Abstract We consider Bose–Einstein condensates with two- and three-body interactions periodically varying in time. Two models of time-dependent three-body interactions, with quadratic and quartic dependence on the two-body atomic scattering length a s , are studied. It is shown that parametric instabilities in the condensate lead to the generation of Faraday waves (FWs), with wavelengths depending on the background scattering length, as well as on the frequency and amplitude of the modulations of a s . From an experimental perspective, this opens a new possibility to tune the period of Faraday patterns by varying not only the frequency of modulations and background scattering length, but also the amplitude of the modulations. The latter effect can be used to estimate the parameters of three-body interactions from the FW experimental results. Theoretical predictions are confirmed by numerical simulations of the corresponding extended Gross–Pitaevskii equation.Abstract We consider Bose–Einstein condensates with two- and three-body interactions periodically varying in time. Two models of time-dependent three-body interactions, with quadratic and quartic dependence on the two-body atomic scattering length a s , are studied. It is shown that parametric instabilities in the condensate lead to the generation of Faraday waves (FWs), with wavelengths depending on the background scattering length, as well as on the frequency and amplitude of the modulations of a s . From an experimental perspective, this opens a new possibility to tune the period of Faraday patterns by varying not only the frequency of modulations and background scattering length, but also the amplitude of the modulations. The latter effect can be used to estimate the parameters of three-body interactions from the FW experimental results. Theoretical predictions are confirmed by numerical simulations of the corresponding extended Gross–Pitaevskii equation.

arXiv:1510.00207Journal of Physics B Atomic Molecular and Optical PhysicsDec 16, 201512 citations

Observation of Faraday Rotation in Cold Atoms in an Integrating Sphere

郑本昌, 成华东, 孟艳玲 +3 more

Chinese Physics LettersJan 1, 20140 citations

Faraday Waves and Collective Modes in Bose-Einstein Condensates

Alexandru I. Nicolin, Ivana Vidanović, Antun Balaž

Advances in intelligent and soft computingJan 1, 20121 citation

Universal three-body bound states in mixed dimensions beyond the Efimov paradigm

Pengfei Zhang, Zhenhua Yu

The Efimov effect was first predicted for three particles interacting at an $s$ -wave resonance in three dimensions. A subsequent study showed that the same effect can be realized by considering two-body and three-body interactions in mixed dimensions. In this work, we consider the three-body problem of two bosonic $A$ atoms interacting with another single $B$ atom in mixed dimensions: The $A$ atoms are confined in a space of dimension ${d}_{A}$ and the $B$ atom in a space of dimension ${d}_{B}$ , and there is an interspecies $s$ -wave interaction in a ${d}_{\mathrm{int}}$ -codimensional space accessible to both species. We find that when the $s$ -wave interaction is tuned on resonance, there emerge an infinite series of universal three-body bound states for ${{d}_{A},{d}_{B},{d}_{\mathrm{int}}}={2,2,0}$ and ${2,3,1}$ . Going beyond the Efimov paradigm, the binding energies of these states follow the scaling $ln|{E}_{n}{|\ensuremath{\sim}\ensuremath{-}s(n\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta})}^{2}/4$, with the scaling factor $s$ being unity for the former case and $\sqrt{{m}_{B}(2{m}_{A}+{m}_{B})}/({m}_{A}+{m}_{B})$ for the latter. We discuss the possibility of realizing our mixed-dimensional systems in a cold-atom experiment and how the effects of these universal three-body bound states may be detected.The Efimov effect was first predicted for three particles interacting at an $s$-wave resonance in three dimensions. A subsequent study showed that the same effect can be realized by considering two-body and three-body interactions in mixed dimensions. In this work, we consider the three-body problem of two bosonic $A$ atoms interacting with another single $B$ atom in mixed dimensions: The $A$ atoms are confined in a space of dimension ${d}_{A}$ and the $B$ atom in a space of dimension ${d}_{B}$, and there is an interspecies $s$-wave interaction in a ${d}_{\mathrm{int}}$-codimensional space accessible to both species. We find that when the $s$-wave interaction is tuned on resonance, there emerge an infinite series of universal three-body bound states for ${{d}_{A},{d}_{B},{d}_{\mathrm{int}}}={2,2,0}$ and ${2,3,1}$. Going beyond the Efimov paradigm, the binding energies of these states follow the scaling $ln|{E}_{n}{|\ensuremath{\sim}\ensuremath{-}s(n\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta})}^{2}/4$, with the scaling factor $s$ being unity for the former case and $\sqrt{{m}_{B}(2{m}_{A}+{m}_{B})}/({m}_{A}+{m}_{B})$ for the latter. We discuss the possibility of realizing our mixed-dimensional systems in a cold-atom experiment and how the effects of these universal three-body bound states may be detected.

arXiv:1704.04754Physical Review ASep 21, 20179 citations

Three-body interactions with cold polar molecules

Hans Peter Büchler, Andrea Micheli, P. Zoller

arXiv:cond-mat/0703688Nature PhysicsJul 22, 2007276 citations

The Efimov effect was first predicted for three particles interacting at an

s

-wave resonance in three dimensions. A subsequent study showed that the same effect can be realized by considering two-body and three-body interactions in mixed dimensions. In this work, we consider the three-body problem of two bosonic

A

atoms interacting with another single

B

atom in mixed dimensions: The

A

atoms are confined in a space of dimension

{d}_{A}

and the

B

atom in a space of dimension

{d}_{B}

, and there is an interspecies

s

-wave interaction in a

{d}_{\mathrm{int}}

-codimensional space accessible to both species. We find that when the

s

-wave interaction is tuned on resonance, there emerge an infinite series of universal three-body bound states for

{{d}_{A},{d}_{B},{d}_{\mathrm{int}}}={2,2,0}

and

{2,3,1}

. Going beyond the Efimov paradigm, the binding energies of these states follow the scaling $ln|{E}_{n}{|\ensuremath{\sim}\ensuremath{-}s(n\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta})}^{2}/4$, with the scaling factor

s

being unity for the former case and

\sqrt{{m}_{B}(2{m}_{A}+{m}_{B})}/({m}_{A}+{m}_{B})

for the latter. We discuss the possibility of realizing our mixed-dimensional systems in a cold-atom experiment and how the effects of these universal three-body bound states may be detected.