Confinement-Induced Resonances in low-dimensional Systems

Institut für Experimentalphysik,
University of Innsbruck, and
Austrian Academy of Sciences,
Innsbruck, Austria

Confinement-Induced Resonances

Most many-body effects change drastically with the number of spatial dimensions available for particle motion. Reducing the dimensionality introduces new phase transitions and serves as a testing ground for theoretical models. In experiments with ultracold gases it is possible to reduce the dimensionality of the system by means of steep optical potentials and to freeze out the particle motion along one or two directions. Such quasi-2D or quasi-1D systems can be realized when the kinetic and the interaction energy of the particles are insufficient to transfer the particles to transversally excited energy levels.


An important requirements to study effects of many-body physics is the ability to tune interparticle interactions. In low-dimensional systems scattering properties are strongly effected by the confining potential, unlike in 3D geometry, where the tuning of interaction is commonly achieved by means of magnetic Feshbach resonances. Whereas the confinement removes motional degrees of freedom, it also provides an additional structure of discrete energy levels that can be used to modify scattering along the unconfined direction and by this to effectively control the interaction properties of the low-dimensional system. Those so-called “confinement-induced resonances” (CIRs) were first predicted by Maxim Olshanii in 1998 [1]. They are caused by a coupling between the incident channel of two incoming particles and a transversally excited molecular state.


lattice beams CIR

Figure 1, An array of 1D systems (red) is formed by interfering two retro-reflected laser beams. We confine the atoms to an array of approximately 3000 independent, horizontally oriented elongated 1D tubes.


In the experiment, we load a Bose-Einstein condensate of cesium atoms into a 2D lattice formed by two retro-reflected lattice beams (Figure 1) and we study the properties of CIRs by measuring particle loss [2]. A typical loss signature is shown in Figure 2 (blue data points). Close to the position of the confinement-induced resonance we observe a abrupt enhancement of atomic loss, followed by a gradual recovery. As we change the relative power in the two lattice beams, we observe a second loss minimum, which we attribute to creation of second confinement induced resonance. The formation of such a double resonance can be explained by the loss of degeneracy of the transversal harmonic oscillator levels [2]. Surprisingly, for strongly anisotropic confinement we observe a broad spectrum of confinement-induced resonances, one of which even persists in the limit of a two-dimensional system [2].


splitting of a CIR

  Figure 2, Loss signature close to a confinement induced resonance. The total atom number is given after a hold time of 200 ms for isotropic and anisotropic transversal confinement.  


top, left to right

Elmar Haller, Johann G. Danzl, Russell Hart, Manfred J. Mark

bottom, left to right
Mattias Gustavsson, Hanns-Christoph Nägerl
, Lukas Reichsöllner

Vladimir Melezhik

Vladimir Melezhik
Bogoliubov Laboratory of Theoretical Physics (Dubna, Russia)


Peter Schmelcher

Peter Schmelcher,

Zentrum fuer Optische Quantentechnologien Universität Hamburg (Germany)


[1]  Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons
M. Olshanii, Phys. Rev. Lett. 81, 938 (1998)  


[2]  Confinement-Induced Resonances in Low-Dimensional Quantum Systems
E. Haller, M.J. Mark, R. Hart, J.G. Danzl, L. Reichsöllner, V. Melezhik, P. Schmelcher, H.-C. Nägerl
Phys. Rev. Lett. 104, 153203 (2010)



Photos for download: ultracold media photos

see also: Super Tonks Girardeau gas

Scattering in confined geometries



The experiments are supported by the START-prize of the Bundesministerium für Wissenschaft und Forschung (BMWF) and the Austrian Science Fund (FWF) .

last change: 10-05-2010 by EH