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arXiv:0712.4191 · Physical Review A

Many-body effects on nonadiabatic Feshbach conversion in bosonic systems

Jie Liu, Bin Liu, Libin Fu

Published Jul 16, 2008• 30 citations
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Abstract

We investigate the dynamics of converting cold bosonic atoms to molecules when an external magnetic field is swept across a Feshbach resonance. Our analysis relies on a quantum microscopic model that accounts for many-body effects in the association process. We show that the picture of two-body molecular production depicted by the Landau-Zener model is significantly altered due to many-body effects. In the nonadiabatic regime, we derive an analytic expression for molecular conversion efficiency that explains the discrepancy between the prediction of the Landau-Zener formula and the experimental data [E. Hodby et al., Phys. Rev. Lett. 94, 120402 (2005)]. Our theory is further extended to the formation of heteronuclear diatomic molecules and gives some interesting predictions.

DOI
10.1103/physreva.78.013618

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We investigate the dynamics of converting cold bosonic atoms to molecules when an external magnetic field is swept across a Feshbach resonance. Our analysis relies on a quantum microscopic model that accounts for many-body effects in the association process. We show that the picture of two-body molecular production depicted by the Landau-Zener model is significantly altered due to many-body effects. In the nonadiabatic regime, we derive an analytic expression for molecular conversion efficiency that explains the discrepancy between the prediction of the Landau-Zener formula and the experimental data [E. Hodby et al., Phys. Rev. Lett. 94, 120402 (2005)]. Our theory is further extended to the formation of heteronuclear diatomic molecules and gives some interesting predictions.
We investigate a generalized many-body model of Feshbach molecule formation that includes the atom-atom, atom-molecule, and molecule-molecule interactions. We show that the picture of two-body molecule production depicted by the Landau-Zener model is significantly altered by the particle interactions. In the adiabatic limit, we work out a formula for the ceiling of conversion efficiency when the interaction strength is larger than a critical value. In the sudden limit, we derive a closed equation for the conversion efficiency using stationary phase approximation. Our theory predicts a significant role of the particle interactions in atom-molecule conversion when the atom density is high and the Feshbach resonance width is narrow.
We consider in detail the situation of applying a time-dependent external magnetic field to a 87 Rb atomic Bose–Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low-energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of Köhler and Burnett (2002 Phys. Rev. A 65 033601) to study the efficiency of the association of molecules in a 87 Rb Bose–Einstein condensate during a linear passage of the magnetic-field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau–Zener, configuration interaction, and two-level mean-field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose–Einstein condensed gas, provided that the magnetic-field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic-field strength, and identify the Landau–Zener coefficient determined by Mies et al (2000 Phys. Rev. A 61 022721) as the main parameter that controls the efficiency.
We investigate the production efficiency of ultracold molecules in bosonic 85Rb and fermionic 40K when the magnetic field is swept across a Feshbach resonance. For adiabatic sweeps of the magnetic field, our novel model shows that the conversion efficiency of both species is solely determined by the phase space density of the atomic cloud, in contrast with a number of theoretical predictions. In the nonadiabatic regime our measurements of the 85Rb molecule conversion efficiency follow a Landau-Zener model.
We investigate the production efficiency of ultracold molecules in bosonic 85 Rb and fermionic 40 K when the magnetic field is swept across a Feshbach resonance.For adiabatic sweeps of the magnetic field, the conversion efficiency of each species is solely determined by the phase space density of the atomic cloud, in contrast to a number of theoretical predictions.Our novel model for the adiabatic pairing process, developed from general physical principles, accurately predicts the conversion efficiency for both ultracold gases of bosons and of fermions.In the non-adiabatic regime our measurements of the 85 Rb molecule conversion efficiency follow a Landau Zener model, with a conversion efficiency that is characterized by the density divided by the time derivative of the magnetic field.
In this thesis I present a nonequilibrium quantum field theory that describes the\nproduction of molecular dimers from a two-component quantum-degenerate atomic\nFermi gas, via a linear downward sweep of a magnetic field across an s-wave Feshbach\nresonance. This problem raises interest because it is presently unclear as to why\ndeviations from the universal Landau-Zener formula for the transition probability at\ntwo-level crossing are observed in the experimentally measured production efficiencies.\nThe approach is based on evaluating real-time Green functions within the Keldysh-\nSchwinger formalism. The effects of quantum statistics associated with Pauli blocking\nfor fermions and induced emission for bosons, characteristic of particle scattering in\na quantum-degenerate many-body medium, are fully accounted for. I show that the\nmolecular conversion efficiency is represented by a power series in terms of a dimensionless\nparameter which, in the zero-temperature limit, depends solely on the initial\ngas density and the Landau-Zener parameter. This result reveals a hindrance of the\ncanonical Landau-Zener transition probability due to many-body effects, and presents\nan explanation for the experimentally observed deviations.\nA second topic treated in this thesis concerns the study of non-adiabatic transitions\nin N-state Landau-Zener systems. In connection to this, I provide a proof of\nthe conjecture put forth by Brundobler and Elser, regarding the survival probability\non the diabatic levels with maximum/minimum slope.
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 $\ensuremath{\Gamma}$ on sweep rate $\ensuremath{\alpha}$, 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 $\ensuremath{\Gamma}\ensuremath{\propto}\ensuremath{\alpha}$ is obtained when the initial molecular fraction is smaller than the 1∕N1∕N1∕N quantum fluctuations, and a cubic-root power law $\ensuremath{\Gamma}\ensuremath{\propto}{\ensuremath{\alpha}}^{1∕3}$ 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.