Abstract We consider the resonant van der Waals (vdW) interaction between two correlated identical two-level atoms (at least one of which being excited) within the framework of macroscopic cavity quantum electrodynamics in linear, dispersing and absorbing media. The interaction of both atoms with the body-assisted electromagnetic field of the cavity is assumed to be strong. Our time-independent evaluation is based on an extended Jaynes–Cummings model. For a system prepared in a superposition of its dressed states, we derive the general form of the vdW forces, using a Lorentzian single-mode approximation. We demonstrate the applicability of this approach by considering the case of a planar cavity and showing the position dependence of Rabi oscillations. We also show that in the limiting case of weak coupling, our results reproduce the perturbative ones for the case where the field is initially in vacuum state while the atomic state is in a superposition of two correlated states sharing one excitation.
Abstract We consider the resonant van der Waals (vdW) interaction between two correlated identical two-level atoms (at least one of which being excited) within the framework of macroscopic cavity quantum electrodynamics in linear, dispersing and absorbing media. The interaction of both atoms with the body-assisted electromagnetic field of the cavity is assumed to be strong. Our time-independent evaluation is based on an extended Jaynes–Cummings model. For a system prepared in a superposition of its dressed states, we derive the general form of the vdW forces, using a Lorentzian single-mode approximation. We demonstrate the applicability of this approach by considering the case of a planar cavity and showing the position dependence of Rabi oscillations. We also show that in the limiting case of weak coupling, our results reproduce the perturbative ones for the case where the field is initially in vacuum state while the atomic state is in a superposition of two correlated states sharing one excitation.
Abstract We study many-atom van der Waals (vdW) forces arising from reversible atom–field interactions in cavity quantum electrodynamics by using a dressed-state approximation. In the most general case, a single-mode Dicke model for atoms, sharing an arbitrary number of excitations, placed in an imperfect cavity, has been developed that leads to the vdW potential of such a system. As special cases, we consider the single-excitation Dicke model and also the case of one atom in the presence of multi-photon excitation inside the cavity. In most of the paper, it is assumed that the atoms are distributed symmetrically with respect to the mode structure. This will decouple all asymmetric states, allowing us to ignore them throughout our calculations. The impact of asymmetric states is taken into account for a system wherein one atom, freely placed in a cavity, together with n − 1 equally-coupled atoms, is interacting with the cavity field. By assuming broadened Lorentzian modes instead of sharp ones, the cavity imperfections have been added to the calculations. The position dependence of the effective Rabi frequency is studied for the example of a planar cavity.
We compute the energies of the interaction between two atoms placed in the middle of a perfectly reflecting planar cavity, in the weak-coupling nondegenerate regime. Both inhibition and enhancement of the interactions can be obtained by varying the size of the cavity. We derive exact expressions for the dyadic Green's function of the cavity field which mediates the interactions and apply time-dependent quantum perturbation theory in the adiabatic approximation. We provide explicit expressions for the van der Waals potentials of two polarizable atomic dipoles and the electrostatic potential of two induced dipoles. We compute the van der Waals potentials in three different scenarios: two atoms in their ground states, two atoms excited, and two dissimilar atoms with one of them excited. In addition, we calculate the phase-shift rate of the two-atom wave function in each case. The effect of the two-dimensional confinement of the electromagnetic field on the dipole-dipole interactions is analyzed. This effect depends on the atomic polarization. For dipole moments oriented parallel to the cavity plates, both the electrostatic and the van der Waals interactions are exponentially suppressed for values of the cavity width much less than the interatomic distance, whereas for values of the width close to the interatomic distance, the strength of both interactions is higher than their values in the absence of cavity. For dipole moments perpendicular to the plates, the strength of the van der Waals interaction decreases for values of the cavity width close to the interatomic distance, while it increases for values of the width much less than the interatomic distance with respect to its strength in the absence of cavity. We illustrate these effects by computing the dipole-dipole interactions between two alkali atoms in circular Rydberg states.
In this dissertation we study the interaction of a single atom with a single mode of the electromagnetic field in an optical cavity. We emphasize strong coupling conditions, where the dipole coupling strength is larger than the dissipation rates of the cavity and the atom. By exciting the coupled atom and cavity mode with an external field, the excited-state spectroscopy of the coupled system is explored. Both quantum mechanical and semiclassical calculations are performed and their results are compared. In the limit of a weak driving field, both results show a two-peak ("vacuum" Rabi) spectrum. With increased strength of the driving field, differences are observed. The quantum calculation shows a multi-peak ( two "vacuum" Rabi peaks plus additional peaks) spectrum, while the semiclassical calculation does not. These additional peaks are produced by transitions between the excited states of the Jaynes-Cummings IV Hamiltonian indicative of the quantum nature of the coupled atom-cavity-mode system.
The strong resonance interaction of a two-level atom with the continuum of quantized electromagnetic modes falling within the contour of a resonance mode of a dielectric microsphere is considered within the framework of quantum electrodynamics. Analytical solutions are derived. As an initial condition, we consider the case when, at time t = 0, the atom is excited and the resonance modes of the microsphere contain a single-photon wavepacket. It is shown that the properties of the emitted photon pair depend crucially on space-time properties of the photon wavepacket contained in the resonator. When the mean square of the electric field of the photon wavepacket at the initial instant of time at the atom position is close to the vacuum value, the radiation of an atom is similar to a spontaneous one and the emitted photon pair has no correlations. On the contrary, if the mean square of the electric field of the photon wavepacket at the initial instant of time at the atom position is substantially greater than the vacuum value, the radiation of an atom has a stimulated nature and the emitted photon pair has very complicated strong correlations. The relationship between the results obtained and the predictions of the dressed states theory are briefly discussed. The results obtained are of a general character and can be applied to the description of the resonant interaction of an excited atom and an excited resonator of an arbitrary shape.
Cavity qed is the domain of quantum optics which studies the behaviour of single atoms and photons coupled together in an electromagnetic resonator. During the last ten years, various spectacular effects have been observed on such systems, either on the atom’s or on the field’s properties. The presence of a cavity around an atom can produce an alteration of the atomic radiative rates which has been observed in several experiments. Ideally, cavity qed deals with two-level atoms coupled resonantly or nearly resonantly to a single cavity mode. This is of course a simplification of real situations, in which atoms have many levels and the cavity sustains more than one mode. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect.
In this chapter, we discuss two more experimental realizations of quantum optical phenomena, namely the interaction of an effective two-level atom with a quantized electromagnetic field in a high Q microwave cavity, the subject usually referred to as cavity QED, or sometimes CQED, and in the quantized motion of a trapped ion. Strictly speaking, these experiments are not optical, but they do realize interactions of exactly the type that are of interest in quantum optics, namely the Jaynes–Cummings interaction between a two-level system (an atom) and a bosonic degree of freedom, a single-mode cavity field in the case of a microwave cavity, and a vibrational mode of the center-of-mass motion of a trapped ion, the quanta being phonons in this case. We shall begin with a description of the useful properties of the so-called Rydberg atoms that are used in the microwave CQED experiments, proceed to discuss some general considerations of the radiative behavior of atoms in cavities, the CQED realization of the Jaynes–Cummings model, and then discuss the use of the dispersive, highly off-resonant, version of the model to generate superpositions of coherent states, i.e. the Schrödinger cat states of the type discussed in Chapters 7 and 9 for traveling wave optical fields but this time for a microwave cavity field. Finally, we discuss the realization of the Jaynes–Cummings interaction in the vibrational motion of a trapped ion.