A brief review of cavity QED

Chapter 1 Introduction

Generally, the spontaneous emission rate were treated as an inherent process, namely, spontaneous emission of atoms would have been independent of the environment. However, the fact is that the spontaneous emission is not an immutable property of an atom but a consequence of atom–vacuum field coupling.

It has long been recognized that the spontaneous emission of an atom in a resonator may be altered from the free-space value, because of a change in the density of modes [1]. In addition, it has not only been known that the rate of spontaneous emission is modified but also the pattern of spontaneous emission can be controlled [2]. The cavity-like effects are a classic theoretical problem which is called cavity quantum electrodynamics (cavity QED).

1.1 A brief review of cavity QED

There are two distinct regimes in cavity QED, i.e., the low-Q regime and the high-Q regime, where Q is the parameter of a resonator for the ability of conserving photon energy. The larger value of Q means that the resonator has smaller loss. A decisive parameter which separates these two regimes (low-Q and high-Q) is the vacuum Rabi frequency,

2 ) the volume of optical cavity. When the vacuum Rabi frequency Ω_R is larger than

2

the decay rate of the photon (γ_photon）or the atomic dipole moment (γ_dipole), the atom-vacuum field coupling is strongly perturbed by the cavity. In this situation, the spontaneous emission becomes reversible and coherent process. However, a laser system will not conform to this conduction because we need cavity loss to obtain sufficient laser output.

In the low-Q case, Ω_R >> γ_photon or γ_dipole, the cavity only weakly perturbs the atom-vacuum field. Spontaneous emission remains an irreversible and incoherent process. Nevertheless, the radiation pattern and the decay rate can still be modified by a cavity as show in Fig. 1-1. In Fig. 1-1 (a), the spontaneous emission will equally radiate to all directions in the free space; but it will be confined in a particular direction by a cavity. The enhancement of coupling strength is proportional to N , where N is number of atoms, which are collectively couple with the cavity field. So the pattern of spontaneous emission in Fig. 1-1 (a) is more localized for N > 1 with the faster decay rate in Fig. 1-1 (b) than for only one single atom in the cavity..

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Fig. 1-1 Modified radiation pattern and decay rate of spontaneous emission intensity by free space, a cavity for a single atom (N=1), and a cavity for many atoms (N>1).

The sketch of Fig. 1-1 means that we could modify or control the pattern and the rate of spontaneous emission by a cavity or number of atoms. The modification of a spontaneous emission rate in the micro-wave cavity was first predicted by Purcell [1]

in 1946, and Drexhage [3] demonstrated it by experiment in the late 1960s. After Purcell’s and Drexhage’s study, the study of cavity QED is toward optical cavity.

The enhanced and inhibited spontaneous emission from atoms placed inside optical cavities had been observed by several groups [4]- [6].

Because of the interference in the micro-cavity, the amplitude of vacuum field is modified in the space. An atom where is located at node or anti-node of vacuum field will have different spontaneous emission rate, such as an atom at the anti-node will enhance spontaneous emission. We let atom as a harmonic oscillator which couples with vacuum field. The radiation intensity will be proportional to P^v12⋅ε^vvac. Therefore the micro-cavity structures are suitable for controlling spontaneous

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emission. Over the past decade, a considerable number of studies have been investigated cavity QED on micro-cavity semiconductor lasers [7][8]. Besides the micro-cavity, the cavity whose cavity length is much larger than the radiation wavelength can also observe the modification of spontaneous emission. In 1987, Heinzen et al., [9] studied on the decay rate of spontaneous emission in a macroscopic cavity which was operated with the confocal resonator. They found that the ytterbium atoms will have enhanced spontaneous emission rate when the atoms are resonant to the cavity mode, but inhibit far from the resonance. Curve (a) of Fig. 1-1 is the photon count rate while the cavity is open. The Airy function is measured by the spontaneous emission. It clearly shows that the spontaneous emission will be modified when the cavity is detuned. Curve (c) shows the counting rate with open cavity, but the laser detuned from the atomic resonance (background). In order to compare with curve (a) and to determine whether spontaneous emission is enhanced or inhibited, curve (b) is normalized counting rate with cavity blocked and multiplied by 2/(T1+T2) to compensate the interference in the cavity, where T1 and T2 are the transmittances of cavity mirrors. So curve (b) shows the counting rate in the free space. We can compare curve (a) and (b) to directly observe the enhanced and inhibited spontaneous emission.

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Fig. 1-2 Photon counting rate for light transmitted through the cavity mirror, as a function of cavity tuning. (Ref. [9]). (a) counting rate with cavity open ; (b) in free space; and (c) background.

So far, the experiments about cavity QED can be categorized by two types.

First, the micro cavity, e.g., in semiconductor, is used to modify vacuum field and then to control spontaneous emission. Another type of experiments, the mode density of macroscopic cavity is modified when the laser resonator operates at degenerate cavity configurations, e.g., mostly at the confocal or concentric cavity.