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

Annual Meeting Optical Society of America

Broadband excitation of the Jaynes–Cummings molecule

Liguang Tian, H. J. Carmichael

Published Jan 1, 1990• 0 citations
Publisher

Abstract

When a single atom interacts with one mode of an optical cavity and the coupling to the cavity mode is sufficiently large, the spectroscopic response of the composite system to a weak probe is a doublet, with peaks located at the eigenfrequencies of the one-quantum excited states of the Jaynes–Cummings Hamiltonian. So far as these one-quantum states are concerned the spectroscopy of the Jaynes–Cummings model is the same as that of coupled, damped harmonic oscillators. This equivalence has been used to observe a doublet spectrum (the so-called "vacuum" Rabi splitting) by exciting a collective dipole oscillator inside an optical cavity.1,2 At higher levels of excitation the spectroscopy of the Jaynes–Cummings model differs markedly from that of coupled harmonic oscillators. Coupled harmonic oscillators give a doublet at all excitation levels; because of its noncommensurate excited state energies the Jaynes–Cummings model gives a multitude of additional peaks. In this paper we show how the excited states of the Jaynes–Cummings Hamiltonian can be probed by driving a cavity containing a single atom with broadband chaotic light. For a sufficiently large dipole coupling strength the spectrum of the light scattered out of the cavity mode shows peaks at the many resonance frequencies of the Jaynes–Cummings Hamiltonian. A similar multipeaked spectrum is seen in transmission. The spectrum of the light reflected from the cavity shows corresponding absorption dips superimposed on the broadband input.

DOI
10.1364/oam.1990.ws3

Related papers

Exploring higher Jaynes-Cummings doublet in cavity quantum electrodynamics system with a broadband squeezed vacuum injection

Daqiang Bao, Chengjie Zhu, Yaping Yang +1 more

We investigate the cavity excitation spectrum and the photon number distribution in a cavity QED system driven by a broadband squeezed vacuum. In an empty cavity, we show that only states with even number of photons can be measured under resonant condition since the squeezed vacuum consists of states with even number of photons only. When a single atom is trapped in the cavity, the strong coupling between the atom and cavity results in energy splittings of the system, and there exist two peaks in the cavity excitation spectrum at two-photon transition frequencies. At the central frequency, however, all photon states can be detected because of the interaction between the atom and cavity. Therefore, it can be used to detect whether a single atom is trapped in the cavity. We also show that the squeezed vacuum can promote multiphoton excitations in the cavity. Using a coherent probe field, it is possible to explore higher Jaynes-Cummings doublet even if the probe field intensity is very weak.

arXiv:1811.11404•Nov 28, 2018•0 citations

Quantum and Semiclassical Calculations of Cavity QED Spectra

L. Tian

In this dissertation we study the interaction of a single atom with a single mode of the electromagnetic field in an optical cavity. We emphasize strong coupling conditions, where the dipole coupling strength is larger than the dissipation rates of the cavity and the atom. By exciting the coupled atom and cavity mode with an external field, the excited-state spectroscopy of the coupled system is explored. Both quantum mechanical and semiclassical calculations are performed and their results are compared. In the limit of a weak driving field, both results show a two-peak ("vacuum" Rabi) spectrum. With increased strength of the driving field, differences are observed. The quantum calculation shows a multi-peak ( two "vacuum" Rabi peaks plus additional peaks) spectrum, while the semiclassical calculation does not. These additional peaks are produced by transitions between the excited states of the Jaynes-Cummings IV Hamiltonian indicative of the quantum nature of the coupled atom-cavity-mode system.

•Jan 1, 1994•0 citations

Dynamically induced atomic resonance fluorescence and cavity transmission spectra in a driven Jaynes-Cummings system

Hyunchul Nha, Young-Tak Chough, Wonho Jhe +1 more

Spectra of the atomic resonance fluorescence and of the cavity-transmitted light in a driven Jaynes-Cummings system are studied theoretically, where the cavity is driven by a classical field of arbitrary strength. In the regime of strong atom-cavity coupling, anomalous resonance peaks occur at $\ifmmode\pm\else\textpm\fi{}\sqrt{n}{g}^{\ensuremath{'}} (n=2,3,\dots{}),$ with the modified vacuum Rabi frequency ${g}^{\ensuremath{'}},$ both in the atomic fluorescence and the cavity transmission. These peaks as well as the observed shift of the vacuum Rabi splitting are explained in terms of the quasienergy levels induced dynamically by the strong driving field. For a stronger driving field, it is shown that the spectrum of the cavity transmission deviates from that of the atomic fluorescence. In the presence of significant damping, the spectrum of the cavity transmission approaches a singlet structure in the strong driving-field limit, and it is found additionally that a bimodal photon-number distribution, which results in a unique quintuplet spectrum of the atomic fluorescence, does not show up in the cavity transmission.

Physical Review A•May 16, 2001•8 citations

The damped and coherently-driven Jaynes$ndash$Cummings model

S. Swain, Z. Ficek

We investigate the influence of a single-mode cavity on the Autler–Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler–Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom–cavity coupling strength g and the cavity damping κ. For an increasing g and/or decreasing κ the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double-dressing' model.

Journal of Optics B Quantum and Semiclassical Optics•Aug 1, 2002•5 citations

Incoherent excitation of the Jaynes-Cummings system

L. Tian, H. J. Carmichael

The authors calculate scattered, transmitted and reflected spectra for a coupled two-level atom and quantized electromagnetic cavity mode driven by broad-band chaotic light. They obtain analytical results in the secular approximation and compare these with exact numerical results. Under cavity QED conditions (strong dipole coupling) the spectra show multiple resonances at the incommensurate transition frequencies of the Jaynes-Cummings Hamiltonian. They obtain expressions for linewidths and transition amplitudes that help them to assess the prospects for an experimental observation of these Jaynes-Cummings resonances.

Quantum Optics Journal of the European Optical Society Part B•Apr 1, 1992•28 citations

Resonance fluorescence spectrum of an atom strongly coupled to a cavity

Craig M. Savage

The spectrum of the resonance fluorescence light from a single two-level atom in a small, high-quality, optical cavity is calculated. The coupling between the atom and cavity is made sufficiently strong compared to the dissipation that single quantum frequency splitting (vacuum Rabi splitting) occurs. Under high excitation qualitatively new fluorescent spectra are predicted. The usual three-peaked resonance fluorescence spectrum now has sidebands whose width is given by the Jaynes-Cummings atom-cavity coupling coefficient rather than by the system dissipation.

Physical Review Letters•Sep 25, 1989•40 citations
When a single atom interacts with one mode of an optical cavity and the coupling to the cavity mode is sufficiently large, the spectroscopic response of the composite system to a weak probe is a doublet, with peaks located at the eigenfrequencies of the one-quantum excited states of the Jaynes–Cummings Hamiltonian. So far as these one-quantum states are concerned the spectroscopy of the Jaynes–Cummings model is the same as that of coupled, damped harmonic oscillators. This equivalence has been used to observe a doublet spectrum (the so-called "vacuum" Rabi splitting) by exciting a collective dipole oscillator inside an optical cavity.1,2 At higher levels of excitation the spectroscopy of the Jaynes–Cummings model differs markedly from that of coupled harmonic oscillators. Coupled harmonic oscillators give a doublet at all excitation levels; because of its noncommensurate excited state energies the Jaynes–Cummings model gives a multitude of additional peaks. In this paper we show how the excited states of the Jaynes–Cummings Hamiltonian can be probed by driving a cavity containing a single atom with broadband chaotic light. For a sufficiently large dipole coupling strength the spectrum of the light scattered out of the cavity mode shows peaks at the many resonance frequencies of the Jaynes–Cummings Hamiltonian. A similar multipeaked spectrum is seen in transmission. The spectrum of the light reflected from the cavity shows corresponding absorption dips superimposed on the broadband input.
We investigate the cavity excitation spectrum and the photon number distribution in a cavity QED system driven by a broadband squeezed vacuum. In an empty cavity, we show that only states with even number of photons can be measured under resonant condition since the squeezed vacuum consists of states with even number of photons only. When a single atom is trapped in the cavity, the strong coupling between the atom and cavity results in energy splittings of the system, and there exist two peaks in the cavity excitation spectrum at two-photon transition frequencies. At the central frequency, however, all photon states can be detected because of the interaction between the atom and cavity. Therefore, it can be used to detect whether a single atom is trapped in the cavity. We also show that the squeezed vacuum can promote multiphoton excitations in the cavity. Using a coherent probe field, it is possible to explore higher Jaynes-Cummings doublet even if the probe field intensity is very weak.
In this dissertation we study the interaction of a single atom with a single mode of the electromagnetic field in an optical cavity. We emphasize strong coupling conditions, where the dipole coupling strength is larger than the dissipation rates of the cavity and the atom. By exciting the coupled atom and cavity mode with an external field, the excited-state spectroscopy of the coupled system is explored. Both quantum mechanical and semiclassical calculations are performed and their results are compared. In the limit of a weak driving field, both results show a two-peak ("vacuum" Rabi) spectrum. With increased strength of the driving field, differences are observed. The quantum calculation shows a multi-peak ( two "vacuum" Rabi peaks plus additional peaks) spectrum, while the semiclassical calculation does not. These additional peaks are produced by transitions between the excited states of the Jaynes-Cummings IV Hamiltonian indicative of the quantum nature of the coupled atom-cavity-mode system.
Spectra of the atomic resonance fluorescence and of the cavity-transmitted light in a driven Jaynes-Cummings system are studied theoretically, where the cavity is driven by a classical field of arbitrary strength. In the regime of strong atom-cavity coupling, anomalous resonance peaks occur at $\ifmmode\pm\else\textpm\fi{}\sqrt{n}{g}^{\ensuremath{'}} (n=2,3,\dots{}),$ with the modified vacuum Rabi frequency ${g}^{\ensuremath{'}},$ both in the atomic fluorescence and the cavity transmission. These peaks as well as the observed shift of the vacuum Rabi splitting are explained in terms of the quasienergy levels induced dynamically by the strong driving field. For a stronger driving field, it is shown that the spectrum of the cavity transmission deviates from that of the atomic fluorescence. In the presence of significant damping, the spectrum of the cavity transmission approaches a singlet structure in the strong driving-field limit, and it is found additionally that a bimodal photon-number distribution, which results in a unique quintuplet spectrum of the atomic fluorescence, does not show up in the cavity transmission.
The damped and coherently-driven JaynesndashndashndashCummings model
We investigate the influence of a single-mode cavity on the Autler–Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler–Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom–cavity coupling strength g and the cavity damping κ. For an increasing g and/or decreasing κ the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double-dressing' model.
The authors calculate scattered, transmitted and reflected spectra for a coupled two-level atom and quantized electromagnetic cavity mode driven by broad-band chaotic light. They obtain analytical results in the secular approximation and compare these with exact numerical results. Under cavity QED conditions (strong dipole coupling) the spectra show multiple resonances at the incommensurate transition frequencies of the Jaynes-Cummings Hamiltonian. They obtain expressions for linewidths and transition amplitudes that help them to assess the prospects for an experimental observation of these Jaynes-Cummings resonances.
The spectrum of the resonance fluorescence light from a single two-level atom in a small, high-quality, optical cavity is calculated. The coupling between the atom and cavity is made sufficiently strong compared to the dissipation that single quantum frequency splitting (vacuum Rabi splitting) occurs. Under high excitation qualitatively new fluorescent spectra are predicted. The usual three-peaked resonance fluorescence spectrum now has sidebands whose width is given by the Jaynes-Cummings atom-cavity coupling coefficient rather than by the system dissipation.