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Journal of Modern Optics

Adiabatic passage through a Feshbach resonance in a degenerate quantum gas

Y. B. Band, Igor Tikhonenkov, E. Pazy, Michael Fleischhauer, Amichay Vardi

Published Aug 23, 2006• 6 citations
Publisher

Abstract

The dynamics of an adiabatic sweep through a Feshbach resonance in a degenerate quantum gas of fermionic atoms to produce a degenerate quantum gas of diatomic molecules are studied using many-body and mean-field methods. We demonstrate that the dependence of the remaining fraction of atoms Γ on sweep rate α varies from exponential Landau–Zener behaviour for a single pair of particles, to a power-law dependence for a large number of atoms, N. Two different power-law behaviours are obtained depending on the initial molecular fraction. The two different regimes are described in terms of quantum fluctuations: a linear power-law, Γ∝α, is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and Γ∝α1/3 when it is larger.

DOI
10.1080/09500340600777771

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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.

•Jun 2, 2009•0 citations
The dynamics of an adiabatic sweep through a Feshbach resonance in a degenerate quantum gas of fermionic atoms to produce a degenerate quantum gas of diatomic molecules are studied using many-body and mean-field methods. We demonstrate that the dependence of the remaining fraction of atoms Γ on sweep rate α varies from exponential Landau–Zener behaviour for a single pair of particles, to a power-law dependence for a large number of atoms, N. Two different power-law behaviours are obtained depending on the initial molecular fraction. The two different regimes are described in terms of quantum fluctuations: a linear power-law, Γ∝α, is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and Γ∝α1/3 when it is larger.
We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction Gamma on the sweep rate alpha varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number N. The power law is linear, Gamma is proportional to alpha, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and Gamma is proportional to alpha(1/3) when it is larger. Experimental data agree well with a linear dependence, but do not conclusively rule out the Landau-Zener model.
We compare various types of adiabatic dynamics that occur during atomic collisions and molecular dynamics. Born–Oppenheimer and non-adiabatic effects in molecular dynamics are contrasted with the time-dependent Landau–Zener transition problem for transitions that occur when a parameter in the Hamiltonian is varied slowly, and these are contrasted with the coherent many-body transitions that occur for a degenerate gas of atoms when an external parameter is tuned slowly near a Feshbach resonance to create loosely bound molecules. Analysis of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms shows that the dependence of the remaining atomic fraction on the sweep rate α varies from exponential Landau–Zener behaviour for a single pair of particles to a power-law dependence for large particle number N.
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.
We consider dynamics of a slowly time-dependent Dicke model, which represents a many-body generalization of the Landau-Zener model. In particular, the model describes narrow Feshbach resonance passage in an ultracold gas of Fermi atoms. Adiabaticity is destroyed when a parameter crosses a critical value, even at very slow sweeping rates of a parameter. The dynamics crucially depends on direction of the sweep. We apply our recent analysis (A. P. Itin and P. T\"orm\"a, e-print arXiv:0901.4778) to the ``inverse'' sweep through the resonance, corresponding (in a context of Feshbach resonance passage) to dissociation of molecules. On a level of the mean-field approximation, the dynamics is equivalent to a molecular condensate formation from Bose atoms within a two-mode model. Mapping the system to a Painlev\'e equation allows us to calculate deviation from adiabaticity at very slow sweeps analytically.
We theoretically examine a zero-temperature system of Fermi degenerate atoms coupled to bosonic molecules via collisionless rapid adiabatic passage across a Feshbach resonance, focusing on saturation of the molecular conversion efficiency at the slowest magnetic-field sweep rates. Borrowing a novel MANY-FERMION Fock-state theory, we find that a proper model of the magnetic-field sweep can systematically remove saturation. We also debunk the common misconception that many-body effects are responsible for molecules existing above the two-body threshold.
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.