Optimized Double-well quantum interferometry with Gaussian squeezed-states

A Mach-Zender interferometer with a gaussian number-difference squeezed input state can exhibit sub-shot-noise phase resolution over a large phase-interval. We obtain the optimal level of squeezing for a given phase-interval $\Delta\theta_0$ and particle number $N$, with the resulting phase-estimation uncertainty smoothly approaching $3.5/N$ as $\Delta\theta_0$ approaches 10/N, achieved with highly squeezed states near the Fock regime. We then analyze an adaptive measurement scheme which allows any phase on $(-\pi/2,\pi/2)$ to be measured with a precision of $3.5/N$ requiring only a few measurements, even for very large $N$. We obtain an asymptotic scaling law of $\Delta\theta\approx (2.1+3.2\ln(\ln(N_{tot}\tan\Delta\theta_0)))/N_{tot}$, resulting in a final precision of $\approx 10/N_{tot}$. This scheme can be readily implemented in a double-well Bose-Einstein condensate system, as the optimal input states can be obtained by adiabatic manipulation of the double-well ground state.Comment: updated versio

Super-rigidity for CR embeddings of real hypersurfaces into hyperquadrics

Let Q^N_l\subset \bC\bP^{N+1} denote the standard real, nondegenerate hyperquadric of signature $l$ and M\subset \bC^{n+1} a real, Levi nondegenerate hypersurface of the same signature $l$. We shall assume that there is a holomorphic mapping H_0\colon U\to \bC\bP^{N_0+1}, where $U$ is some neighborhood of $M$ in \bC^{n+1}, such that $H_0(M)\subset Q^{N_0}_l$ but $H(U)\not\subset Q^{N_0}_l$. We show that if $N_0-n<l$ then, for any $N\geq N_0$, any holomorphic mapping H\colon U\to \bC\bP^{N+1} with $H(M)\subset Q^{N}_l$ and $H(U)\not\subset Q^{N_0}_l$ must be the standard linear embedding of $Q^{N_0}_l$ into $Q^N_l$ up to conjugation by automorphisms of $Q^{N_0}_l$ and $Q^N_l$

Collisions of Jets of Particles from Active Galactic Nuclei with Neutralino Dark Matter

We examine the possibility that energetic Standard Model particles contained in the jets produced by active galactic nuclei (AGN) may scatter off of the dark matter halo which is expected to surround the AGN. In particular, if there are nearby states in the dark sector which can appear resonantly in the scattering, the cross section can be enhanced and a distinctive edge feature in the energy spectrum may appear. We examine bounds on supersymmetric models which may be obtained from the Fermi Gamma-ray Space Telescope observation of the nearby AGN Centaurus A.Comment: 20 pages, 9 figures; v2: version published in JCA

Transition Temperature of a Uniform Imperfect Bose Gas

We calculate the transition temperature of a uniform dilute Bose gas with repulsive interactions, using a known virial expansion of the equation of state. We find that the transition temperature is higher than that of an ideal gas, with a fractional increase K_0(na^3)^{1/6}, where n is the density and a is the S-wave scattering length, and K_0 is a constant given in the paper. This disagrees with all existing results, analytical or numerical. It agrees exactly in magnitude with a result due to Toyoda, but has the opposite sign.Comment: Email correspondence to [email protected] ; 2 pages using REVTe

Degenerate Fermi gas in a combined harmonic-lattice potential

In this paper we derive an analytic approximation to the density of states for atoms in a combined optical lattice and harmonic trap potential as used in current experiments with quantum degenerate gases. We compare this analytic density of states to numerical solutions and demonstrate its validity regime. Our work explicitly considers the role of higher bands and when they are important in quantitative analysis of this system. Applying our density of states to a degenerate Fermi gas we consider how adiabatic loading from a harmonic trap into the combined harmonic-lattice potential affects the degeneracy temperature. Our results suggest that occupation of excited bands during loading should lead to more favourable conditions for realizing degenerate Fermi gases in optical lattices.Comment: 11 pages, 9 figure

On-demand generation of entanglement of atomic qubits via optical interferometry

The problem of on-demand generation of entanglement between single-atom qubits via a common photonic channel is examined within the framework of optical interferometry. As expected, for a Mach-Zehnder interferometer with coherent laser beam as input, a high-finesse optical cavity is required to overcome sensitivity to spontaneous emission. We show, however, that with a twin-Fock input, useful entanglement can in principle be created without cavity-enhancement. Both approaches require single-photon resolving detectors, and best results would be obtained by combining both cavity-feedback and twin-Fock inputs. Such an approach may allow a fidelity of $.99$ using a two-photon input and currently available mirror and detector technology. In addition, we study interferometers based on NOON states and show that they perform similarly to the twin-Fock states, yet without the need for high-precision photo-detectors. The present interferometrical approach can serve as a universal, scalable circuit element for quantum information processing, from which fast quantum gates, deterministic teleportation, entanglement swapping $etc.$, can be realized with the aid of single-qubit operations.Comment: To be published in PR

Effects of collisions against thermal impurities in the dynamics of a trapped fermion gas

We present a theoretical study of the dynamical behavior of a gas made of ultracold fermionic atoms, which during their motions can collide with a much smaller number of thermal bosonic impurities. The atoms are confined inside harmonic traps and the interactions between the two species are treated as due to s-wave scattering with a negative scattering length modeling the 40K-87Rb fermion-boson system. We set the fermions into motion by giving a small shift to their trap center and examine two alternative types of initial conditions, referring to (i) a close-to-equilibrium situation in which the two species are at the same temperature (well below the Fermi temperature and well above the Bose-Einstein condensation temperature); and (ii) a far-from-equilibrium case in which the impurities are given a Boltzmann distribution of momenta while the fermions are at very low temperatures. The dynamics of the gas is evaluated by the numerical solution of the Vlasov-Landau equations for the one-body distribution functions, supported by some analytical results on the collisional properties of a fermion gas. We find that the trapped gaseous mixture is close to the collisionless regime for values of the parameters corresponding to current experiments, but can be driven towards a collisional regime even without increasing the strength of the interactions, either by going over to heavier impurity masses or by matching the width of the momentum distribution of the impurities to the Fermi momentum of the fermion gas.Comment: 7 pages, 4 figures, RevTeX 4, accepted in PR

Ultra-bright omni-directional collective emission of correlated photon pairs from atomic vapors

Spontaneous four-wave mixing can generate highly correlated photon pairs from atomic vapors. We show that multi-photon pumping of dipole-forbidden transitions in a recoil-free geometry can result in ultra-bright pair-emission in the full 4\pi solid angle, while strongly suppresses background Rayleigh scattering and associated atomic heating, Such a system can produce photon pairs at rates of ~ 10 ^12 per second, given only moderate optical depths of 10 ~ 100, or alternatively, the system can generate paired photons with sub-natural bandwidths at lower production rates. We derive a rate-equation based theory of the collective atomic population and coherence dynamics, and present numerical simulations for a toy model, as well as realistic model systems based on 133 Cs and 171 Yb level structures. Lastly, we demonstrate that dark-state adiabatic following (EIT) and/or timescale hierarchy protects the paired photons from reabsorption as they propagate through an optically thick sample