Absolute frequency measurements of the D2D_2 line and fine-structure interval in 39^{39}K

We report a value for the $D_2$-line frequency of $^{39}$K with 0.25 ppb uncertainty. The frequency is measured using an evacuated ring-cavity resonator whose length is calibrated against a reference laser. The $D_2$ line presents a problem in identifying the line center because the closely-spaced energy levels of the excited state are not resolved. We use computer modelling of the measured spectrum to extract the line center and obtain a value of 391 015 578.040(75) MHz. In conjunction with our previous measurement of the $D_1$ line, we determine the fine-structure interval in the $4P$ state to be 1 729 997.132(90) MHz. The results represent significant improvement over previous values.Comment: 4 pages, 3 figure

Giant optical Faraday rotation induced by a single electron spin in a quantum dot: Applications to entangling remote spins via a single photon

We propose a quantum non-demolition method - giant Faraday rotation - to detect a single electron spin in a quantum dot inside a microcavity where negatively-charged exciton strongly couples to the cavity mode. Left- and right-circularly polarized light reflected from the cavity feels different phase shifts due to cavity quantum electrodynamics and the optical spin selection rule. This yields giant and tunable Faraday rotation which can be easily detected experimentally. Based on this spin-detection technique, a scalable scheme to create an arbitrary amount of entanglement between two or more remote spins via a single photon is proposed.Comment: 5 pages, 3 figure

Extreme non-linear response of ultra-narrow optical transitions in cavity QED for laser stabilization

We explore the potential of direct spectroscopy of ultra-narrow optical transitions of atoms localized in an optical cavity. In contrast to stabilization against a reference cavity, which is the approach currently used for the most highly stabilized lasers, stabilization against an atomic transition does not suffer from Brownian thermal noise. Spectroscopy of ultra-narrow optical transitions in a cavity operates in a very highly saturated regime in which non-linear effects such as bistability play an important role. From the universal behavior of the Jaynes-Cummings model with dissipation, we derive the fundamental limits for laser stabilization using direct spectroscopy of ultra-narrow atomic lines. We find that with current lattice clock experiments, laser linewidths of about 1 mHz can be achieved in principle, and the ultimate limitations of this technique are at the 1 $\mu$ Hz level.Comment: 5 pages, 4 figure

Quantum turbulence in condensate collisions: an application of the classical field method

We apply the classical field method to simulate the production of correlated atoms during the collision of two Bose-Einstein condensates. Our non-perturbative method includes the effect of quantum noise, and provides for the first time a theoretical description of collisions of high density condensates with very large out-scattered fractions. Quantum correlation functions for the scattered atoms are calculated from a single simulation, and show that the correlation between pairs of atoms of opposite momentum is rather small. We also predict the existence of quantum turbulence in the field of the scattered atoms--a property which should be straightforwardly measurable.Comment: 5 pages, 3 figures: Rewritten text, replaced figure

Entanglement of formation for symmetric Gaussian states

We show that for a fixed amount of entanglement, two-mode squeezed states are those that maximize Einstein-Podolsky-Rosen-like correlations. We use this fact to determine the entanglement of formation for all symmetric Gaussian states corresponding to two modes. This is the first instance in which this measure has been determined for genuine continuous variable systems.Comment: 4 pages, revtex

A high bandwidth quantum repeater

We present a physical- and link-level design for the creation of entangled pairs to be used in quantum repeater applications where one can control the noise level of the initially distributed pairs. The system can tune dynamically, trading initial fidelity for success probability, from high fidelity pairs (F=0.98 or above) to moderate fidelity pairs. The same physical resources that create the long-distance entanglement are used to implement the local gates required for entanglement purification and swapping, creating a homogeneous repeater architecture. Optimizing the noise properties of the initially distributed pairs significantly improves the rate of generating long-distance Bell pairs. Finally, we discuss the performance trade-off between spatial and temporal resources.Comment: 5 page

Influence of External Fields and Environment on the Dynamics of Phase Qubit-Resonator System

We analyze the dynamics of a qubit-resonator system coupled with a thermal bath and external electromagnetic fields. Using the evolution equations for the set of Heisenberg operators, that describe the whole system, we derive an expression for the resonator field, accounting for the resonator-drive,-bath, and -qubit interaction. The renormalization of the resonator frequency, caused by the qubit-resonator interaction, is accounted for. Using solutions for the resonator field, we derive the equation describing qubit dynamics. The influence of the qubit evolution during the measurement time on the fidelity of a single-shot measurement is studied. The relation between the fidelity and measurement time is shown explicitly. Also, an expression describing relaxation of the superposition qubit state towards its stationary value is derived. The possibility of controlling this state, by varying the amplitude and frequency of drive, is shown.Comment: 15 page

Squashed States of Light: Theory and Applications to Quantum Spectroscopy

Using a feedback loop it is possible to reduce the fluctuations in one quadrature of an in-loop field without increasing the fluctuations in the other. This effect has been known for a long time, and has recently been called ``squashing'' [B.C. Buchler et al., Optics Letters {\bf 24}, 259 (1999)], as opposed to the ``squeezing'' of a free field in which the conjugate fluctuations are increased. In this paper I present a general theory of squashing, including simultaneous squashing of both quadratures and simultaneous squeezing and squashing. I show that a two-level atom coupled to the in-loop light feels the effect of the fluctuations as calculated by the theory. In the ideal limit of light squeezed in one quadrature and squashed in the other, the atomic decay can be completely suppressed.Comment: 8 pages plus one figure. Submitted to JEOS-B for Dan Walls Special Issu

Intensity fluctuations in steady state superradiance

Alkaline-earth like atoms with ultra-narrow optical transitions enable superradiance in steady state. The emitted light promises to have an unprecedented stability with a linewidth as narrow as a few millihertz. In order to evaluate the potential usefulness of this light source as an ultrastable oscillator in clock and precision metrology applications it is crucial to understand the noise properties of this device. In this paper we present a detailed analysis of the intensity fluctuations by means of Monte-Carlo simulations and semi-classical approximations. We find that the light exhibits bunching below threshold, is to a good approximation coherent in the superradiant regime, and is chaotic above the second threshold.Comment: 8 pages, 5 figure

Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement

We propose a cavity QED setup which implements a dissipative Lipkin-Meshkov-Glick model -- an interacting collective spin system. By varying the external model parameters the system can be made to undergo both first-and second-order quantum phase transitions, which are signified by dramatic changes in cavity output field properties, such as the probe laser transmission spectrum. The steady-state entanglement between pairs of atoms is shown to peak at the critical points and can be experimentally determined by suitable measurements on the cavity output field. The entanglement dynamics also exhibits pronounced variations in the vicinities of the phase transitions.Comment: 19 pages, 18 figures, shortened versio