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arXiv:1604.08302

Superradiance from few emitters with non-radiative decay

Игорь Евгеньевич Проценко, Alexander V. Uskov

Published Apr 28, 2016• 1 citation
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Abstract

Description of superradiance of few quantum emitters with non-radiative decay in terms of quantum states is presented. Quantum efficiencies (QE) of SR of two and three emitters are calculated and compared with the case of two and three independent emitters. Maximum increase in QE is 8% for two emitters and 16% for three emitters, it is reached at certain ratios between non-radiative and radiative rates. Approach can be generalized with inclusion of the incoherent pump, dephasing and delay in emitter-emitter interaction.

DOI
10.48550/arxiv.1604.08302

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Description of superradiance of few quantum emitters with non-radiative decay in terms of quantum states is presented. Quantum efficiencies (QE) of SR of two and three emitters are calculated and compared with the case of two and three independent emitters. Maximum increase in QE is 8% for two emitters and 16% for three emitters, it is reached at certain ratios between non-radiative and radiative rates. Approach can be generalized with inclusion of the incoherent pump, dephasing and delay in emitter-emitter interaction.
Description of superradiance (SR) of few quantum emitters with non-radiative decay is carried out in the frame of Schrödinger picture taking into account non-equilibrium bath states. Quantum efficiencies (QE) of SR of two and three emitters are calculated and compared with QE of spontaneous emission of two and three independent emitters. Maximum increase of QE is 9% for two emitters and 16% for three emitters, it is reached at certain relationships between non-radiative and radiative decay rates and at non-equilibrium in baths of non-radiative decay.
Determining the peak photon emission time and rate for an ensemble of NNN quantum systems undergoing collective superradiant decay typically requires tracking the time evolution of the density operator. Generally, the dimension of the density operator grows exponentially (∼ ⁣2N\sim \! 2^N∼2N) with the number of emitters, in the absence of any symmetries such as in Dicke superradiance with full or partial permutational symmetry. We present a detailed study of the superradiant peak emission rate and time for initially fully excited quantum emitter ensembles, for one-, two- and three-dimensional arrays in free-space and emitter chains coupled to waveguide reservoirs. For few emitters (N≲14N\lesssim 14N≲14) we utilize the full quantum master equation, and for mesoscopic emitter numbers (N≲400N\lesssim 400N≲400) we use a second- and third-order cumulant expansion of the operator averages to track the time evolution of the system.
Super-radiance is a striking phenomenon resulting from the collective interaction of emitters with light, and it is fundamentally related to the appearance of long-range correlations between the dipole moments of the emitters. As such, it represents a distinct phase of dissipative many-body systems compared to the case of independent emitters, similarly to how ferromagnetism stands out in magnetic materials in contrast to paramagnetism. In this work we address the conditions under which the transition to super-radiance can occur in ensembles of emitters subject to dephasing and individual decay -- a situation which is particularly relevant to the case of emitters in the solid state. The simplifying assumption of an ensemble of permutationally invariant emitters allows for the efficient solution of both the dissipative dynamics after a pulsed excitation, as well as of the steady state under incoherent pumping. This exact solution allows us to benchmark a truncated cumulant expansion approach, which can give predictions for arbitrarily big system sizes. We show that super-radiance is fundamentally robust to sizable dephasing and non-radiative decay rates, both under a pulsed excitation, as well as under continuous pumping. This robustness is the result of the collective acceleration effect of super-radiant emission with respect to the individual coupling to a local environment. We establish the universal critical scaling laws at the transition between normal radiance and super-radiance; and we show that, in the super-radiant phase, significant finite-size crossovers can be observed before reaching the asymptotic scaling regime. Our results pave the way for future experiments to provide a quantitative characterization of the scaling properties of super-radiance, seen as a distinct non-equilibrium many-body phase in ensembles of incoherently pumped emitters.
Superradiance is a quantum phenomenon in which coherence between emitters results in enhanced and directional radiative emission. Many quantum optical phenomena can be characterized by the two-time quantum correlation function g(2)(t,τ)g^{(2)}(t,τ)g(2)(t,τ), which describes the photon statistics of emitted radiation. However, the critical task of determining g(2)(t,τ)g^{(2)}(t,τ)g(2)(t,τ) becomes intractable for large emitter ensembles due to the exponential scaling of the Hilbert space dimension with the number of emitters. Here, we analyse and benchmark two approximate numerical sampling methods applicable to emitter arrays embedded within electromagnetic environments, which generally provide upper and lower bounds for g(2)(t,0)g^{(2)}(t,0)g(2)(t,0). We also introduce corrections to these methods (termed offset corrections) that significantly improve the quality of the predictions. The optimal choice of method depends on the total number of emitters, such that taken together, the two approaches provide accurate descriptions across a broad range of important regimes. This work therefore provides new theoretical tools for studying the well-known yet complex phenomenon of superradiance in large ensembles of quantum emitters.
In conventional lasers, the emitters are typically incoherent, radiating photons independently; in superradiant lasers, many coherent emitters radiate photons collectively, but they essentially do not interact with each other. Here, we present the concept of quantum many-body lasers, in which the emitters interact coherently and radiate collectively. In this proof-of-concept study, we consider a cavity coupled to many pumped spin-1/2 emitters with all-to-all interaction. We find that the squeezing induced by the coherent many-body interaction can be transferred from the spins to photons through superradiant lasing. This work illustrates the concept of using a pumped quantum many-body system to generate bright quantum light with quantum correlations beyond conventional optical coherence, which can facilitate quantum technologies and the study of nonlinear optics in the quantum realm.