Alessio Recati

Numerical observation of Hawking radiation from acoustic black holes in atomic Bose-Einstein condensates

We report numerical evidence of Hawking emission of Bogoliubov phonons from a sonic horizon in a flowing one-dimensional atomic Bose–Einstein condensate. The presence of Hawking radiation is revealed from peculiar long-range patterns in the density–density correlation function of the gas. Quantitative agreement between our fully microscopic calculations and the prediction of analog models is obtained in the hydrodynamic limit. New features are predicted and the robustness of the Hawking signal against a finite temperature discussed.

Normal state of a polarized fermi gas at unitarity.

We study the Fermi gas at unitarity and at T=0 by assuming that, at high polarizations, it is a normal Fermi liquid composed of weakly interacting quasiparticles associated with the minority spin atoms. With a quantum Monte Carlo approach we calculate their effective mass and binding energy, as well as the full equation of state of the normal phase as a function of the concentration x=n downward arrow/n upward arrow of minority atoms. We predict a first order phase transition from normal to superfluid at x(c)=0.44 corresponding, in the presence of harmonic trapping, to a critical polarization P(c)=(N upward arrow - N downward arrow/(N upward arrow + N downward arrow)=77%. We calculate the radii and the density profiles in the trap and predict that the frequency of the spin dipole mode will be increased by a factor of 1.23 due to interactions.

Overcritical Rotation of a Trapped Bose-Einstein Condensate

The rotational motion of an interacting Bose-Einstein condensate confined by a harmonic trap is investigated by solving the hydrodynamic equations of superfluids, with the irrotationality constraint for the velocity field. We point out the occurrence of an overcritical branch where the system can rotate with angular velocity larger than the oscillator frequencies. We show that in the case of isotropic trapping the system exhibits a bifurcation from an axisymmetric to a triaxial configuration, as a consequence of the interatomic forces. The dynamical stability of the rotational motion with respect to the dipole and quadrupole oscillations is explicitly discussed.

Normal state of highly polarized fermi gases: simple many-body approaches

We consider the problem of a single downward arrow atom in the presence of a Fermi sea of upward arrow atoms, in the vicinity of a Feshbach resonance. We calculate the chemical potential and the effective mass of the downward arrow atom using two simple approaches: a many-body variational wave function and a T-matrix approximation. These two methods lead to the same results and are in good agreement with existing quantum Monte Carlo calculations performed at unitarity and, in one dimension, with the known exact solution. Surprisingly, our results suggest that, even at unitarity, the effect of interactions is fairly weak and can be accurately described using single particle-hole excitations. We also consider the case of unequal masses.

Nonlocal density correlations as a signature of Hawking radiation from acoustic black holes

We have used the analogy between gravitational systems and nonhomogeneous fluid flows to calculate the density-density correlation function of an atomic Bose-Einstein condensate in the presence of an acoustic black hole. The emission of correlated pairs of phonons by Hawking-like process results into a peculiar long-range density correlation. Quantitative estimations of the effect are provided for realistic experimental configurations.

Photon energy lifter

We propose a time-dependent, spatially periodic photonic structure which is able to shift the carrier frequency of an optical pulse which propagates through it. Taking advantage of the slow group velocity of light in periodic photonic structures, the wavelength conversion process can be performed with an efficiency close to 1 and without affecting the shape and the coherence of the pulse. Quantitative Finite Difference Time Domain simulations are performed for realistic systems with optical parameters of conventional silicon technology.

Exactly Solvable Model of the BCS-BEC Crossover

We discuss an integrable model of interacting fermions in one dimension that allows a complete description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 fermions to the Lieb-Liniger model of repulsive bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from -infinity to +infinity while the system evolves from a BCS-like state through a Tonks-Girardeau gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed.

Radiation induced force between two planar waveguides

Abstract.We study the electromagnetic force exerted on a pair of parallel slab waveguides by the light propagating through them. We have calculated the dependence of the force on the slab separation by means of the Maxwell–Stress tensor formalism and we have discussed its main features for the different propagation modes: spatially symmetric (antisymmetric) modes give rise to an attractive (repulsive) interaction. We have derived the asymptotic behaviors of the force at small and large separation and we have quantitatively estimated the mechanical deflection induced on a realistic air-bridge structure.

Quantum fluctuations around black hole horizons in Bose-Einstein condensates

We study several realistic configurations allowing to realize an acoustic horizon in the flow of a one dimensional Bose-Einstein condensate. In each case we give an analytical description of the flow pattern, of the spectrum of Hawking radiation and of the associated quantum fluctuations. Our calculations confirm that the non local correlations of the density fluctuations previously studied in a simplified model provide a clear signature of Hawking radiation also in realistic configurations. In addition we explain by direct computation how this non local signal relates to short range modifications of the density correlations.

Acoustic white holes in flowing atomic Bose–Einstein condensates

We study acoustic white holes in a steadily flowing atomic Bose–Einstein condensate. A white hole configuration is obtained when the flow velocity goes from a super-sonic value in the upstream region to a sub-sonic one in the downstream region. The scattering of phonon wavepackets on a white hole horizon is numerically studied in terms of the Gross–Pitaevskii equation of mean-field theory: dynamical stability of the acoustic white hole is found, as well as a signature of a nonlinear back-action of the incident phonon wavepacket onto the horizon. The correlation pattern of density fluctuations is numerically studied by means of the truncated-Wigner method, which includes quantum fluctuations. Signatures of the white hole radiation of correlated phonon pairs by the horizon are characterized; analogies and differences with Hawking radiation from acoustic black holes are discussed. In particular, a short wavelength feature is identified in the density correlation function, whose amplitude steadily grows in time since the formation of the horizon. The numerical observations are quantitatively interpreted by means of an analytical Bogoliubov theory of quantum fluctuations for a white hole configuration within the step-like horizon approximation.