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Physical Review A

Formation of fermionic molecules via interisotope Feshbach resonances

E. G. M. van Kempen, Bout Marcelis, S. J. J. M. F. Kokkelmans

Published Nov 19, 2004• 31 citations
Publisher

Abstract

We perform an analysis of recent experimental measurements and improve the lithium interaction potentials. For $^{6}\mathrm{Li}$ a consistent description can be given. We discuss theoretical uncertainties for the position of the wide $^{6}\mathrm{Li}$ Feshbach resonance, and we present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the $^{6}\mathrm{Li}\text{\ensuremath{-}}^{7}\mathrm{Li}$ system, and their importance for different types of crossover superfluidity models is discussed.

DOI
10.1103/physreva.70.050701

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Formation of fermionic molecules via interisotope Feshbach resonances

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We perform an analysis of recent experimental measurements and improve the lithium interaction potentials. For $^6$Li a consistent description can be given. We discuss theoretical uncertainties for the position of the wide $^6$Li Feshbach resonance, and we present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the $^6$Li-$^7$Li system, and their importance for different types of crossover superfluidity models is discussed.

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Experiments on ultra-cold fermionic /sup 6/Li confined in a crossed dipole trap. /sup 6/Li possesses Feshbach resonances both in the s-wave and p-wave channels. This features enables the exploration of both s-wave and p-wave pairing mechanisms. We first discuss our observation of Bose-Einstein condensation of /sup 6/Li/sub 2/ molecules in the low-magnetic field wing the s-wave Feshbach located at /spl sim/ 834 G. The molecular BEC offers a good starting point for the exploration of the BEC-BCS (Bardeen-Cooper-Schrieffer) crossover. We have also located p-wave Feshbach resonances in the two lowest hyperfine states of /sup 6/Li. The experimental positions of these resonances are in good agreement with those predicted by coupled channel calculations. We have studied the atom losses close to these resonances and have developed a semi-analytical model capturing our experimental findings.

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We propose to realize a strongly interacting Fermi superfluid near a narrow Feshbach resonance using the recently discovered ``orbital Feshbach resonance.'' The orbital Feshbach resonance is a type of magnetic field tunable scattering resonance theoretically predicted and experimentally observed recently in the alkaline-earth-metal-like $^{173}\mathrm{Yb}$ atom. We first show that the orbital Feshbach resonance is a narrow resonance in energy, while it is hundreds Gauss wide in terms of magnetic field strength, taking the advantage that the magnetic moment difference between the open and closed channels is quite small. Therefore, this is an ideal platform for the experimental realization of a strongly interacting Fermi superfluid with narrow resonance. We further show that the transition temperature for the Fermi superfluid in this system, especially at the BCS side of the resonance, is even higher than that in a wide resonance, which is also due to the narrow character of this resonance. Our results will encourage experimental efforts to realize Fermi superfluid in the alikaline-earth-metal-like $^{173}\mathrm{Yb}$ system, the properties of which will be complementary to extensively studied Fermi superfluids nearby a wide resonance in alkali-metal $^{40}\mathrm{K}$ and $^{6}\mathrm{Li}$ systems.

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Feshbach resonances in cold atomic gases

E. G. M. van Kempen

The research described in this thesis is part of an international effort with the aim of studying ultracold quantum degenerate gas samples like Bose-Einstein condensates and Fermi degenerate systems, consisting of atoms confined in magnetic or optical traps. The behavior of such samples is governed by the inter-atomic interactions and the resulting properties of the atom-atom scattering. At the relevant temperatures of 1nK to 10µK a key property is the atom-atom scattering length a. In chapter 2 a theoretical method is presented which enables one to describe the interaction and scattering of (ultra)cold atoms to unprecedented precision. It is also unparalleled in comprehensiveness: it allows the prediction of a large and varied set of experimental data for all isotopes of the same element. The method relies on the extraction from experiments of a few (phase) parameters which completely summarize the behavior of the atoms in the (ultra)cold regime. In chapter 3 the method is applied to the "workhorses" of cold-atom physics: the atomic species 85Rb and 87Rb. We extract the foregoing parameters to a very high precision from several recent high precision experiments, allowing us to predict e.g. the 87Rb spinor condensate to be ferromagnetic: a prediction for which the scattering length has to be calculated with a precision better than 1%. We also predict Feshbach resonances at experimentally accessible magnetic field strengths; resonances searched for and found by the experimental group of Rempe. In close collaboration with his group we "fine-tune" the interaction parameters found previously, by making use of only one of the observed resonances. We then obtain agreement with 42 out of the observed 43 resonance field strengths and are able to identify bound states inducing the Feshbach resonances at these locations. Chapter 4 describes the results of this research. With a thorough understanding of the rubidium interactions, we then switch to lithium which has a fermionic (6Li) and a bosonic (7Li) isotope. Both are being used in cold-atom experiments. In chapter 5 we evaluate the interaction parameters for lithium allowing us to predict magnetic field strengths for which a sample of fermionic 6Li atoms can be regarded as strongly interacting. Furthermore, a three-level method for measuring mean-field shifts, based on radio-frequency techniques, is introduced. For weak interactions we find proportionality of resonance shifts to interaction strengths. In the strongly interacting regime, however, these shifts become very small reflecting the quantum unitarity limit and many-body effects. Most interesting is the fact that in this regime the shifts are small both for large positive a and for large negative a, likely reflecting the universality of the interaction energy. In chapters 6 and 7 the interactions between lithium atoms are reinvestigated, making use of newly available experimental data and with the updated interaction parameters special attention is paid to locating field strengths at which magnetically tunable Feshbach resonances occur in the scattering of lithium atoms. In chapter 6 scattering events in a gas of (fermionic) 6Li atoms are studied. In chapter 7 we show that a consistent description of the 6Li+6Li system can be given. We discuss theoretical uncertainties for the position of the wide 6Li Feshbach resonance and present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the 6Li-7Li system, and their importance for different types of crossover superfluidity models is discussed. Molecules created by magnetically sweeping over these resonances will have a fermionic character. One magnetic field strength is predicted at which two different fermionic molecules can be created simultaneously.

•Jan 1, 2006•1 citation
We perform an analysis of recent experimental measurements and improve the lithium interaction potentials. For 6Li^{6}\mathrm{Li}6Li a consistent description can be given. We discuss theoretical uncertainties for the position of the wide 6Li^{6}\mathrm{Li}6Li Feshbach resonance, and we present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the 6Li\ensuremath-7Li^{6}\mathrm{Li}\text{\ensuremath{-}}^{7}\mathrm{Li}6Li\ensuremath-7Li system, and their importance for different types of crossover superfluidity models is discussed.
We perform an analysis of recent experimental measurements and improve the lithium interaction potentials. For 6^66Li a consistent description can be given. We discuss theoretical uncertainties for the position of the wide 6^66Li Feshbach resonance, and we present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the 6^66Li-7^77Li system, and their importance for different types of crossover superfluidity models is discussed.
Experiments on ultra-cold fermionic /sup 6/Li confined in a crossed dipole trap. /sup 6/Li possesses Feshbach resonances both in the s-wave and p-wave channels. This features enables the exploration of both s-wave and p-wave pairing mechanisms. We first discuss our observation of Bose-Einstein condensation of /sup 6/Li/sub 2/ molecules in the low-magnetic field wing the s-wave Feshbach located at /spl sim/ 834 G. The molecular BEC offers a good starting point for the exploration of the BEC-BCS (Bardeen-Cooper-Schrieffer) crossover. We have also located p-wave Feshbach resonances in the two lowest hyperfine states of /sup 6/Li. The experimental positions of these resonances are in good agreement with those predicted by coupled channel calculations. We have studied the atom losses close to these resonances and have developed a semi-analytical model capturing our experimental findings.
We have observed 26 interspecies Feshbach resonances at fields up to 2050 G in ultracold 6Li+23Na{}^{6}\text{Li}+{}^{23}\text{Na}6Li+23Na mixtures for different spin-state combinations. Applying the asymptotic bound-state model to assign the resonances, we found that most resonances have ddd-wave character. This analysis serves as guidance for a coupled-channel calculation, which uses modified interaction potentials to describe the positions of the Feshbach resonances well within the experimental uncertainty and to calculate their widths. The scattering length derived from the improved interaction potentials is experimentally confirmed and deviates from previously reported values in sign and magnitude. We give prospects for 7Li+23Na{}^{7}\text{Li}+{}^{23}\text{Na}7Li+23Na and predict broad Feshbach resonances suitable for tuning.
We propose to realize a strongly interacting Fermi superfluid near a narrow Feshbach resonance using the recently discovered ``orbital Feshbach resonance.'' The orbital Feshbach resonance is a type of magnetic field tunable scattering resonance theoretically predicted and experimentally observed recently in the alkaline-earth-metal-like 173Yb^{173}\mathrm{Yb}173Yb atom. We first show that the orbital Feshbach resonance is a narrow resonance in energy, while it is hundreds Gauss wide in terms of magnetic field strength, taking the advantage that the magnetic moment difference between the open and closed channels is quite small. Therefore, this is an ideal platform for the experimental realization of a strongly interacting Fermi superfluid with narrow resonance. We further show that the transition temperature for the Fermi superfluid in this system, especially at the BCS side of the resonance, is even higher than that in a wide resonance, which is also due to the narrow character of this resonance. Our results will encourage experimental efforts to realize Fermi superfluid in the alikaline-earth-metal-like 173Yb^{173}\mathrm{Yb}173Yb system, the properties of which will be complementary to extensively studied Fermi superfluids nearby a wide resonance in alkali-metal 40K^{40}\mathrm{K}40K and 6Li^{6}\mathrm{Li}6Li systems.
We systematically study the BCS-BEC crossover and the quantum phase transition in ultracold 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K atoms across a wide Feshbach resonance. The background scattering lengths for 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K have opposite signs, which lead to very different behaviors for these two types of atoms. For 40K^{40}\mathrm{K}40K, both the two-body and the many-body calculations show that the system always has two branches of solutions: one corresponds to a deeply bound molecule state; and the other, the one accessed by the current experiments, corresponds to a weakly bound state with population always dominantly in the open channel. For 6Li^{6}\mathrm{Li}6Li, there is only a unique solution with the standard crossover from the weakly bound Cooper pairs to the deeply bound molecules as one sweeps the magnetic field through the crossover region. Because of this difference, for the experimentally accessible state of 40K^{40}\mathrm{K}40K, there is a quantum phase transition at zero temperature from the superfluid to the normal Fermi gas at the positive detuning of the magnetic field where the sss-wave scattering length passes its zero point. For 6Li^{6}\mathrm{Li}6Li, however, the system changes continuously across the zero point of the scattering length. For both types of atoms, we also give a detailed comparison between the results from the two-channel and the single-channel model over the whole region of the magnetic field detuning.
The research described in this thesis is part of an international effort with the aim of studying ultracold quantum degenerate gas samples like Bose-Einstein condensates and Fermi degenerate systems, consisting of atoms confined in magnetic or optical traps. The behavior of such samples is governed by the inter-atomic interactions and the resulting properties of the atom-atom scattering. At the relevant temperatures of 1nK to 10µK a key property is the atom-atom scattering length a. In chapter 2 a theoretical method is presented which enables one to describe the interaction and scattering of (ultra)cold atoms to unprecedented precision. It is also unparalleled in comprehensiveness: it allows the prediction of a large and varied set of experimental data for all isotopes of the same element. The method relies on the extraction from experiments of a few (phase) parameters which completely summarize the behavior of the atoms in the (ultra)cold regime. In chapter 3 the method is applied to the "workhorses" of cold-atom physics: the atomic species 85Rb and 87Rb. We extract the foregoing parameters to a very high precision from several recent high precision experiments, allowing us to predict e.g. the 87Rb spinor condensate to be ferromagnetic: a prediction for which the scattering length has to be calculated with a precision better than 1%. We also predict Feshbach resonances at experimentally accessible magnetic field strengths; resonances searched for and found by the experimental group of Rempe. In close collaboration with his group we "fine-tune" the interaction parameters found previously, by making use of only one of the observed resonances. We then obtain agreement with 42 out of the observed 43 resonance field strengths and are able to identify bound states inducing the Feshbach resonances at these locations. Chapter 4 describes the results of this research. With a thorough understanding of the rubidium interactions, we then switch to lithium which has a fermionic (6Li) and a bosonic (7Li) isotope. Both are being used in cold-atom experiments. In chapter 5 we evaluate the interaction parameters for lithium allowing us to predict magnetic field strengths for which a sample of fermionic 6Li atoms can be regarded as strongly interacting. Furthermore, a three-level method for measuring mean-field shifts, based on radio-frequency techniques, is introduced. For weak interactions we find proportionality of resonance shifts to interaction strengths. In the strongly interacting regime, however, these shifts become very small reflecting the quantum unitarity limit and many-body effects. Most interesting is the fact that in this regime the shifts are small both for large positive a and for large negative a, likely reflecting the universality of the interaction energy. In chapters 6 and 7 the interactions between lithium atoms are reinvestigated, making use of newly available experimental data and with the updated interaction parameters special attention is paid to locating field strengths at which magnetically tunable Feshbach resonances occur in the scattering of lithium atoms. In chapter 6 scattering events in a gas of (fermionic) 6Li atoms are studied. In chapter 7 we show that a consistent description of the 6Li+6Li system can be given. We discuss theoretical uncertainties for the position of the wide 6Li Feshbach resonance and present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the 6Li-7Li system, and their importance for different types of crossover superfluidity models is discussed. Molecules created by magnetically sweeping over these resonances will have a fermionic character. One magnetic field strength is predicted at which two different fermionic molecules can be created simultaneously.