Decay Rate in Anharmonic Potentials

Yuri Kondratiev, Yuri V. Kozitsky

K. S. Viswanathan

Eric L. Bolda, Eite Tiesinga, Paul S. Julienne

We investigate a process by which an optical lattice potential can transfer two unbound ultracold atoms in a lattice site to an untrapped dimer. The transition is mediated by the anharmonic terms in the lattice potential, which couple the relative and center-of-mass coordinates of the two atoms. We calculate the rate of decay from the ground state in a lattice cell to the last bound dimer state as a function of the -wave scattering length and optical lattice depth. The decay rate has a maximum value of , where is the atomic recoil energy. Consequently typical molecular production rates are much smaller than . Explicit results are given for atoms tuned near a Feshbach resonance.

J. Cruz-Sampedro

Vincent Pouthier

The lifetime of two-vibron bound states in the overtone region of a one-dimensional anharmonic molecular lattice is investigated. The anharmonicity, introduced within an attractive Hubbard Hamiltonian for bosons, is responsible for the formation of bound states which belong to a finite linewidth band located below the continuum of two-vibron free states. The decay of these bound states into either bound or free states is described by considering the coupling between the vibrons and a thermal bath formed by a set of low-frequency acoustic phonons. The relaxation rate is expressed in terms of the spectral distribution of the vibron/phonon coupling and of the two-vibron Green operator which is calculated exactly by using the number states method. The behavior of the two-vibron bound states relaxation rate is analyzed with a special emphasis on the influence of the anharmonicity. It is shown that the rate exhibits two distinct regimes depending on the thermal bath dimension. When the bath dimension is equal to unity, the rate increases with the anharmonicity and the decay of the two-vibron bound states into the other bound states appears as the main contribution of the rate. By contrast, when the bath dimension is equal to 2 and 3, the rate decreases as the anharmonicity increases, indicating that the two-vibron bound states decay into the two-vibron free states continuum.

Michele Battezzati

A procedure previously developed by us for the evaluation of the diffusion coefficient and drift velocity of a charged Newtonian particle in a zero-point field is applied here to a sextic potential-one-dimensional system, for which an exact solution to the related Hamilton-Jacobi-Yasue-Riccati equation is available. This potential energy function represents either a stiff single well or a triple well. For this model, the averaged diffusion coefficient has been evaluated by assuming that the particle under study is confined for a long time inside one anharmonic well, that is, in the limit of infinite relaxation time, and the results are compared with quantum-mechanical predictions. A double-well model potential is subsequently examined.