Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms

Abstract

The problem of molecular production from degenerate gas of fermions at a wide Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction leads to significant renormalization of the gap between adiabatic levels. In contrast to static problem the close vicinity of exact resonance does not play substantial role. Two main physical results of our theory is the high sensitivity of molecular production to the initial value of magnetic field and generation of a large BCS condensate distributed over a broad range of momenta in inverse process of the molecule dissociation.In recent years there have been numerous achievements in the area of ultra-cold atomic physics. The major experimental tool for it is the use of the Feshbach resonances (FR) [1,2,3,4,5,6,7], which occurs when the energy of a quasibound molecular state becomes equal to the energy of two free alkali atoms. The magneticfield dependence of the resonance allows precise tuning of the atom-atom interaction strength in an ultracold gas [1]. Moreover, time-dependent magnetic fields can be used to reversibly convert atom pairs into weakly bound molecules [8,9,10,11,12,13,14,15]. This technique has proved to be extremely effective in converting degenerate atomic gases of fermions [8,9,10,11,16,17,18] and bosons [14,15,19] into bosonic dimer molecules.The Feshbach resonance proceeds at sufficiently strong magnetic fields so that electronic spins are polarized. The collisions in s-channel of such Fermi-atoms is possible only if they have different states of nuclear spins. In a typical experiment [8,17] an admixture of atoms of 40 K with the same total atomic spin 9/2 but different spin projection quantum numbers −7/2 and −9/2 was used.Theoretical works on the molecular production can be roughly divided in two categories. The first is a phenomenology suggesting that the pairs of molecules perform independently the Landau-Zener (LZ) transitions [4,6]. Therefore the total number of molecules in the end of the process is the LZ transition probability multiplied by the number of pairs. The most problematic in this approach is what should be accepted for the LZ transition matrix element ∆ (further we call it the LZ gap). Direct calculation of the transition probability from a microscopic Hamiltonian up to the 4-th order in the interaction constant [20] shows that, in contrast to the assumption of phenomenological works, the many-body effects are very essential. Another category includes the works based on a simplified model [21], in which molecules have only one available state mimicking the condensate [22,23,24]. Though the numerical works of this category displayed a reasonable temperature dependence, they could not give a clear physical picture and detailed dependencies on parameters of the problem. The series of semi-analytical works by Pazy et al. [22,25,26,27] were based on two contradicting assumptions as we show later.In this letter we consider the process of molecule production from fermi...

Solvable multistate model of Landau-Zener transitions in cavity QED

“…A number of approximate methods have been used to study transition probabilities in the model (33), including Keldysh technique and adiabatic approximation [30,31]. It is also known that some of the simpler solvable multistate LZ models correspond to specific limits of the model (33) [32,33]. Therefore, behavior of the model (33) is considered well understood, at least in the limit of a large spin (S 1).…”

Nonadiabaticity and large fluctuations in a many-particle Landau-Zener problem

“…2, b). (Although the initial full occupancy of the flat fermion band assumed in AG may not be adequate to the description of the experimental situation [16], see section VIII below.) 2.…”

Landau-Zener-Stueckelberg Physics with a Singular Continuum of States

“…4 one can see that except the region h 3 ∼ w ∼ γ 2 0 ∆, the numerical result is well captured by at least one of the three analytical expressions, Eqs. (7), (13), and (14). Remarkably, at w γ 2 0 ∆, the Stueckelberg oscillations are reproduced both by the Markovian Eq.…”