arXiv:cond-mat/0405178 · Physical Review Letters

Atom-Molecule Coexistence and Collective Dynamics Near a Feshbach Resonance of Cold Fermions

Roman A. Barankov, Leonid S Levitov

Published Sep 22, 2004• 66 citations

Abstract

Degenerate Fermi gas interacting with molecules near a Feshbach resonance is unstable with respect to the formation of a mixed state, in which atoms and molecules coexist as a coherent superposition. A theory of this state is developed using a mapping to the Dicke model, treating the molecular field in the single mode approximation. The results are accurate in the strong coupling regime relevant for current experimental efforts. The exact solution of the Dicke model is exploited to study stability, phase diagram, and nonadiabatic dynamics of the molecular field in the mixed state.

DOI: 10.1103/physrevlett.93.130403

Related papers

Collective Molecule Formation in a Degenerate Fermi Gas via a Feshbach Resonance

Juha Javanainen, Marijan Koštrun, Yi Zheng +6 more

arXiv:physics/0406077Physical Review LettersMay 20, 200441 citations

Fermi-Bose mixture across a Feshbach resonance

Luca Salasnich, Flavio Toigo

arXiv:cond-mat/0701098Physical Review AJan 25, 200722 citations

Phase diagram of a Bose gas near a wide Feshbach resonance

Lan Yin

arXiv:0710.5318Physical Review AApr 25, 200812 citations

Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms

Deqiang Sun, Ar. Abanov, V. L. Pokrovsky

arXiv:0707.3630Europhysics Letters (EPL)Jun 12, 200818 citations

Molecular production at a broad Feshbach resonance in Fermi-gas of cooled atoms

Deqiang Sun, Ar. Abanov, V. L. Pokrovsky

Bulletin of the American Physical SocietyMar 13, 20080 citations

Degenerate atom-molecule mixture in a cold Fermi gas

S. J. J. M. F. Kokkelmans, Georgy V. Shlyapnikov, Ch Salomon

We show that the atom-molecule mixture formed in a degenerate atomic Fermi gas with interspecies repulsion near a Feshbach resonance constitutes a peculiar system where the atomic component is almost nondegenerate but quantum degeneracy of molecules is important. We develop a thermodynamic approach for studying this mixture, explain experimental observations, and predict optimal conditions for achieving molecular Bose-Einstein condensation.

arXiv:cond-mat/0308384Physical Review AMar 23, 200431 citations

arXiv:cond-mat/0405178 · Physical Review Letters

Atom-Molecule Coexistence and Collective Dynamics Near a Feshbach Resonance of Cold Fermions

Roman A. Barankov, Leonid S Levitov

Published Sep 22, 2004• 66 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.93.130403

Related papers

Collective Molecule Formation in a Degenerate Fermi Gas via a Feshbach Resonance

Juha Javanainen, Marijan Koštrun, Yi Zheng +6 more

We model collisionless collective conversion of a degenerate Fermi gas of atoms into bosonic molecules via a Feshbach resonance, treating the bosonic molecules as a classical field and seeding the pairing amplitudes with random phases. A dynamical instability of the Fermi sea against association with molecules drives the conversion. The model qualitatively reproduces several experimental observations [Regal et al., Nature (London), (2003)]. We predict that the initial temperature of the Fermi gas sets the limit for the efficiency of atom-molecule conversion.We model collisionless collective conversion of a degenerate Fermi gas of atoms into bosonic molecules via a Feshbach resonance, treating the bosonic molecules as a classical field and seeding the pairing amplitudes with random phases. A dynamical instability of the Fermi sea against association with molecules drives the conversion. The model qualitatively reproduces several experimental observations [Regal et al., Nature (London), (2003)]. We predict that the initial temperature of the Fermi gas sets the limit for the efficiency of atom-molecule conversion.

arXiv:physics/0406077Physical Review LettersMay 20, 200441 citations

Fermi-Bose mixture across a Feshbach resonance

Luca Salasnich, Flavio Toigo

We study a dilute mixture of degenerate bosons and fermions across a Feshbach resonance of the Fermi-Fermi scattering length ${a}_{F}$ . This scattering length is renormalized by the boson-induced interaction between fermions and its value is crucial to determine the phase diagram of the system. For the mixture in a box and a positive Bose-Fermi scattering length, we show that there are three possibilities: A single uniform mixed phase, a purely fermionic phase coexisting with a mixed phase, and a purely fermionic phase coexisting with a purely bosonic one. As $1∕{a}_{F}$ is increased from a negative value to the Feshbach resonance $(1∕{a}_{F}=0)$ , the region of pure separation increases and the other two regions are strongly reduced. Above the Feshbach resonance $(1∕{a}_{F}>0)$ , pairs of Fermi atoms become Bose-condensed molecules. We find that these molecules are fully spatially separated from the bosonic atoms when $1∕{a}_{F}$ exceeds a critical value. For a negative Bose-Fermi scattering length we deduce the condition for collapse, which coincides with the onset of dynamical instability of the fully mixed phase. We consider also the mixture in a harmonic trap and determine the conditions for partial demixing, full demixing, and collapse. The experimental implications of our results are investigated by analyzing mixtures of $^{6}\mathrm{Li}\text{\ensuremath{-}}^{23}\mathrm{Na}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ atoms.We study a dilute mixture of degenerate bosons and fermions across a Feshbach resonance of the Fermi-Fermi scattering length ${a}_{F}$. This scattering length is renormalized by the boson-induced interaction between fermions and its value is crucial to determine the phase diagram of the system. For the mixture in a box and a positive Bose-Fermi scattering length, we show that there are three possibilities: A single uniform mixed phase, a purely fermionic phase coexisting with a mixed phase, and a purely fermionic phase coexisting with a purely bosonic one. As $1∕{a}_{F}$ is increased from a negative value to the Feshbach resonance $(1∕{a}_{F}=0)$, the region of pure separation increases and the other two regions are strongly reduced. Above the Feshbach resonance $(1∕{a}_{F}>0)$, pairs of Fermi atoms become Bose-condensed molecules. We find that these molecules are fully spatially separated from the bosonic atoms when $1∕{a}_{F}$ exceeds a critical value. For a negative Bose-Fermi scattering length we deduce the condition for collapse, which coincides with the onset of dynamical instability of the fully mixed phase. We consider also the mixture in a harmonic trap and determine the conditions for partial demixing, full demixing, and collapse. The experimental implications of our results are investigated by analyzing mixtures of $^{6}\mathrm{Li}\text{\ensuremath{-}}^{23}\mathrm{Na}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ atoms.

arXiv:cond-mat/0701098Physical Review AJan 25, 200722 citations

Phase diagram of a Bose gas near a wide Feshbach resonance

Lan Yin

In this paper, we study the phase diagram of a homogeneous Bose gas with a repulsive interaction near a wide Feshbach resonance at zero temperature. The Bose-Einstein-condensation (BEC) state of atoms is a metastable state. When the scattering length $a$ exceeds a critical value depending on the atom density $n$ , $n{a}^{3}>0.035$ , the molecular excitation energy is imaginary and the atomic BEC state is dynamically unstable against molecule formation. The BEC state of diatomic molecules has lower energy, where the atomic excitation is gapped and the molecular excitation is gapless. However, when the scattering length is above another critical value, $n{a}^{3}>0.0164$ , the molecular BEC state becomes an unstable coherent mixture of atoms and molecules. In both BEC states, the binding energy of diatomic molecules is reduced due to the many-body effect.In this paper, we study the phase diagram of a homogeneous Bose gas with a repulsive interaction near a wide Feshbach resonance at zero temperature. The Bose-Einstein-condensation (BEC) state of atoms is a metastable state. When the scattering length $a$ exceeds a critical value depending on the atom density $n$, $n{a}^{3}>0.035$, the molecular excitation energy is imaginary and the atomic BEC state is dynamically unstable against molecule formation. The BEC state of diatomic molecules has lower energy, where the atomic excitation is gapped and the molecular excitation is gapless. However, when the scattering length is above another critical value, $n{a}^{3}>0.0164$, the molecular BEC state becomes an unstable coherent mixture of atoms and molecules. In both BEC states, the binding energy of diatomic molecules is reduced due to the many-body effect.

arXiv:0710.5318Physical Review AApr 25, 200812 citations

Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms

Deqiang Sun, Ar. Abanov, V. L. Pokrovsky

The problem of molecular production from a degenerate gas of fermions at a broad Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction and induced coherence lead to significant renormalization of the gap between adiabatic levels. The essential region of energies near the resonance contributing to the atom-molecule transformation strongly exceeds the Fermi energy of the weakly interacting gas. The close vicinity of the exact resonance does not play as substantial a role as in the static problem. Our main results are: i) The molecular production is sensitive to the initial magnetic field. ii) In the inverse process of molecule dissociation a large BCS condensate distributed over a broad range of momenta is generated.The problem of molecular production from a degenerate gas of fermions at a broad Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction and induced coherence lead to significant renormalization of the gap between adiabatic levels. The essential region of energies near the resonance contributing to the atom-molecule transformation strongly exceeds the Fermi energy of the weakly interacting gas. The close vicinity of the exact resonance does not play as substantial a role as in the static problem. Our main results are: i) The molecular production is sensitive to the initial magnetic field. ii) In the inverse process of molecule dissociation a large BCS condensate distributed over a broad range of momenta is generated.

arXiv:0707.3630Europhysics Letters (EPL)Jun 12, 200818 citations

Molecular production at a broad Feshbach resonance in Fermi-gas of cooled atoms

Deqiang Sun, Ar. Abanov, V. L. Pokrovsky

\n The problem of molecular production from a degenerate gas of fermions at a broad Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction and induced coherence lead to significant renormalization of the gap between adiabatic levels. The essential region of energies near the resonance contributing to the atom-molecule transformation strongly exceeds the Fermi energy of the weakly interacting gas. The close vicinity of the exact resonance does not play as substantial a role as in the static problem. Our main results are: i) The molecular production is sensitive to the initial magnetic field. ii) In the inverse process of molecule dissociation a large BCS condensate distributed over a broad range of momenta is generated.\n\n The problem of molecular production from a degenerate gas of fermions at a broad Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction and induced coherence lead to significant renormalization of the gap between adiabatic levels. The essential region of energies near the resonance contributing to the atom-molecule transformation strongly exceeds the Fermi energy of the weakly interacting gas. The close vicinity of the exact resonance does not play as substantial a role as in the static problem. Our main results are: i) The molecular production is sensitive to the initial magnetic field. ii) In the inverse process of molecule dissociation a large BCS condensate distributed over a broad range of momenta is generated.\n

Bulletin of the American Physical SocietyMar 13, 20080 citations

Degenerate atom-molecule mixture in a cold Fermi gas

S. J. J. M. F. Kokkelmans, Georgy V. Shlyapnikov, Ch Salomon

arXiv:cond-mat/0308384Physical Review AMar 23, 200431 citations

We study a dilute mixture of degenerate bosons and fermions across a Feshbach resonance of the Fermi-Fermi scattering length

{a}_{F}

. This scattering length is renormalized by the boson-induced interaction between fermions and its value is crucial to determine the phase diagram of the system. For the mixture in a box and a positive Bose-Fermi scattering length, we show that there are three possibilities: A single uniform mixed phase, a purely fermionic phase coexisting with a mixed phase, and a purely fermionic phase coexisting with a purely bosonic one. As

1∕{a}_{F}

is increased from a negative value to the Feshbach resonance

(1∕{a}_{F}=0)

, the region of pure separation increases and the other two regions are strongly reduced. Above the Feshbach resonance

(1∕{a}_{F}>0)

, pairs of Fermi atoms become Bose-condensed molecules. We find that these molecules are fully spatially separated from the bosonic atoms when

1∕{a}_{F}

exceeds a critical value. For a negative Bose-Fermi scattering length we deduce the condition for collapse, which coincides with the onset of dynamical instability of the fully mixed phase. We consider also the mixture in a harmonic trap and determine the conditions for partial demixing, full demixing, and collapse. The experimental implications of our results are investigated by analyzing mixtures of $^{6}\mathrm{Li}\text{\ensuremath{-}}^{23}\mathrm{Na}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ atoms.

a

exceeds a critical value depending on the atom density

n

n{a}^{3}>0.035

, the molecular excitation energy is imaginary and the atomic BEC state is dynamically unstable against molecule formation. The BEC state of diatomic molecules has lower energy, where the atomic excitation is gapped and the molecular excitation is gapless. However, when the scattering length is above another critical value,

n{a}^{3}>0.0164

, the molecular BEC state becomes an unstable coherent mixture of atoms and molecules. In both BEC states, the binding energy of diatomic molecules is reduced due to the many-body effect.