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Cavity Quantum Electrodynamics of Systems from Few Atoms to Controlled Ensembles

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Cavity Quantum Electrodynamics of Systems from Few Atoms to Controlled Ensembles Hungarian Scientific Research Fund NF proposal Cavity quantum electrodynamics of systems from few atoms to controlled ensembles Peter Domokos Research Institute for Solid State Physics and Optics of the Hungarian Academy of Sciences 1 INTRODUCTION 1 1 Introduction The interaction of the electromagnetic field and atoms is significantly changed if, instead of being in free space, the field is limited by boundaries. The substantial modification of the radiative properties of single atoms or ensembles in a cavity is of fundamental interest, and has an impact on spectroscopy as well as on the current evolution of nanoscale technologies. Cavity quantum electrodynamics (cavity QED, CQED) has been studied for several decades now, however, it is in the last few years that this subject has undergone a breathtaking progress in the laboratories. Recent spectacular advances include, for example, the tracking of atomic trajectories [Hood et al., 2000; Pinkse et al., 2000], the realization of single-atom lasing [McKeever et al., 2003a] and that of deterministic single- photon source [Keller et al., 2004], the cooling of atomic motion by cavity fields [Maunz et al., 2004], the generation of Fock states of the cavity field [Varcoe et al., 2000], and a test of the complementarity principle [Bertet et al., 2001]. The prototype system of cavity QED is a single atomic dipole coupled to the elec- tromagnetic radiation field in a tiny, high-finesse resonator (cavity) composed of mirrors with extremely high reflection coefficients. The interaction is strongly enhanced due to “recycling” the photons by reflections. Whereas lasers act on atoms merely as external fields, the resonator mode becomes a genuine dynamical variable of the coupled system. The atom exerts a significant back-action on the field while evolving under its influence. Cavity QED can be viewed as a model system extending the range of light-matter inter- action. The usual scenario of an external field can be rendered with a parameter setting that yields a low number of photon round-trips. At the same time, the coupling can be continuously tuned to achieve a highly correlated atom-photon dynamics. This general- ization opens an avenue towards new applications based on the strong nonlinearities in the dynamics and on the resulting correlation between the subsystems. In this project, cavity QED will be connected to the subject of manipulating the gross motion of neutral massive particles by optical means. On the microscopic level, the me- chanical effect of radiation becomes appreciable and gives rise to a wealth of interesting phenomena. With the use of spatially and temporally coherent light sources, i.e. lasers, the mechanical interaction can be designed and the center-of-mass degree of freedom can be controlled by light. As the most spectacular application we mention the various methods developed for the trapping and cooling of neutral particles, which have had an immense impact on today’s atomic, molecular, and optical physics [Chu, 1998; Cohen- Tannoudji, 1998; Phillips, 1998]. The importance of eliminating thermal noise cannot be overestimated since it allows to push measurement precision to the ultimate quantum noise limit given by the uncertainty principle. Owing to optical cooling methods, the quantum degenerate, Bose-condensed state of alkali atom gases has been reached [Cornell and Wieman, 2002; Ketterle, 2002], and later, that of many other species even including molecules [Jochim et al., 2003]. The project objectives are closely related to these out- standing scientific achievements, awarded by the Nobel prizes in 1997 (laser cooling and trapping), 2001 (Bose-Einstein condensation), and 2005 (optical coherence). The guiding principle of the project is that the manipulation of atoms by lasers and related effects must be revisited in the context of cavity QED. One example where this extension has already opened new directions of research is cavity cooling, a recently pre- dicted [Horak et al., 1997] and demonstrated [Maunz et al., 2004] method of efficiently cooling atoms by means of dynamically varying cavity fields. Cavity cooling can poten- tially be applied to arbitrary massive particle with linear polarizability and is therefore a major research topic in several laboratories and theoretical groups today. 2 PROJECT OBJECTIVES 2 Cavity QED can greatly contribute to our knowledge of light-matter interaction con- cerning composite systems. Cavity-induced forces on a dilute gas of atoms are distin- guished by the inherent role of many-body effects: the evolution cannot be interpreted in terms of independent single-atom processes as opposed to free space schemes. There is a cavity-mediated interaction between remote atoms, which can alter the dynamics dramat- ically. It is through the electromagnetic field that a collective behaviour of an ensemble of polarizable particles arises, and the back-reaction of those particles on the field is am- plified by the collectivity. For example, a gas of laser-driven atoms scattering light into a cavity has been shown to produce a phase transition between the homogeneous spatial distribution and a regular pattern bound by the electromagnetic field of the cavity. We found that the efficiency of cavity cooling in this scheme can significantly improve owing to the collective action of the atoms: they self-organize into a regular pattern and dis- sipate motional energy by superradiant scattering into the cavity [Domokos and Ritsch, 2002]. The novelty of the proposed research subject is that we study many-body phenomena in a cavity at a very fundamental level, including a precise modeling of the atom-atom interaction. This initiative is motivated by the fact that the collective effects in an atom cloud depend heavily on the properties of the atom-atom interaction. Therefore we need to complete the previous models with two additional interaction channels. In a dense cloud of cold atoms illuminated by quasi-resonant laser fields, the anisotropic dipole-dipole coupling is the dominant interaction, mediated by the electromagnetic vac- uum field. This coupling amounts to a measurable modification of the optical properties of the cloud, e. g., a nonlinear density dependence of the refractive index [Morice et al., 1995]. As a consequence, slow diffusion of light [Labeyrie et al., 2003] and an instabil- ity of the homogeneous distribution [Sesko et al., 1991] have been observed in a dense atom cloud. Furthermore, as one of the major components of this project, we take into account the short range atom-atom interaction resulting from the electron exchange of overlapping atoms. Its effect on the optical properties of colliding atoms has never been explored before. This model will enable us to study photoassociation of atoms into bound molecules. Ultimately, equipped with the full model we can address the regime of ultracold atoms, where the material component manifests wavelike behavior. This is a research direction of fundamental interest in many-body physics. Quantum statistical properties can be investigated in well-controlled, weakly interacting atomic ensembles. A unique feature of the system is that the collisional properties are partially tunable. The necessary ultra- low temperature regime can be achieved today, phase transition into a Bose-Einstein condensate is being routinely realized with alkali atoms. Various other manifestations of quantum statistics, superfluidity, etc., can be observed. The strongly coupled dynamics of electromagnetic radiation field and matter, where this latter is represented by a quantum degenerate gas has not yet been explored at all. Experiments are in construction, the first results have recently been reported on the coupling of Bose-Einstein condensates to a high-finesse resonator [Ottl et al., 2005], strongly motivating our effort on the theoretical description. 2 Project objectives Our general objective is to study the dynamics of composite quantum systems with in- creasing degrees of complexity in their dimensionality, where the different degrees of free- 2 PROJECT OBJECTIVES 3 dom communicate via their common coupling to the same cavity field modes. Neither simple theoretical models, nor brute force numerical simulations are efficient to describe such systems of interest. Instead, sophisticated phase-space and Monte Carlo methods of quantum optics will be invoked, which enable us to properly treat the quantum noise in open, nonlinear systems. We aim at providing the theoretical ground for exploring new regimes of light-matter interaction in the case of few-atom systems, molecules, Bose- Einstein condensates and Fermi gases. gf(x) η(ω) κ γ ηt(ω) Figure 1: Schematic representation of the general system to be studied. Atoms moving in an optical resonator are strongly coupled to a sinusoidal mode of the cavity [gf(x)]. The system can be excited by injecting a laser field (η) into the resonator through the partially transmitting mirror or the atoms can be directly laser-driven from the side (ηt). The atoms radiate into free space as well, giving rise to an atom-atom coupling through the vacuum field modes. Depending on the temperature, the atoms can behave as pointlike small wavepackets (see Sect. 2.1), or can extend into large wavefunctions at ultracold temperatures (see Sect. 2.3). The contact interaction between colliding atoms will be studied in detail (see Sect. 2.3). The system has irreversible loss channels: beside the spontaneous emission into the free vacuum field, the resonator photons escape at rate κ. 2.1 Cavity cooling and dipole-dipole interaction in a cavity We consider cold neutral atoms that can be described by small wave-packets, well localized on the radiation wavelength scale. Besides1 being commonly coupled to selected modes of a resonator field, they interact through the broadband reservoir of vacuum field modes: a dipole-dipole coupling arises from the reabsorption of spontaneously emitted photons. This interaction has previously been neglected, assuming a relatively low density of the atom gas. However, thanks to the efficient cavity cooling schemes, the gas may become significantly compressed in the vicinity of antinodes of the resonator mode.
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