Full observation of single-atom dynamics in cavity QED

We report the use of broadband heterodyne spectroscopy to perform continuous measurement of the interaction energy between one atom and a high-finesse optical cavity, during individual transit events of $\sim 250$ $\mu$s duration. Measurements over a wide range of atom-cavity detunings reveal the transition from resonant to dispersive coupling, via the transfer of atom-induced signals from the amplitude to the phase of light transmitted through the cavity. By suppressing all sources of excess technical noise, we approach a measurement regime in which the broadband photocurrent may be interpreted as a classical record of conditional quantum evolution in the sense of recently developed quantum trajectory theories.Comment: Submitted to Applied Physics B. Uses Revtex, 13 pages with 11 EPS figure

Evaluation of heating effects on atoms trapped in an optical trap

We solve a stochastic master equation based on the theory of Savard et al. [T. A. Savard. K. M. O'Hara, and J. E. Thomas, Phys, Rev. A 56, R1095 (1997)] for heating arising from fluctuations in the trapping laser intensity. We compare with recent experiments of Ye et al. [J. Ye, D. W. Vernooy, and H. J. Kimble, Phys. Rev. Lett. 83, 4987 (1999)], and find good agreement with the experimental measurements of the distribution of trap occupancy times. The major cause of trap loss arises from the broadening of the energy distribution of the trapped atom, rather than the mean heating rate, which is a very much smaller effect

Pressure Dependence of Wall Relaxation in Polarized 3^3He Gaseous Cells

We have observed a linear pressure dependence of longitudinal relaxation time ($T_1$) at 4.2 K and 295 K in gaseous $^3$He cells made of either bare pyrex glass or Cs/Rb-coated pyrex due to paramagnetic sites in the cell wall. The paramagnetic wall relaxation is previously thought to be independent of $^3$He pressure. We develop a model to interpret the observed wall relaxation by taking into account the diffusion process, and our model gives a good description of the data

Bregman distances and Chebyshev sets

A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in Euclidean spaces a closed set is Chebyshev if and only if the set is convex. In this paper, from the more general perspective of Bregman distances, we show that if every point in the space has a unique nearest point in a closed set, then the set is convex. We provide two approaches: one is by nonsmooth analysis; the other by maximal monotone operator theory. Subdifferentiability properties of Bregman nearest distance functions are also given

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.Comment: 8 pages, 4 figure