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

Nonlinear Dynamics in Optical Systems

Spontaneous Dressed-State Polarization of a Coupled Atom and Cavity Mode

H. J. Carmichael, P. M. Alsing

Published Jan 1, 1990• 4 citations
Publisher

Abstract

The interaction between two-state atoms and the modes of an optical cavity has been studied extensively over many years; in particular, in connection with lasers and optical bistability. These are dissipative systems, and it has been usual in their study to assume that dissipation rates are, in some sense, large compared with the coupling strength between the atoms and the field. Recent work has shown that interesting new dynamical behavior occurs when this is not so. For example, spontaneous emission linewidths can be altered,1,2 and if the coupling is very strong, an emission line can be split into a pair of resonances identified with the normal- mode frequencies of coupled oscillators describing the atomic polarization and the cavity field.3.4 Altered linewidths and normal-mode splitting are features of weak excitation; both are explained by a coupled damped harmonic oscillator model. In this paper we report new results obtained for strong excitation.

DOI
10.1364/nldos.1990.stqe600

Related papers

Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators

H. J. Carmichael, Robert J. Brecha, Mark G. Raizen +2 more

We calculate the spontaneous-emission spectrum and the spectrum of weakly driven fluorescence for a two-level atom coupled to a resonant-cavity mode. For strong atom-cavity coupling the spectra split into two peaks that can have subnatural linewidths. If the cavity linewidth is negligible, the spontaneous-emission spectrum has half the radiative linewidth of the atom; the spectrum of weakly driven fluorescence shows an additional 36% squeezing-induced narrowing. These effects can be observed using coupled-field and collective-polarization oscillators excited in a cavity containing N two-level atoms.

Physical Review A•Nov 1, 1989•203 citations

Spontaneous dressed-state polarization of a coupled atom and cavity mode

P. M. Alsing, H. J. Carmichael

The authors calculate the asymptotic quantum state of a driven cavity mode interacting with a two-state atom when the dipole coupling constant is much larger than the atomic and cavity linewidths. They show that a novel symmetry breaking transition occurs as the strength of the driving field is increased. Although the driving field, the cavity mode, and the atom are all resonant, above the transition threshold the intracavity field shows a bimodality in phase. The bimodality results from an intensity-dependent detuning between the driving field and the transition frequencies of the composite atom-cavity-mode 'molecule.' Well above the transition threshold the driven cavity mode plus atom behaves as a driven harmonic oscillator with randomly switched detuning; the detuning (and hence the phase of the interactivity field) changes sign each time the atom makes a spontaneous transition between dressed states.

Quantum Optics Journal of the European Optical Society Part B•Feb 1, 1991•124 citations

Dissipative Quantum Dynamics in Cavity Quantum Electrodynamics

H. Jeff. Kimble, G. Rempe, R. J. Thompson +1 more

Of fundamental importance in quantum optics has been the investigation of the radiative coupling of a collection of atoms to the field of a resonant cavity1. Within this context we are conducting a research program to investigate the interaction of optically prepared two-state atoms with the fields of high finesse optical cavities. With regard to our specific observations, we have employed a sodium atomic beam apparatus to make direct spectroscopic measurements of the normal-mode splitting for the coupled oscillator system formed by the collective atomic polarization of N two-state atoms and a single mode of a resonator of finesse of approximately 2x10⁴. At the transition wavelength of 589 nm (³, S_(1/2), F = 2, m_F = 2→3 P_(3/2), m_F = 3 and for one of our spherical mirror standing-wave cavities, the relevant parameters for the system are as follows: transverse atomic decay rate γ_⊥ = 2πX5X10⁶/S, cavity damping rate K/γ⊥= 0.18, and single-atom coupling coefficient g/γ_⊥ = 0.2.

Foundations of Quantum Mechanics•Apr 1, 1992•1 citation

Novel fluorescent spectra from an atom strongly coupled to a driven cavity

Craig M. Savage

Recently there has been both theoretical [1-3] and experimental [4] interest in atoms strongly coupled to single mode optical cavities. Strong coupling means that the energy level splitting due to a single quantum of excitation is comparable to the dissipative linewidth of the system. Single quantum frequency splitting has been observed for as few as 20 atoms strongly coupled to a cavity [4].

Digest on Nonlinear Optics: Materials, Phenomena and Devices•Jan 1, 1990•0 citations

Composite structure for two-state atoms in an optical cavity

M. G. Raizen, R. J. Brecha, R. J. Thompson +1 more

Experimental and theoretical investigations of the radiative processes of a collection of two-state atoms contained in a high-finesse optical cavity are reported. To make contact with previous work on this subject, we consider the usual regimens in which either the cavity or the atomic damping is dominant. However, of greater interest and relevance to our experiments is the regime of strong coupling that generates splittings and new features in the normal-mode structure of the composite atom-field system. We identify possible mechanisms for producing line shapes with subnatural linewidths. Our experimental investigations are conducted with two-state sodium atoms that interact with a single mode of an ultra-high-finesse optical cavity. The incoherent spectral density of the transmitted field is detected by optical heterodyne. We obtain good qualitative agreement between theory and experiment for the general features of the composite atom-field system as manifested in the spectral density of the transmitted field. Experiments to probe the response of the system to weak modulation of the incident field are in progress.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Dynamics of Coherently Excited Semiconductor Microcavities

June‐Koo Kevin Rhee, Theodore B. Norris, Yasuhiko Arakawa +2 more

Recently, cavity quantum electrodynamic (QED) effects in semiconductor microcavities have been of considerable interest since, in the weak-coupling regime they play an important role in selectively increasing spontaneous emission into the lasing mode of vertical-cavity surface-emitting lasers (VCSEL’s) [1,2], enabling low-threshold, high speed, and high efficiency. In a strong-coupling regime, the normal modes of the coupled system are superpositions of the exciton and cavity modes. Hence the impulsively excited system will evolve in time with the energy oscillating between the exciton and cavity modes. This is known as a vacuum-Rabi oscillation (VRO), with a frequency of Ω=d¯⋅E¯/@@h, where d¯ is the transition dipole moment of atoms and E¯ the vacuum-field strength. Of course, VRO are observable only when the cavity lifetime and exciton dephasing time are long enough compared to VRO period. Recently, Weisbuch et al. [3] have reported an observation of the normal-mode vacuum Rabi splitting in 2-D-exciton/planar-DBR microcavities. The observed splittings were as large as 6 meV in reflection and transmission spectra, implying 690-fs vacuum Rabi oscillations.

International Conference on Ultrafast Phenomena•Jan 1, 1994•0 citations
The interaction between two-state atoms and the modes of an optical cavity has been studied extensively over many years; in particular, in connection with lasers and optical bistability. These are dissipative systems, and it has been usual in their study to assume that dissipation rates are, in some sense, large compared with the coupling strength between the atoms and the field. Recent work has shown that interesting new dynamical behavior occurs when this is not so. For example, spontaneous emission linewidths can be altered,1,2 and if the coupling is very strong, an emission line can be split into a pair of resonances identified with the normal- mode frequencies of coupled oscillators describing the atomic polarization and the cavity field.3.4 Altered linewidths and normal-mode splitting are features of weak excitation; both are explained by a coupled damped harmonic oscillator model. In this paper we report new results obtained for strong excitation.
We calculate the spontaneous-emission spectrum and the spectrum of weakly driven fluorescence for a two-level atom coupled to a resonant-cavity mode. For strong atom-cavity coupling the spectra split into two peaks that can have subnatural linewidths. If the cavity linewidth is negligible, the spontaneous-emission spectrum has half the radiative linewidth of the atom; the spectrum of weakly driven fluorescence shows an additional 36% squeezing-induced narrowing. These effects can be observed using coupled-field and collective-polarization oscillators excited in a cavity containing N two-level atoms.
The authors calculate the asymptotic quantum state of a driven cavity mode interacting with a two-state atom when the dipole coupling constant is much larger than the atomic and cavity linewidths. They show that a novel symmetry breaking transition occurs as the strength of the driving field is increased. Although the driving field, the cavity mode, and the atom are all resonant, above the transition threshold the intracavity field shows a bimodality in phase. The bimodality results from an intensity-dependent detuning between the driving field and the transition frequencies of the composite atom-cavity-mode 'molecule.' Well above the transition threshold the driven cavity mode plus atom behaves as a driven harmonic oscillator with randomly switched detuning; the detuning (and hence the phase of the interactivity field) changes sign each time the atom makes a spontaneous transition between dressed states.
Of fundamental importance in quantum optics has been the investigation of the radiative coupling of a collection of atoms to the field of a resonant cavity1. Within this context we are conducting a research program to investigate the interaction of optically prepared two-state atoms with the fields of high finesse optical cavities. With regard to our specific observations, we have employed a sodium atomic beam apparatus to make direct spectroscopic measurements of the normal-mode splitting for the coupled oscillator system formed by the collective atomic polarization of N two-state atoms and a single mode of a resonator of finesse of approximately 2x10⁴. At the transition wavelength of 589 nm (³, S_(1/2), F = 2, m_F = 2→3 P_(3/2), m_F = 3 and for one of our spherical mirror standing-wave cavities, the relevant parameters for the system are as follows: transverse atomic decay rate γ_⊥ = 2πX5X10⁶/S, cavity damping rate K/γ⊥= 0.18, and single-atom coupling coefficient g/γ_⊥ = 0.2.
Experimental and theoretical investigations of the radiative processes of a collection of two-state atoms contained in a high-finesse optical cavity are reported. To make contact with previous work on this subject, we consider the usual regimens in which either the cavity or the atomic damping is dominant. However, of greater interest and relevance to our experiments is the regime of strong coupling that generates splittings and new features in the normal-mode structure of the composite atom-field system. We identify possible mechanisms for producing line shapes with subnatural linewidths. Our experimental investigations are conducted with two-state sodium atoms that interact with a single mode of an ultra-high-finesse optical cavity. The incoherent spectral density of the transmitted field is detected by optical heterodyne. We obtain good qualitative agreement between theory and experiment for the general features of the composite atom-field system as manifested in the spectral density of the transmitted field. Experiments to probe the response of the system to weak modulation of the incident field are in progress.
Recently, cavity quantum electrodynamic (QED) effects in semiconductor microcavities have been of considerable interest since, in the weak-coupling regime they play an important role in selectively increasing spontaneous emission into the lasing mode of vertical-cavity surface-emitting lasers (VCSEL’s) [1,2], enabling low-threshold, high speed, and high efficiency. In a strong-coupling regime, the normal modes of the coupled system are superpositions of the exciton and cavity modes. Hence the impulsively excited system will evolve in time with the energy oscillating between the exciton and cavity modes. This is known as a vacuum-Rabi oscillation (VRO), with a frequency of Ω=d¯⋅E¯/@@h, where d¯ is the transition dipole moment of atoms and E¯ the vacuum-field strength. Of course, VRO are observable only when the cavity lifetime and exciton dephasing time are long enough compared to VRO period. Recently, Weisbuch et al. [3] have reported an observation of the normal-mode vacuum Rabi splitting in 2-D-exciton/planar-DBR microcavities. The observed splittings were as large as 6 meV in reflection and transmission spectra, implying 690-fs vacuum Rabi oscillations.