Collisional oscillations of trapped boson-fermion mixtures approaching collapse

We study the collective modes of a confined gaseous cloud of bosons and fermions with mutual attractive interactions at zero temperature. The cloud consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a spherical harmonic trap and the coupling between the two species is varied by increasing either the magnitude of the interspecies s-wave scattering length or the number of bosons. The mode frequencies are obtained in the collisional regime by solving the equations of generalized hydrodynamics and are compared with the spectra calculated in the collisionless regime within a random-phase approximation. We find that, as the mixture is driven towards the collapse instability, the frequencies of the modes of fermionic origin show a blue shift which can become very significant for large numbers of bosons. Instead the modes of bosonic origin show a softening, which becomes most pronounced in the very proximity of collapse. Explicit illustrations of these trends are given for the monopolar spectra, but similar trends are found for the dipolar and quadrupolar spectra except for the surface (n=0) modes which are essentially unaffected by the interactions.Comment: 9 pages, 5 figures, revtex

From an insulating to a superfluid pair-bond liquid

We study an exchange coupled system of itinerant electrons and localized fermion pairs resulting in a resonant pairing formation. This system inherently contains resonating fermion pairs on bonds which lead to a superconducting phase provided that long range phase coherence between their constituents can be established. The prerequisite is that the resonating fermion pairs can become itinerant. This is rendered possible through the emergence of two kinds of bond-fermions: individual and composite fermions made of one individual electron attached to a bound pair on a bond. If the strength of the exchange coupling exceeds a certain value, the superconducting ground state undergoes a quantum phase transition into an insulating pair-bond liquid state. The gap of the superfluid phase thereby goes over continuously into a charge gap of the insulator. The change-over from the superconducting to the insulating phase is accompanied by a corresponding qualitative modification of the dispersion of the two kinds of fermionic excitations. Using a bond operator formalism, we derive the phase diagram of such a scenario together with the elementary excitations characterizing the various phases as a function of the exchange coupling and the temperature.Comment: 10 pages, 5 figure

Proton-tetraneutron elastic scattering

We analyze the elastic scattering of protons on a 4n system. This was used as part of the detection technique of a recent experiment [1] to search for the 4n (tetraneutron) as a bound particle. We show that it is unlikely that this process alone could yield the events reported in ref. [1], unless the 4n has an anomalously large backward elastic scattering amplitude.Comment: 6 pages, 2 figures, accepted for publication in Phys. Rev.

Measurement of interaction energy near a Feshbach resonance in a 6Li Fermi gas

We investigate the strongly interacting regime in an optically trapped $^6$Li Fermi mixture near a Feshbach resonance. The resonance is found at $800(40)$G in good agreement with theory. Anisotropic expansion of the gas is interpreted by collisional hydrodynamics. We observe an unexpected and large shift ($80$G) between the resonance peak and both the maximum of atom loss and the change of sign of the interaction energy.Comment: 4 pages, 4 figure

Solvable relativistic quantum dots with vibrational spectra

For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where spectrum is roughly equidistant and where a fine-tuning of the levels is mediated by PT-symmetric interactions composed of imaginary delta functions which mimic creation/annihilation processes.Comment: Int. Worskhop "Pseudo-Hermitian Hamiltonians in Quantum Physics III" (June 20 - 22, 2005, Koc Unversity, Istanbul(http://home.ku.edu.tr/~amostafazadeh/workshop/workshop.htm) a part of talk (9 pages

Adiabatic Fidelity for Atom-Molecule Conversion in a Nonlinear Three-Level \Lambda-system

We investigate the dynamics of the population transfer for atom-molecule three-level $\Lambda$-system on stimulated Raman adiabatic passage(STIRAP). We find that the adiabatic fidelity for the coherent population trapping(CPT) state or dark state, as the function of the adiabatic parameter, approaches to unit in a power law. The power exponent however is much less than the prediction of linear adiabatic theorem. We further discuss how to achieve higher adiabatic fidelity for the dark state through optimizing the external parameters of STIRAP. Our discussions are helpful to gain higher atom-molecule conversion yield in practical experiments.Comment: 4 pages, 5 figure

New method for extracting quasi-bound states from the continuum

A new parameter-free method is proposed for treatment of single-particle resonances in the real-energy continuum shell model. This method yields quasi-bound states embedded in the continuum which provide a natural generalization of weakly bound single-particle states.Comment: 22 pages, 10 figure

Control of Ultra-cold Inelastic Collisions by Feshbash Resonances and Quasi-One-Dimensional Confinement

Cold inelastic collisions of atoms or molecules are analyzed using very general arguments. In free space, the deactivation rate can be enhanced or suppressed together with the scattering length of the corresponding elastic collision via a Feshbach resonance, and by interference of deactivation of the closed and open channels. In reduced dimensional geometries, the deactivation rate decreases with decreasing collision energy and does not increase with resonant elastic scattering length. This has broad implications; e.g., stabilization of molecules in a strongly confining two-dimensional optical lattice, since collisional decay of the highly vibrationally excited states due to inelastic collisions is suppressed. The relation of our results with those based on the Lieb-Liniger model are addressed.Comment: 5 pages, 1 figur

Irreversible quantum graphs

Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently strong coupling, the spectrum of the system admits a new continuum mode which exists even if the graph is compact, and a {\it single} harmonic oscillator is coupled to it. This mechanism is shown to imply that the quantum dynamics is irreversible. Moreover, it demonstrates the surprising result that irreversibility can be introduced by a "bath" which consists of a {\it single} harmonic oscillator