Number of closed-channel molecules in the BEC-BCS crossover

Low dimensional behavior of two ultra-cold atoms trapped in two-and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used, allowing an exhaustive analysis of low-dimensional resonant scattering behavior and of the confinement induced bound states. The role of the different parameters of the resonance is depicted in this context. Results are compared with the ones of the zero-range approach. The relevance of the effective range approximation in low dimensions is studied. Examples of known resonances are used to illustrate the bound state properties.

Section: Discussionmentioning

confidence: 99%

Ultracold-atom collisions in atomic waveguides: A two-channel analysis

Kristensen

Pricoupenko

2015

“…What makes these relations remarkable is that they hold for any finite-energy state of the system, it does not matter whether the system is few-or many-body, superfluid or normal, weakly or strongly interacting, in equilibrium or nonequilibrium, at zero or finite temperature. These universal relations have more recently been rederived using many other approaches including the quantum field theoretical techniques [1,[5][6][7][8][9], and have also been verified via numerical few-body calculations [10].…”

Section: Introductionmentioning

confidence: 95%

Isothermal-sweep theorems for ultracold quantum gases in a canonical ensemble

Iskin

2011

After deriving the isothermal Hellmann-Feynman theorem (IHFT) that is suitable for mixed states in a canonical ensemble, we use this theorem to obtain the isothermal magnetic-field sweep theorems for the free, average and trapping energies, and for the entropy, specific heat, pressure and atomic compressibility of stronglycorrelated ultra-cold quantum gases. In particular, we apply the sweep theorems to two-component Fermi gases in the weakly-interacting BCS and BEC limits, showing that the temperature dependence of the contact parameter can be determined by the variation of either the entropy or specific heat with respect to the scattering length. We also use the IHFT to obtain the Virial theorem in a canonical ensemble, and discuss its implications for quantum gases.

“…In our single impurity problem, N cc is less than or equal to one, and can also be interpreted as the occupation probability (or population) of the closed channel. When the system is prepared in an eigenstate of energy E, and relative energy ∆E = E − E FS (N ) with respect to the non-interacting Fermi sea, with a fixed total momentum P if desired, a direct application of the Hellmann-Feynman theorem gives [42]:…”

Section: Closed Channel Populationmentioning

confidence: 99%

“…Taking as a parameter the inverse scattering length rather than E mol , as in [42], and using Eqs. (5) and (6) we can rewrite N cc in the more convenient form…”

Section: Closed Channel Populationmentioning

confidence: 99%

Impurity in a Fermi sea on a narrow Feshbach resonance: A variational study of the polaronic and dimeronic branches

Trefzger

Castin

2012

We study the problem of a single impurity of mass M immersed in a Fermi sea of particles of mass m. The impurity and the fermions interact through a s-wave narrow Feshbach resonance, so that the Feshbach length R * naturally appears in the system. We use simple variational ansatz, limited to at most one pair of particle-hole excitations of the Fermi sea and we determine for the polaronic and dimeronic branches the phase diagram between absolute ground state, local minimum, thermodynamically unstable regions (with negative effective mass), and regions of complex energies (with negative imaginary part). We also determine the closed channel population which is experimentally accessible. Finally we identify a non-trivial weakly attractive limit where analytical results can be obtained, in particular for the crossing point between the polaronic and dimeronic energy branches.