Full observation of single-atom dynamics in cavity QED

We report the use of broadband heterodyne spectroscopy to perform continuous measurement of the interaction energyEint between one atom and a high-finesse optical cavity, during individual transit events of ≈ 250μs duration. We achieve a fractional sensitivity ≈ 4×10−4/√Hz to variations inEint/h within a measurement bandwidth that covers 2.5 decades of frequency ( 1–300 kHz). Our basic procedure is to drop cold cesium atoms into the cavity from a magnetooptic trap while monitoring the cavity’s complex optical susceptibility with a weak probe laser. The instantaneous value of the atom–cavity interaction energy, which in turn determines the coupled system’s optical susceptibility, depends on both the atomic position and (Zeeman) internal state. 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 c nditionalquantum evolution in the sense of recently developed quantum trajectory theories. PACS: 03.65.Bz; 06.20.Dk; 42.50 Optical-cavity quantum electrodynamics (QED) in the strongcoupling regime [1] provides a unique experimental paradigm for real-time observation of quantum dynamical processes at thesingle-atomlevel. Whereas spectacular advances have certainly been made in the preparation and tomography of quantum states of motion for a single trapped ion [2, 3], all such experiments have involved the accumulation of ensemble-averaged data over many successive realizations of the process being studied. Recent studies of single-molecule dynamics have likewise demonstrated the “immediate” detection of photochemical [4] or conformational [5] events, but such experiments presently lack the potential that cavity QED provides for observing quantum processes on a timescale that ∗ E-mail: hmabuchi@cco.caltech.edu makes coherent control /intervention a tangible possibility. We wish here to look beyond the mere detection of quantum jumps, and to focus on the development of a broadband, single-shotmeasurement technique that achieves signal-tonoise ratio> 1 over a bandwidth that includes all characteristic frequencies of a quantum dynamical process. Real-time observation of quantum dynamics in manyatom systems has recently become an important theme in atomic physics, with notable demonstrations involving vibrational excitations of a trapped Bose–Einstein condensate [6] and the decay of coherent oscillations of an ensemble of atoms in an optical lattice [7, 8]. In contrast to programs like these, for which the scientific emphasis lies on noninvasive observation of a system’s intrinsic dynamical processes, experiments in single-atom cavity QED hold great potential for nabling precise investigations of how measurement backaction altersthe dynamical behavior of a continuously observed open quantum system [9–12, 55]. A sophisticated theoretical basis for understanding such issues is presently maturing in the form of quantum trajectory theories [13–16], but significant technical challenges remain to be solved before definitive experiments can be performed in the lab. Our purpose in the present work is to report substantial progress towards surmounting such obstacles in the context of cavity QED, and hence towards achieving the essential experimental capabilities required to perform quantitative tests of measurement-based stochastic master equations. We ultimately hope to be able to implement some recently proposed “applications” of the continuous observation of dissipative quantum dynamics, in fields such as quantum measurement [17, 20], quantum chaos [18, 19], and quantum feedback control [20, 21, 23, 24]. This article focuses on a detailed description of our recent experiments that record the complete time-evolution of interaction energy between one atom and a high-finesse optical cavity, during individual transit events of ≈ 250μs duration. With characteristic atom–cavity interaction energiesEint/h≈ 10 MHz, we achieve measurement sensitivities Sg ' 4.5 kHz/ √ Hz over a bandwidth that covers the dominant rates of variation inEint (1–300 kHz). Unlike typical pump-probe measurements of scattering dynamics in real