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:0707.3599 · Physical Review Letters

Theory for p -Wave Feshbach Molecules

K. B. Gubbels, Henk T. C. Stoof

Published Nov 8, 2007• 26 citations
arXivHTMLPDF

Abstract

We determine the physical properties of p-wave Feshbach molecules in doubly spin-polarized 40K and find excellent agreement with recent experiments. We show that these molecules have a large probability Z to be in the closed channel or bare molecular state responsible for the Feshbach resonance. In the superfluid state this allows for observation of Rabi oscillations between the molecular and atomic components of the Bose-Einstein condensed pairs, which contains a characteristic signature of the quantum phase transition that occurs as a function of applied magnetic field.

DOI
10.1103/physrevlett.99.190406

Related papers

Dressed molecules in atomic quantum gases

M. W. J. Romans

The use of Feshbach resonances in the field of ultracold gases has received a lot of attention recently. In first instance it was realized that these resonances can be used to alter the interaction strength in an atomic gas, by means of tuning an external magnetic field. Furthermore, by sweeping the magnetic field from one side of the resonance to the other, a degenerate gas of bosonic molecules can be created, a significant accomplishment. By making the interactions between fermionic atoms strongly attractive, a fermionic superfluid was recently made, a feat that has drawn a lot of attention in the physics community and from the media. We present work that describes these many-particle systems near a Feshbach resonance in a comprehensive way by using the concept of dressed molecules. These dressed molecules are essentially two-particle states that are a superposition of a tightly bound bare molecule, and two unbound bare atoms. This description reduces to the correct paired wave-function in the two-body limit. Moreover it gives a physically correct description of all the phenomena mentioned above: the Bose-condensation of a gas near a Feshbach resonance, that contains molecules, is more correctly interpreted as a Bose-condensation of dressed molecules. The fermionic superfluid contains a condensate of bosonic pairs, normally called Cooper pairs, that can be understood as the dressed molecules. For the latter case, the dressed-molecule picture also gives an elegant characterization of the crossover between a Bose condensate of pure molecules on one side of the resonance, to a fermionic Bardeen-Cooper-Schrieffer superfluid on the other side. Then, the dressed molecules change continuously from being mostly a bare molecule, to being mostly a loose pair of two atoms. It is clear that the nature of the dressed molecules is much determined by the probability for it to be in the bare-molecular state. This probability we denote with a single parameter Z. We present various ways of calculating it, and study how it affects the macroscopic physics.

•Feb 7, 2007•1 citation

Quantum phase transition in a 2D atomic Bose gas with a g-wave Feshbach resonance

Zhang, Fan, Yin, Lan

Recent repoet on the formation of two-dimensional Bose-Einstein condensates (BECs) of spinning g-wave molecules is surprise. Here we study quantum phase transition in the quasi-2D atomic Bose gas with a g-wave Feshbach resonance, and show that there are two phase transitions in this system: from a phase with only a atomic Bose-Einstein condensate to a phase with coexistence of atomic and molecular condensation and from the coexistence phase to a phase with only a molecular Bose-Einstein condensate. We show that the g-wave resonance Feshbach has two features in the phase transitions, a phase with only a atomic Bose-Einstein condensate is no longer forbidden and resonance effects appear only at levels beyond the mean-field. We determine the T=0 beyond mean-field phase diagram of the gas as a function of magnetic field and molecular condensation density. We also detemine the ratio of atomic to molecular condensation in the coexistence phase, which can be tested in experiments.

arXiv:2505.19070•May 25, 2025•0 citations

Atom—Molecule Coherence Near a Feshbach Resonance in a Bose-Einstein Condensate

Sarah T. Thompson, N. R. Claussen, Elizabeth A. Donley +1 more

Atom–molecule coherence in a Bose-Einstein condensate (BEC) has been demonstrated. Sudden changes were made to the magnetic field near a Feshbach resonance such that oscillations between atomic and molecular states were excited. The frequency of these oscillations was measured over a large range of magnetic fields and was found to be in excellent quantitative agreement with the predicted energy difference between two colliding atoms and the bound molecular state. This agreement indicates that we have created a quantum superposition of atoms and diatomic molecules, which are chemically different species. 1

International Conference on Atomic Physics (ICAP)•Apr 1, 2003•0 citations

Rarified Liquid Properties of Hybrid Atomic-Molecular Bose-Einstein Condensates

Eddy Timmermans, Paolo Tommasini, Robin Côté +2 more

In the atomic Bose-Einstein condensate, the interactions that bring a binary atom system to an intermediate state molecule in the Feshbach resonance create a second condensate component of molecules. The atomic and molecular condensates coherently exchange pairs of atoms. We discuss a signature of the coherent intercondensate exchange: Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the energy detuning. The dependence of the many-body ground state energy on volume suggests that the on-resonant ground state is a dilute condensate with the liquidlike property of a self-determined density.

Physical Review Letters•Oct 4, 1999•136 citations

Microscopic many-body theory of atomic Bose gases near a Feshbach resonance

R. A. Duine, Henk T. C. Stoof

A Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.

arXiv:cond-mat/0210544•Journal of Optics B Quantum and Semiclassical Optics•Apr 1, 2003•49 citations

Stability and dynamics of atom-molecule superfluids near a narrow Feshbach resonance

Zhiqiang Wang, Ke Wang, Zhendong Zhang +3 more

The recent observations of a stable molecular condensate emerging from a condensate of bosonic atoms and related ``super-chemical'' dynamics have raised an intriguing set of questions. Here we provide a microscopic understanding of this unexpected stability and dynamics in atom-molecule superfluids; we show one essential element behind these phenomena is an extremely narrow Feshbach resonance in $^{133}\mathrm{Cs}$ at 19.849G. Comparing theory and experiment, we demonstrate how this narrow resonance enables the dynamical creation of a large closed-channel molecular fraction superfluid, appearing in the vicinity of unitarity. Theoretically, the observed superchemistry (i.e., Bose-enhanced reactions of atoms and molecules) is found to be assisted by the formation of Cooper-like pairs of bosonic atoms that have opposite momenta. Importantly, this narrow resonance opens the possibility to explore the quantum critical point of a molecular Bose superfluid and related phenomena which would not be possible near a more typically broad Feshbach resonance.

arXiv:2310.01639•Physical Review A•Jul 11, 2024•5 citations
We determine the physical properties of p-wave Feshbach molecules in doubly spin-polarized 40K and find excellent agreement with recent experiments. We show that these molecules have a large probability Z to be in the closed channel or bare molecular state responsible for the Feshbach resonance. In the superfluid state this allows for observation of Rabi oscillations between the molecular and atomic components of the Bose-Einstein condensed pairs, which contains a characteristic signature of the quantum phase transition that occurs as a function of applied magnetic field.
The use of Feshbach resonances in the field of ultracold gases has received a lot of attention recently. In first instance it was realized that these resonances can be used to alter the interaction strength in an atomic gas, by means of tuning an external magnetic field. Furthermore, by sweeping the magnetic field from one side of the resonance to the other, a degenerate gas of bosonic molecules can be created, a significant accomplishment. By making the interactions between fermionic atoms strongly attractive, a fermionic superfluid was recently made, a feat that has drawn a lot of attention in the physics community and from the media. We present work that describes these many-particle systems near a Feshbach resonance in a comprehensive way by using the concept of dressed molecules. These dressed molecules are essentially two-particle states that are a superposition of a tightly bound bare molecule, and two unbound bare atoms. This description reduces to the correct paired wave-function in the two-body limit. Moreover it gives a physically correct description of all the phenomena mentioned above: the Bose-condensation of a gas near a Feshbach resonance, that contains molecules, is more correctly interpreted as a Bose-condensation of dressed molecules. The fermionic superfluid contains a condensate of bosonic pairs, normally called Cooper pairs, that can be understood as the dressed molecules. For the latter case, the dressed-molecule picture also gives an elegant characterization of the crossover between a Bose condensate of pure molecules on one side of the resonance, to a fermionic Bardeen-Cooper-Schrieffer superfluid on the other side. Then, the dressed molecules change continuously from being mostly a bare molecule, to being mostly a loose pair of two atoms. It is clear that the nature of the dressed molecules is much determined by the probability for it to be in the bare-molecular state. This probability we denote with a single parameter Z. We present various ways of calculating it, and study how it affects the macroscopic physics.
Recent repoet on the formation of two-dimensional Bose-Einstein condensates (BECs) of spinning g-wave molecules is surprise. Here we study quantum phase transition in the quasi-2D atomic Bose gas with a g-wave Feshbach resonance, and show that there are two phase transitions in this system: from a phase with only a atomic Bose-Einstein condensate to a phase with coexistence of atomic and molecular condensation and from the coexistence phase to a phase with only a molecular Bose-Einstein condensate. We show that the g-wave resonance Feshbach has two features in the phase transitions, a phase with only a atomic Bose-Einstein condensate is no longer forbidden and resonance effects appear only at levels beyond the mean-field. We determine the T=0 beyond mean-field phase diagram of the gas as a function of magnetic field and molecular condensation density. We also detemine the ratio of atomic to molecular condensation in the coexistence phase, which can be tested in experiments.
Atom–molecule coherence in a Bose-Einstein condensate (BEC) has been demonstrated. Sudden changes were made to the magnetic field near a Feshbach resonance such that oscillations between atomic and molecular states were excited. The frequency of these oscillations was measured over a large range of magnetic fields and was found to be in excellent quantitative agreement with the predicted energy difference between two colliding atoms and the bound molecular state. This agreement indicates that we have created a quantum superposition of atoms and diatomic molecules, which are chemically different species. 1
In the atomic Bose-Einstein condensate, the interactions that bring a binary atom system to an intermediate state molecule in the Feshbach resonance create a second condensate component of molecules. The atomic and molecular condensates coherently exchange pairs of atoms. We discuss a signature of the coherent intercondensate exchange: Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the energy detuning. The dependence of the many-body ground state energy on volume suggests that the on-resonant ground state is a dilute condensate with the liquidlike property of a self-determined density.
A Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.
The recent observations of a stable molecular condensate emerging from a condensate of bosonic atoms and related ``super-chemical'' dynamics have raised an intriguing set of questions. Here we provide a microscopic understanding of this unexpected stability and dynamics in atom-molecule superfluids; we show one essential element behind these phenomena is an extremely narrow Feshbach resonance in 133Cs^{133}\mathrm{Cs}133Cs at 19.849G. Comparing theory and experiment, we demonstrate how this narrow resonance enables the dynamical creation of a large closed-channel molecular fraction superfluid, appearing in the vicinity of unitarity. Theoretically, the observed superchemistry (i.e., Bose-enhanced reactions of atoms and molecules) is found to be assisted by the formation of Cooper-like pairs of bosonic atoms that have opposite momenta. Importantly, this narrow resonance opens the possibility to explore the quantum critical point of a molecular Bose superfluid and related phenomena which would not be possible near a more typically broad Feshbach resonance.