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Journal of Physics B Atomic Molecular and Optical Physics

Cavity-QED interactions of several atoms

Saeideh Esfandiarpour, Hassan Safari, Stefan Yoshi Buhmann

Published Dec 6, 2018• 3 citations
Publisher

Abstract

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.

DOI
10.1088/1361-6455/aaf6d7

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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.
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.
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.
Abstract Simulating cavity quantum electrodynamics in synthetic platforms offers a route to studying light--matter physics without real photons. We reassess the frequently invoked analogy between harmonically trapped, spin--orbit-coupled atoms and the quantum Rabi and Dicke models, with particular emphasis on squeezing and entanglement. A single non-interacting atom realizes the quantum Rabi Hamiltonian exactly, up to elementary spin and phase-space rotations. For NNN non-interacting atoms, however, the center-of-mass mode is only one member of a complete orthonormal set containing N−1N-1N−1 relative modes. We prove that, after all modes are included, the spin--spin terms generated by the collective mode cancel exactly against those generated by the relative modes. Equivalently, the original Hamiltonian is a sum of independent one-particle Hamiltonians and therefore cannot create interparticle entanglement from a separable state. Contact interactions invalidate this cancellation but do not remove the relative modes or turn the exact many-body Hamiltonian into a Dicke model. A one-mode Dicke description can arise only as a controlled low-energy approximation after all relevant relative excitations have been shown to be spectrally suppressed. We discuss this distinction together with experimental scales, finite temperature, and possible mode-selection strategies. We also distinguish the single-particle interference underlying density fringes from the interaction-stabilized stripe supersolid observed in many-body condensates.
Summary form only given. The topic of quantum cavity electrodynamics is to describe the coupling between the fluctuations of an atomic system and the vacuum e.m. field, when special boundary conditions are imposed by a cavity to the vacuum field. A realistic description of these boundary conditions is hence of crucial importance. For such a purpose, the unavoidable dispersive spectral properties of any material cavity cannot be ignored when dealing with (temporal) fluctuations. For these reasons, we have embarked on an (experimental) analysis of the resonant long-range coupling between atomic excitation and the surface modes of a cavity (most often restricted to a simple wall, i.e. a flat open cavity). In our present investigations, we are concerned with the exploration of the dissipative counterpart of the resonant atom-surface van der Waals coupling.
Abstract We investigate a hybrid quantum system consisting of two coupled optical cavities, each containing an ensemble of coherently pumped artificial or real two-level atoms. The system is modelled within the dressed-state formalism, accounting for coherent driving and dissipative interactions with independent electromagnetic reservoirs. Focusing on the regime where the Rabi frequency greatly exceeds the collective spontaneous emission and cavity decay rates, respectively, we derive the equations of motion characterizing the system and analyse its steady-state behaviours. Special attention is given to the scenario in which only one cavity contains a pumped multi-atom ensemble, and as a consequence, coherent excitation transfer to the second cavity occurs via cavity–cavity coupling. In this case, the mean photon number in the second cavity mode scales proportional to the squared number of atoms, i.e., N2 from the first cavity. The proposed model offers insight into light–matter interaction in composite systems and suggests viable mechanisms for engineering collective interactions and non-local excitation transport in quantum optical platforms.
Over the past ten years, our group has investigated the effects of confinement on atoms inside metallic micron–sized cavities in order to elucidate some basic phenomena in the field of cavity quantum electrodynamics (QED). The first of these was the inhibition of spontaneous emission from an atom inside a cavity. This was followed by a laser spectroscopic measurement of the van der Waals interaction between a single Rydberg atom and a gold cavity, which showed that a simple electrostatic model of the atom–cavity interaction is correct when the cavity is small enough. More recently, the retarded Casimir–Polder force was measured between a ground state sodium atom and a large cavity, demonstrating that the van der Waals potential fails at long enough range and that the vacuum fluctuations of the field then have an important role in the interaction of the atom with the cavity. Our group is now pushing forward these investigations to study cavities whose walls have losses and dispersion, where the theory of cavity QED is significantly more complicated. With real surfaces, we have to deal with the complex dielectric response ε(ω) of the material, which exhibits frequency–dependent absorption and dispersion. One particularly interesting case is when a downward transition in the atom is resonant with an excitation of the cavity walls. This opens a new branch for the atomic decay: as an alternative to creating a photon within the space surrounded by the cavity walls the atomic decay can now create an electromagnetic excitation of the walls themselves. Another novel feature of our experiments is that the Bohr frequencies of the atom are close to the kT/h, where T is room temperature. We therefore expect to be able to measure effects associated with QED at finite temperature; in other words, to study how the blackbody radiation affects our experiments. By conducting experiments with real surfaces, we hope to elucidate and perhaps simplify the theoretical models used to describe these systems.