Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0707.0859 · Physical Review Letters

Coherence and Clock Shifts in Ultracold Fermi Gases with Resonant Interactions

Gordon Baym, C. J. Pethick, Zhenhua Yu, Martin W. Zwierlein

Published Nov 8, 2007• 95 citations
arXivHTMLPDF

Abstract

Using arguments based on sum rules, we derive a general result for the average shifts of rf lines in Fermi gases in terms of interatomic interaction strengths and two-particle correlation functions. We show that near an interaction resonance shifts vary inversely with the atomic scattering length, rather than linearly as in dilute gases, thus accounting for the experimental observation that clock shifts remain finite at Feshbach resonances.

DOI
10.1103/physrevlett.99.190407

Related papers

Quasiparticles, coherence, and nonlinearity: Exact simulations of rf spectroscopy of strongly interacting one-dimensional Fermi gases

M. J. Leskinen, V. Apaja, J. Kajala +1 more

We consider rf spectroscopy of ultracold Fermi gases by exact simulations of the many-body state and the coherent dynamics in one dimension. Deviations from the linear response sum rule result are found to suppress the pairing contribution to the rf line shifts. We compare the coherent rotation and quasiparticle descriptions of rf spectroscopy which are analogous to NMR experiments in superfluid $^{3}\mathrm{He}$ and tunneling in solids, respectively. We suggest that rf spectroscopy in ultracold gases provides an interesting crossover between these descriptions that could be used for studying decoherence in quantum measurement, in the context of many-body quantum states.

arXiv:0802.1882•Physical Review A•Aug 1, 2008•4 citations

Dimer-Projection Contact and the Clock Shift of a Unitary Fermi Gas

Kevin G. S. Xie, Colin J. Dale, Kiera Pond Grehan +5 more

Understanding the dynamics of short-range correlations is a central challenge in strongly interacting Fermi gases. In ultracold gases, these correlations are quantified by the contact parameter, yet measurements to date have been limited to equilibrium systems or relatively slow, global dynamics. Here, we introduce a rapid spectroscopic technique based on projection of the interacting state onto an alternate scattering channel with a low-lying dimer state. We demonstrate contact measurements on the microsecond timescale-faster than the inverse Fermi energy. Using ^{40}K near a broad s-wave Feshbach resonance, we show that the strength of the dimer-projection feature scales proportionally with the contact parameter extracted from the high-frequency tail of radio-frequency spectroscopy, in agreement with coupled-channels calculations. Analysis of the spectra further reveals that the dimer feature provides the dominant contribution to the clock shift of the unitary Fermi gas, allowing the first experimental bound on this quantity. The observed deviations from universal predictions highlight the importance of multichannel effects. Our results open new avenues for studying contact correlators, hydrodynamic attractors, and quantum critical behavior.

arXiv:2506.13707•Physical Review Letters•Jan 28, 2026•2 citations

Many-particle physics with ultracold gases

Matthias Punk

This thesis is concerned with different aspects of many-particle-physics in the context of ultracold quantum gases. The first part deals with the theoretical basis of radio-frequency-spectroscopy of ultracold Fermi gases near Feshbach-resonances. In particular, we calculate spectral functions and the corresponding rf-spectra of strongly interacting Fermi gases at unitarity. Furthermore, we study the polaron-to-molecule transition using variational methods. We calculate the critical value of the interaction strength and compare it to experimental results. The last part deals with non-equilibrium dynamics of Heisenberg-spin-chains, where the unitary time evolution of a Néel-state is analyzed. Quite generally, the antiferromagnetic order parameter relaxes exponentially and the corresponding relaxation time exhibits a minimum at the isotropic Heisenberg point.

•Jan 1, 2010•3 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

Clock Shift in a Strongly Interacting Two-Dimensional Fermi Gas

Christian B. Langmack, Marcus Barth, W. Zwerger +1 more

We derive universal relations for the rf spectroscopy of a two-dimensional Fermi gas consisting of two spin states interacting through an $S$-wave scattering length. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like $1/({\ensuremath{\omega}}^{2}{ln}^{2}\ensuremath{\omega})$. Its coefficient is proportional to ${ln}^{2}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})$, where ${a}_{2\mathrm{D}}$ and ${a}_{2\mathrm{D}}^{\ensuremath{'}}$ are the two-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to $\mathrm{ln}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})$. If $|\mathrm{ln}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})|\ensuremath{\gg}1$, the clock shift arises as a cancellation between much larger contributions proportional to ${ln}^{2}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})$ from bound-bound and bound-free rf transitions.

arXiv:1111.0999•Physical Review Letters•Feb 9, 2012•49 citations

Theory of rf-Spectroscopy of Strongly Interacting Fermions

Matthias Punk, W. Zwerger

We show that strong pairing correlations in Fermi gases lead to the appearance of a gaplike structure in the rf spectrum, both in the balanced superfluid and in the normal phase above the Clogston-Chandrasekhar limit. The average rf shift of a unitary gas is proportional to the ratio of the Fermi velocity and the scattering length with the final state. In the strongly imbalanced case, the rf spectrum measures the binding energy of a minority atom to the Fermi sea of majority atoms. Our results provide a qualitative understanding of recent experiments by Schunck et al.

arXiv:0707.0792•Physical Review Letters•Oct 25, 2007•126 citations
Using arguments based on sum rules, we derive a general result for the average shifts of rf lines in Fermi gases in terms of interatomic interaction strengths and two-particle correlation functions. We show that near an interaction resonance shifts vary inversely with the atomic scattering length, rather than linearly as in dilute gases, thus accounting for the experimental observation that clock shifts remain finite at Feshbach resonances.
We consider rf spectroscopy of ultracold Fermi gases by exact simulations of the many-body state and the coherent dynamics in one dimension. Deviations from the linear response sum rule result are found to suppress the pairing contribution to the rf line shifts. We compare the coherent rotation and quasiparticle descriptions of rf spectroscopy which are analogous to NMR experiments in superfluid 3He^{3}\mathrm{He}3He and tunneling in solids, respectively. We suggest that rf spectroscopy in ultracold gases provides an interesting crossover between these descriptions that could be used for studying decoherence in quantum measurement, in the context of many-body quantum states.
Understanding the dynamics of short-range correlations is a central challenge in strongly interacting Fermi gases. In ultracold gases, these correlations are quantified by the contact parameter, yet measurements to date have been limited to equilibrium systems or relatively slow, global dynamics. Here, we introduce a rapid spectroscopic technique based on projection of the interacting state onto an alternate scattering channel with a low-lying dimer state. We demonstrate contact measurements on the microsecond timescale-faster than the inverse Fermi energy. Using ^{40}K near a broad s-wave Feshbach resonance, we show that the strength of the dimer-projection feature scales proportionally with the contact parameter extracted from the high-frequency tail of radio-frequency spectroscopy, in agreement with coupled-channels calculations. Analysis of the spectra further reveals that the dimer feature provides the dominant contribution to the clock shift of the unitary Fermi gas, allowing the first experimental bound on this quantity. The observed deviations from universal predictions highlight the importance of multichannel effects. Our results open new avenues for studying contact correlators, hydrodynamic attractors, and quantum critical behavior.
This thesis is concerned with different aspects of many-particle-physics in the context of ultracold quantum gases. The first part deals with the theoretical basis of radio-frequency-spectroscopy of ultracold Fermi gases near Feshbach-resonances. In particular, we calculate spectral functions and the corresponding rf-spectra of strongly interacting Fermi gases at unitarity. Furthermore, we study the polaron-to-molecule transition using variational methods. We calculate the critical value of the interaction strength and compare it to experimental results. The last part deals with non-equilibrium dynamics of Heisenberg-spin-chains, where the unitary time evolution of a Néel-state is analyzed. Quite generally, the antiferromagnetic order parameter relaxes exponentially and the corresponding relaxation time exhibits a minimum at the isotropic Heisenberg point.
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.
We derive universal relations for the rf spectroscopy of a two-dimensional Fermi gas consisting of two spin states interacting through an SSS-wave scattering length. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like $1/({\ensuremath{\omega}}^{2}{ln}^{2}\ensuremath{\omega})$. Its coefficient is proportional to ${ln}^{2}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})$, where a2D{a}_{2\mathrm{D}}a2D​ and ${a}_{2\mathrm{D}}^{\ensuremath{'}}$ are the two-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to $\mathrm{ln}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})$. If $|\mathrm{ln}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})|\ensuremath{\gg}1$, the clock shift arises as a cancellation between much larger contributions proportional to ${ln}^{2}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})$ from bound-bound and bound-free rf transitions.
We show that strong pairing correlations in Fermi gases lead to the appearance of a gaplike structure in the rf spectrum, both in the balanced superfluid and in the normal phase above the Clogston-Chandrasekhar limit. The average rf shift of a unitary gas is proportional to the ratio of the Fermi velocity and the scattering length with the final state. In the strongly imbalanced case, the rf spectrum measures the binding energy of a minority atom to the Fermi sea of majority atoms. Our results provide a qualitative understanding of recent experiments by Schunck et al.