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Superradiant Decay and Dipole-Dipole Interaction of Distant Atoms in a Two-Way Cascaded Cavity QED System

Steffen Zeeb, Changsuk Noh, A. S. Parkins, H. J. Carmichael

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We investigate theoretically the modification of atomic spontaneous emission in a two-way cascaded cavity QED system consisting of microtoroidal resonators connected via an optical fiber. Under appropriate conditions, atoms coupled to different resonators can undergo either superradiant decay or coherent dipole-dipole interaction.
DOI
10.1364/iqec.2011.i947

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We investigate a two-way cascaded cavity QED system consisting of microtoroidal resonators coupled through an optical fiber. Each microtoroidal cavity supports two counterpropagating whispering-gallery modes coupled to single atoms through their evanescent fields. We focus on a pair of atom-microtoroid systems and compute the spectrum of spontaneous emission into the fiber with one atom initially excited. Explicit results are presented for strong-coupling and bad-cavity regimes, where the latter allows the effective atom-atom interaction to be controlled through the atom-cavity coupling and detuning: the atoms exhibit either collective spontaneous emission with no dipole-dipole interaction or a (coherent) dipole-dipole interaction and independent (single-atom) emission. This capacity for switching the character of the interaction is a feature of bidirectional coupling and connects our two-way cascaded system to work on one-dimensional waveguides. Building upon our bad-cavity results, we generalize to many atom-microtoroid systems coupled through an optical fiber.
The cooperative dynamics of a microlaser consisting of two threelevel atoms interacting with a pump field and two quantized cavity modes forming a radiative cascade are studied. Adiabatic elimination of one mode leads to a strong dynamical entanglement between the internal states of the atoms which allows us to study the effects of a cavity-mediated dipole-dipole interaction. We show that the coherent dynamics of the two-atom system will preferentially couple symmetrical linear combinations of internal states. If this coupling dominates the dynamics, the two-atom system will behave like a single atom with correspondingly larger dipole moment, that is a superradiant two-atom system. Even very small spontaneous decay causes transitions from symmetrical to antisymmetrical states and conversely. The hopping between two subsets of the state space can give rise to intriguing phenomena such as bistability of the laser mode intensity. By a randomization of the two coupling phases we recover the standard independent-atom laser theory.
Enhanced and inhibited spontaneous emission of two close atoms in an overdamped cavity is studied taking into account the dipole-dipole interaction between them. The system is described in the minimal-coupling scheme and the advantages of this choice for our problem are discussed. The dynamics is investigated using both quantum Langevin equations and Master equation techniques. This last approach allows one to describe the behavior of the atoms plus field system as a one-step process. The case in which both atoms are initially in their excited state and the mode is in its vacuum state is discussed in some detail. It is shown that, different from what occurs to two close atoms in free space, in an overdamped cavity dipolar interaction may modify the decay rate. In particular, we find that the two transitions the atomic system performs to reach its equilibrium configuration can have different rates, and that for a suitable choice of the detuning between the cavity mode and the unperturbed atomic frequency, one of the transitions occurs at an enhanced rate while the second is inhibited.
The transversely confined propagating modes of an optical fiber mediate virtually infinite range energy exchanges among atoms placed within their field, which adds to the inherent free space dipole–dipole coupling. Typically, the single atom free space decay rate largely surpasses the emission rate into the guided fiber modes. However, scaling up the atom number as well as the system size amounts to entering a collective emission regime, where fiber-induced superradiant spontaneous emission dominates over free space decay. We numerically study this super- and subradiant decay of highly excited atomic states for one or several transverse fiber modes as present in hollow core fibers. As particular excitation scenarios we compare the decay of a totally inverted state to the case of π /2 pulses applied transversely or along the fiber axis as in standard Ramsey or Rabi interferometry. While a mean field approach fails to correctly describe the initiation of superradiance, a second-order approximation accounting for pairwise atom–atom quantum correlations generally proves sufficient to reliably describe superradiance of ensembles from two to a few hundred particles. In contrast, a full account of subradiance requires the inclusion of all higher order quantum correlations. Considering multiple guided modes introduces a natural effective cut-off for the interaction range emerging from the dephasing of different fiber contributions.
We propose to turn two resonant distant cavities effectively into one by coupling them via an optical fiber which is coated with two-level atoms [J. D. Franson et al., Phys. Rev. A 70, 062302 (2004)]. The purpose of the atoms is to destructively measure the evanescent electric field of the fiber on a time scale which is long compared to the time it takes a photon to travel from one cavity to the other. Moreover, the boundary conditions imposed by the setup should support a small range of standing waves inside the fiber, including one at the frequency of the cavities. In this way, the fiber provides an additional decay channel for one common cavity field mode but not for the other. If the corresponding decay rate is sufficiently large, this mode decouples effectively from the system dynamics. A single nonlocal resonator mode is created.