Feshbach resonances in ultracold gases

In this chapter, we describe scattering resonance phenomena in general, and focus on the mechanism of Feshbach resonances, for which a multi-channel treatment is required. We derive the dependence of the scattering phase shift on magnetic field and collision energy. From this, the scattering length and effective range coefficient can be extracted, expressions which are particularly useful for ultracold gases.Comment: 23 pages, 3 figures. This article will be published as Chapter 4 in "Quantum gas experiments - exploring many-body states", edited by P. T\"orm\"a and K. Sengstock, Imperial College Press, London, to be published 201

Ramsey fringes in a Bose-Einstein condensate between atoms and molecules

In a recent experiment, a Feshbach scattering resonance was exploited to observe Ramsey fringes in a $^{85}$Rb Bose-Einstein condensate. The oscillation frequency corresponded to the binding energy of the molecular state. We show that the observations are remarkably consistent with predictions of a resonance field theory in which the fringes arise from oscillations between atoms and molecules.Comment: 5 pages, 5 figure

BCS-BEC crossover in a strongly correlated Fermi gas

We study the BCS-BEC crossover in the strongly correlated regime of an ultra-cold rotating two component Fermi gas. Strong correlations are shown to generate an additional long-range interaction which results in a modified crossover region compared to the non-rotating situation. The two-particle correlation function reveals a smooth crossover between the s-wave paired fermionic fractional quantum Hall state and the bosonic Laughlin state.Comment: 4 pages, 3 figure

Simulating polaron biophysics with Rydberg atoms

Transport of excitations along proteins can be formulated in a quantum physics context, based on the periodicity and vibrational modes of the structures. Exact solutions are very challenging to obtain on classical computers, however, approximate solutions based on the Davydov ansatz have demonstrated the possibility of stabilized solitonic excitations along the protein. We propose an alternative study based on a chain of ultracold atoms. We investigate the experimental parameters to control such a quantum simulator based on dressed Rydberg atoms. We show that there is a feasible range of parameters where a quantum simulator can directly mimic the Davydov equations and their solutions. Such a quantum simulator opens up new directions for the study of transport phenomena in a biophysical context.Transport of excitations along proteins can be formulated in a quantum physics context, based on the periodicity and vibrational modes of the structures. Exact solutions are very challenging to obtain on classical computers, however, approximate solutions based on the Davydov ansatz have demonstrated the possibility of stabilized solitonic excitations along the protein. We propose an alternative study based on a chain of ultracold atoms. We investigate the experimental parameters to control such a quantum simulator based on dressed Rydberg atoms. We show that there is a feasible range of parameters where a quantum simulator can directly mimic the Davydov equations and their solutions. Such a quantum simulator opens up new directions for the study of transport phenomena in a biophysical context

Feshbach resonances and collapsing Bose-Einstein condensates

We investigate the quantum state of burst atoms seen in the recent Rb-85 experiments at JILA. We show that the presence of a resonance scattering state can lead to a pairing instability generating an outflow of atoms with energy comparable to that observed. A resonance effective field theory is used to study this dynamical process in an inhomogeneous system with spherical symmetry

Trapped electrons in the quantum degenerate regime

A full strength Coulomb interaction between trapped electrons can be felt only in absence of a neutralizing background. In order to study quantum degenerate electrons without such a background, an external trap is needed to compensate for the strong electronic repulsion. As a basic model for such a system, we study a trapped electron pair in a harmonic trap with an explicit inclusion of its Coulomb interaction. We find the eigenenergy of the ground state, confirming earlier work in the context of harmonium. We extend this to a complete set of properly scaled energies for any value of the trapping strength, including the excited states. The problem is solved either numerically or by making harmonic approximations to the potential. As function of the trapping strength a crossover can be made from the strongly to the weakly-coupled regime, and we show that in both regimes perturbative methods based on a pair-wise electron description would be effective for a many-particle trapped electron system, which resembles a Wigner crystal in the ground state of the strongly coupled limit

Feshbach resonances in Cesium at Ultra-low Static Magnetic Fields

We have observed Feshbach resonances for 133Cs atoms in two different hyperfine states at ultra-low static magnetic fields by using an atomic fountain clock. The extreme sensitivity of our setup allows for high signal-to-noise-ratio observations at densities of only 2*10^7 cm^{-3}. We have reproduced these resonances using coupled-channels calculations which are in excellent agreement with our measurements. We justify that these are s-wave resonances involving weakly-bound states of the triplet molecular Hamiltonian, identify the resonant closed channels, and explain the observed multi-peak structure. We also describe a model which precisely accounts for the collisional processes in the fountain and which explains the asymmetric shape of the observed Feshbach resonances in the regime where the kinetic energy dominates over the coupling strength.Comment: 5 pages, 4 figures, 1 tabl

Scattering hypervolume for ultracold bosons from weak to strong interactions

The elastic scattering properties of three bosons at low energy enter the many-body description of ultracold Bose gases via the three-body scattering hypervolume $D$. We study this quantity for identical bosons that interact via a pairwise finite-range potential. Our calculations cover the regime from strongly repulsive potentials towards attractive potentials supporting multiple two-body bound states and are consistent with the few existing predictions for $D$. We present the first numerical confirmation of the universal predictions for $D$ in the strongly interacting regime, where Efimov physics dominates, for a local nonzero-range potential. Our findings highlight how $D$ is influenced by three-body quasibound states with strong $d$-wave or $g$-wave characteristics in the weakly interacting regime.Comment: 13 pages, 8 figure