Squeezing the Efimov effect

Abstract

The quantum mechanical three-body problem is a source of continuing interest due to its complexity and not least due to the presence of fascinating solvable cases. The prime example is the Efimov effect where infinitely many bound states of identical bosons can arise at the threshold where the two-body problem has zero binding energy. An important aspect of the Efimov effect is the effect of spatial dimensionality; it has been observed in three dimensional systems, yet it is believed to be impossible in two dimensions. Using modern experimental techniques, it is possible to engineer trap geometry and thus address the intricate nature of quantum few-body physics as function of dimensionality. Here we present a framework for studying the three-body problem as one (continuously) changes the dimensionality of the system all the way from three, through two, and down to a single dimension. This is done by considering the Efimov favorable case of a mass-imbalanced system and with an external confinement provided by a typical experimental case with a (deformed) harmonic trap.

11 pages, 4 figures, comments are most welcome

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Observation of an Efimov spectrum in an atomic system
• Observation of universality in ultracold 7Li three-body recombination
• Observation of an Efimov-like resonance in ultracold atom-dimer scattering
• Observation of heteronuclear atomic Efimov resonances
• Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance
• Radio Frequency Association of Efimov Trimers
• Universal Fermi gases in mixed dimensions
• Universal properties of Fermi gases in arbitrary dimensions
• Observation of Efimov molecules created from a resonantly interacting Bose gas
• Heteronuclear Efimov scenario with positive intraspecies scattering length
• Universal low-energy properties of three two-dimensional particles
• Universal three-body parameter in ultracold 4He*
• Weakly bound states of two- and three-boson systems in the crossover from two to three dimension

Cited by in corpus (22)

• Feshbach resonances in $p$-wave three-body recombination within Fermi-Fermi mixtures of open-shell ${}^6$Li and closed-shell ${}^{173}$Yb atoms
• A Pure Confinement Induced Trimer in One-Dimensional Atomic Waveguides
• Efimov effect in $D$ spatial dimensions in $AAB$ systems
• Few-body quantum method in a $d$-dimensional space
• Universality in a one-dimensional three-body system
• Confinement of two-body systems and calculations in $d$ dimensions
• Three identical bosons: Properties in non-integer dimensions and in external fields
• Efimov effect in a $D$-dimensional Born-Oppenheimer approach
• Efimov states of three unequal bosons in non-integer dimensions
• D-dimensional three-body bound-state problem with zero range interactions
• Efimov effect in non-integer dimensions induced by an external field
• Universality of excited three-body bound states in one dimension
• Efimov resonance position near a narrow Feshbach resonance in ${}^6$Li-${}^{133}$Cs mixture
• Three-body continuum states and Efimov physics in non-integer geometry
• Correlated Gaussian Approach to Anisotropic Resonantly Interacting Few-Body Systems
• Dimensional crossover in non-relativistic effective field theory
• Long-lived trimers in a quasi-two-dimensional Fermi system
• Confinement of $N$-body systems and non-integer dimensions
• Two-body continuum states in non-integer geometry
• Dimensional effects in Efimov physics
• Emergence of N-body tunable interactions in universal few-atom system
• Few-body techniques using momentum space for bound and continuum states