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arXiv:0902.0818 · AIP conference proceedings

Optical Spectra of the Jaynes-Cummings Ladder

Fabrice P. Laussy, Elena del Valle, M. R. Singh, R. H. Lipson

Published Jan 1, 2009• 4 citations
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Abstract

We explore how the Jaynes‐Cummings ladder transpires in the emitted spectra of a two‐level system in strong coupling with a single mode of light. We focus on the case of very strong coupling, that would be achieved with systems of exceedingly good quality (very long lifetimes for both the emitter and the cavity). We focus on the incoherent regime of excitation, that is realized with semiconductors quantum dots in microcavities, and discuss how reasonable is the understanding of the systems in terms of transitions between dressed states of the Jaynes‐Cummings Hamiltonian.

DOI
10.1063/1.3183476

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AIP conference proceedings•Jan 1, 2011•0 citations
We explore how the Jaynes‐Cummings ladder transpires in the emitted spectra of a two‐level system in strong coupling with a single mode of light. We focus on the case of very strong coupling, that would be achieved with systems of exceedingly good quality (very long lifetimes for both the emitter and the cavity). We focus on the incoherent regime of excitation, that is realized with semiconductors quantum dots in microcavities, and discuss how reasonable is the understanding of the systems in terms of transitions between dressed states of the Jaynes‐Cummings Hamiltonian.
Abstract. We explore how the Jaynes-Cummings ladder transpires in the emitted spectra of a twolevel system in strong coupling with a single mode of light. We focus on the case of very strong coupling, that would be achieved with systems of exceedingly good quality (very long lifetimes for both the emitter and the cavity). We consider the incoherent regime of excitation, that is realized with semiconductors quantum dots in microcavities, and discuss how reasonable is the understanding of the systems in terms of transitions between dressed states of the Jaynes-Cummings Hamiltonian.
Light and matter can be unified under the strong coupling regime, creating superpositions of both, called dressed states or polaritons. After initially being demonstrated in bulk semiconductors and atomic systems ,strong coupling phenomena have been realized in solid state optical microcavities. They form an essential ingredient in the exciting physics spanning from many-body quantum coherence phenomena, like Bose-Einstein condensation and superfluidity, to cavity quantum electrodynamics (cQED). A widely used approach within cQED is the Jaynes-Cummings (JC) model that describes the interaction of a single fermionic two-level system with a single bosonic photon mode. For a photon number larger than one, known as quantum strong coupling (QSC), a significant anharmonicity is predicted for the ladder-like spectrum of dressed states. For optical transitions in semiconductor nanostructures, first signatures of the quantum strong coupling were recently published. In our latest report we applied advanced coherent nonlinear spectroscopy to explore a strongly coupled exciton-cavity system. Specifically, we measured and simulated its four-wave mixing (FWM) response, granting direct access to the first two rungs of the JC ladder. This paper summarizes the main results of Ref. 15 and adds FWM experiments obtained on a micropillar cavity in which a doublet of quantum dot (QD) excitons interacts with the cavity mode in the limit of weak to strong coupling.
We study experimentally and theoretically a coherently driven strongly coupled quantum dot--microcavity system. Our focus is on physics of the unexplored intermediate excitation regime where the resonant laser field dresses a strongly coupled single exciton-photon (polariton) system resulting in a ladder of laser-dressed Jaynes-Cummings states. In that case, both the coupling of the emitter to the confined light field of the microcavity and to the light field of the external laser are equally important, as proved by observation of injection pulling of the polariton branches by an external laser. This intermediate interaction regime is of particular interest since it connects the purely quantum mechanical Jaynes-Cummings ladder and the semiclassical Autler-Townes ladder. Exploring the driving strength dependence of the mutually coupled system we establish the maximum in the resonance fluorescence signal to be a robust fingerprint of the intermediate regime and observe signatures indicating the laser-dressed Jaynes-Cummings ladder. In order to address the underlying physics we excite the coupled system via the matter component of fermionic nature undergoing saturation---in contrast to commonly used cavity-mediated excitation.
The Jaynes-Cummings model, describing the interaction between a single two-level system and a photonic mode, has been used to describe a large variety of systems, ranging from cavity quantum electrodynamics, trapped ions, to superconducting qubits coupled to resonators. Recently there has been renewed interest in studying the quantum strong-coupling (QSC) regime, where states with photon number greater than one are excited. This regime has been recently achieved in semiconductor nanostructures, where a quantum dot is trapped in a planar microcavity. Here we study the quantum strong-coupling regime by calculating its photoluminescence (PL) properties under a pulsed excitation. We discuss the changes in the PL as the QSC regime is reached, which transitions between a peak around the cavity resonance to a doublet. We particularly examine the variations of the PL in the time domain, under regimes of short and long pulse times relative to the microcavity decay time.
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.
We study the effect of pure dephasing on the strong‐coupling of a two‐level system (typically, a quantum dot) with the single mode of a microcavity. Whereas dephasing merely broadens the line in the linear regime, it results in a new spectral shape when transitions between higher manifolds of the Jaynes‐Cummings ladder are involved, namely, a triplet, that we show does not imply weak‐coupling. Higher excitation brings the system into lasing. Description of this intermediate triplet allows to demonstrate quantum nonlinearities even in noisy systems and to measure the magnitude of dephasing.