arXiv:1203.2850 · Physical Review A

Controlling integrability in a quasi-one-dimensional atom-dimer mixture

Dmitry S. Petrov, V. Lebedev, Jook T. M. Walraven

Published Jun 28, 2012• 9 citations

Abstract

We analytically study the atom-dimer scattering problem in the near-integrable limit when the oscillator length ${l}_{0}$ of the transverse confinement is smaller than the dimer size, $\ensuremath{\sim}{l}_{0}^{2}/|a|$, where $a<0$ is the interatomic scattering length. The leading contributions to the atom-diatom reflection and break-up probabilities are proportional to ${a}^{6}$ in the bosonic case and to ${a}^{8}$ for the $\ensuremath{\uparrow}$-$\ensuremath{\uparrow}\ensuremath{\downarrow}$ scattering in a two-component fermionic mixture. We show that by tuning $a$ and ${l}_{0}$ one can control the ``degree of integrability'' in a quasi-1D atom-dimer mixture in an extremely wide range leaving thermodynamic quantities unchanged. We find that the relaxation to deeply bound states in the fermionic (bosonic) case is slower (faster) than transitions between different Bethe ansatz states. We propose a realistic experiment for detailed studies of the crossover from integrable to nonintegrable dynamics.

DOI: 10.1103/physreva.85.062711

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Controlling integrability in a quasi-1D atom-dimer mixture

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arXiv:1203.2850 · Physical Review A

Controlling integrability in a quasi-one-dimensional atom-dimer mixture

Dmitry S. Petrov, V. Lebedev, Jook T. M. Walraven

Published Jun 28, 2012• 9 citations

arXiv HTML PDF

Abstract

We analytically study the atom-dimer scattering problem in the near-integrable limit when the oscillator length

{l}_{0}

of the transverse confinement is smaller than the dimer size,

\ensuremath{\sim}{l}_{0}^{2}/|a|

, where

a<0

is the interatomic scattering length. The leading contributions to the atom-diatom reflection and break-up probabilities are proportional to

{a}^{6}

in the bosonic case and to

{a}^{8}

for the

\ensuremath{\uparrow}

\ensuremath{\uparrow}\ensuremath{\downarrow}

scattering in a two-component fermionic mixture. We show that by tuning

a

and

{l}_{0}

one can control the ``degree of integrability'' in a quasi-1D atom-dimer mixture in an extremely wide range leaving thermodynamic quantities unchanged. We find that the relaxation to deeply bound states in the fermionic (bosonic) case is slower (faster) than transitions between different Bethe ansatz states. We propose a realistic experiment for detailed studies of the crossover from integrable to nonintegrable dynamics.

DOI: 10.1103/physreva.85.062711

Related papers

Controlling integrability in a quasi-1D atom-dimer mixture

Dmitry S. Petrov, Lebedev, V., Jook T. M. Walraven

We analytically study the atom-dimer scattering problem in the near-integrable limit when the oscillator length l_0 of the transverse confinement is smaller than the dimer size, ~l_0^2/|a|, where a<0 is the interatomic scattering length. The leading contributions to the atom-diatom reflection and break-up probabilities are proportional to a^6 in the bosonic case and to a^8 for the up-(up-down) scattering in a two-component fermionic mixture. We show that by tuning a and l_0 one can control the "degree of integrability" in a quasi-1D atom-dimer mixture in an extremely wide range leaving thermodynamic quantities unchanged. We find that the relaxation to deeply bound states in the fermionic (bosonic) case is slower (faster) than transitions between different Bethe ansatz states. We propose a realistic experiment for detailed studies of the crossover from integrable to nonintegrable dynamics.We analytically study the atom-dimer scattering problem in the near-integrable limit when the oscillator length l_0 of the transverse confinement is smaller than the dimer size, ~l_0^2/|a|, where a<0 is the interatomic scattering length. The leading contributions to the atom-diatom reflection and break-up probabilities are proportional to a^6 in the bosonic case and to a^8 for the up-(up-down) scattering in a two-component fermionic mixture. We show that by tuning a and l_0 one can control the "degree of integrability" in a quasi-1D atom-dimer mixture in an extremely wide range leaving thermodynamic quantities unchanged. We find that the relaxation to deeply bound states in the fermionic (bosonic) case is slower (faster) than transitions between different Bethe ansatz states. We propose a realistic experiment for detailed studies of the crossover from integrable to nonintegrable dynamics.

Jan 1, 20120 citations

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Motivated by a recent experiment by ENS group on the mixture of Bose and Fermi superfluids (arxiv:1404.2548), we investigate the effective scattering between a bosonic atom and a molecule(dimer) of fermion atoms. It is found that the mean-field prediction of the atom-dimer scattering length ( $a_{ad}$ ), as simply given by the boson-fermion scattering length ( $a_{bf}$ ), generically fails. Instead, $a_{ad}$ crucially depends on the ratio between $a_{bf}$ and $a_{ff}$ (the fermion-fermion scattering length), and in addition log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing $a_{ad}$ for a wide range of $a_{ff}$ in the molecular side of the fermion-fermion Feshbach resonance, and further demonstrate that the atom-dimer many-body system can become unstable against either phase separation or collapse as tuning $a_{ff}$ . Our results have practical implications to the atom loss and collective mode measurement in ENS experiment.Motivated by a recent experiment by ENS group on the mixture of Bose and Fermi superfluids (arxiv:1404.2548), we investigate the effective scattering between a bosonic atom and a molecule(dimer) of fermion atoms. It is found that the mean-field prediction of the atom-dimer scattering length ($a_{ad}$), as simply given by the boson-fermion scattering length ($a_{bf}$), generically fails. Instead, $a_{ad}$ crucially depends on the ratio between $a_{bf}$ and $a_{ff}$ (the fermion-fermion scattering length), and in addition log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing $a_{ad}$ for a wide range of $a_{ff}$ in the molecular side of the fermion-fermion Feshbach resonance, and further demonstrate that the atom-dimer many-body system can become unstable against either phase separation or collapse as tuning $a_{ff}$. Our results have practical implications to the atom loss and collective mode measurement in ENS experiment.

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Atom-dimer scattering and stability of Bose and Fermi mixtures

Xiaoling Cui

Motivated by a recent experiment by the Ecole Normale Sup\'erieure de Lyon (ENS) group on the mixture of Bose and Fermi superfluids [I. Ferrier-Barbut et al., Science 345, 1035 (2014)], we investigate the effective scattering between a bosonic atom and a molecule (dimer) of fermion atoms. It is found that the mean-field prediction of the atom-dimer scattering length $({a}_{\mathrm{ad}})$ , as simply given by the boson-fermion scattering length $({a}_{\mathrm{bf}})$ , generically fails. Instead, ${a}_{\mathrm{ad}}$ crucially depends on the ratio between ${a}_{\mathrm{bf}}$ and ${a}_{\mathrm{ff}}$ (the fermion-fermion scattering length), and in addition it log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing ${a}_{\mathrm{ad}}$ for a wide range of ${a}_{\mathrm{ff}}$ in the molecular side of the fermion-fermion Feshbach resonance, and further demonstrate that the atom-dimer many-body system can become unstable against either phase separation or collapse as tuning ${a}_{\mathrm{ff}}$ . Our results have some implications for the ENS experiment.Motivated by a recent experiment by the Ecole Normale Sup\'erieure de Lyon (ENS) group on the mixture of Bose and Fermi superfluids [I. Ferrier-Barbut et al., Science 345, 1035 (2014)], we investigate the effective scattering between a bosonic atom and a molecule (dimer) of fermion atoms. It is found that the mean-field prediction of the atom-dimer scattering length $({a}_{\mathrm{ad}})$, as simply given by the boson-fermion scattering length $({a}_{\mathrm{bf}})$, generically fails. Instead, ${a}_{\mathrm{ad}}$ crucially depends on the ratio between ${a}_{\mathrm{bf}}$ and ${a}_{\mathrm{ff}}$ (the fermion-fermion scattering length), and in addition it log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing ${a}_{\mathrm{ad}}$ for a wide range of ${a}_{\mathrm{ff}}$ in the molecular side of the fermion-fermion Feshbach resonance, and further demonstrate that the atom-dimer many-body system can become unstable against either phase separation or collapse as tuning ${a}_{\mathrm{ff}}$. Our results have some implications for the ENS experiment.

arXiv:1406.1242Physical Review AOct 21, 201427 citations

We analytically study the atom-dimer scattering problem in the near-integrable limit when the oscillator length

{l}_{0}

of the transverse confinement is smaller than the dimer size,

\ensuremath{\sim}{l}_{0}^{2}/|a|

, where

a<0

is the interatomic scattering length. The leading contributions to the atom-diatom reflection and break-up probabilities are proportional to

{a}^{6}

in the bosonic case and to

{a}^{8}

for the

\ensuremath{\uparrow}

\ensuremath{\uparrow}\ensuremath{\downarrow}

scattering in a two-component fermionic mixture. We show that by tuning

a

and

{l}_{0}

a

and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths

{a}_{\mathit{ad}}

and

{b}_{\mathit{ad}}

. In the tightly bound ``dimer limit'' ${a}_{\ensuremath{\perp}}∕a\ensuremath{\rightarrow}\ensuremath{\infty}$, we find

{b}_{\mathit{ad}}=0

and

{a}_{\mathit{ad}}

is linked to the 3D atom-dimer scattering length. In the weakly bound ``BCS limit'' ${a}_{\ensuremath{\perp}}∕a\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, a connection to the Bethe ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is nonuniversal:

{a}_{\mathit{ad}}

and

{b}_{\mathit{ad}}

depend both on ${a}_{\ensuremath{\perp}}∕a$ and on a parameter

{R}^{*}

related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.

a_{ad}

), as simply given by the boson-fermion scattering length (

a_{bf}

), generically fails. Instead,

a_{ad}

crucially depends on the ratio between

a_{bf}

and

a_{ff}

(the fermion-fermion scattering length), and in addition log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing

a_{ad}

for a wide range of

a_{ff}

in the molecular side of the fermion-fermion Feshbach resonance, and further demonstrate that the atom-dimer many-body system can become unstable against either phase separation or collapse as tuning

a_{ff}

. Our results have practical implications to the atom loss and collective mode measurement in ENS experiment.

({a}_{\mathrm{ad}})

, as simply given by the boson-fermion scattering length

({a}_{\mathrm{bf}})

, generically fails. Instead,

{a}_{\mathrm{ad}}

crucially depends on the ratio between

{a}_{\mathrm{bf}}

and

{a}_{\mathrm{ff}}

(the fermion-fermion scattering length), and in addition it log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing

{a}_{\mathrm{ad}}

for a wide range of

{a}_{\mathrm{ff}}

in the molecular side of the fermion-fermion Feshbach resonance, and further demonstrate that the atom-dimer many-body system can become unstable against either phase separation or collapse as tuning

{a}_{\mathrm{ff}}

. Our results have some implications for the ENS experiment.