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arXiv:1104.1561 · Physical Review Letters

Inelastic Confinement-Induced Resonances in Low-Dimensional Quantum Systems

Simon Sala, Philipp‐Immanuel Schneider, Alejandro Sáenz

Published Aug 16, 2012• 60 citations
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Abstract

A theoretical model is presented describing the confinement-induced resonances observed in the recent loss experiment of Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)]. These resonances originate from possible molecule formation due to the coupling of center-of-mass and relative motion. A corresponding model is verified by ab initio calculations and predicts the resonance positions in 1D as well as in 2D confinement in agreement with the experiment. This resolves the contradiction of the experimental observations to previous theoretical predictions.

DOI
10.1103/physrevlett.109.073201

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A theoretical model is presented describing the confinement-induced resonances observed in the recent loss experiment of Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)]. These resonances originate from possible molecule formation due to the coupling of center-of-mass and relative motion. A corresponding model is verified by ab initio calculations and predicts the resonance positions in 1D as well as in 2D confinement in agreement with the experiment. This resolves the contradiction of the experimental observations to previous theoretical predictions.
A detailed study of the anharmonicity-induced resonances caused by the coupling of center-of-mass and relative motion is presented for a system of two ultracold atoms in single-well potentials. As has been confirmed experimentally, these inelastic confinement-induced resonances are of interest since they can lead to coherent molecule formation, losses, and heating in ultracold atomic gases. A perturbative model is introduced to describe the resonance positions and the coupling strengths. The validity of the model and the behavior of the resonances for different confinement geometries are analyzed in comparison with exact numerical ab initio calculations. While such resonances have so far only been detected for large positive values of the s-waves\text{-wave}s-wave scattering length, it is found that they are present also for negative s-waves\text{-wave}s-wave scattering lengths, i.e., for attractive interactions. The possibility to coherently tune the resonances by a variation of the external confinement geometry might pave the way for coherent molecule association where magnetic Feshbach resonances are inaccessible.
We perform a theoretical and experimental study of a system of two ultracold atoms with tunable interaction in an elongated trapping potential. We show that the coupling of center-of-mass and relative motion due to an anharmonicity of the trapping potential leads to a coherent coupling of a state of an unbound atom pair and a molecule with a center of mass excitation. By performing the experiment with exactly two particles we exclude three-body losses and can therefore directly observe coherent molecule formation. We find quantitative agreement between our theory of inelastic confinement-induced resonances and the experimental results. This shows that the effects of center-of-mass to relative-motion coupling can have a significant impact on the physics of quantum systems near center-of-mass to relative-motion coupling resonances.
Recently, it was shown that the coupling of center-of-mass and relative motion in atomic systems leads to inelastic confinement-induced resonances (ICIRs) [Phys. Rev. Lett. 109, 073201 (2012)]. In the present work, the possible occurrence of ICIRs in quantum dots is investigated. Particularly, electron-hole and electron-electron two-body systems with long-range Coulomb interaction are considered using the material parameters of GaAs. ICIRs are identified for the electron-hole system verifying the universal nature of the ICIR and, additionally, resonances due to the coupling of center-of-mass and relative motion are found also for the electron-electron system. In analogy to the coherent molecule formation appearing at ICIR in atomic systems a significant change in the mean distance between electrons and holes at the resonance is observed. By using the redistribution of the particle densities at the resonance position in modern quantum-dot experiments, the ICIR can provide a new technique for the control of the electron distribution in quantum dots and for the generation of single photons on demand.
We theoretically investigate the confinement-induced resonance for quasi-one-dimensional quantum systems under transversely anisotropic confinement, using a two-body sss-wave-scattering model in the zero-energy collision limit. We predict a single resonance for any transverse anisotropy, whose position shows a slight downshift with increasing anisotropy. We compare our prediction with the recent experimental result by Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)], in which two resonances are observed in the presence of transverse anisotropy. The discrepancy between theory and experiment remains to be resolved.
We report on the observation of confinement-induced resonances for strong three-dimensional (3D) confinement in a lattice potential. Starting from a Mott-insulator state with predominantly single-site occupancy, we detect loss and heating features at specific values for the confinement length and the 3D scattering length. Two independent models, based on the coupling between the center-of-mass and the relative motion of the particles as mediated by the lattice, predict the resonance positions to a good approximation, suggesting a universal behavior. Our results extend confinement-induced resonances to any dimensionality and open up an alternative method for interaction tuning and controlled molecule formation under strong 3D confinement.
We report on the observation of confinement-induced resonances for strong three-dimensional (3D) confinement in a lattice potential. Starting from a Mott-insulator state with predominantly single-site occupancy, we detect loss and heating features at specific values for the confinement length and the 3D scattering length. Two independent models, based on the coupling between the center-of-mass and the relative motion of the particles as mediated by the lattice, predict the resonance positions to a good approximation, suggesting a universal behavior. Our results extend confinement-induced resonances to any dimensionality and open up an alternative method for interaction tuning and controlled molecule formation under strong 3D confinement.