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

Physical Review A

Elementary excitations and universal interaction in Bose-Einstein condensates at large scattering lengths

Risto Sarjonen, M. Saarela, Ferran Mazzanti

Published Oct 10, 2011• 2 citations
Publisher

Abstract

We present a theoretical analysis of excitation modes in Bose-Einstein condensates of ultracold alkali-metal gases for large scattering lengths, showing clear deviations from the Bogoliubov prediction as seen by Papp et al. [Phys. Rev. Lett. 101, 135301 (2008)]. We construct the atom-atom interaction by deriving the $T$ matrix of such systems from two coupled (open and closed) channels assuming that the Feshbach resonance dominates the latter. We calculate molecular bound-state energies as a function of the magnetic field and compare with available experiments. The $s$-wave phase shifts determine the local effective interaction with long-ranged repulsion and short-ranged attraction. We show that it becomes a universal function at large scattering lengths. Finally, we use this interaction to characterize the ground-state and elementary excitations of ${}^{85}$Rb, ${}^{87}$Rb, and ${}^{23}$Na gases. Good agreement with line shift experiments in ${}^{85}$Rb is achieved. We find that, at large scattering lengths, Bragg scattering experiments could directly measure the momentum dependence of the effective two-body potential.

DOI
10.1103/physreva.84.041602

Related papers

Elementary Excitations in Bose-Einstein Condensates at Large Scattering Lengths

Risto Sarjonen, M. Saarela, Ferran Mazzanti

We present a theoretical analysis of excitation modes in Bose-Einstein condensates in ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We assume that the effective interaction in the metastable, single channel, gaseous phase has a well defined Fourier transform that scales with the scattering length. Based on this we show that for increasing scattering lengths or equivalently increasing densities the system becomes less correlated and that at large values of the scattering length Bragg scattering measures directly the Fourier transform of the effective two-body potential. We construct model potentials which fit the recently measured line shifts in $^{85}$Rb by Papp et al. (Phys. Rev. Lett. {\bf 101}, 135301 (2008)), and show that they fix the low momentum expansion of the effective range function. We find excellent agreement with the experimental data when the effective range is $\ll 1$ and the coefficient of the $k^4$-term is $-7.5 \pm 0.5$ in scattering length units. The resolution in Bragg scattering experiments so far does not reveal details of the frequency dependence in the dynamic structure function $S(k,ω)$ and we show that the Feynman spectrum determines the measured line shifts. We propose the possibility of a transition to a novel density wave state.

arXiv:0912.3336•Dec 17, 2009•0 citations

Effective Field Theory for Atom-Molecule Systems II: Stationary Solutions and Bogoliubov Excitations in Atom-Molecule Systems

Catarina E. Sahlberg, Crispin W. Gardiner

We formulate the basic theoretical methods for Bose-Einstein Condensation of atoms close to a Feshbach resonance, in which the tunable scattering length of the atoms is described using a system of coupled atom and molecule fields. These include the Thomas-Fermi description of the condensate profile, the c-field equations, and the Bogoliubov-de Gennes equations, and the Bogoliubov excitation spectrum for a homogenous condensed system. We apply this formalism to the special case of Bragg scattering from a uniform condensate, and find that for moderate and large scattering lengths, there is a dramatic difference in the shift of the peak of the Bragg spectra, compared to that based on a structureless atom model. The result is compatible with the experimental results of Papp et al. [S. B. Papp et al., Phys. Rev. Lett., 101(13):135301, Sep 2008].

arXiv:1109.2971•Sep 14, 2011•2 citations

Large scattering lengths and long-range interactions in ultracold atomic gases

Risto Sarjonen

This thesis studies bosonic and fermionic quantum gases. In the first part, a variational many-body theory is used to explain a Bragg scattering experiment carried out on a bosonic quantum gas [S.B. Papp et al. Bragg Spectroscopy of a Strongly Interacting 85Rb Bose-Einstein Condensate. Phys. Rev. Lett. 101, 135301 (2008)]. A key feature in the experiment was the use of a Feshbach resonance, which made large values of the scattering length accessible. Due to the large values of the scattering length, existing models such as the Beliaev model could not be used to explain the observations, and therefore the experiment was a particularly interesting one to analyze. In our first approach, we constructed ad hoc potentials that fitted the observed excitation spectrum, and later we improved our approach by using T-matrix formalism to describe the Feshbach resonant system. All in all, the phenomenological model we developed fits the observed excitation spectrum and yields correct molecular Feshbach resonance state energies in certain cases. The second part of this thesis studies fermionic quantum gases. We focus on studying a gas of spin-1/2 particles confined to a spin-dependent optical lattice. The lattice geometry is such that the up-spin component is loaded in a honeycomb lattice, and the down-spin component is confined to the underlying triangular lattice. We considered attractive on-site and nearest-neighbor interactions, and formulated the nearest-neighbor interaction term in such a way that it takes into account the possibility of spontaneous time-reversal symmetry breaking. Furthermore, we took into account the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which breaks spatial symmetry. Within a mean-field approximation, we showed that the FFLO state is the ground state of the system in many instances. In addition, we found out that the system spontaneously breaks time-reversal symmetry if the nearest-neighbor interaction strength is large. Due to the time-reversal symmetry breaking, the system has topologically non-trivial phases characterized by nonzero Chern numbers. Finally, there were also cases where the time-reversal symmetry was broken in the FFLO phase, and thus we found a phase where spatial and time-reversal symmetries are simultaneously broken.

•Jan 1, 2015•1 citation

Classical-field methods for atom-molecule systems

Catarina E. Sahlberg, Crispin W. Gardiner

We extend classical-field methods [Blakie et al., Adv. Phys. 57, 363 (2008)] to provide a description of atom-molecule systems. We use a model of Bose-Einstein condensation of atoms close to a Feshbach resonance, in which the tunable scattering length of the atoms is described using a system of coupled atom and molecule fields [Holland et al., Phys. Rev. Lett. 86, 1915 (2001)]. We formulate the basic theoretical methods for a coupled atom-molecule system, including the determination of the phenomenological parameters in our system, the Thomas-Fermi description of Bose-Einstein condensate, the Bogoliubov--de Gennes equations, and the Bogoliubov excitation spectrum for a homogenous condensed system. We apply this formalism to the special case of Bragg scattering from a uniform condensate and find that for moderate and large scattering lengths, there is a dramatic difference in the shift of the peak of the Bragg spectra, compared to that based on a structureless atom model. The result is compatible with the experimental results of Papp et al. [Phys. Rev. Lett 101, 135301 (2008)] for Bragg scattering from a nonuniform condensate.

Physical Review A•Feb 27, 2013•2 citations

Cold quantum gases with resonant interactions

Bout Marcelis

We study ultracold gases of alkali-metal atoms in the quantum degenerate regime. The interatomic interactions in these type of systems can be tuned using resonances induced by magnetic or electric fields. The tunability of the interactions, together with the possibility of confining the atoms with several kinds of external potentials, allows for a completely novel approach to study basic problems in many-body physics, and moreover, allows to enter regimes which have never been accessible in condensed matter or nuclear physics. For example, this has led to the experimental demonstration of an intimate relation between two types of superfluidity: the crossover from Bose-Einstein condensation of tightly bound molecules to the superfluid behavior related to weakly bound BCS-like pairs. Another experimental landmark was reached when the existence of universal Efimov three-body bound states was proven in experiments with ultracold bosonic cesium atoms. In this thesis, we study several aspects of these strongly interacting and ultracold atomic gases. We develop an analytical model that encapsulates all of the relevant scattering physics in atomic systems where open-channel shape resonances and closedchannel Feshbach resonances give rise to complicated and non-trivial scattering properties. This model provides lots of physical insight and is shown to describe important quantities, such as the molecular energies and scattering phase shifts, with a high level of accuracy. The model is compared to full numerical coupled-channel calculations in two atomic systems: rubidium and lithium. We study the BCS-BEC crossover using a many-body description of the ultracold gas that includes the non-trivial energy dependence of the scattering model. We show that it gives rise to superfluid behavior associated with the formation of BCS-like pairs while the low-energy interactions are repulsive in character. The energy dependence of the interactions is crucial, as it gives rise to attractive interactions at the Fermi energy, necessary for the formation of Cooper pairs. We demonstrate new ways of controlling the interatomic interactions using a combination of magnetic and electric fields. This leads to experimental control of, for instance, the three-body parameter in the context of Efimov physics and of non-universal behavior in the BCS-BEC crossover in fermionic gases. Using a four-body method based on first principles, we solve the molecule-molecule scattering problem to calculate several important properties of bosonic and fermionic Summary 145 molecules that consist of light and heavy atoms. These type of molecules are of current experimental interest, and we predict several exciting relations between three- and four-body observables in these type of systems.

•Jan 1, 2008•0 citations

Dynamic effects of a Feshbach resonance on Bragg scattering from a Bose-Einstein condensate

Catarina E. Sahlberg, R. J. Ballagh, Crispin W. Gardiner

We present a theoretical model for Bragg scattering from a Bose-Einstein condensate (BEC) in the vicinity of a magnetic Feshbach resonance, using a two-$c$-field formalism, one $c$ field for the atom and the other for a molecule formed of two atoms. We use this model to numerically simulate an experiment [Papp et al., Phys. Rev. Lett. 101, 135301 (2008)] investigating the effects of strong interactions on the Bragg spectrum from a ${}^{85}$Rb BEC. Results from these simulations and from our previous calculations using an atom-molecule Bogoliubov approach are in very good quantitative agreement with the experimental results, confirming the importance of the resonance bound state in the dynamics of the condensate for fast experiments like Bragg scattering.

Physical Review A•Apr 15, 2013•3 citations
We present a theoretical analysis of excitation modes in Bose-Einstein condensates of ultracold alkali-metal gases for large scattering lengths, showing clear deviations from the Bogoliubov prediction as seen by Papp et al. [Phys. Rev. Lett. 101, 135301 (2008)]. We construct the atom-atom interaction by deriving the TTT matrix of such systems from two coupled (open and closed) channels assuming that the Feshbach resonance dominates the latter. We calculate molecular bound-state energies as a function of the magnetic field and compare with available experiments. The sss-wave phase shifts determine the local effective interaction with long-ranged repulsion and short-ranged attraction. We show that it becomes a universal function at large scattering lengths. Finally, we use this interaction to characterize the ground-state and elementary excitations of 85{}^{85}85Rb, 87{}^{87}87Rb, and 23{}^{23}23Na gases. Good agreement with line shift experiments in 85{}^{85}85Rb is achieved. We find that, at large scattering lengths, Bragg scattering experiments could directly measure the momentum dependence of the effective two-body potential.
We present a theoretical analysis of excitation modes in Bose-Einstein condensates in ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We assume that the effective interaction in the metastable, single channel, gaseous phase has a well defined Fourier transform that scales with the scattering length. Based on this we show that for increasing scattering lengths or equivalently increasing densities the system becomes less correlated and that at large values of the scattering length Bragg scattering measures directly the Fourier transform of the effective two-body potential. We construct model potentials which fit the recently measured line shifts in 85^{85}85Rb by Papp et al. (Phys. Rev. Lett. {\bf 101}, 135301 (2008)), and show that they fix the low momentum expansion of the effective range function. We find excellent agreement with the experimental data when the effective range is ≪1\ll 1≪1 and the coefficient of the k4k^4k4-term is −7.5±0.5-7.5 \pm 0.5−7.5±0.5 in scattering length units. The resolution in Bragg scattering experiments so far does not reveal details of the frequency dependence in the dynamic structure function S(k,ω)S(k,ω)S(k,ω) and we show that the Feynman spectrum determines the measured line shifts. We propose the possibility of a transition to a novel density wave state.
We formulate the basic theoretical methods for Bose-Einstein Condensation of atoms close to a Feshbach resonance, in which the tunable scattering length of the atoms is described using a system of coupled atom and molecule fields. These include the Thomas-Fermi description of the condensate profile, the c-field equations, and the Bogoliubov-de Gennes equations, and the Bogoliubov excitation spectrum for a homogenous condensed system. We apply this formalism to the special case of Bragg scattering from a uniform condensate, and find that for moderate and large scattering lengths, there is a dramatic difference in the shift of the peak of the Bragg spectra, compared to that based on a structureless atom model. The result is compatible with the experimental results of Papp et al. [S. B. Papp et al., Phys. Rev. Lett., 101(13):135301, Sep 2008].
This thesis studies bosonic and fermionic quantum gases. In the first part, a variational many-body theory is used to explain a Bragg scattering experiment carried out on a bosonic quantum gas [S.B. Papp et al. Bragg Spectroscopy of a Strongly Interacting 85Rb Bose-Einstein Condensate. Phys. Rev. Lett. 101, 135301 (2008)]. A key feature in the experiment was the use of a Feshbach resonance, which made large values of the scattering length accessible. Due to the large values of the scattering length, existing models such as the Beliaev model could not be used to explain the observations, and therefore the experiment was a particularly interesting one to analyze. In our first approach, we constructed ad hoc potentials that fitted the observed excitation spectrum, and later we improved our approach by using T-matrix formalism to describe the Feshbach resonant system. All in all, the phenomenological model we developed fits the observed excitation spectrum and yields correct molecular Feshbach resonance state energies in certain cases. The second part of this thesis studies fermionic quantum gases. We focus on studying a gas of spin-1/2 particles confined to a spin-dependent optical lattice. The lattice geometry is such that the up-spin component is loaded in a honeycomb lattice, and the down-spin component is confined to the underlying triangular lattice. We considered attractive on-site and nearest-neighbor interactions, and formulated the nearest-neighbor interaction term in such a way that it takes into account the possibility of spontaneous time-reversal symmetry breaking. Furthermore, we took into account the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which breaks spatial symmetry. Within a mean-field approximation, we showed that the FFLO state is the ground state of the system in many instances. In addition, we found out that the system spontaneously breaks time-reversal symmetry if the nearest-neighbor interaction strength is large. Due to the time-reversal symmetry breaking, the system has topologically non-trivial phases characterized by nonzero Chern numbers. Finally, there were also cases where the time-reversal symmetry was broken in the FFLO phase, and thus we found a phase where spatial and time-reversal symmetries are simultaneously broken.
We extend classical-field methods [Blakie et al., Adv. Phys. 57, 363 (2008)] to provide a description of atom-molecule systems. We use a model of Bose-Einstein condensation of atoms close to a Feshbach resonance, in which the tunable scattering length of the atoms is described using a system of coupled atom and molecule fields [Holland et al., Phys. Rev. Lett. 86, 1915 (2001)]. We formulate the basic theoretical methods for a coupled atom-molecule system, including the determination of the phenomenological parameters in our system, the Thomas-Fermi description of Bose-Einstein condensate, the Bogoliubov--de Gennes equations, and the Bogoliubov excitation spectrum for a homogenous condensed system. We apply this formalism to the special case of Bragg scattering from a uniform condensate and find that for moderate and large scattering lengths, there is a dramatic difference in the shift of the peak of the Bragg spectra, compared to that based on a structureless atom model. The result is compatible with the experimental results of Papp et al. [Phys. Rev. Lett 101, 135301 (2008)] for Bragg scattering from a nonuniform condensate.
We study ultracold gases of alkali-metal atoms in the quantum degenerate regime. The interatomic interactions in these type of systems can be tuned using resonances induced by magnetic or electric fields. The tunability of the interactions, together with the possibility of confining the atoms with several kinds of external potentials, allows for a completely novel approach to study basic problems in many-body physics, and moreover, allows to enter regimes which have never been accessible in condensed matter or nuclear physics. For example, this has led to the experimental demonstration of an intimate relation between two types of superfluidity: the crossover from Bose-Einstein condensation of tightly bound molecules to the superfluid behavior related to weakly bound BCS-like pairs. Another experimental landmark was reached when the existence of universal Efimov three-body bound states was proven in experiments with ultracold bosonic cesium atoms. In this thesis, we study several aspects of these strongly interacting and ultracold atomic gases. We develop an analytical model that encapsulates all of the relevant scattering physics in atomic systems where open-channel shape resonances and closedchannel Feshbach resonances give rise to complicated and non-trivial scattering properties. This model provides lots of physical insight and is shown to describe important quantities, such as the molecular energies and scattering phase shifts, with a high level of accuracy. The model is compared to full numerical coupled-channel calculations in two atomic systems: rubidium and lithium. We study the BCS-BEC crossover using a many-body description of the ultracold gas that includes the non-trivial energy dependence of the scattering model. We show that it gives rise to superfluid behavior associated with the formation of BCS-like pairs while the low-energy interactions are repulsive in character. The energy dependence of the interactions is crucial, as it gives rise to attractive interactions at the Fermi energy, necessary for the formation of Cooper pairs. We demonstrate new ways of controlling the interatomic interactions using a combination of magnetic and electric fields. This leads to experimental control of, for instance, the three-body parameter in the context of Efimov physics and of non-universal behavior in the BCS-BEC crossover in fermionic gases. Using a four-body method based on first principles, we solve the molecule-molecule scattering problem to calculate several important properties of bosonic and fermionic Summary 145 molecules that consist of light and heavy atoms. These type of molecules are of current experimental interest, and we predict several exciting relations between three- and four-body observables in these type of systems.
We present a theoretical model for Bragg scattering from a Bose-Einstein condensate (BEC) in the vicinity of a magnetic Feshbach resonance, using a two-ccc-field formalism, one ccc field for the atom and the other for a molecule formed of two atoms. We use this model to numerically simulate an experiment [Papp et al., Phys. Rev. Lett. 101, 135301 (2008)] investigating the effects of strong interactions on the Bragg spectrum from a 85{}^{85}85Rb BEC. Results from these simulations and from our previous calculations using an atom-molecule Bogoliubov approach are in very good quantitative agreement with the experimental results, confirming the importance of the resonance bound state in the dynamics of the condensate for fast experiments like Bragg scattering.