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Physical Review A

Stochastic initiation of superradiance in a cavity: Decoherence through pseudospin exchange

Hyunchul Nha, H. J. Carmichael

Published Nov 14, 2002• 2 citations
Publisher

Abstract

We study superradiance from a fully inverted medium in the presence of two channels for atomic relaxation. Spontaneous emission from individual atoms is included and competes with the collective emission responsible for superradiance. We compare exact results within the quantum trajectory formalism with a previous approximation [J. P. Clemens and H. J. Carmichael, Phys. Rev. A 65, 023815 (2002)] which neglects the reexcitation of an atom after it spontaneously emits. The approximation underestimates the decoherence during the second half of an emitted pulse.

DOI
10.1103/physreva.66.053806

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We study superradiance from a fully inverted medium in the presence of two channels for atomic relaxation. Spontaneous emission from individual atoms is included and competes with the collective emission responsible for superradiance. We compare exact results within the quantum trajectory formalism with a previous approximation [J. P. Clemens and H. J. Carmichael, Phys. Rev. A 65, 023815 (2002)] which neglects the reexcitation of an atom after it spontaneously emits. The approximation underestimates the decoherence during the second half of an emitted pulse.
We investigate the stochastic initiation of superradiant emission from a collection of excited two-state atoms coupled through a low-Q cavity mode. Noncollective emission into other modes of the electromagnetic field is included, allowing us to describe the transition from predominantly noncollective to collective behavior as the number of atoms is increased. We examine the dependence of the photon statistics on the number of atoms and the ratio of collective to noncollective decay rates. Numerical results for a few to 106{10}^{6}106 atoms are obtained using an approximation scheme developed within the framework of quantum trajectory theory. Results are compared with those for a pure collective emission process and an earlier treatment of noncollective effects.
This paper presents a semiclassical treatment of the evolution of an initially inverted system into a superradiant state in an extended, optically thick medium. In this process spontaneous emission and background thermal radiation initiate the collective radiative decay and produce a superradiant output pulse of intensity proportional to the square of the number of radiators. The treatment is based on the coupled Maxwell-Schr\"odinger equations, modified to include a fluctuating polarization source properly constructed to account for the effects of spontaneous emission. Computer results show that for a high-gain system only two parameters significantly influence the evolution process: TR{T}_{R}TR​, the characteristic radiation damping time of the collective system; and ${\ensuremath{\theta}}_{0}$, a function of the conditions which initiate the superradiant process. In this limit one obtains a normalized emission curve and simple analytical expressions for the time delay, pulse width, and peak intensity of the output radiation. These results are in good agreement with experiments. A comparison of our model with previous treatments of superradiance is given.
We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to 10310^3103 emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.
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.
Superradiance is an extensive cooperative spontaneous emission phenomenon, exhibited by some atomic collective-spin states. However, distinct initial states differ in their decay dynamics. Dicke states ∣j,m⟩|j,m\rangle∣j,m⟩ with distinct numbers of excitations n=m+jn=m+jn=m+j, driven by vacuum fluctuations, have their peak emission intensity shifted in time. Rotating Dicke states relative to the decay axis introduces an interesting parity structure that affects the pulse profile and photon correlations. Squeezed-bath prepared states undergo a squeezing-controlled crossover to the rotated Dicke states, making the emission character dependent on the amount of squeezing transferred from light to the atomic state. For semiclassical states with a macroscopic dipole moment, like the atomic coherent state, the emission intensity depends on their polarization. We present detailed results on the superradiant dynamics of a representative selection of states expanded in Dicke states to highlight the initial state as an independent dynamical control parameter. For large-NNN, we are able to predict fairly accurately the pulse profile in each case using the mean-field approximation, an approach based on the Fokker--Planck equation. We also present comparative results on the intensity correlation function, quantify the coherent and incoherent contributions of the emission, and contrast between small and large ensembles.
The emission of radiation from a spatially extended amplifying medium is shown to exhibit new coherence effects when the medium is modeled by inverted atoms which possess a degeneracy allowing Q(J) transitions. In particular, it is predicted that media of this type for which J=2 can emit leading pulses which are doubly peaked or asymmetric within both the regimes of superfluorescence and oscillating fluorescence. Dissipative processes can radically alter the character of the emission; an output consisting of two well-separated pulses appears feasible, but the precise behavior in the present model depends upon the magnitude of the field losses and the initiation statistics.