Many-body effects on adiabatic passage through Feshbach resonances

Abstract

We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms Gamma on sweep rate alpha, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $Gamma\propto alpha$ is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law $Gamma\propto alpha^{1/3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.Comment: 9 pages, 9 figure

Role of particle interactions in a many-body model of Feshbach-molecule formation in bosonic systems

“…The nonlinearity stems both from the diagonal and off-diagonal terms and is preserved even without taking into account the particle interactions. In addition, the absence of hermicity as well as the lack of U (1) invariance of the Hamiltonian restrict the mean-field motion to a "tear-drop" shaped equal-single-pair-entropy surface [15,16], rather than the surface of a Bloch sphere. As we will show latter, the interplay of these new features leads to a very different energy level structure and conversion dynamics.…”

Molecules with an induced dipole moment in a stochastic electric field

“…II, and are valid for arbitrary direction of E. The mean-field theory treatment takes the expectation values of Eqs. (9) and (10), replacing the expectation value of the productL ×n by the product of the expectation values [10,11,13,14] and taking the limit as → 0 on the RHS of (9):…”

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

“…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-gas of atoms after the FR is swept across the Fermi sea. The accepted model is valid under assumption of strong interaction equivalent to the condition of wide resonance [28].…”

“…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.…”

“…The same criterion allows to neglect the dispersion of molecules. This approximation has been used earlier [26,29] and numerical proof of its validity has been reported in [27].…”