the direction of the applied magnetic field. We consider the relevant schemes that ensure the determination of the mutual spatial orientation of the atoms and the distance between them by entirely optical means. A corresponding theoretical description is given accounting for the dipole-dipole interaction between the two atoms in the presence of a magnetic field and for polarizations of the quantum field interacting with magnetic sublevels of the two-atom system.
The term of atom optics is due to the natural analogy with light optics or the optics of photons. Some elements of the optics of atoms and molecules, based on the interaction between spatially nonuniform static magnetic or electrical fields and the magnetic or electrical dipole moment of the particles, have long been known and used fairly successfully in experimental physics. In the presence of a magnetic or electric field, the quantum state of atom or molecule is shifted, the shift depending on the initial quantum state of the particle and the field strength. A particle in nonuniform magnetic field is acted upon by the force directed along the field strength gradient. The focusing properties of a magnetic lens depend on the magnetic sublevel of atoms.
Several effects of quantum interference in spectroscopy of a system of two atoms are discussed. (i) In the system of spatially separated atoms in a one-dimensional (1D) geometry (a single-mode waveguide or photon crystal), a (meta)stable excited entangled state can be formed, its decay being very sensitive to the distance between the atoms and to perturbations which cause a difference between their resonance frequencies. (ii) In a system of closely located atoms in 3D space, the extreme sensitivity of absorption and fluorescence spectra to the direction of the applied magnetic field is demonstrated. These theoretical predictions can be useful for the quantum information processing and ultrasensitive measurements.
We present an analysis of the spontaneous emission by two identical two-level atoms a distance R apart, both of which are initially in the upper state. This analysis applies for two interacting atoms emitting both in a free space and in a cavity structure. In this paper we use the Heisenberg picture. We work under the dipole approximation and the rotating-wave approximation. We assume that all the field modes are initially in the vacuum state and the two atoms A and B are in the upper state. We will concentrate on the motion of the product of the dipole operators of two atoms. Because we have two excitations at t=0, and because we work under rotating-wave approximation, we will always have two excitations, i.e., two excited atoms, or one excited atom plus one photon, or two unexcited atoms with two photons.
The polarization of the resonance fluorescence of interacting atoms and the transfer of coherence, due to the exchange of excitation, are studied theoretically. The treatment is for the general case where both the excited and the ground states can have arbitrary angular momenta, except that they can be connected to each other by an allowed transition. Electrostatic dipole–dipole interaction and electromagnetic radiative interaction are considered simultaneously as the perturbations on the system. Heitler and Ma's generalized time-dependent perturbation method is used. The system is quantized with respect to the space-fixed z axis and a static magnetic field along the z axis may be present, so that the magnetic sublevels (m, m′, etc., for the excited state J, and α, β, etc., for the ground state J′) are not necessarily degenerate. The intensity of the scattered light of a given polarization, in a given direction, is expressed as a function of kR (where ℏck is the energy of excitation and R is the internuclear distance), and of the orientation of R with respect to z axis. The matrix elements (ℏ / 2)γmβ,αm′ and Vmβ,αm′, which cause resonant transfer of excitation between two atoms through radiative and electrostatic interaction, respectively, are also expressed as a function of kR, and of the orientation of R. For randomly oriented atoms, the polarization after being averaged over the random orientation of R becomes a function of kR. Numerical calculations have been carried out for S01 → 1P1 transition. The coherence is shown to be conserved upon resonant transfer of excitation when R is parallel to the quantization axis.
Abstract Using the example of two closely spaced localized alkaline-earth atoms, we consider the possibilities of the quantum beat method (a version of the level-crossing spectroscopy in a magnetic field) in finding two parameters characterizing the system, namely, the direction from one atom to another and the distance between them. The applicability of the method to the nanoscopy of systems of closely spaced quantum dots, vacancy centers (NV centers, etc.), and impurity atoms (molecules) in crystals is discussed.
The excitation spectrum arising from the interaction between two identical atoms (molecules), one of which is excited in the presence of a resonant strong electromagnetic field (pump field), is investigated. The excitation spectrum is found to consist of those describing the symmetric and antisymmetric modes, respectively. The form of both spectra depends on the relation between the distance R separating the atoms and the wavelength $\ensuremath{\lambda}$ of the transition from the ground state to the excited state. For $R<\ensuremath{\lambda}$, and when certain conditions prevail, the spectral function for the symmetric modes consists of three Lorentzian lines describing the central peak and the two sidebands whose radiative widths are equal to ${\ensuremath{\gamma}}_{0}$, $\frac{3{\ensuremath{\gamma}}_{0}}{2}$, and $\frac{3{\ensuremath{\gamma}}_{0}}{2}$, which are twice the corresponding ones arising from an isolated single atom interacting with the pump field. For the antisymmetric modes the central peak has a $\ensuremath{\delta}$-function distribution indicating the stability of the mode in question, while, when certain conditions are satisfied, the two sidebands are described by Lorentzian lines each having a radiative width of the order of $\frac{{\ensuremath{\gamma}}_{0}}{2}$, which is equal to the natural linewidth for a photon spontaneously emitted from an isolated atom. For both the symmetric and antisymmetric modes, the dipole-dipole interaction between the atoms brings about small energy shifts. For $R>\ensuremath{\lambda}$, apart from the small energy shifts caused by the dipole-dipole interaction, the spectral functions for symmetric and antisymmetric modes are similar to that for the single atom interacting with the pump field.