C. J. Hood

Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity

An extensive characterization of high-finesse optical cavities used in cavity QED experiments is described. Different techniques in the measurement of the loss and phase shifts associated with the mirror coatings are discussed and their agreement shown. Issues of cavity-field mode structure supported by the dielectric coatings are related to our effort to achieve the strongest possible coupling between an atom and the cavity.

Trapping of single atoms with single photons in cavity QED

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.

Quantum manipulation and measurement of single atoms in optical cavity QED

Summary form only given. Using cold atoms strongly interacting with individual photons inside a high finesse cavity, we are approaching an ideal quantum system in which both matter (internal and external degrees of freedom) and light exhibit strong quantum character and the systems coherent evolution dominates decoherence processes. With this system we have performed real-time continuous measurement of single atomic spatial trajectories. The measurement protocol involves the determination of the phase of the cavity output field, which is far-detuned from the atomic resonance to minimize the measurement back action on the center-of-mass (CM) motion. The real-time evolution of the complex field amplitude is efficiently recorded at high bandwidth and with good signal-to-noise ratio, limited respectively by the rate of coherent coupling between atom and cavity mode and the photodetection shot noise. This nearly optimal detection technique has already revealed atomic CM motion inside the cavity standing-wave field of single photons, and should eventually lead to the strong conditioning of system evolution on measurement results and the realization of quantum feedback control. Another related but independent experiment concentrates on quantum manipulation of the CM motion. Owing to the highest coherent coupling rate between cavity field and individual atoms achieved to date, the mechanical coupling between atom and cavity can be significantly larger than the kinetic energy of laser cooled atoms, even under very low cavity excitation. Indeed, evidence of mechanical light forces for intracavity photon number <1 has already been observed. The origin of this mechanical force is radically different from that in conventional laser trapping where photon scattering (coherent or incoherent) drives the atomic CM motion. The spatial variation of the standing cavity mode (and hence of the atom-field coupling), produce optical potentials capable of localizing atoms inside the cavity. With the initial evidence of prolonged atomic transit through the cavity field (by 3/spl times/) when the suitable trapping state (the lower dressed state of the atom-cavity system) was excited, we are working towards suppression of the atomic momentum diffusion to achieve long-term atomic confinement via quantum feedback.

Optical Cavity QED

The experiments of our group in optical cavity QED are characterized by the strong coupling of a small collection of atoms to a single mode of an optical resonator. Recent progress has led to systems in which the interaction of single atoms and cavity fields with an average photon number \(\bar n \)≪ 1 can be observed. Optical cavity QED thus offers unique possibilities to investigate quantum phenomena of the atom-field dynamics. Examples include nonlinear spectroscopy of the atom-cavity system with sub-photon fields, the generation of arbitrary states of the quantized radiation field, the efficient coupling of an atom to squeezed light and the detection of single atoms with high probability.

Real-time tracking and trapping of single atoms in cavity QED

Cavity quantum electrodynamics (QED) offers powerful possibilities for the deterministic control of atom-photon interactions quantum by quantum [1]. Indeed, modern experiments in cavity QED have achieved the exceptional circumstance of strong coupling, for which single quanta can profoundly impact the dynamics of the atom-cavity system. The diverse accomplishments of this field set the stage for advances into yet broader frontiers in quantum information science for which cavity QED offers unique advantages, such as the realization of quantum networks by way of multiple atom-cavity systems linked by optical interconnects [2,3].

Real-time cavity QED with single atoms

We report the first measurement of the real-time evolution of the complex field amplitude brought on by single atom transits. We show the variation in time of both quadrature amplitudes (simultaneously recorded) of the light transmitted through the cavity, as well the resultant optical phase for a single atom transit event. In this particular measurement, the cavity and laser were both detuned by 10 MHz from the Cs resonance.

Cavity Quantum Electrodynamics with a Capital Q

With recent developments in optical cavity QED pioneered in the Quantum Optics Group at Caltech, optical physics has progressed to a domain wherein processes are driven by single atoms interacting with optical fields with average energy corresponding to much less than one photon. This unique situation opens doors for new and exciting phenomena which manifestly rely on the quantum nature of the atom-field interaction. The system that we have developed to access this realm consists of an atom strongly coupled to a single mode of a high finesse optical resonator [1]. To introduce the notation, the dipole coupling of the atom to the cavity mode is described by a rate g, while the dissipative rates are γ || for atomic energy decay (with the polarization decay rate γ ┴ = γ || /2 as appropriate for purely radiative relaxation) and k for cavity decay.

Dynamics of single-atom, single-photon trapping in cavity QED

Single atoms are trapped via strong coupling to single-photon fields in optical cavity QED. Properties of the atom-cavity interaction are explored through experimental observation of trapped-atom dynamics and lifetimes as trap parameters are systematically varied.

Quantum communication and computation in quantum optics

Summary form only given. In the quantum optics group at Caltech, we are attempting to lay the foundations for quantum information science by way of advances on several fronts in optical physics. Within the setting of cavity QED, single atoms are strongly coupled to the field of a high finesse optical cavity at the single photon level, with current work directed toward trapping and localization of atoms inside the cavity. Although there are daunting technical problems to overcome, a principal scientific objective is the creation of quantum networks to implement fundamental quantum communication protocols and for distributed quantum computation. Beyond quantum information processing with internal atomic states and photons serving as qubits, we are also investigating algorithms for continuous quantum variables. A recent example is our realization of quantum teleportation for the quadrature amplitudes of a beam of light. The experiment utilizes squeezed-state entanglement to achieve unconditional quantum teleportation.

Measurement and control of single atom motions in the quantum regime

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.