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arXiv:1904.04877 · Physical Review A

Collective dynamics of inhomogeneously broadened emitters coupled to an optical cavity with narrow linewidth

Kamanasish Debnath, Yuan Zhang, Klaus Mølmer

Published Nov 11, 2019• 19 citations
arXivHTMLPDF

Abstract

We study collective effects in an inhomogeneously broadened ensemble of two-level emitters coupled to an optical cavity with narrow linewidth. Using second-order mean-field theory we find that the emitters within a few times the cavity linewidth exhibit synchronous behavior and undergo collective Rabi oscillations. Under proper conditions, the synchronized oscillations give rise to a modulated intracavity field which can excite emitters detuned by many linewidths from the cavity resonance. To study the synchronization in further detail, we simplify the model and consider two ensembles and study steady-state properties when the emitters are subjected to an incoherent drive.

DOI
10.1103/physreva.100.053821

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We study collective effects in an inhomogeneously broadened ensemble of two-level emitters coupled to an optical cavity with narrow linewidth. Using second-order mean-field theory we find that the emitters within a few times the cavity linewidth exhibit synchronous behavior and undergo collective Rabi oscillations. Under proper conditions, the synchronized oscillations give rise to a modulated intracavity field which can excite emitters detuned by many linewidths from the cavity resonance. To study the synchronization in further detail, we simplify the model and consider two ensembles and study steady-state properties when the emitters are subjected to an incoherent drive.
The interplay between collective optical response and molecular static and dynamic disorder is studied using simple effective Hamiltonians for an ensemble of two-level emitters inside and outside a single-mode cavity. We model environmental disorder by randomly modulating the molecular transition frequencies and the coupling between the emitters and the electromagnetic field. We also consider effects of intermolecular interactions and orientational disorder. We investigate how these effects lead to new features in the steady state absorption (outside the cavity), transmission spectra (inside the cavity) and the yield of local molecular processes such as a unimolecular reaction. Outside the cavity, the collective behavior is manifested in the linewidth of the steady state absorption, the emission spectrum, and the local chemical yield. Inside the cavity, however, the collective behavior primarily determines the Rabi splitting. Effects of intermolecular interactions under orientational disorder are also studied. For the most part, for all types of disorder, if we increase disorder, we find a reduction in the collective nature of the molecular response (smaller effective N), and therefore, the Rabi splitting contraction occurs with orientational disorder. Moreover, we find that static disorder is more destructive to collective behavior than dynamic disorder.
The interplay between collective optical response and molecular static and dynamic disorder is studied using simple effective Hamiltonians for an ensemble of two-level emitters inside and outside a single-mode cavity. We model environmental disorder by randomly modulating the molecular transition frequencies and the coupling between the emitters and the electromagnetic field. We also consider the effects of intermolecular interactions and orientational disorder. We investigate how these effects lead to new features in the steady-state absorption (outside the cavity), transmission spectra (inside the cavity), and the yield of local molecular processes such as a unimolecular reaction. Outside the cavity, the collective behavior is manifested in the linewidth of the steady-state absorption, the emission spectrum, and the local chemical yield. Inside the cavity, however, the collective behavior primarily determines the Rabi splitting. The effects of intermolecular interactions under orientational disorder are also studied. For the most part, for all types of disorder, if we increase disorder, we find a reduction in the collective nature of the molecular response (smaller effective NNN) and therefore the Rabi splitting contraction occurs with orientational disorder. Moreover, we find that static disorder is more destructive to collective behavior than dynamic disorder.
The enhanced collective coupling to weak quantum fields may turn atomic or spin ensembles into an important component in quantum information processing architectures. Inhomogeneous broadening can, however, significantly reduce the coupling and the lifetime of the collective excitation that represent the quantum information. In this paper we show that the width and shape of the inhomogeneous broadening have a striking influence on the dynamics of the cavity-ensemble system and may lead to narrowing of the linewidth of the collective states. We underpin our findings with the examples of a Gaussian and a Lorentzian profile of the inhomogeneity.
Summary form only given. The interaction strength of light and matter can be greatly influenced by altering the environment of the emitters and the electric field. In a photonic cavity the emitter-field coupling strength may become sufficiently large that the emitters and the field can exchange an excitation multiple times before it decays, giving rise to Rabi oscillations. In a passive cavity with one (several) two-level emitter(s), this manifests itself as a (collective) Rabi splitting of the transmissions spectrum [1-3], and it has recently been shown that incoherently pumped single emitters in cavities may exhibit Rabi splitting of the emission spectrum at large coupling strengths [4,5]. We present a fully analytical model describing a large collection of incoherently pumped two-level emitters in a single-mode cavity (e.g. quantum dots in a nano-cavity) and show that collective Rabi splitting of the emission spectrum can occur in these systems as well [6]. We derive a condition in terms of system parameters for the splitting to occur, and show that this is different from the condition typically associated with strong emitter-field coupling. Moreover, we show that the collective Rabi splitting decreases with increasing pump rate P, giving a transition from the strong-coupling regime to the weak-coupling regime, and possibly lasing at large P (Fig. 1(a)).
We study the quantum dynamics of many-body arrays of two-level atoms in a driven cavity subject to collective decay and interactions mediated by the cavity field. We work in the bad cavity limit accessible, for example, using long-lived electronic clock states of alkaline-earth atoms, for which the bare atomic linewidth is much less than the cavity linewidth. In the absence of interactions, our system reduces to previously studied models of collective fluorescence. We show that while interactions do not qualitatively change the steady-state properties they lead to a drastic change in the dynamical properties. We find that, for some intervals of driving strengths, the system shows two very distinct types of transient behaviors that depend on the initial state of the system. In particular, there is a parameter regime where the system features oscillatory dynamics with a period of oscillation that becomes much shorter than the duration of the overall transient dynamics as the atom number increases. We use both mean-field and exact numerical calculations of the quantum system to investigate the dynamics.
Background: Theoretical studies of superradiant lasing on optical clock transitions predict a superb frequency accuracy and precision closely tied to the bare atomic linewidth. Such a superradiant laser is also robust against cavity fluctuations when the spectral width of the lasing mode is much larger than that of the atomic medium. Recent predictions suggest that this unique feature persists even for a hot and thus strongly broadened ensemble, provided the effective atom number is large enough. Methods: Here we use a second-order cumulant expansion approach to study the power, linewidth and lineshifts of such a superradiant laser as a function of the inhomogeneous width of the ensemble including variations of the spatial atom-field coupling within the resonator. Results: We present conditions on the atom numbers, the pump and coupling strengths required to reach the buildup of collective atomic coherence as well as scaling and limitations for the achievable laser linewidth. Conclusions: We show how sufficiently large numbers of atoms subject to strong optical pumping can induce synchronization of the atomic dipoles over a large bandwidth. This generates collective stimulated emission of light into the cavity mode leading to narrow-band laser emission at the average of the atomic frequency distribution. The linewidth is orders of magnitudes smaller than that of the cavity as well as the inhomogeneous gain broadening and exhibits reduced sensitivity to cavity frequency noise.