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Physical Review Letters

Real-Time Cavity QED with Single Atoms

Christina J. Hood, Michael Chapman, T. W. Lynn, Harry J. Kimble

Published May 11, 1998• 394 citations
Publisher

Abstract

The combination of cold atoms and large coherent coupling enables investigations in a new regime in cavity QED with single-atom trajectories monitored in real time with high signal-to-noise ratio. The underlying ``vacuum-Rabi'' splitting is clearly reflected in the frequency dependence of atomic transit signals recorded atom by atom, with evidence for mechanical light forces for intracavity photon number $<1$. The nonlinear optical response of one atom in a cavity is observed to be in accord with the one-atom quantum theory but at variance with semiclassical predictions.

DOI
10.1103/physrevlett.80.4157

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The combination of cold atoms and large coherent coupling enables investigations in a new regime in cavity QED with single-atom trajectories monitored in real time with high signal-to-noise ratio. The underlying ``vacuum-Rabi'' splitting is clearly reflected in the frequency dependence of atomic transit signals recorded atom by atom, with evidence for mechanical light forces for intracavity photon number <1<1<1. The nonlinear optical response of one atom in a cavity is observed to be in accord with the one-atom quantum theory but at variance with semiclassical predictions.
Using laser-cooled atoms strongly coupled to a high finesse optical cavity, we have performed real-time continuous measurements of single atomic trajectories in terms of the interaction energy (E/sub int/) with the cavity. Individual transit events reveal a shot-noise limited measurement (fractional) sensitivity of 4/spl times/10/sup -4///spl radic/Hz to variations in E/sub int///spl planck/ within a bandwidth of 1300 kHz. The strong coupling of atom and cavity leads to a maximum interaction energy greater than the kinetic energy of an intracavity laser-cooled atom, even under weak cavity excitation. Evidence of mechanical light forces for intracavity photon number <1 has been observed. The quantum character of the nonlinear optical response of the atom-cavity system is manifested for the trajectory of a single atom.
Cavity quantum electrodynamics (QED), the system of a single atom interacting with a single mode of a high finesse optical resonator, has tremendous potential for use in quantum logic, quantum information processing, and in enabling observation of quantum mechanical effects in the laboratory. The work of this thesis demonstrates a number of steps toward realizing these goals, by employing an experimental system with the strongest atom-field coupling achieved to date in optical cavity QED. The effects of strong coupling in cavity QED are studied for single cold atoms measured one at a time, in real time. The passage of single atoms through the cavity is employed to map out the frequency response of the system, and to demonstrate that quantum rather than semiclassical theory provides the correct theoretical model. The mechanical effects of strong coupling on single atoms are explored, these experiments demonstrating the first trapping of single atoms with single photons. Additionally, strong coupling enables high signal-to-noise ratio for monitoring atomic position at single photon field strengths; this capability is employed to investigate the motion of atoms trapped within the cavity. The transmitted cavity field is used to reconstruct the trajectories of single atoms, thereby realizing a new form of microscopy - the Atom-Cavity Microscope. Technical developments necessary to create the cavities used in this experiment are detailed. Ideas for future extensions to the experiment are proposed; a zero light-shift dipole force trap, and measurement of photon statistics of a single strongly coupled atom (which realizes a photon blockade device) are discussed.
Using cold atoms strongly coupled to a high finesse optical cavity, we have performed real-time continuous measurement of single atomic trajectories in terms of the interaction energy (Eint) with the cavity. Individual transit events reveal a shot-noise limited measurement (fractional) sensitivity of 4×10−4/Hz to variations in Eint/ℏ within a bandwidth of 1–300 kHz. The strong coupling of atom and cavity leads to a maximum interaction energy greater than the kinetic energy of an intracavity laser-cooled atom, even under weak cavity excitation. Evidence of mechanical light forces for intracavity photon number <1 has been observed. The quantum character of the nonlinear optical response of the atom-cavity system is manifested for the trajectory of a single atom.
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.
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.
We report on recent progress in our lab involving cavity quantum electrodynamics with optically trapped atoms. \n \nIn particular, we will focus on a recent measurement of the Vacuum-Rabi splitting for one atom strongly coupled to the field of a high finesse optical resonator. This splitting is characteristic of the normal modes in the eigenvalue spectrum of the atom-cavity system. 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 in cavity QED that have required averaging over many atoms.