Summary form only given. A new regime in cavity QED is realized in which single atoms interact with the cavity field for very long times (i.e., many Rabi cycles) and in which the atomic kinetic energy is comparable to or smaller than the dipole coupling energy. The mechanical effects of just a few-photon light field should therefore enable single atoms to be trapped in effective potential wells. We consider such a situation in the far detuned dispersive regime of cavity QED, where a single atom is confined in the lower (quantized) bound states of the effective optical potential formed around an antinode of the standing wave cavity field.
Summary form only given. A new regime in cavity QED is realized in which single atoms interact with the cavity field for very long times (i.e., many Rabi cycles) and in which the atomic kinetic energy is comparable to or smaller than the dipole coupling energy. The mechanical effects of just a few-photon light field should therefore enable single atoms to be trapped in effective potential wells. We consider such a situation in the far detuned dispersive regime of cavity QED, where a single atom is confined in the lower (quantized) bound states of the effective optical potential formed around an antinode of the standing wave cavity field.
By integrating the techniques of laser cooling and trapping with those of cavity quantum electrodynamics (QED), single cesium atoms have been trapped within the mode of a small, high finesse optical cavity in a regime of strong coupling. The observed lifetime for individual atoms trapped within the cavity mode is $\ensuremath{\tau}\ensuremath{\approx}28\mathrm{ms}$, and is limited by fluctuations of light forces arising from the far-detuned intracavity field. This initial realization of trapped atoms in cavity QED should enable diverse protocols in quantum information science.
Two recent experiments have reported the trapping of individual atoms inside optical resonators by the mechanical forces associated with single photons [Hood et al., Science 287, 1447 (2000); Pinkse et al., Nature (London) 404, 365 (2000)]. Here we analyze the trapping dynamics in these settings, focusing on two points of interest. First, we investigate the extent to which light-induced forces in these experiments are distinct from their free-space counterparts, and whether or not there are qualitatively different effects of optical forces at the single-photon level within the setting of cavity QED. Second, we explore the quantitative features of the resulting atomic motion, and how these dynamics are mapped onto experimentally observable variations of the intracavity field. Toward these ends, we present results from extensive numerical simulations of the relevant forces and their fluctuations, as well as a detailed derivation of our numerical simulation method, based on the full quantum-mechanical master equation. Not surprisingly, qualitatively distinct atomic dynamics arise as the coupling and dissipative rates are varied. For the experiment of Hood et al., we show that atomic motion is largely conservative and is predominantly in radial orbits transverse to the cavity axis. A comparison with the free-space theory demonstrates that the fluctuations of the dipole force are suppressed by an order of magnitude. This effect is based upon the Jaynes-Cummings eigenstates of the atom-cavity system and represents distinct physics for optical forces at the single-photon level within the context of cavity QED. By contrast, even in a regime of strong coupling in the experiment of Pinkse et al., there are only small quantitative distinctions between the potentials and heating rates in the free-space theory and the quantum theory, so it is not clear that a description of this experiment as a novel single-quantum trapping effect is necessary. The atomic motion is strongly diffusive, leading to an average localization time comparable to the time for an atom to transit freely through the cavity, and to a reduction in the ability to infer aspects of the atomic motion from the intracavity photon number.
Cavity quantum electrodynamics (cavity QED) describes the interactions of single atoms and single photons in a resonator. In the laboratory, state-of-the-art experiments are able to observe the dynamics of these simple yet fundamental quantum systems. The recent development of quantum information science has also introduced a new role for cavity QED systems as quantum interfaces, in which information can be coherently mapped between photonic and atomic quantum bits. Groundbreaking optical cavity QED experiments in the past twenty years would not have been possible without the technological development of mirror coatings with extremely low scatter and absorption losses. Thermal noise has typically played a smaller role in cavity QED experiments but in certain instances is nevertheless important to consider. In this chapter, we begin with an overview of optical cavity QED experiments and some of the central questions that they address. It is hoped that this description, while by no means exhaustive, will provide a window for the nonspecialist into basic techniques and motivations in the field. We then turn to focus on the roles played by scattering and absorption loss and mechanical loss. We discuss how these losses have set limits on feasible experiments and the extent to which improvements may be possible. Experimental realizations of cavity QED systems An idealized cavity QED system consists of one atom placed between two highly reflective mirrors (Figure 17.1). In this model, a single atomic transition interacts with photons in a single cavity mode; the atom is often pictured at an antinode of the cavity standing wave, where it has a maximal dipole interaction with the cavity field.
Two recent experiments are discussed which demonstrate real-time trapping and monitoring of single atoms within a high-finesse optical resonator. A single atom moving within the resonator generates large variations in the transmission of a weak probe laser, which are recorded in real time. These cavity QED signals are used to trigger ON a confining potential to trap the atom. In the first experiment, the confining potential is provided by the single-photon forces associated with the cavity QED interaction. An inversion algorithm allows individual atom trajectories to be reconstructed from the record of cavity transmission, and reveals single atoms bound in orbit by the mechanical forces associated with single photons. In a second experiment, an additional classical standing-wave dipole trap provides the trapping, enabling a 28 ms trap lifetime for single strongly coupled atoms.
Cavity qed is the domain of quantum optics which studies the behaviour of single atoms and photons coupled together in an electromagnetic resonator. During the last ten years, various spectacular effects have been observed on such systems, either on the atom’s or on the field’s properties. The presence of a cavity around an atom can produce an alteration of the atomic radiative rates which has been observed in several experiments. Ideally, cavity qed deals with two-level atoms coupled resonantly or nearly resonantly to a single cavity mode. This is of course a simplification of real situations, in which atoms have many levels and the cavity sustains more than one mode. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect.
The experiments discussed in this thesis focus on the interaction of a single trapped atom with the single mode of a high-finesse optical cavity, in the regime of strong coupling. Chapter 1 gives a brief introduction, after which Chapter 2 describes our recent measurements of the transmission spectrum of the atom-cavity system. The spectrum exhibits a clearly resolved vacuum-Rabi splitting, in good quantitative agreement with theoretical predictions. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements of this type that have required averaging over 10^3-10^5 atoms. Chapter 3 discusses our observations of photon blockade for the transmitted light in the presence of one trapped atom. Excitation of the atom-cavity system by a first photon blocks the transmission of a second one, thereby converting an incident Poissonian stream of photons into a sub-Poissonian, anti-bunched stream, as confirmed by measurements of the photon statistics of the transmitted field. The intensity correlations of the cavity transmission also reveal the energy distribution for oscillatory motion of the trapped atom. Chapter 4 details a set of simple but necessary measurements of relevant experimental parameters such as cavity geometry, linewidth, mirror properties, birefringence, and detection efficiency. The thesis concludes with Appendix A, describing the efficient laser setup we use for our magneto-optical traps.