Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Exciton-photon dynamics in quantum dots embedded in photonic cavities

Thomas Tunstall Allcock

Published Dec 1, 2020• 0 citations
OpenAlex

Abstract

We develop an exact analytical approach to four-wave mixing and higher-order optical nonlinearities of a quantum dot-microcavity system. This approach allows us \nto analyse the non-linear response in terms of coherent transitions between rungs \nof the Jaynes-Cummings ladder, finding their complex amplitudes and frequencies. \nIncreasing the pulse area of the excitation field, a transition from quantum strong \ncoupling to coherent classical regime is observed, which manifests itself in a formation of the famous Mollow triplet, with the observation in the three-level model \nof a quantum dot, including a biexciton, to predict two new effects: One is the \nexistence of a Mollow-like quintuplet, the other is a complete elimination of the \nfour-wave-mixing optical non-linearity under certain parameter constraints. We further develop a simple and accurate approximation in the low-damping limit of the \nJaynes-Cummings model of the quantum dot-microcavity system, for nonlinear response of any order in a closed analytic form, predicting the positions and widths \nof the spectral lines. For higher damping, we demonstrate a strong relaxation down \nthe ladder, shown by both numerical and analytic calculation.

Related papers

Quantum Mollow Quadruplet in Nonlinear Cavity QED

Thomas Allcock, Wolfgang Langbein, Egor A. Muljarov

We develop an exact analytical approach to the optical response of a two-level system coupled to a microcavity for arbitrary excitation strengths. The response is determined in terms of the complex amplitudes of transitions between the rungs of the Jaynes-Cummings ladder, explicitly isolating nonlinearities of different orders. Increasing the pulse area of the excitation field, we demonstrate the formation of a quantum Mollow quadruplet (QMQ), quantizing the semiclassical Mollow triplet into a coherent superposition of a large number of transitions between rungs of the ladder, with inner and outer doublets of the QMQ formed by densely lying inner and outer quantum transitions between the split rungs. Remarkably, a closed-form analytic approximation for the QMQ of any order of nonlinearity is found in the high-field low-damping limit.

arXiv:2107.01203•Physical Review Letters•Mar 24, 2022•5 citations

Coherence dynamics and quantum-to-classical crossover in an exciton–cavity system in the quantum strong coupling regime

Jacek Kasprzak, Kanchana Sivalertporn, Ferdinand Albert +7 more

Interaction between light and matter generates optical nonlinearities, which are particularly pronounced in the quantum strong coupling regime. When a single bosonic mode couples to a single fermionic mode, a Jaynes–Cummings (JC) ladder is formed, which we realize here using cavity photons and quantum dot excitons. We measure and model the coherent anharmonic response of this strongly coupled exciton–cavity system at resonance. Injecting two photons into the cavity, we demonstrate a larger polariton splitting with respect to the vacuum Rabi splitting. This is achieved using coherent nonlinear spectroscopy, specifically four-wave mixing, where the coherence between the ground state and the first (second) rung of the JC ladder can be interrogated for positive (negative) delays. With increasing excitation intensity and thus rising average number of injected photons, we observe spectral signatures of the quantum-to-classical crossover of the strong coupling regime.

New Journal of Physics•Apr 22, 2013•15 citations

Impact of the phonon environment on the nonlinear quantum-dot cavity QED. II. Analytical approach

L. S. Sirkina, Egor A. Muljarov

The effect of phonons on a nonlinear optical response of a quantum dot-cavity system in quantum strong coupling regime can be accounted for by a fully analytical treatment, provided that the exciton-phonon dynamics is much faster than the exciton-cavity dynamics. Modern experiments involving semiconductor quantum dots embedded in optical microcavities typically meet this criterion. We find that, for a relatively small exciton-cavity coupling, the effect of phonons is concentrated mainly in the polaron shift of the exciton frequency and reduction of exciton-cavity coupling by the Huang-Rhys factor. We have generalized this result to an arbitrary optical nonlinearity and demonstrated a good agreement with the exact solution in a wide range of temperatures. This generalization provides access to higher rungs of the Jaynes-Cummings ladder, where exact numerical approaches are impractical or even impossible. At larger coupling strengths and low temperatures, our approximation is also in good agreement with the exact solution, which makes it a very useful tool for addressing the phonon contribution to the coherent dynamics of a nonlinear optical system. We demonstrate our results for third-order optical polarization with varying observation time and delay time between excitation pulses in the form of two-dimensional spectra. These spectra provide useful information about the coherent coupling between the exciton and the cavity modes. The presented analytical approach is also compared with another useful approximation, having the form of a matrix product, which is a special case of the asymptotically exact solution in the limit of a short phonon memory time.

arXiv:2306.16579•Jun 28, 2023•0 citations

Impact of the phonon environment on the nonlinear quantum-dot–cavity QED: Path-integral approach

L. S. Sirkina, Egor A. Muljarov

We demonstrate a strong influence of the phonon environment on the coherent dynamics of the quantum dot (QD)-cavity system in the quantum strong coupling regime. This regime is implemented in the nonlinear QD-cavity QED and can be reliably measured by heterodyne spectral interferometry. We present a semianalytic asymptotically exact path integral-based approach to the nonlinear optical response of this system, which includes two key ingredients: Trotter's decomposition and linked-cluster expansion. Applied to the four-wave-mixing optical polarization, this approach provides access to different excitation and measurement channels, as well as to higher-order optical nonlinearities and quantum correlators. Furthermore, it allows us to extract useful analytic approximations and analyze the nonlinear optical response in terms of quantum transitions between phonon-dressed states of the anharmonic Jaynes-Cummings (JC) ladder. Being well described by these approximations at low temperatures and small exciton-cavity coupling, the exact solution deviates from them for stronger couplings and higher temperatures, demonstrating remarkable non-Markovian effects, spectral asymmetry, and strong phonon renormalization of the JC ladder.

arXiv:2306.17722•Physical review. B./Physical review. B•Sep 28, 2023•5 citations

Theoretical analysis of four-wave mixing on semiconductor quantum dot ensembles with quantum light

Hendrik Rose, Stefan Grisard, Artur V. Trifonov +5 more

The nonlinear optical response of an ensemble of semiconductor quantum dots is analyzed by wave-mixing processes, where we focus on four-wave mixing with two incident pulses. Wave-mixing experiments are often described with semiclassical models, where the light is modeled classically and the material quantum mechanically. Here, however, we use a fully quantized model, where the light is given by a quantum state of light. Quantum light involves more degrees of freedom than classical light as e.g., its photon statistics and quantum correlations, which is a promising resource for quantum devices, such as quantum memories. The light-matter interaction is treated with a Jaynes-Cummings type model and the quantum field is given by a single mode since the quantum dots are embedded in a microcavity. We present numerical simulations of the four-wave-mixing response of a homogeneous system for pulse sequences and find a significant dependence of the result on the photon statistics of the incident pulses. The model constitutes a problem with a large state space which arises from the frequency distribution of the transition energies of the inhomogeneously broadened quantum dot ensemble that is coupled with a quantum light mode. Here we approximate the dynamics by summing over individual quantum dot-microcavity systems. Photon echoes arising from the excitation with different quantum states of light are simulated and compared.

Ultrafast Phenomena and Nanophotonics•Mar 15, 2023•0 citations

Four-wave mixing dynamics of a strongly coupled quantum-dot–microcavity system driven by up to 20 photons

Daniel Groll, Daniel Wigger, Kevin Jürgens +6 more

The Jaynes-Cummings (JC) model is at the heart of cavity QED and suitable to describe many different systems. Here, the authors use it to investigate a quantum dot strongly coupled to a micropillar cavity. Supported by experiments, they apply four-wave mixing spectroscopy to study the system's dynamics. They push the limits of JC physics by injecting up to $\ensuremath{\sim}20$ photons using ultrashort laser pulses. Starting with complicated dynamics, the signal evolves into a single-frequency oscillation monitoring the relaxation down the JC ladder.

arXiv:2006.07337•Physical review. B./Physical review. B•Jun 4, 2020•13 citations
We develop an exact analytical approach to four-wave mixing and higher-order optical nonlinearities of a quantum dot-microcavity system. This approach allows us \nto analyse the non-linear response in terms of coherent transitions between rungs \nof the Jaynes-Cummings ladder, finding their complex amplitudes and frequencies. \nIncreasing the pulse area of the excitation field, a transition from quantum strong \ncoupling to coherent classical regime is observed, which manifests itself in a formation of the famous Mollow triplet, with the observation in the three-level model \nof a quantum dot, including a biexciton, to predict two new effects: One is the \nexistence of a Mollow-like quintuplet, the other is a complete elimination of the \nfour-wave-mixing optical non-linearity under certain parameter constraints. We further develop a simple and accurate approximation in the low-damping limit of the \nJaynes-Cummings model of the quantum dot-microcavity system, for nonlinear response of any order in a closed analytic form, predicting the positions and widths \nof the spectral lines. For higher damping, we demonstrate a strong relaxation down \nthe ladder, shown by both numerical and analytic calculation.
We develop an exact analytical approach to the optical response of a two-level system coupled to a microcavity for arbitrary excitation strengths. The response is determined in terms of the complex amplitudes of transitions between the rungs of the Jaynes-Cummings ladder, explicitly isolating nonlinearities of different orders. Increasing the pulse area of the excitation field, we demonstrate the formation of a quantum Mollow quadruplet (QMQ), quantizing the semiclassical Mollow triplet into a coherent superposition of a large number of transitions between rungs of the ladder, with inner and outer doublets of the QMQ formed by densely lying inner and outer quantum transitions between the split rungs. Remarkably, a closed-form analytic approximation for the QMQ of any order of nonlinearity is found in the high-field low-damping limit.
Interaction between light and matter generates optical nonlinearities, which are particularly pronounced in the quantum strong coupling regime. When a single bosonic mode couples to a single fermionic mode, a Jaynes–Cummings (JC) ladder is formed, which we realize here using cavity photons and quantum dot excitons. We measure and model the coherent anharmonic response of this strongly coupled exciton–cavity system at resonance. Injecting two photons into the cavity, we demonstrate a larger polariton splitting with respect to the vacuum Rabi splitting. This is achieved using coherent nonlinear spectroscopy, specifically four-wave mixing, where the coherence between the ground state and the first (second) rung of the JC ladder can be interrogated for positive (negative) delays. With increasing excitation intensity and thus rising average number of injected photons, we observe spectral signatures of the quantum-to-classical crossover of the strong coupling regime.
The effect of phonons on a nonlinear optical response of a quantum dot-cavity system in quantum strong coupling regime can be accounted for by a fully analytical treatment, provided that the exciton-phonon dynamics is much faster than the exciton-cavity dynamics. Modern experiments involving semiconductor quantum dots embedded in optical microcavities typically meet this criterion. We find that, for a relatively small exciton-cavity coupling, the effect of phonons is concentrated mainly in the polaron shift of the exciton frequency and reduction of exciton-cavity coupling by the Huang-Rhys factor. We have generalized this result to an arbitrary optical nonlinearity and demonstrated a good agreement with the exact solution in a wide range of temperatures. This generalization provides access to higher rungs of the Jaynes-Cummings ladder, where exact numerical approaches are impractical or even impossible. At larger coupling strengths and low temperatures, our approximation is also in good agreement with the exact solution, which makes it a very useful tool for addressing the phonon contribution to the coherent dynamics of a nonlinear optical system. We demonstrate our results for third-order optical polarization with varying observation time and delay time between excitation pulses in the form of two-dimensional spectra. These spectra provide useful information about the coherent coupling between the exciton and the cavity modes. The presented analytical approach is also compared with another useful approximation, having the form of a matrix product, which is a special case of the asymptotically exact solution in the limit of a short phonon memory time.
We demonstrate a strong influence of the phonon environment on the coherent dynamics of the quantum dot (QD)-cavity system in the quantum strong coupling regime. This regime is implemented in the nonlinear QD-cavity QED and can be reliably measured by heterodyne spectral interferometry. We present a semianalytic asymptotically exact path integral-based approach to the nonlinear optical response of this system, which includes two key ingredients: Trotter's decomposition and linked-cluster expansion. Applied to the four-wave-mixing optical polarization, this approach provides access to different excitation and measurement channels, as well as to higher-order optical nonlinearities and quantum correlators. Furthermore, it allows us to extract useful analytic approximations and analyze the nonlinear optical response in terms of quantum transitions between phonon-dressed states of the anharmonic Jaynes-Cummings (JC) ladder. Being well described by these approximations at low temperatures and small exciton-cavity coupling, the exact solution deviates from them for stronger couplings and higher temperatures, demonstrating remarkable non-Markovian effects, spectral asymmetry, and strong phonon renormalization of the JC ladder.
The nonlinear optical response of an ensemble of semiconductor quantum dots is analyzed by wave-mixing processes, where we focus on four-wave mixing with two incident pulses. Wave-mixing experiments are often described with semiclassical models, where the light is modeled classically and the material quantum mechanically. Here, however, we use a fully quantized model, where the light is given by a quantum state of light. Quantum light involves more degrees of freedom than classical light as e.g., its photon statistics and quantum correlations, which is a promising resource for quantum devices, such as quantum memories. The light-matter interaction is treated with a Jaynes-Cummings type model and the quantum field is given by a single mode since the quantum dots are embedded in a microcavity. We present numerical simulations of the four-wave-mixing response of a homogeneous system for pulse sequences and find a significant dependence of the result on the photon statistics of the incident pulses. The model constitutes a problem with a large state space which arises from the frequency distribution of the transition energies of the inhomogeneously broadened quantum dot ensemble that is coupled with a quantum light mode. Here we approximate the dynamics by summing over individual quantum dot-microcavity systems. Photon echoes arising from the excitation with different quantum states of light are simulated and compared.
The Jaynes-Cummings (JC) model is at the heart of cavity QED and suitable to describe many different systems. Here, the authors use it to investigate a quantum dot strongly coupled to a micropillar cavity. Supported by experiments, they apply four-wave mixing spectroscopy to study the system's dynamics. They push the limits of JC physics by injecting up to $\ensuremath{\sim}20$ photons using ultrashort laser pulses. Starting with complicated dynamics, the signal evolves into a single-frequency oscillation monitoring the relaxation down the JC ladder.