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Observation of a Feshbach Resonance in Cold Atom Scattering

Daniel J. Heinzen, Ph. W. Courteille, R. S. Freeland

Published May 3, 1998• 0 citations
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Abstract

Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.

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Atoms and molecules in a Bose-Einstein condensate with strong interactions

S. J. J. M. F. Kokkelmans

With help of a Feshbach scattering resonance it is possible to change the effective two-body interaction of ultra-cold atoms from repulsive to attractive, from weak to strong. Regular field theory for the description of Bose-Einstein condensates is based on a single interaction parameter only, the scattering length. Such a description, however, is not valid anymore for the resonance regime. We formulated a field-theory that incorporated the microscopic energy-dependent two-body interactions, that also takes pair correlations into account. This theory allowed us to explain an experiment at JILA where Ramsey fringes were observed in a ^85Rb Bose-Einstein condensate by making use of a Feshbach resonance. The theory and experiment show that coherent molecules are created, a first step in the direction of molecular BEC. For non-resonant interactions, the self-energy corresponding to the atom-atom interactions is proportional to the scattering length. Close to resonance, however, this relationship no longer applies, and the energy will level off to a finite value on resonance. We investigate this resonance self-energy, and compare it with experimental results from strongly interacting Fermi systems.

APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts•May 1, 2003•0 citations

Observation of a Feshbach Resonance in Cold Atom Scattering

Ph. W. Courteille, R. S. Freeland, Daniel J. Heinzen +2 more

We probe $s$-wave collisions of laser-cooled ${}^{85}\mathrm{Rb}({f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2)$ atoms with Zeeman-resolved photoassociation spectroscopy. We observe that these collisions exhibit a magnetically tunable Feshbach resonance, and determine that this resonance tunes to zero energy at a magnetic field of $164\ifmmode\pm\else\textpm\fi{}7\mathrm{G}$. This result indicates that the self-interaction energy of an ${}^{85}\mathrm{Rb}$ Bose-Einstein condensate can be magnetically tuned. We also demonstrate that Zeeman-resolved photoassociation spectroscopy provides a useful new tool for the study of ultracold atomic collisions.

Physical Review Letters•Jul 6, 1998•554 citations

[sup 85]Rb BEC near a Feshback resonance

N. R. Claussen

Bose-Einstein condensation has been achieved in a magnetically trapped sample of 85Rb atoms. Stable condensates of up to 104 atoms have been created by using a magnetic-field-induced Feshbach resonance to reverse the sign of the zero-field scattering length. These condensates provide unique opportunities for the study of BEC physics. The variation of the scattering length near the resonance has been used to magnetically tune the condensate self-interaction energy over a very wide range. This range extended from very strong repulsive self-interactions to large attractive ones. The effect of moving the condensate through the Feshbach resonance has been studied and compared with theory. Long-lived metastable condensates with attractive interactions have been produced near the zero of the Feshbach resonance. The transition from repulsive to attractive interactions can lead to a “collapse” of the condensate in which the cloud shrinks below our resolution limit, loses a significant number of atoms due to inelastic losses, and emits a burst of high-energy atoms.

AIP conference proceedings•Jan 1, 2001•0 citations

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

Stable 85Rb Bose-Einstein Condensates with Widely Tunable Interactions

Simon L. Cornish, N. R. Claussen, Jacob Roberts +2 more

Bose-Einstein condensation has been achieved in a magnetically trapped sample of 85Rb atoms. Long-lived condensates of up to 10(4) atoms have been produced by using a magnetic-field-induced Feshbach resonance to reverse the sign of the scattering length. This system provides new opportunities for the study of condensate physics. The variation of the scattering length near the resonance has been used to magnetically tune the condensate self-interaction energy over a wide range, extending from strong repulsive to large attractive interactions. When the interactions were switched from repulsive to attractive, the condensate shrank to below our resolution limit, and after approximately 5 ms emitted a burst of high-energy atoms.

arXiv:cond-mat/0004290•Physical Review Letters•Aug 28, 2000•899 citations

A tunable Bose-Einstein condensate of cesium atoms

Tino Weber, Jens Herbig, Manfred J. Mark +2 more

The achievement of a Bose-Einstein condensate of cesium in the lowest internal state (F=3, m/sub F/=3) by evaporative cooling in an optical trap is reported. The corresponding scattering length shows a strong dependence on magnetic field, varying from large negative to large positive values in a conveniently accessible magnetic field range due to a unusual combination of broad and narrow Feshbach resonances. The inelastic processes resulting from this complex scattering behavior in thermal ensembles is studied. These measurements have been of crucial importance for identifying a suitable path in phase space towards condensation. In first experiments, the strong dependence of the condensate mean-field energy on the magnetic field is demonstrated. By briefly switching to different scattering lengths just before releasing the sample from the trap, imploding, exploding, and non-interacting 'frozen' condensates are produced. We will employ the tunable interaction in further experiments by looking at molecule formation on Feshbach resonances and exploring condensate dynamics at extreme values of the scattering length.

European Quantum Electronics Conference (EQEC)•Jan 1, 2003•0 citations
Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.
With help of a Feshbach scattering resonance it is possible to change the effective two-body interaction of ultra-cold atoms from repulsive to attractive, from weak to strong. Regular field theory for the description of Bose-Einstein condensates is based on a single interaction parameter only, the scattering length. Such a description, however, is not valid anymore for the resonance regime. We formulated a field-theory that incorporated the microscopic energy-dependent two-body interactions, that also takes pair correlations into account. This theory allowed us to explain an experiment at JILA where Ramsey fringes were observed in a ^85Rb Bose-Einstein condensate by making use of a Feshbach resonance. The theory and experiment show that coherent molecules are created, a first step in the direction of molecular BEC. For non-resonant interactions, the self-energy corresponding to the atom-atom interactions is proportional to the scattering length. Close to resonance, however, this relationship no longer applies, and the energy will level off to a finite value on resonance. We investigate this resonance self-energy, and compare it with experimental results from strongly interacting Fermi systems.
We probe sss-wave collisions of laser-cooled ${}^{85}\mathrm{Rb}({f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2)$ atoms with Zeeman-resolved photoassociation spectroscopy. We observe that these collisions exhibit a magnetically tunable Feshbach resonance, and determine that this resonance tunes to zero energy at a magnetic field of $164\ifmmode\pm\else\textpm\fi{}7\mathrm{G}$. This result indicates that the self-interaction energy of an 85Rb{}^{85}\mathrm{Rb}85Rb Bose-Einstein condensate can be magnetically tuned. We also demonstrate that Zeeman-resolved photoassociation spectroscopy provides a useful new tool for the study of ultracold atomic collisions.
Bose-Einstein condensation has been achieved in a magnetically trapped sample of 85Rb atoms. Stable condensates of up to 104 atoms have been created by using a magnetic-field-induced Feshbach resonance to reverse the sign of the zero-field scattering length. These condensates provide unique opportunities for the study of BEC physics. The variation of the scattering length near the resonance has been used to magnetically tune the condensate self-interaction energy over a very wide range. This range extended from very strong repulsive self-interactions to large attractive ones. The effect of moving the condensate through the Feshbach resonance has been studied and compared with theory. Long-lived metastable condensates with attractive interactions have been produced near the zero of the Feshbach resonance. The transition from repulsive to attractive interactions can lead to a “collapse” of the condensate in which the cloud shrinks below our resolution limit, loses a significant number of atoms due to inelastic losses, and emits a burst of high-energy atoms.
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.
Bose-Einstein condensation has been achieved in a magnetically trapped sample of 85Rb atoms. Long-lived condensates of up to 10(4) atoms have been produced by using a magnetic-field-induced Feshbach resonance to reverse the sign of the scattering length. This system provides new opportunities for the study of condensate physics. The variation of the scattering length near the resonance has been used to magnetically tune the condensate self-interaction energy over a wide range, extending from strong repulsive to large attractive interactions. When the interactions were switched from repulsive to attractive, the condensate shrank to below our resolution limit, and after approximately 5 ms emitted a burst of high-energy atoms.
The achievement of a Bose-Einstein condensate of cesium in the lowest internal state (F=3, m/sub F/=3) by evaporative cooling in an optical trap is reported. The corresponding scattering length shows a strong dependence on magnetic field, varying from large negative to large positive values in a conveniently accessible magnetic field range due to a unusual combination of broad and narrow Feshbach resonances. The inelastic processes resulting from this complex scattering behavior in thermal ensembles is studied. These measurements have been of crucial importance for identifying a suitable path in phase space towards condensation. In first experiments, the strong dependence of the condensate mean-field energy on the magnetic field is demonstrated. By briefly switching to different scattering lengths just before releasing the sample from the trap, imploding, exploding, and non-interacting 'frozen' condensates are produced. We will employ the tunable interaction in further experiments by looking at molecule formation on Feshbach resonances and exploring condensate dynamics at extreme values of the scattering length.