Collective generation of quantum states of light by entangled atoms

We present a theoretical framework to describe the collective emission of light by entangled atomic states. Our theory applies to the low excitation regime, where most of the atoms are initially in the ground state, and relies on a bosonic description of the atomic excitations. In this way, the problem of light emission by an ensemble of atoms can be solved exactly, including dipole-dipole interactions and multiple light scattering. Explicit expressions for the emitted photonic states are obtained in several situations, such as those of atoms in regular lattices and atomic vapors. We determine the directionality of the photonic beam, the purity of the photonic state, and the renormalization of the emission rates. We also show how to observe collective phenomena with ultracold atoms in optical lattices, and how to use these ideas to generate photonic states that are useful in the context of quantum information.Comment: 15 pages, 10 figure

Quantum simulation of the hexagonal Kitaev model with trapped ions

We present a detailed study of quantum simulations of coupled spin systems in surface-electrode ion-trap arrays, and illustrate our findings with a proposed implementation of the hexagonal Kitaev model [A. Kitaev, Annals of Physics 321,2 (2006)]. The effective (pseudo)spin interactions making up such quantum simulators are found to be proportional to the dipole-dipole interaction between the trapped ions, and are mediated by motion which can be driven by state-dependent forces. The precise forms of the trapping potentials and the interactions are derived in the presence of a surface electrode and a cover electrode. These results are the starting point to derive an optimized surface-electrode geometry for trapping ions in the desired honeycomb lattice of Kitaev's model, where we design the dipole-dipole interactions in a way that allows for coupling all three bond types of the model simultaneously, without the need for time discretization. Finally we propose a simple wire structure that can be incorporated in a microfabricated chip to generate localized state-dependent forces which drive the couplings prescribed by this particular model; such a wire structure should be adaptable to many other situations.Comment: 24 pages, 7 figures. v2: simplified the derivation of (28) without changing conclusions; minor edits. v3: minor edit

Far-from-equilibrium noise heating and laser cooling dynamics in radio-frequency Paul traps

We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.Comment: 23 pages, 7 figure

Electrostatics of Gapped and Finite Surface Electrodes

We present approximate methods for calculating the three-dimensional electric potentials of finite surface electrodes including gaps between electrodes, and estimate the effects of finite electrode thickness and an underlying dielectric substrate. As an example we optimize a radio-frequency surface-electrode ring ion trap, and find that each of these factors reduces the trapping secular frequencies by less than 5% in realistic situations. This small magnitude validates the usual assumption of neglecting the influences of gaps between electrodes and finite electrode extent.Comment: 9 pages, 9 figures (minor changes

Experiments towards quantum information with trapped Calcium ions

Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. With resolved sideband cooling on the optical S1/2 - D5/2 quadrupole transition we have cooled one and two 40Ca+ ions to the ground state of vibration with up to 99.9% probability. With a novel cooling scheme utilizing electromagnetically induced transparency on the S1/2 - P1/2 manifold we have achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the motional ground state we have demonstrated coherent quantum state manipulation on the S1/2 - D5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations within 1.4 ms have been observed in the motional ground state and in the n=1 Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more than 5 micron for up to 4 ions. We are able to cool two ions to the ground state in the trap and individually address the ions with laser pulses through a special optical addressing channel.Comment: Proceedings of the ICAP 2000, Firenz

Fluorescence during Doppler cooling of a single trapped atom

We investigate the temporal dynamics of Doppler cooling of an initially hot single trapped atom in the weak binding regime using a semiclassical approach. We develop an analytical model for the simplest case of a single vibrational mode for a harmonic trap, and show how this model allows us to estimate the initial energy of the trapped particle by observing the fluorescence rate during the cooling process. The experimental implementation of this temperature measurement provides a way to measure atom heating rates by observing the temperature rise in the absence of cooling. This method is technically relatively simple compared to conventional sideband detection methods, and the two methods are in reasonable agreement. We also discuss the effects of RF micromotion, relevant for a trapped atomic ion, and the effect of coupling between the vibrational modes on the cooling dynamics.Comment: 12 pages, 11 figures, Submitted to Phys. Rev.

Rabi oscillations in a quantum dot-cavity system coupled to a non-zero temperature phonon bath

We study a quantum dot strongly coupled to a single high-finesse optical microcavity mode. We use a rotating wave approximation method, commonly used in ion-laser interactions, tegether with the Lamb-Dicke approximation to obtain an analytic solution of this problem. The decay of Rabi oscillations because of the electron-phonon coupling are studied at arbitrary temperature and analytical expressions for the collapse and revival times are presented. Analyses without the rotating wave approximation are presented by means of investigating the energy spectrum.Comment: 7 pages, 5 figures; Revised versio