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arXiv:0710.2421 · Physical Review A

Spontaneous emission spectrum of a two-level atom in a very-high- Q cavity

Alexia Auffèves, Benjamin Besga, Jean‐Michel Gérard, J.-Ph. Poizat

Published Jun 25, 2008• 54 citations
arXivHTMLPDF

Abstract

In this paper we consider an initially excited two-level system coupled to a monomode cavity, and compute exact expressions for the spectra spontaneously emitted by each system in the general case where they have arbitrary linewidths and frequencies. Our method is based on the fact that this problem has an easily solvable classical counterpart, which provides a clear interpretation of the evidenced phenomena. We show that if the cavity linewidth is much lower than the atomic linewidth, photons are emitted at the cavity frequency, even if the atom and the cavity are strongly detuned. We also study the links between the spontaneous emission spectra and the fluorescence spectra emitted when the atom is driven by a classical field of tunable frequency in the low excitation limit.

DOI
10.1103/physreva.77.063833

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In this paper we consider an initially excited two-level system coupled to a monomode cavity, and compute exact expressions for the spectra spontaneously emitted by each system in the general case where they have arbitrary linewidths and frequencies. Our method is based on the fact that this problem has an easily solvable classical counterpart, which provides a clear interpretation of the evidenced phenomena. We show that if the cavity linewidth is much lower than the atomic linewidth, photons are emitted at the cavity frequency, even if the atom and the cavity are strongly detuned. We also study the links between the spontaneous emission spectra and the fluorescence spectra emitted when the atom is driven by a classical field of tunable frequency in the low excitation limit.
In this paper we investigate a coupled system of an initially excited two-level atom coupled to a monomode cavity,and compute spontaneous emission spectrum and mean population density emitted by the atom and the cavity using the quantum theory that accounts for theoretical derviation and numerical calculation.The spectra emitted separately by the atom and the cavity in of strong coupling region are dramatically different from those in weak coupling region at resonance.The cavity spectrum line splitting in the strong coupling region,however,a hole exists in the atomic spectrum in the weak coupling region.We study systematically the emission spectra when the atom and the cavity are detuned,and the results show that if the cavity linewidth is much smaller than the atomic linewidth(good cavity regime),photons are emitted at the cavity frequency even if the atom and the cavity are strongly detuned,and provide theoretic foundation for the apparently puzzling feature observed in the recent experiment.In this paper we computate the atomic and the cavity mean population densities each as a function of time and their relation to the luminous intensity, and offer a new insight into civity induced transparency effect.
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 spontaneous emission spectrum for a three-level cascade configuration atom in a single mode high-Q cavity coupled to a zero temperature reservoir of continuum external modes is determined from the atom–cavity mode master equation using the quantum regression theorem. Initially the atom is in its upper state and the cavity mode empty of photons. Following Glauber, the spectrum is defined via the response of a detector atom. Spectra are calculated for the detector located inside the cavity (case A), outside the cavity end mirror (case B—end emission), or placed for emission out the side of the cavity (case C). The spectra for case A and case B are found to be essentially the same. In all the cases the predicted lineshapes are free of instrumental effects and only due to cavity decay. Spectra are presented for intermediate and strong coupling regime situations (where both atomic transitions are resonant with the cavity frequency), for cases of non-zero cavity detuning, and for cases where the two atomic transition frequencies differ. The spectral features for cases B(A) and C are qualitatively similar, with six spectral peaks for resonance cases and eight for detuned cases. These general features of the spectra can be understood via the dressed atom model. However, case B and C spectra differ in detail, with the latter exhibiting a deep spectral hole at the cavity frequency due to quantum interference effects.
We solve the spontaneous-emission problem for an atom coupled to a standing-wave cavity mode. The interaction between the atom and the cavity mode is treated nonperturbatively with the quantized motion of the atom along the cavity axis included. Results are presented for the spontaneous-emission spectrum and the final momentum distribution of the atom. For equal atomic and cavity linewidths analytical results are obtained using a Bloch-state basis (eigenstates of the coupled atom and cavity mode); these are compared with results calculated in the Raman-Nath approximation. The case of unequal linewidths may be solved numerically using the eigenstates of the uncoupled atom and cavity mode as a basis, or analytically by making a secular approximation in the Bloch-state basis. The distribution of final atomic momentum shows that under strong-coupling conditions the atom is diffracted by its radiation reaction field. We compare the spontaneous emission spectra with spectra calculated by treating the motion of the atom classically. Generally there is good agreement when the classical results are averaged over the quantum-mechanical uncertainty in the initial position of the atom. The agreement is lost for sufficiently strong dipole coupling or sufficiently light atoms. Then, spectra that are symmetric in the classical treatment are asymmetric in the quantum treatment due to energy exchange between the internal degrees of freedom and center-of-mass degrees of freedom of the atom.
There is increasing interest in the photon statistics and spectroscopic properties of the radiation from atoms confined in an optical cavity. Effects such as the cavity enhancement and inhibition of spontaneous emission, which were first observed using microwave cavities, have recently been measured at optical frequencies.1 Recent measurements of squeezing and the dynamic effects of single-quantum-level splittings also demonstrate the possibilities for quantum-statistical studies of coupled atom-cavity systems at optical frequencies.2 We study a single two-level atom confined inside an optical cavity which is driven by coherent light in resonance with both cavity and atom. For weak driving field intensities we have calculated the spectrum of the light transmitted by the cavity and fluorescence out the sides of the cavity.