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

Physical Review A

Competing three-photon and one-photon transitions in cavity quantum electrodynamics

Iyyanki V. Jyotsna, G. S. Agarwal

Published Aug 1, 1994• 15 citations
Publisher

Abstract

We examine a model of two-channel cavity quantum electrodynamics (QED) consisting of three-photon and one-photon absorption processes, i.e., we present a cavity-QED version of a nonlinear optical balance. We give detailed numerical results for the evolution of the atomic populations and the number of photons at the fundamental and third harmonic frequencies. We also show the behavior of the system if the fields are treated semiclassically, and we find the quantum effects to be rather dominant.

DOI
10.1103/physreva.50.1770

Related papers

Semiclassical and quantum nonlinear spectra of a strongly coupled single Λ-type three-level atom-cavity QED system

Mohamed Musa, Helmi Temimi, Y. Zhu

We present detailed numerical simulations of semiclassical and quantum spectra of a cavity QED system consisting of a single three-level atom in Λ-configuration interacting with a quantized cavity mode through one of its transitions while its other transition is driven by a coherent classical field. We compute the semiclassical and quantum spectra of the system under various levels of external driving field strengths. In the semiclassical approach, we neglect the correlations between the cavity and atomic operators, whereas in the quantum case no such assumption is made. Our results show that the two approaches yield identical results under sufficiently weak driving field conditions. However, the two approaches yield starkly different results at stronger driving field intensities: the fully quantum approach yields a well-defined multiphoton spectrum whereas the semiclassical approach results in a bistable spectrum. Furthermore, our calculations reveal a complex Raman structure at the position of the dark-state transition.

arXiv:1907.12391•Journal of Modern Optics•Mar 4, 2022•1 citation

Cavity quantum electrodynamics

Tracy E. Northup

Cavity quantum electrodynamics (cavity QED) describes the interactions of single atoms and single photons in a resonator. In the laboratory, state-of-the-art experiments are able to observe the dynamics of these simple yet fundamental quantum systems. The recent development of quantum information science has also introduced a new role for cavity QED systems as quantum interfaces, in which information can be coherently mapped between photonic and atomic quantum bits. Groundbreaking optical cavity QED experiments in the past twenty years would not have been possible without the technological development of mirror coatings with extremely low scatter and absorption losses. Thermal noise has typically played a smaller role in cavity QED experiments but in certain instances is nevertheless important to consider. In this chapter, we begin with an overview of optical cavity QED experiments and some of the central questions that they address. It is hoped that this description, while by no means exhaustive, will provide a window for the nonspecialist into basic techniques and motivations in the field. We then turn to focus on the roles played by scattering and absorption loss and mechanical loss. We discuss how these losses have set limits on feasible experiments and the extent to which improvements may be possible. Experimental realizations of cavity QED systems An idealized cavity QED system consists of one atom placed between two highly reflective mirrors (Figure 17.1). In this model, a single atomic transition interacts with photons in a single cavity mode; the atom is often pictured at an antinode of the cavity standing wave, where it has a maximal dipole interaction with the cavity field.

Cambridge University Press eBooks•Jan 6, 2012•0 citations

Dark states and interferences in cascade transitions of ultracold atoms in a cavity

R. Arun, G. S. Agarwal

We examine the competition among one- and two-photon processes in an ultracold, three-level atom undergoing cascade transitions as a result of its interaction with a bimodal cavity. We show parameter domains where two-photon transitions are dominant, and we also study the effect of two-photon emission on the mazer action in the cavity. The two-photon emission leads to the loss of detailed balance and therefore we obtain the photon statistics of the cavity field by the numerical integration of the master equation. The photon distribution in each cavity mode exhibits sub- and super-Poissonian behaviors depending on the strength of atom-field coupling. The photon distribution becomes identical to a Poisson distribution when the atom-field coupling strengths of the modes are equal.

arXiv:quant-ph/0204023•Physical Review A•Oct 24, 2002•19 citations

TWO-PHOTON NONLINEAR INTERACTION MEDIATED BY CAVITY QUANTUM ELECTRODYNAMICS SYSTEMS

Kazuki Koshino, Hajime Ishihara

Exploiting the field-amplification effect of a cavity, the possibility of optical nonlinearity by only two photons was indicated experimentally. In the present article, we review our recent analysis of the two-photon dynamics in a cavity quantum electrodynamics (QED) system. Since a cavity-QED system is highly dispersive around its resonances, the shapes of photonic pulses are significantly deformed through interaction with the system. Thus, the present analysis is based on a formalism beyond single-mode approximations. The external photon field is treated rigorously as a continuum, which enables us to handle the two-photon wavefunction in the space representation. The degree of optical nonlinearity in a two-photon state is quantified by comparing the output wavefunction with the linear output wavefunction. It is revealed that the semiclassical optical response theory can be applied for evaluation of the two-photon optical nonlinearity. The two-photon nonlinearity appears not purely as a phase shift in the output wavefunction. The degradation of the fidelity between the output wavefunction and the linear output wavefunction always occurs, which hinders the application of this nonlinear effect as a quantum phase gate. The optimum condition for maximizing the two-photon nonlinearity is clarified, suggesting that pulse shape control is more essential than the Q-value control of the cavity QED system.

International Journal of Modern Physics B•Jul 20, 2006•4 citations

Deterministic three-photon down-conversion by a passive ultrastrong cavity-QED system

Kazuki Koshino, Tomohiro Shitara, Ziqiao Ao +1 more

In ultra- and deep-strong cavity quantum electrodynamics (QED) systems, many intriguing phenomena that do not conserve the excitation number are expected to occur. In this paper, we theoretically analyze the optical response of an ultrastrong cavity-QED system in which an atom is coupled to the first and third harmonic modes of a cavity, and report the possibility of deterministic three-photon down-conversion of itinerant photons upon reflection at the cavity. In the conventional parametric down-conversion, a strong input field is needed because of the smallness of the transition matrix elements of the higher-order processes. However, if we use an atom-cavity system in an unprecedentedly strong-coupling region, even a weak field in the linear-response regime is sufficient to cause this rare event involving the fourth-order transitions.

arXiv:2109.02764•Physical Review Research•Jan 6, 2022•8 citations

Low-lying bifurcations in cavity quantum electrodynamics

Michael A. Armen, Hideo Mabuchi

The interplay of quantum fluctuations with nonlinear dynamics is a central topic in the study of open quantum systems, connected to fundamental issues (such as decoherence and the quantum-classical transition) and practical applications (such as coherent information processing and the development of mesoscopic sensors and amplifiers). With this context in mind, we here present a computational study of some elementary bifurcations that occur in a driven and damped cavity quantum electrodynamics (cavity QED) model at low intracavity photon number. In particular, we utilize the single-atom cavity QED master equation and associated stochastic Schr\"odinger equations to characterize the equilibrium distribution and dynamical behavior of the quantized intracavity optical field in parameter regimes near points in the semiclassical (mean-field, Maxwell-Bloch) bifurcation set. Our numerical results show that the semiclassical limit sets are qualitatively preserved in the quantum stationary states, although quantum fluctuations apparently induce phase diffusion within periodic orbits and stochastic transitions between attractors. We restrict our attention to an experimentally realistic parameter regime.

arXiv:quant-ph/0602170•Physical Review A•Jun 1, 2006•87 citations
We examine a model of two-channel cavity quantum electrodynamics (QED) consisting of three-photon and one-photon absorption processes, i.e., we present a cavity-QED version of a nonlinear optical balance. We give detailed numerical results for the evolution of the atomic populations and the number of photons at the fundamental and third harmonic frequencies. We also show the behavior of the system if the fields are treated semiclassically, and we find the quantum effects to be rather dominant.
We present detailed numerical simulations of semiclassical and quantum spectra of a cavity QED system consisting of a single three-level atom in Λ-configuration interacting with a quantized cavity mode through one of its transitions while its other transition is driven by a coherent classical field. We compute the semiclassical and quantum spectra of the system under various levels of external driving field strengths. In the semiclassical approach, we neglect the correlations between the cavity and atomic operators, whereas in the quantum case no such assumption is made. Our results show that the two approaches yield identical results under sufficiently weak driving field conditions. However, the two approaches yield starkly different results at stronger driving field intensities: the fully quantum approach yields a well-defined multiphoton spectrum whereas the semiclassical approach results in a bistable spectrum. Furthermore, our calculations reveal a complex Raman structure at the position of the dark-state transition.
Cavity quantum electrodynamics (cavity QED) describes the interactions of single atoms and single photons in a resonator. In the laboratory, state-of-the-art experiments are able to observe the dynamics of these simple yet fundamental quantum systems. The recent development of quantum information science has also introduced a new role for cavity QED systems as quantum interfaces, in which information can be coherently mapped between photonic and atomic quantum bits. Groundbreaking optical cavity QED experiments in the past twenty years would not have been possible without the technological development of mirror coatings with extremely low scatter and absorption losses. Thermal noise has typically played a smaller role in cavity QED experiments but in certain instances is nevertheless important to consider. In this chapter, we begin with an overview of optical cavity QED experiments and some of the central questions that they address. It is hoped that this description, while by no means exhaustive, will provide a window for the nonspecialist into basic techniques and motivations in the field. We then turn to focus on the roles played by scattering and absorption loss and mechanical loss. We discuss how these losses have set limits on feasible experiments and the extent to which improvements may be possible. Experimental realizations of cavity QED systems An idealized cavity QED system consists of one atom placed between two highly reflective mirrors (Figure 17.1). In this model, a single atomic transition interacts with photons in a single cavity mode; the atom is often pictured at an antinode of the cavity standing wave, where it has a maximal dipole interaction with the cavity field.
We examine the competition among one- and two-photon processes in an ultracold, three-level atom undergoing cascade transitions as a result of its interaction with a bimodal cavity. We show parameter domains where two-photon transitions are dominant, and we also study the effect of two-photon emission on the mazer action in the cavity. The two-photon emission leads to the loss of detailed balance and therefore we obtain the photon statistics of the cavity field by the numerical integration of the master equation. The photon distribution in each cavity mode exhibits sub- and super-Poissonian behaviors depending on the strength of atom-field coupling. The photon distribution becomes identical to a Poisson distribution when the atom-field coupling strengths of the modes are equal.
Exploiting the field-amplification effect of a cavity, the possibility of optical nonlinearity by only two photons was indicated experimentally. In the present article, we review our recent analysis of the two-photon dynamics in a cavity quantum electrodynamics (QED) system. Since a cavity-QED system is highly dispersive around its resonances, the shapes of photonic pulses are significantly deformed through interaction with the system. Thus, the present analysis is based on a formalism beyond single-mode approximations. The external photon field is treated rigorously as a continuum, which enables us to handle the two-photon wavefunction in the space representation. The degree of optical nonlinearity in a two-photon state is quantified by comparing the output wavefunction with the linear output wavefunction. It is revealed that the semiclassical optical response theory can be applied for evaluation of the two-photon optical nonlinearity. The two-photon nonlinearity appears not purely as a phase shift in the output wavefunction. The degradation of the fidelity between the output wavefunction and the linear output wavefunction always occurs, which hinders the application of this nonlinear effect as a quantum phase gate. The optimum condition for maximizing the two-photon nonlinearity is clarified, suggesting that pulse shape control is more essential than the Q-value control of the cavity QED system.
In ultra- and deep-strong cavity quantum electrodynamics (QED) systems, many intriguing phenomena that do not conserve the excitation number are expected to occur. In this paper, we theoretically analyze the optical response of an ultrastrong cavity-QED system in which an atom is coupled to the first and third harmonic modes of a cavity, and report the possibility of deterministic three-photon down-conversion of itinerant photons upon reflection at the cavity. In the conventional parametric down-conversion, a strong input field is needed because of the smallness of the transition matrix elements of the higher-order processes. However, if we use an atom-cavity system in an unprecedentedly strong-coupling region, even a weak field in the linear-response regime is sufficient to cause this rare event involving the fourth-order transitions.
The interplay of quantum fluctuations with nonlinear dynamics is a central topic in the study of open quantum systems, connected to fundamental issues (such as decoherence and the quantum-classical transition) and practical applications (such as coherent information processing and the development of mesoscopic sensors and amplifiers). With this context in mind, we here present a computational study of some elementary bifurcations that occur in a driven and damped cavity quantum electrodynamics (cavity QED) model at low intracavity photon number. In particular, we utilize the single-atom cavity QED master equation and associated stochastic Schr\"odinger equations to characterize the equilibrium distribution and dynamical behavior of the quantized intracavity optical field in parameter regimes near points in the semiclassical (mean-field, Maxwell-Bloch) bifurcation set. Our numerical results show that the semiclassical limit sets are qualitatively preserved in the quantum stationary states, although quantum fluctuations apparently induce phase diffusion within periodic orbits and stochastic transitions between attractors. We restrict our attention to an experimentally realistic parameter regime.