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arXiv:0803.1297 · Physical Review A

Atom-to-molecule conversion efficiency and adiabatic fidelity

Li-Hua Lü, You‐Quan Li

Published May 20, 2008• 24 citations
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Abstract

The efficiency of converting two-species fermionic atoms into bosonic molecules is investigated in terms of mean-field Lagrangian density. We find that the stimulated Raman adiabatic passage technique aided by Feshbach resonance is more effective than the bare Feshbach resonance for $^{6}\text{L}\text{i}$ atoms rather than $^{40}\text{K}$ atoms. We also generally consider the symmetry and its relevant conservation law, which enables us to introduce a natural definition of adiabatic fidelity for a coherent population trapping state. The calculated values of the fidelity are presented and then we provide an explanation of why the conversion efficiencies for $^{40}\text{K}$ and $^{6}\text{L}\text{i}$ are distinctly different.

DOI
10.1103/physreva.77.053611

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The efficiency of converting two-species fermionic atoms into bosonic molecules is investigated in terms of mean-field Lagrangian density. We find that the stimulated Raman adiabatic passage technique aided by Feshbach resonance is more effective than the bare Feshbach resonance for 6Li^{6}\text{L}\text{i}6Li atoms rather than 40K^{40}\text{K}40K atoms. We also generally consider the symmetry and its relevant conservation law, which enables us to introduce a natural definition of adiabatic fidelity for a coherent population trapping state. The calculated values of the fidelity are presented and then we provide an explanation of why the conversion efficiencies for 40K^{40}\text{K}40K and 6Li^{6}\text{L}\text{i}6Li are distinctly different.
We give a brief description of theoretical studies on multi-component systems and detailed discussions on systems with atom-to-molecule conversion. The conversion of two species of atoms into stable molecules through the Feshbach resonance assisted by stimulated Raman adiabatic passage in photoassociation is studied with the help of mean-field Langrange density. The conversion efficiency is large for the fully bosonic system as well as the boson-fermion mixture as long as the general two-photon resonance condition is satisfied.
In the present paper, we investigate the linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules through the stimulated Raman adiabatic passage aided by Feshbach resonance. We analytically obtain the regions for the appearance of linear instability. Moreover, taking 40 K and 6 Li atom—molecule conversion systems as examples, we give the unstable regions numerically. We also attempt to obtain the adiabatic criterion for this nonlinear system with classical adiabatic dynamics and study the adibaticity of the dark state with the adiabatic condition.
We study the conversion of 40K^{40}\mathrm{K}40K and 87Rb^{87}\mathrm{Rb}87Rb atoms into stable molecules through the stimulated Raman adiabatic passage (STIRAP) in photoassociation assisted with Feshbach resonance. Starting with the mean-field Lagrange density, we show that the atom-to-molecule conversion efficiency by STIRAP aided by Feshbach resonance is much larger than that by bare Feshbach resonance. We also study the influence of the population imbalance on the atom-to-molecule conversion.
On the basis of the stimulated Raman adiabatic passage technology, we study the conversion of ultracold atoms into diatomic molecules by using a square-shaped pulse field. By the method of adiabatic fidelity, we analyze the dynamical evolution process of the coherent population trapping state for the atom-molecule conversion system. We introduce two adiabatic fidelities to describe the efficiency of ultracold atom-molecule conversion, i.e.:1) the final adiabatic fidelity, which gives the value of the adiabatic fidelity at the end of the evolution:the closer to 1 it is, the higher the conversion efficiency is; 2) the final maximum adiabatic fidelity, which denotes the maximum value that can be achieved at the end of evolution, indicating the highest conversion efficiency. With these two quantities, we discuss how to achieve higher adiabatic fidelity for the coherent population trapping state through optimizing the pulse-delay time and the pulse-laser intensity of the stimulated Raman adiabatic passage. In addition, we also discuss the effects of the width of pulses on the ultracold atom-molecule conversion efficiency and the feasibility of continuous light. It is shown that the final adiabatic fidelity of the coherent population trapping state demonstrates a large periodic oscillation with the pulse-laser intensity. By calculating and analyzing the final adiabatic fidelity and the final maximum adiabatic fidelity, we obtain the conditions for higher efficiency conversion, which gives the best choice of the pulse-laser intensity, the pulse-delay time, and the width of pulses. The results show that the scheme of square-shaped pulses we discussed has obvious advantages compared with that of Gaussian-shaped pulses, which can achieve high adiabatic fidelity and realize higher ultracold atom-molecule conversion efficiency via employing the pulse-laser field with low intensity. Further detailed comparison between the square-shaped pulses and the Gaussian-shaped pulses is also given. Particularly, we find that the final adiabatic fidelity shows a periodic oscillation with the pulse width, which means that the high efficiency atom-molecule conversion can be achieved by using a pulse field with small width. Moreover, we find that the high efficiency conversion can also be achieved by using special continuous light under certain conditions.
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.