Phase Coherence in a Driven Double-Well System

We analyze the dynamics of the molecular field incoherently pumped by the photoassociation of fermionic atoms and coupled by quantum tunnelling in a double-well potential. The relative phase distribution of the molecular modes in each well and their phase coherence are shown to build up owing to quantum mechanical fluctuations starting from the vacuum state. We identify three qualitatively different steady-state phase distributions, depending on the ratio of the molecule-molecule interaction strength to interwell tunnelling, and examine the crossover from a phase-coherent regime to a phase-incoherent regime as this ratio increases.Comment: 5 pages, 2 figure

Suppression of Magnetic State Decoherence Using Ultrafast Optical Pulses

It is shown that the magnetic state decoherence produced by collisions in a thermal vapor can be suppressed by the application of a train of ultrafast optical pulses.Comment: 5 pages, 3 figure

Phase Conjugation of a Quantum-Degenerate Atomic Fermi Beam

We discuss the possibility of phase-conjugation of an atomic Fermi field via nonlinear wave mixing in an ultracold gas. It is shown that for a beam of fermions incident on an atomic phase-conjugate mirror, a time reversed backward propagating fermionic beam is generated similar to the case in nonlinear optics. By adopting an operational definition of the phase, we show that it is possible to infer the presence of the phase-conjugate field by the loss of the interference pattern in an atomic interferometer

Diffraction of ultra-cold fermions by quantized light fields: Standing versus traveling waves

We study the diffraction of quantum degenerate fermionic atoms off of quantized light fields in an optical cavity. We compare the case of a linear cavity with standing wave modes to that of a ring cavity with two counter-propagating traveling wave modes. It is found that the dynamics of the atoms strongly depends on the quantization procedure for the cavity field. For standing waves, no correlations develop between the cavity field and the atoms. Consequently, standing wave Fock states yield the same results as a classical standing wave field while coherent states give rise to a collapse and revivals in the scattering of the atoms. In contrast, for traveling waves the scattering results in quantum entanglement of the radiation field and the atoms. This leads to a collapse and revival of the scattering probability even for Fock states. The Pauli Exclusion Principle manifests itself as an additional dephasing of the scattering probability

Molecule formation as a diagnostic tool for second order correlations of ultra-cold gases

We calculate the momentum distribution and the second-order correlation function in momentum space, $g^{(2)}({\bf p},{\bf p}',t)$ for molecular dimers that are coherently formed from an ultracold atomic gas by photoassociation or a Feshbach resonance. We investigate using perturbation theory how the quantum statistics of the molecules depend on the initial state of the atoms by considering three different initial states: a Bose-Einstein condensate (BEC), a normal Fermi gas of ultra-cold atoms, and a BCS-type superfluid Fermi gas. The cases of strong and weak coupling to the molecular field are discussed. It is found that BEC and BCS states give rise to an essentially coherent molecular field with a momentum distribution determined by the zero-point motion in the confining potential. On the other hand, a normal Fermi gas and the unpaired atoms in the BCS state give rise to a molecular field with a broad momentum distribution and thermal number statistics. It is shown that the first-order correlations of the molecules can be used to measure second-order correlations of the initial atomic state.Comment: revtex, 15 pages,8 figure

Boson-Fermion coherence in a spherically symmetric harmonic trap

We consider the photoassociation of a low-density gas of quantum-degenerate trapped fermionic atoms into bosonic molecules in a spherically symmetric harmonic potential. For a dilute system and the photoassociation coupling energy small compared to the level separation of the trap, only those fermions in the single shell with Fermi energy are coupled to the bosonic molecular field. Introducing a collective pseudo-spin operator formalism we show that this system can then be mapped onto the Tavis-Cummings Hamiltonian of quantum optics, with an additional pairing interaction. By exact diagonalization of the Hamiltonian, we examine the ground state and low excitations of the Bose-Fermi system, and study the dynamics of the coherent coupling between atoms and molecules. In a semiclassical description of the system, the pairing interaction between fermions is shown to result in a self-trapping transition in the photoassociation, with a sudden suppression of the coherent oscillations between atoms and molecules. We also show that the full quantum dynamics of the system is dominated by quantum fluctuations in the vicinity of the self-trapping solution.Comment: 16 pages, 14 figure

Dynamics of Fermionic Four-Wave Mixing

We study the dynamics of a beam of fermions diffracted off a density grating formed by fermionic atoms in the limit of a large grating. An exact description of the system in terms of particle-hole operators is developed. We use a combination of analytical and numerical methods to quantitatively explore the Raman-Nath and the Bragg regimes of diffraction. We discuss the limits in diffraction efficiency resulting from the dephasing of the grating due the distribution of energy states occupied by the fermions. We propose several methods to overcome these limits, including the novel technique of ``atom echoes''.Comment: 8 pages, 7 figure

Atomtronics: ultracold atom analogs of electronic devices

Atomtronics focuses on atom analogs of electronic materials, devices and circuits. A strongly interacting ultracold Bose gas in a lattice potential is analogous to electrons in solid-state crystalline media. As a consequence of the band structure, cold atoms in a lattice can exhibit insulator or conductor properties. P-type and N-type material analogs can be created by introducing impurity sites into the lattice. Current through an atomtronic wire is generated by connecting the wire to an atomtronic battery which maintains the two contacts at different chemical potentials. The design of an atomtronic diode with a strongly asymmetric current-voltage curve exploits the existence of superfluid and insulating regimes in the phase diagram. The atomtronic analog of a bipolar junction transistor exhibits large negative gain. Our results provide the building blocks for more advanced atomtronic devices and circuits such as amplifiers, oscillators and fundamental logic gates

Measuring dark energy spatial inhomogeneity with supernova data

The gravitational lensing distortion of distant sources by the large-scale distribution of matter in the Universe has been extensively studied. In contrast, very little is known about the effects due to the large-scale distribution of dark energy. We discuss the use of Type Ia supernovae as probes of the spatial inhomogeneity and anisotropy of dark energy. We show that a shallow, almost all-sky survey can limit rms dark energy fluctuations at the horizon scale down to a fractional energy density of ~10^-4Comment: 4 pages; PRL submitte

How close can an Inhomogeneous Universe mimic the Concordance Model?

Recently, spatially inhomogeneous cosmological models have been proposed as an alternative to the LCDM model, with the aim of reproducing the late time dynamics of the Universe without introducing a cosmological constant or dark energy. This paper investigates the possibility of distinguishing such models from the standard LCDM using background or large scale structure data. It also illustrates and emphasizes the necessity of testing the Copernican principle in order to confront the tests of general relativity with the large scale structure.Comment: 15 pages, 7 figure