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Dicke enhancement of light-matter interaction for a single quasi-degenerate multilevel emitter

Tommaso Tufarelli, Daniel Friedrich, Heiko Groß, Joachim M. Hamm, Ortwin G. Hess, Bert Hecht

Published Oct 23, 2020• 0 citations
OpenAlex

Abstract

We study a quantum emitter with N nearly degenerate excited states (sublevels) coupled to the ground state via the same optical resonance. We show that in such circumstances an approximate Jaynes-Cummings system emerges, with an effective coupling constant scaling with the square root of N. While our conclusions hold in general, we also present detailed analytical derivations for the instructive case N=2. Employing a quantum optical master equation we further observe that our system can closely match the spectral line shapes and photon autocorrelation functions typical of Jaynes-Cummings physics. Interestingly, we find that finite emitter dephasing can improve the quality of the approximation in some cases. By showing a novel route to increase the effective light-matter coupling strength, our findings may facilitate the control and detection of single-photon nonlinearities at ambient conditions.

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Jaynes–Cummings model breaks down when the cavity geometry significantly reduces free-space emission

Martin Blaha, Arno Rauschenbeutel, Jürgen Volz

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 decay 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.

Journal of the Optical Society of America B•Jun 17, 2024•2 citations
We study a quantum emitter with N nearly degenerate excited states (sublevels) coupled to the ground state via the same optical resonance. We show that in such circumstances an approximate Jaynes-Cummings system emerges, with an effective coupling constant scaling with the square root of N. While our conclusions hold in general, we also present detailed analytical derivations for the instructive case N=2. Employing a quantum optical master equation we further observe that our system can closely match the spectral line shapes and photon autocorrelation functions typical of Jaynes-Cummings physics. Interestingly, we find that finite emitter dephasing can improve the quality of the approximation in some cases. By showing a novel route to increase the effective light-matter coupling strength, our findings may facilitate the control and detection of single-photon nonlinearities at ambient conditions.
Coupling NNN identical emitters to the same field mode is a well-established method to enhance light-matter interaction. However, the resulting N\sqrt{N}N​ boost of the coupling strength comes at the cost of a ``linearized'' (effectively semiclassical) dynamics. Here, we instead demonstrate a new approach for enhancing the coupling constant of a single quantum emitter, while retaining the nonlinear character of the light-matter interaction. We consider a single quantum emitter with NNN nearly degenerate transitions that are collectively coupled to the same field mode. We show that in such conditions an effective Jaynes-Cummings model emerges with a boosted coupling constant of order N\sqrt{N}N​. The validity and consequences of our general conclusions are analytically demonstrated for the instructive case N=2N=2N=2. We further observe that our system can closely match the spectral line shapes and photon autocorrelation functions typical of Jaynes-Cummings physics, proving that quantum optical nonlinearities are retained. Our findings match up very well with recent broadband plasmonic nanoresonator strong-coupling experiments and will, therefore, facilitate the control and detection of single-photon nonlinearities at ambient conditions.
The interaction of an ensemble of NNN two-level quantum emitters with a single-mode electromagnetic field is described by the Tavis-Cummings model. There, the collectively enhanced light-matter coupling strength is given by gN=Ng‾1{g}_{N}=\sqrt{N}{\overline{g}}_{1}gN​=N​g​1​, where g‾1{\overline{g}}_{1}g​1​ is the ensemble-averaged single-emitter coupling strength. This model has been employed to describe and to analyze numerous cavity-based experiments. Here, we show that this is only justified if the effective scattering rate into noncavity modes is negligible compared to the cavity's free-spectral range. In terms of experimental parameters, this requires that the optical depth of the ensemble is low, a condition that is violated in several state-of-the-art experiments. We give quantitative conditions for the validity of the Tavis-Cummings model and derive a more general Hamiltonian description that takes into account the cascaded interaction of the photons with all consecutive emitters. We show that the predictions of our cascaded model can differ quantitatively and even qualitatively from those obtained with the Tavis-Cummings model. Finally, we present experimental data, for which the deviation from the predictions of the Tavis-Cummings model is apparent. Our findings are relevant for all experiments in which optically dense ensembles of quantum emitters are coupled to an optical resonator.
Environmental influences on the dynamics of a coupled qubit-oscillator system are studied analytically in a regime where deviations from the exactly solvable Jaynes–Cummings model are important. We investigate the case of a quasi-degenerate qubit within the ultra-strong coupling regime for which the qubit frequency is much smaller than the frequency of the oscillator, and the coupling between the qubit and the oscillator is large, both of which invalidate the usually employed rotating wave approximation. In contrast to the standard quantum optics master equation, we explicitly take the qubit-oscillator coupling into account while microscopically deriving a dressed state master equation. Using the derived master equation, we discuss a spectroscopic technique which can be used to probe the dressed energy-level structure of the qubit-oscillator system.
Analytical solution for the stationary density matrix is derived, by using the Morris-Shore transformation, for an open Jaynes-Cummings system of a two-level atom with Zeeman sublevel degeneracy coupled to an arbitrary-polarized cavity mode. In the limit of weak excitation with the number of quantum in the system not exceeding one, we have obtained the stationary solution of the master equation up to the first order of the driving field intensity. We have also derived the analytic expressions for the excitation spectra of atomic spontaneous emission and cavity transmission. Our results show that the system can be regarded as a non-degenerate two-level system with a single effective coupling constant which depends only on the elliptic angle of the driving field as long as the atom-cavity coupling is not too strong. A precise condition for this approximation is derived. This work provides a theoretical ground for experimentally realizing a Jaynes-Cummings system with a coupling constant continuously varied for various cavity quantum electrodynamics studies.
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.
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 decay 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.