T. W. Lynn

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.

APPLICATIONS OF OPTICAL CAVITIES IN MODERN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS

Publisher Summary This chapter discusses applications of optical cavities in modern atomic, molecular, and optical physics. For many contemporary physics experiments, the use of an optical cavity has become a powerful tool for enhancement in detection sensitivities, nonlinear interactions, and quantum dynamics. Indeed, an optical cavity allows one to extend the interaction length between matter and field, to build up the optical power, to impose a well-defined mode structure on the electromagnetic field, to enable extreme nonlinear optics, and to study manifestly quantum mechanical behavior associated with the modified vacuum structure and/or the large field associated with a single photon confined to a small volume. Experimental activities that have benefited from the use of optical cavities appear in such diverse areas as ultra-sensitive detection for classical laser spectroscopy, nonlinear optical devices, optical frequency metrology and precision measurement, and cavity quantum electrodynamics (cavity QED). One of the important themes in laser spectroscopy is to utilize an extended interaction length between matter and field inside a high finesse cavity for increased detection sensitivity. Two key ingredients are needed to achieve the highest sensitivity possible in detection of atomic and molecular absorptions: enhancement of the absorption signal and elimination of technical noise. The chapter discusses exploration of quantum dynamics associated with the enhanced interaction between atoms and cavity field; where the structure of the cavity enables a large field amplitude associated with single intracavity photons, the system dynamics can become manifestly quantum and nonlinear.

Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement

Measuring an entangled state of two particles is crucial to many quantum communication protocols. Yet Bell-state distinguishability using a finite apparatus obeying linear evolution and local measurement is theoretically limited. We extend known bounds for Bell-state distinguishability in one and two variables to the general case of entanglement in n two-state variables. We show that at most 2{sup n+1}-1 classes out of 4{sup n} hyper-Bell states can be distinguished with one copy of the input state. With two copies, complete distinguishability is possible. We present optimal schemes in each case.

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.

Search for correlated high energy cosmic ray events with CHICOS

We present the results of a search for time correlations in high energy cosmic ray data (primary E > 10^14 eV) collected by the California HIgh school Cosmic ray ObServatory (CHICOS) array. Data from 60 detector sites spread over an area of 400 km^2 were studied for evidence of isolated events separated by more than 1 km with coincidence times ranging from 1 µs up to 1 s. The results are consistent with the absence of excess coincidences except for a 2.9σ excess observed for coincidence times less than 10 µs. We report upper limits for the coincidence probability as a function of coincidence time.

Cavity QED with Strong Coupling — Toward the Deterministic Control of Quantum Dynamics

Many of the current efforts to control the dynamics of individual quantum systems take place within the setting of cavity quantum electrodynamics (QED). The coupling of an atomic dipole to the mode of an optical resonator has historically produced important quantum effects in the regime of weak coupling between dipole and cavity mode; more recent experiments access the regime of strong coupling and begin to enable control of the quantum states of single atoms and single-photon fields through a coherent coupling that exceeds dissipative rates in the system. We briefly review the historicl path to strong coupling and the variety of experiments involving single-quantum cavity QED. Current achievements and future challenges are illustrated through further discussion of two ongoing experiments in out group: one pursuing quantum feedback to trap single atoms in a cavity mode with single photons, the other building capability for quantum logic by using a FORT to hold atoms within a cavity mode. [Note that the presentation on which this paper is based can be accessed at http://www.its.caltech.edu/qoptics/cqed.html]

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.

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.