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Quantum Electronics and Laser Science Conference

Evolution of the vacuum Rabi peaks in a many-atom system

S. L. Mielke, J. Gripp, Luis A. Orozco

Published Jun 7, 1996• 0 citations
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Abstract

Summary form only given. The two peaks of the vacuum Rabi splitting behave like simple harmonic oscillators for very weak excitation. The transmission spectrum of a cavity filled with a collection of two-level atoms shows this doublet and, for sufficiently high intensities, its evolution into a single peak. As the excitation increases anharmonicity grows in the oscillators to a point where frequency hysteresis appears in the transmission spectrum. The saturation of the transition of the two-level atoms is responsible for the nonlinearity that causes the anharmonicity. This work investigates the transition from the doublet into the singlet. We include the possibility of a detuning between the atomic and cavity resonances.

Related papers

Evolution of the vacuum Rabi peaks in a many-atom system

J. Gripp, Luis A. Orozco

The two peaks of the vacuum Rabi splitting behave like simple harmonic oscillators for very weak excitation. The transmission spectrum of a cavity filled with two-level atoms shows this doublet at low values of the driving intensity, but only a single peak at high values. The evolution from a doublet to a singlet is governed by the anharmonic response of the system as the driving intensity increases. The anharmonicity can grow to a point where frequency hysteresis appears in the transmission spectrum. This work investigates theoretically with a semiclassical model the transition from the doublet into the singlet. The stability of the different solutions is analysed as the parameters of atomic and cavity detuning vary. The model is extended to include the experimentally relevant transverse profile of the cavity mode as well as the standing wave structure of the field.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Aug 1, 1996•13 citations

Anharmonicity of the vacuum Rabi peaks in a many-atom system

J. Gripp, S. L. Mielke, Luis A. Orozco +1 more

We have experimentally observed the evolution of the vacuum Rabi doublet into a singlet in the transmission spectrum of a cavity filled with a collection of two-level atoms. For very weak excitation the peaks behave like simple harmonic oscillators, but become anharmonic as the excitation increases. The anharmonicity grows to a point where hysteresis appears in the transmission spectrum, eventually causing the two peaks to merge into one.

Physical Review A•Nov 1, 1996•57 citations

Evolution of the vacuum Rabi peaks in a detuned atom-cavity system

J. Gripp, S. L. Mielke, Luis A. Orozco

We measure the transmission spectrum of an optical cavity filled with two-level atoms. For small intensities, the coupling between atoms and a single mode of the cavity splits the spectrum into two normal modes: the vacuum Rabi peaks. We gradually decouple the system in two ways and study the evolution of the vacuum Rabi peaks. First we lower the atom-cavity coupling frequency through its intensity dependence, showing that the peaks shift, deform, exhibit frequency hysteresis, and eventually merge into a single peak that approaches the empty cavity resonance. Second we detune the atoms and the cavity mode and observe an avoided crossing. The normal modes of the coupled system transform into the two resonances of the uncoupled system. We map out the transition region and find good agreement with theoretical predictions.

Physical Review A•Oct 1, 1997•76 citations

Modification of a vacuum Rabi splitting via a frequency-modulated cavity mode

C. K. Law, S.-Y. Zhu, Muhammad Suhail Zubairy

The spectrum radiated by an initially excited two-level atom in a very-high-Q cavity is studied. We consider the situation where the frequency of the vacuum field cavity mode is varied time-dependently during Rabi cycles. Under the resonance condition where the modulation frequency is the same as the vacuum Rabi frequency, we show that the vacuum Rabi splitting can be further split into two doublets. The relative heights of spectral peaks are shown to depend on the modulation phase. Furthermore, we show that the interference between different spectral peaks can break the symmetry of the spectrum.

Physical Review A•Nov 1, 1995•46 citations

Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime

Julio R. Gea-Banacloche, Haibin Wu, Min Xiao

We present the theory of ``normal mode splitting'' (sometimes also called, in the low-intensity limit, ``vacuum Rabi splitting'') for a Doppler-broadened two-level medium in an optical cavity, and illustrate it with experimental results. We note that, in the extreme Doppler limit, the absorptive and dispersive properties of the medium are due to almost completely different groups of atoms, and hence it is possible, in principle, to partially saturate the absorbing atoms without changing the dispersion very much; as a result of this, for a sufficiently high probe intensity, transmission peaks well within the Doppler absorption profile are visible, even though the medium is optically dense. Some interesting features exhibited by this system in various regimes are transmission peaks that are unrelated to the ``zero-phase'' condition, and three-peaked transmission spectra for high atomic density and high cavity input power.

Physical Review A•Aug 19, 2008•23 citations

Broadband excitation of the Jaynes–Cummings molecule

Liguang Tian, H. J. Carmichael

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.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations
Summary form only given. The two peaks of the vacuum Rabi splitting behave like simple harmonic oscillators for very weak excitation. The transmission spectrum of a cavity filled with a collection of two-level atoms shows this doublet and, for sufficiently high intensities, its evolution into a single peak. As the excitation increases anharmonicity grows in the oscillators to a point where frequency hysteresis appears in the transmission spectrum. The saturation of the transition of the two-level atoms is responsible for the nonlinearity that causes the anharmonicity. This work investigates the transition from the doublet into the singlet. We include the possibility of a detuning between the atomic and cavity resonances.
The two peaks of the vacuum Rabi splitting behave like simple harmonic oscillators for very weak excitation. The transmission spectrum of a cavity filled with two-level atoms shows this doublet at low values of the driving intensity, but only a single peak at high values. The evolution from a doublet to a singlet is governed by the anharmonic response of the system as the driving intensity increases. The anharmonicity can grow to a point where frequency hysteresis appears in the transmission spectrum. This work investigates theoretically with a semiclassical model the transition from the doublet into the singlet. The stability of the different solutions is analysed as the parameters of atomic and cavity detuning vary. The model is extended to include the experimentally relevant transverse profile of the cavity mode as well as the standing wave structure of the field.
We measure the transmission spectrum of an optical cavity filled with two-level atoms. For small intensities, the coupling between atoms and a single mode of the cavity splits the spectrum into two normal modes: the vacuum Rabi peaks. We gradually decouple the system in two ways and study the evolution of the vacuum Rabi peaks. First we lower the atom-cavity coupling frequency through its intensity dependence, showing that the peaks shift, deform, exhibit frequency hysteresis, and eventually merge into a single peak that approaches the empty cavity resonance. Second we detune the atoms and the cavity mode and observe an avoided crossing. The normal modes of the coupled system transform into the two resonances of the uncoupled system. We map out the transition region and find good agreement with theoretical predictions.
The spectrum radiated by an initially excited two-level atom in a very-high-Q cavity is studied. We consider the situation where the frequency of the vacuum field cavity mode is varied time-dependently during Rabi cycles. Under the resonance condition where the modulation frequency is the same as the vacuum Rabi frequency, we show that the vacuum Rabi splitting can be further split into two doublets. The relative heights of spectral peaks are shown to depend on the modulation phase. Furthermore, we show that the interference between different spectral peaks can break the symmetry of the spectrum.
We present the theory of ``normal mode splitting'' (sometimes also called, in the low-intensity limit, ``vacuum Rabi splitting'') for a Doppler-broadened two-level medium in an optical cavity, and illustrate it with experimental results. We note that, in the extreme Doppler limit, the absorptive and dispersive properties of the medium are due to almost completely different groups of atoms, and hence it is possible, in principle, to partially saturate the absorbing atoms without changing the dispersion very much; as a result of this, for a sufficiently high probe intensity, transmission peaks well within the Doppler absorption profile are visible, even though the medium is optically dense. Some interesting features exhibited by this system in various regimes are transmission peaks that are unrelated to the ``zero-phase'' condition, and three-peaked transmission spectra for high atomic density and high cavity input power.
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.