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arXiv:1101.5300 · Physical Review A

Superradiance of cold atoms coupled to a superconducting circuit

Daniel Braun, J. E. Hoffman, Eite Tiesinga

Published Jun 6, 2011• 7 citations
arXivHTMLPDF

Abstract

We investigate superradiance of an ensemble of atoms coupled to an integrated superconducting $\mathit{LC}$ circuit. Particular attention is paid to the effect of inhomogeneous coupling constants. Combining perturbation theory in the inhomogeneity and numerical simulations, we show that inhomogeneous coupling constants can significantly affect the superradiant relaxation process. Incomplete relaxation terminating in ``dark states'' can occur, from which the only escape is through individual spontaneous emission on a much longer time scale. The relaxation dynamics can be significantly accelerated or retarded, depending on the distribution of the coupling constants. On the technical side, we also generalize the previously known propagator of superradiance for identical couplings in the completely symmetric sector to the full exponentially large Hilbert space.

DOI
10.1103/physreva.83.062305

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We investigate superradiance of an ensemble of atoms coupled to an integrated superconducting LC\mathit{LC}LC circuit. Particular attention is paid to the effect of inhomogeneous coupling constants. Combining perturbation theory in the inhomogeneity and numerical simulations, we show that inhomogeneous coupling constants can significantly affect the superradiant relaxation process. Incomplete relaxation terminating in ``dark states'' can occur, from which the only escape is through individual spontaneous emission on a much longer time scale. The relaxation dynamics can be significantly accelerated or retarded, depending on the distribution of the coupling constants. On the technical side, we also generalize the previously known propagator of superradiance for identical couplings in the completely symmetric sector to the full exponentially large Hilbert space.
The collective spontaneous emission of a fully inverted inhomogeneously broadened ensemble of N two-level systems coupled to a single-mode low-Q cavity is investigated numerically using Monte Carlo wave function technique. An intrinsically bi-exponential emission dynamics is found when the time scales of superradiance tau(sr) and inhomogeneous dephasing T2* approximately 1/Deltaomega(inh) become comparable: a fast superradiant is followed by a slow subradiant decay. Experimental configurations using ensembles of quantum dots coupled to optical microcavities are proposed as possible candidates to observe the combined superradiant and subradiant energy relaxation.
The interaction of an ensemble of atoms with common vacuum modes may lead to an enhanced emission into these modes. This phenomenon, known as superradiance, highlights the coherent nature of spontaneous emission, resulting in macroscopic entangled states in mundane situations. The complexity of the typical observations of superradiance, however, masks its quantum nature, allowing alternative classical interpretations. Here we stress how this picture changed with the implementation ten years ago of a new process for single-photon generation from atomic ensembles. We present then the last piece of evidence for the superradiant nature of such a process, reporting the observation of an accelerated emission of the photon with a rate that may be tuned by controllably changing the number of atoms in the ensemble. We hope such an investigation will help open up a new bottom-up approach to the study of superradiance.
The problem of superradiant emission from a small atomic system is treated under conditions in which the effects of inhomogeneous broadening are important, as in a solid. The treatment is semiclassical, with the assumption that all atoms see the same electromagnetic field. A set of coupled integrodifferential equations is obtained characterizing the state of each atom of resonant frequency \ensuremath{\omega} at time ttt. It is found that, in general, atoms of different frequencies evolve differently in time, whether or not they start from the same initial state. The effect of the inhomogeneous broadening is generally to delay the onset and to reduce the amplitude of the superradiant pulse. Some effects of inhomogeneous broadening are manifest even when the inhomogeneous lifetime is much longer than the usual superradiance time. When the atomic system starts in the ground state and is then exposed to a coherent excitation pulse, superradiant effects can appear even when the inhomogeneous lifetime is very short compared with the usual superradiance time.
Superconducting flux qubits are a promising candidate for realizing quantum information processing and quantum simulations. Such devices behave like artificial atoms, with the advantage that one can easily tune the ``atoms'' internal properties. Here, by harnessing this flexibility, we propose a technique to minimize the inhomogeneous broadening of a large ensemble of flux qubits by tuning only the external flux. In addition, as an example of many-body physics in such an ensemble, we show how to observe superradiance, and its quadratic scaling with ensemble size, using a tailored microwave control pulse that takes advantage of the inhomogeneous broadening itself to excite only a subensemble of the qubits. Our scheme opens up an approach to using superconducting circuits to explore the properties of quantum many-body systems.
Since Dicke's seminal paper on coherence in spontaneous radiation by atomic ensembles, superradiance has been extensively studied. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to nonradiative decoherence processes. Here, we report the experimental observation of subradiance in an extended and dilute cold-atom sample containing a large number of particles. We use a far detuned laser to avoid multiple scattering and observe the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we detect a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical depth of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model.
We study a bosonic analog of the paradigmatic Dicke model of superradiance, comprising interacting bosonic modes subject to fully symmetric collective decay. Depending on the interaction strength, we uncover qualitatively distinct regimes of emission. For strong interactions, the emission closely resembles Dicke superradiance, with perturbative corrections arising from the presence of additional levels. For weaker interactions, the bosonic statistics qualitatively changes the dynamics, leading to a crossover to subradiant emission. Remarkably, we show that the dynamics in this regime can be described by rate equations analogous to those of the Dicke model despite the large accessible bosonic Hilbert space. Our findings are based on a combination of analytical arguments and large-scale numerics enabled by the permutational symmetry of the problem and may be probed in circuit QED experiments.