Open quantum systems approach to atomtronics

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 tabl

The Super-Strong Coupling Regime of Cavity Quantum Electrodynamics

We describe a qualitatively new regime of cavity quantum electrodynamics, the super strong coupling regime. This regime is characterized by atom-field coupling strengths of the order of the free spectral range of the cavity, resulting in a significant change in the spatial mode functions of the light field. It can be reached in practice for cold atoms trapped in an optical dipole potential inside the resonator. We present a nonperturbative scheme that allows us to calculate the frequencies and linewidths of the modified field modes, thereby providing a good starting point for a quantization of the theory.Comment: Figures rearranged and introduction rewritte

Number statistics of molecules formed from ultra-cold atoms

We calculate the number statistics of a single-mode molecular field excited by photoassociation or via a Feshbach resonance from an atomic Bose-Einstein condensate (BEC), a normal atomic Fermi gas and a Fermi system with pair correlations (BCS state). We find that the molecule formation from a BEC is a collective process that leads for short times to a coherent molecular state in the quantum optical sense. Atoms in a normal Fermi gas, on the other hand, are converted into molecules independently of each other and result for short times in a molecular state analogous to that of a classical chaotic light source. The BCS situation is intermediate between the two and goes from producing an incoherent to a coherent molecular field with increasing gap parameter.Comment: 5 pages, 4 figure

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

Spin squeezing in optical lattice clocks via lattice-based QND measurements

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 versio

Cavity QED determination of atomic number statistics in optical lattices

We study the reflection of two counter-propagating modes of the light field in a ring resonator by ultracold atoms either in the Mott insulator state or in the superfluid state of an optical lattice. We obtain exact numerical results for a simple two-well model and carry out statistical calculations appropriate for the full lattice case. We find that the dynamics of the reflected light strongly depends on both the lattice spacing and the state of the matter-wave field. Depending on the lattice spacing, the light field is sensitive to various density-density correlation functions of the atoms. The light field and the atoms become strongly entangled if the latter are in a superfluid state, in which case the photon statistics typically exhibit complicated multimodal structures.Comment: 10 pages revtex, 13 figure

Reconstruction of the phase of matter-wave fields using a momentum resolved cross-correlation technique

We investigate the potential of the so-called XFROG cross-correlation technique originally developed for ultrashort laser pulses for the recovery of the amplitude and phase of the condensate wave function of a Bose-Einstein condensate. Key features of the XFROG method are its high resolution, versatility and stability against noise and some sources of systematic errors. After showing how an analogue of XFROG can be realized for Bose-Einstein condensates, we illustrate its effectiveness in determining the amplitude and phase of the wave function of a vortex state. The impact of a reduction of the number of measurements and of typical sources of noise on the field reconstruction are also analyzed.Comment: 7 pages; 9 figures; article with higher resolution figures available from author

Coupled dynamics of atoms and radiation pressure driven interferometers

We consider the motion of the end mirror of a cavity in whose standing wave mode pattern atoms are trapped. The atoms and the light field strongly couple to each other because the atoms form a distributed Bragg mirror with a reflectivity that can be fairly high. We analyze how the dipole potential in which the atoms move is modified due to this backaction of the atoms. We show that the position of the atoms can become bistable. These results are of a more general nature and can be applied to any situation where atoms are trapped in an optical lattice inside a cavity and where the backaction of the atoms on the light field cannot be neglected. We analyze the dynamics of the coupled system in the adiabatic limit where the light field adjusts to the position of the atoms and the light field instantaneously and where the atoms move much faster than the mirror. We calculate the side band spectrum of the light transmitted through the cavity and show that these spectra can be used to detect the coupled motion of the atoms and the mirror.Comment: 11 pages; 13 figures; two added references and other minor correction