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Lasing and steady state superradiance are two phenomena that may appear at first glance to be distinct. In a laser, phase information is maintained by a macroscopic intracavity light field, and the robustness of this phase is what leads to the coherence of the output light. In contrast, the coherence of steady-state superradiant systems derives from the macroscopic collective dipole of a many-atom ensemble. In this paper, we develop a quantum theory that connects smoothly between these two extreme limits. We show that lasing and steady-state superradiance should be thought of as the two extreme limits of a continuous crossover. The properties of systems that lie in the superradiance, lasing, and crossover parameter regions are compared. We find that for a given output intensity a narrower linewidth can be obtained by operating closer to the superradiance side of the crossover. We also find that the collective phase is robust against cavity frequency fluctuations in the superradiant regime and against atomic level fluctuations in the lasing regime., Comment: 10 pages, 4 figures

We investigate laser cooling of an ensemble of atoms in an optical cavity. We demonstrate that when atomic dipoles are sychronized in the regime of steady-state superradiance, the motion of the atoms may be subject to a giant frictional force leading to potentially very low temperatures. The ultimate temperature limits are determined by a modified atomic linewidth, which can be orders of magnitude smaller than the cavity linewidth. The cooling rate is enhanced by the superradiant emission into the cavity mode allowing reasonable cooling rates even for dipolar transitions with ultranarrow linewidth.

We consider the phase stability of a local oscillator (or laser) locked to a cavity QED system comprised of atoms with an ultra-narrow optical transition. The atoms are cooled to millikelvin temperatures and then released into the optical cavity. Although the atomic motion introduces Doppler broadening, the standing wave nature of the cavity causes saturated absorption features to appear, which are much narrower than the Doppler width. These features can be used to achieve an extremely high degree of phase stabilization, competitive with the current state-of-the-art. Furthermore, the inhomogeneity introduced by finite atomic velocities can cause optical bistability to disappear, resulting in no regions of dynamic instability and thus enabling a new regime accessible to experiments where optimum stabilization may be achieved.

We investigate Ramsey spectroscopy performed on a synchronized ensemble of two-level atoms. The synchronization is induced by the collective coupling of the atoms to a heavily damped mode of an optical cavity. We show that, in principle, with this synchronized system it is possible to observe Ramsey fringes indefinitely, even in the presence of spontaneous emission and other sources of individual-atom dephasing. This could have important consequences for atomic clocks and a wide range of precision metrology applications.

We propose a system for observing the correlated phase dynamics of two mesoscopic ensembles of atoms through their collective coupling to an optical cavity. We find a dynamical quantum phase transition induced by pump noise and cavity output-coupling. The spectral properties of the superradiant light emitted from the cavity show that at a critical pump rate the system undergoes a transition from the independent behavior of two disparate oscillators to the phase-locking that is the signature of quantum synchronization., Comment: 4 pages, 4 figures

We study an optomechanical system in which a microwave field and an optical field are coupled to a common mechanical resonator. We explore methods that use these mechanical resonators to store quantum mechanical states and to transduce states between the electromagnetic resonators from the perspective of the effect of mechanical decoherence. Besides being of fundamental interest, this coherent quantum state transfer could have important practical implications in the field of quantum information science, as it potentially allows one to overcome intrinsic limitations of both microwave and optical platforms. We discuss several state transfer protocols and study their transfer fidelity using a fully quantum mechanical model that utilizes quantum state-diffusion techniques. This work demonstrates that mechanical decoherence should not be an insurmountable obstacle in realizing high fidelity storage and transduction., Comment: 10 pages, 10 figures

We show that open quantum systems of two-level atoms symmetrically coupled to a single-mode photon field can be efficiently simulated by applying a SU(4) group theory to quantum master equations. This is important since many foundational examples in quantum optics fall into this class. We demonstrate the method by finding exact solutions for many-atom open quantum systems such as lasing and steady state superradiance.

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 figures

We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate atomic transport across a variety of lattice configurations. We demonstrate how the behavior of an electronic diode, a field-effect transistor, and a bipolar junction transistor can be realized with neutral, ultracold atoms trapped in optical lattices. An analysis of the current fluctuations is provided for the case of the atomtronic diode. Finally, we show that it is possible to demonstrate AND logic gate behavior in an optical lattice., Comment: 10 pages, 10 figures, 1 table

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 figures

Earth-alkaline-like atoms with ultra-narrow transitions open the door to a new regime of cavity quantum electrodynamics. That regime is characterized by a critical photon number that is many orders of magnitude smaller than what can be achieved in conventional systems. We show that it is possible to achieve superradiance in steady state with such systems. We discuss the basic underlying mechanisms as well as the key experimental requirements, Comment: 5 pages, 3 figures

We propose a new light source based on having alkaline-earth atoms in an optical lattice collectively emit photons on an ultra-narrow clock transition into the mode of a high Q-resonator. The resultant optical radiation has an extremely narrow linewidth in the mHz range, even smaller than that of the clock transition itself due to collective effects. A power level of order $10^{-12}W$ is possible, sufficient for phase-locking a slave optical local oscillator. Realizing this light source has the potential to improve the stability of the best clocks by two orders of magnitude., Comment: minor revisions + shortening; factor 2 algebra mistake corrected

Interferometry with Heisenberg limited phase resolution may play an important role in the next generation of atomic clocks, gravitational wave detectors, and in quantum information science. For experimental implementations the robustness of the phase resolution is crucial since any experimental realization will be subject to imperfections. In this article we study the robustness of phase reconstruction with two number states as input subject to fluctuations in the state preparation. We find that the phase resolution is insensitive to fluctuations in the total number of particles and robust against noise in the number difference at the input. The phase resolution depends on the uncertainty in the number difference in a universal way that has a clear physical interpretation: Fundamental noise due to the Heisenberg limit and noise due to state preparation imperfection contribute essentially independently to the total uncertainty in the phase. For number difference uncertainties less than one the first noise source is dominant and the phase resolution is essentially Heisenberg limited. For number difference uncertainties greater than one the noise due to state preparation imperfection is dominant and the phase resolution deteriorates linearly with the number difference uncertainty., Comment: 13 pages, 6 figures; high-resolution version can be obtained from authors

The ability to control spins in semiconductors is important in a variety of fields including spintronics and quantum information processing. Due to the potentially fast dephasing times of spins in the solid state [1-3], spin control operating on the picosecond or faster timescale may be necessary. Such speeds, which are not possible to attain with standard electron spin resonance (ESR) techniques based on microwave sources, can be attained with broadband optical pulses. One promising ultrafast technique utilizes single broadband pulses detuned from resonance in a three-level Lambda system [4]. This attractive technique is robust against optical pulse imperfections and does not require a fixed optical reference phase. Here we demonstrate the principle of coherent manipulation of spins theoretically and experimentally. Using this technique, donor-bound electron spin rotations with single-pulse areas exceeding pi/4 and two-pulses areas exceeding pi/2 are demonstrated. We believe the maximum pulse areas attained do not reflect a fundamental limit of the technique and larger pulse areas could be achieved in other material systems. This technique has applications from basic solid-state ESR spectroscopy to arbitrary single-qubit rotations [4, 5] and bang-bang control[6] for quantum computation., Comment: 15 pages, 4 figures, submitted 12/2008. Since the submission of this work we have become aware of related work: J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, Science 320: 349-352 (2008)

Quantum projection noise will soon limit the best achievable precision of optical atomic clocks based on lattice-confined neutral atoms. Squeezing the collective atomic pseudo-spin via measurement of the clock state populations during Ramsey interrogation suppresses the projection noise. We show here that the lattice laser field can be used to perform ideal quantum non-demolition measurements without clock shifts or decoherence and explore the feasibility of such an approach in theory with the lattice field confined in a ring-resonator. Detection of the motional sideband due to the atomic vibration in the lattice wells can yield signal sizes a hundredfold above the projection noise limit., Comment: Substantially expanded version

We report a novel hemispherical micro-cavity that is comprised of a planar integrated semiconductor distributed Bragg reflector (DBR) mirror, and an external, concave micro-mirror having a radius of curvature $50\mathrm{\mu m}$. The integrated DBR mirror containing quantum dots (QD), is designed to locate the QDs at an antinode of the field in order to maximize the interaction between the QD and the cavity. The concave micro-mirror, with high-reflectivity over a large solid-angle, creates a diffraction-limited (sub-micron) mode-waist at the planar mirror, leading to a large coupling constant between cavity mode and QD. The half-monolithic design gives more spatial and spectral tuning abilities, relatively to fully monolithic structures. This unique micro-cavity design will potentially enable us to both reach the cavity quantum electrodynamics (QED) strong coupling regime and realize the deterministic generation of single photons on demand., Comment: 15 pages, 17 figures, final version

In high-purity n-type GaAs under strong magnetic field, we are able to isolate a lambda system composed of two Zeeman states of neutral-donor bound electrons and the lowest Zeeman state of bound excitons. When the two-photon detuning of this system is zero, we observe a pronounced dip in the excited-state photoluminescence indicating the creation of the coherent population-trapped state. Our data are consistent with a steady-state three-level density-matrix model. The observation of coherent population trapping in GaAs indicates that this and similar semiconductor systems could be used for various EIT-type experiments., Comment: 5 pages, 4 figures replaced 6/25/2007 with PRL version