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Continuous observation of quantum dynamics

Hideo Mabuchi

Published Mar 17, 2006• 1 citation
Publisher

Abstract

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.

DOI
10.7907/sgc8-n788

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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.
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.
The experiments discussed in this thesis focus on the interaction of a single trapped atom with the single mode of a high-finesse optical cavity, in the regime of strong coupling. Chapter 1 gives a brief introduction, after which Chapter 2 describes our recent measurements of the transmission spectrum of the atom-cavity system. The spectrum exhibits a clearly resolved vacuum-Rabi splitting, in good quantitative agreement with theoretical predictions. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements of this type that have required averaging over 10^3-10^5 atoms. Chapter 3 discusses our observations of photon blockade for the transmitted light in the presence of one trapped atom. Excitation of the atom-cavity system by a first photon blocks the transmission of a second one, thereby converting an incident Poissonian stream of photons into a sub-Poissonian, anti-bunched stream, as confirmed by measurements of the photon statistics of the transmitted field. The intensity correlations of the cavity transmission also reveal the energy distribution for oscillatory motion of the trapped atom. Chapter 4 details a set of simple but necessary measurements of relevant experimental parameters such as cavity geometry, linewidth, mirror properties, birefringence, and detection efficiency. The thesis concludes with Appendix A, describing the efficient laser setup we use for our magneto-optical traps.
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.
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.
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.
We report on recent progress in our lab involving cavity quantum electrodynamics with optically trapped atoms. \n \nIn particular, we will focus on a recent measurement of the Vacuum-Rabi splitting for one atom strongly coupled to the field of a high finesse optical resonator. This splitting is characteristic of the normal modes in the eigenvalue spectrum of the atom-cavity system. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements in cavity QED that have required averaging over many atoms.