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arXiv:1606.05591 · Physical Review A

Strong light-matter coupling in the presence of lasing

Christopher Gies, F. Gericke, P. Gärtner, Steffen Holzinger, Caspar Hopfmann, Tobias Heindel, Janik Wolters, C. Schneider, Matthias Florian, F. Jahnke, Sven Höfling, Martin Kamp, Stephan Reitzenstein

Published Aug 3, 2017• 24 citations
arXivHTMLPDF

Abstract

The regime of strong light-matter coupling is typically associated with weak excitation. With current realizations of cavity-QED systems, strong coupling may persevere even at elevated excitation levels sufficient to cross the threshold to lasing. In the presence of stimulated emission, the vacuum-Rabi doublet in the emission spectrum is modified and the established criterion for strong coupling no longer applies. We provide a generalized criterion for strong coupling and the corresponding emission spectrum, which includes the influence of higher Jaynes-Cummings states. The applicability is demonstrated in a theory-experiment comparison of a few-emitter quantum-dot--micropillar laser as a particular realization of the driven dissipative Jaynes-Cummings model. Furthermore, we address the question if and for which parameters true single-emitter lasing can be achieved and provide evidence for the coexistence of strong coupling and lasing in our system in the presence of background emitter contributions.

DOI
10.1103/physreva.96.023806

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The regime of strong light-matter coupling is typically associated with weak excitation. With current realizations of cavity-QED systems, strong coupling may persevere even at elevated excitation levels sufficient to cross the threshold to lasing. In the presence of stimulated emission, the vacuum-Rabi doublet in the emission spectrum is modified and the established criterion for strong coupling no longer applies. We provide a generalized criterion for strong coupling and the corresponding emission spectrum, which includes the influence of higher Jaynes-Cummings states. The applicability is demonstrated in a theory-experiment comparison of a few-emitter quantum-dot--micropillar laser as a particular realization of the driven dissipative Jaynes-Cummings model. Furthermore, we address the question if and for which parameters true single-emitter lasing can be achieved and provide evidence for the coexistence of strong coupling and lasing in our system in the presence of background emitter contributions.
The development and physical understanding of high-beta nanolasers operating in regime of cavity-quantum-electrodynamics (cQED) is a highly interdisciplinary field of research, involving important aspects of nanotechnology, quantum optics, and semiconductor physics. Of particular interest is the quantum limit of operation, in which a few or even a single emitter act as gain material. The regime of strong light-matter coupling is typically associated with weak excitation. With current realizations of cQED systems, strong coupling may persevere even at elevated excitation levels sufficient to cross the threshold to lasing. In the presence of stimulated emission, the vacuum-Rabi doublet in the emission spectrum is modified and the established criterion for strong coupling no longer applies. Based on an analytic approach, we provide a generalized criterion for strong coupling and the corresponding emission spectrum that includes the influence of higher Jaynes-Cummings states. The applicability is demonstrated in a theory-experiment comparison of a state-of-the-art few-emitter quantum-dot (QD)–micropillar laser as a particular realization of the driven dissipative Jaynes-Cummings model [1]. Furthermore, we address the question if and for which parameters true single-emitter lasing can be achieved. By using a master-equation approach for up to 8 QDs coupled to the mode, we provide evidence for the coexistence of strong coupling and lasing in our system in the presence of background emitter contributions by identifying signatures in the mean-photon number, the photon-autocorrelation function, and the emission linewidth. [1] C. Gies et al., accepted for publication in PRA, arxiv:1606.05591
A criterion for strong coupling between two quantum emitters and a single resonant light mode in a cavity is presented. The criterion takes into account the escape of cavity photons and the spontaneous emission of the emitters, which are modeled as two-level systems. By using such a criterion, the dissipative Tavis-Cummings ladder of states is constructed, and it is shown that the inclusion of one more emitter with respect to the Jaynes-Cummings (single emitter) case increases the effective parameter region in which nthn\text{th}nth-order Rabi splitting is observed.
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 present a systematic study of the properties of systems composed of NNN two-level quantum emitters coupled to a single cavity mode, for light-matter interaction strengths ranging from the weak to the ultrastrong and deep-strong coupling regimes. Beginning with an analysis of the energy spectrum as a function of the light-matter coupling strength, we examine systems with varying numbers of emitters, from a pair to large collections, approaching the thermodynamic limit $(N\ensuremath{\rightarrow}\ensuremath{\infty})$. Additionally, we explore the emission properties of these systems under incoherent excitation of the emitters, employing a general theoretical framework for open cavity-QED systems, which is valid across all light-matter interaction regimes and preserves gauge invariance within truncated Hilbert spaces. Furthermore, we study the influence of the emitter-environment interaction on the spectral properties of the system. Specifically, when each emitter interacts independently with its own reservoir, we observe the emergence of an emission peak at the cavity's resonant frequency for even values of NNN. Our analysis also clarifies the evolution of the system as the number of emitters increases, ultimately converging toward an equivalent system composed of two interacting single-mode bosonic fields.
We study a two-level system (atom, superconducting qubit, or quantum dot) strongly coupled to a single photonic mode of a cavity, in the presence of incoherent pumping and including detuning and dephasing. This system displays a striking quantum-to-classical transition. On the grounds of several approximations that reproduce to various degrees exact results obtained numerically, we separate five regimes of operations, that we term ``linear,'' ``quantum,'' ``lasing,'' ``quenching,'' and ``thermal.'' In the fully quantized picture, the lasing regime arises as a condensation of dressed states and manifests itself as a Mollow triplet structure in the direct emitter photoluminescence spectrum, which embeds fundamental features of the full-field quantization description of light-matter interaction.
Strong coupling between a single resonator mode and a single quantum emitter is key to a plethora of experiments and applications in quantum science and technology and is commonly described by means of the Jaynes-Cummings model. Here, we show that the Jaynes-Cummings model only applies when the cavity does not significantly change the emitter's emission rate into free-space. Most notably, the predictions made by the Jaynes-Cummings model become increasingly wrong when approaching the ideal emitter-resonator systems with no free-space decay channels. We present a Hamiltonian that provides, within the validity range of the rotating wave approximation, a correct theoretical description that applies to all regimes. As minimizing the coupling to free-space modes is paramount for many cavity-based applications, a correct description of strong light-matter interaction is therefore crucial for developing and optimizing quantum protocols.