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AIP conference proceedings

Measurement and control of single atom motions in the quantum regime

Jun Ye, Christina J. Hood, T. W. Lynn, Hideo Mabuchi, David W. Vernooy, Harry J. Kimble

Published Jan 1, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.57479

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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.

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Laser Physics•Jan 1, 2001•4 citations
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.
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.
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Previous work in cavity quantum electrodynamics has focused principally on achieving the condition of strong coupling, such that the single-photon Rabi frequency for one atom in a cavity dominates the rates associated with all forms of dissipation and dephasing. Although strong coupling was convincingly demonstrated in these experiments, the use of thermal atomic beams as a source of atoms invariably limited the intracavity dwell time of any given atom to values marginally longer than the system's characteristic dynamical timescales. Accordingly, the observation of single-atom effects in these experiments required integration over the transits of many successive atoms through the optical resonator. In such ensemble-averaged experiments, the quantitative effects of dissipation and measurement could always be understood from the perspective of Master Equation formalisms. By contrast, our most recent work has incorporated laser cooling techniques to accomplish a thousand-fold increase in the dwell time of individual atoms while maintaining conditions of strong coupling. With this extreme separation of timescales, the effects of individual atoms on the cavity transmission can clearly be resolved. Moreover, detailed information on each individual atom's spatial trajectory through the cavity can be inferred from the time-varying amplitude and phase of the transmitted light. Understanding the exact nature of such correlations in real laboratory measurements requires not only a careful characterization of excess technical noise, but also an in-depth study of how (and when) aspects of continuous quantum measurement theory should properly be applied. This thesis primarily contains a detailed description of an experiment in which we used broadband heterodyne spectroscopy to record the complete time-evolution of interaction energy between one atom and a high-finesse optical cavity, during individual scattering events of [...] duration. With a characteristic interaction energy scale [...], we achieve a shot-noise limited measurement sensitivity [...] over a bandwidth that covers the dominant rates of variation in [...]. I also include two brief studies in quantum measurement theory, which highlight the significance of the experimental work for continuing research on conditional quantum dynamics. The first investigates quantum limits to broadband measurement of position and force, and the second proposes a novel trajectory-based approach to quantum system identification.
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.
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.
Cavity quantum electrodynamics (QED) in the strong-coupling regime provides the opportunity to monitor and control the dynamics of a simple quantum system. A single Cesium atom interacts strongly with single-photon fields in the mode of a high-finesse optical cavity. When the resulting coherent coupling rate dominates dissipation in the system, strong coupling is realized and the system displays distinctively quantum behavior. The coupling between atomic internal states and the quantized cavity field allows for diverse protocols in quantum state preparation, quantum communication, and quantum logic. However, the atom's external or motional state must also be taken into account. My research develops cavity QED in the limit where the coherent atom-field coupling dominates the atomic kinetic energy and thus significantly affects the atomic center-of-mass motion. In this regime, the interaction of the atom with the cavity field provides both a means of controlling atomic motion and a signal for detecting that motion in real time with high signal-to-noise. The sensing capability of the ``atom-cavity microscope" is exploited to trap single atoms with single-photon fields and to monitor their orbits in real time as they are bound in the cavity. Such real-time position sensing is the basis for a detailed strategy and ongoing experiment to actively stabilize select aspects of an atom's motion within the cavity. As the cavity-enabled position measurement approaches the standard quantum limit, this work begins to realize a quantum servo for atomic position and to address questions of optimal state estimation and state preparation. In combination with other progress in cavity QED, it furthers the goal of controlled atom-field interactions for quantum information science.
Two recent experiments are discussed which demonstrate real-time trapping and monitoring of single atoms within a high-finesse optical resonator. A single atom moving within the resonator generates large variations in the transmission of a weak probe laser, which are recorded in real time. These cavity QED signals are used to trigger ON a confining potential to trap the atom. In the first experiment, the confining potential is provided by the single-photon forces associated with the cavity QED interaction. An inversion algorithm allows individual atom trajectories to be reconstructed from the record of cavity transmission, and reveals single atoms bound in orbit by the mechanical forces associated with single photons. In a second experiment, an additional classical standing-wave dipole trap provides the trapping, enabling a 28 ms trap lifetime for single strongly coupled atoms.