Confinement-induced resonance

A scattering resonance in a tightly confined quantum gas caused by coupling between transverse confinement modes and particle interactions. It can occur even when the underlying three-dimensional interaction is not resonant.

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Olshanii formula: A relation connecting the effective one-dimensional coupling constant to three-dimensional scattering length and transverse confinement. It predicts the confinement-dependent coupling divergence that defines the resonance.
Quantum waveguide: A structure that confines quantum particles in some directions while allowing propagation in others. The resonance is studied when particles move through a tightly confined waveguide.
Tonks–Girardeau gas: A one-dimensional gas of impenetrable bosons whose spatial correlations resemble those of free fermions. Strong repulsion near the resonance can drive a gas toward this regime.
Mikhail Olshanii: A theoretical physicist known for predicting confinement-induced resonance in a one-dimensional atomic waveguide. His calculation identified the resonance produced by transverse confinement.
Transverse mode: A quantized state of motion perpendicular to an elongated system’s free direction. Virtual excitation of higher transverse modes changes the effective scattering amplitude.
Quasi-one-dimensional system: A system confined strongly in two directions but with appreciable motion along a third. This geometry leaves transverse modes available to mediate the resonance.
Lieb–Liniger model: An exactly solvable model of one-dimensional bosons with contact interactions. The resonance provides experimental control over the model’s interaction strength.
Confinement-induced resonance in waveguides: The original setting in which transverse confinement was shown to produce a resonance in effective one-dimensional scattering. This formulation made the mode-coupling mechanism explicit.
Scattering length: A low-energy parameter that characterizes the strength and sign of two-body scattering. Its value and the confinement length determine where the effective one-dimensional interaction diverges.
Two-body scattering: The quantum collision of two particles, described by their incoming and outgoing states. The resonance is defined through a change in the effective two-particle scattering amplitude.