Pure confinement-induced trimer in one-dimensional atomic waveguides

Shallow trimers composed of three bosonic atoms in one-dimensional harmonic waveguides are studied in the vicinity of a Feshbach resonance. It is shown that for arbitrarily large values of the one-dimensional scattering length, an excited trimer branch exists in coexistence with the dimer and the trimer of the Lieb-Liniger model.

Figure 1

Solid line: relative difference between the lowest quasi-1D trimer obtained from Eq. (4) and the McGuire trimer as a function of the small parameter ${(a_{\perp }/a_{1\mathrm{D}})}^2$ in the vicinity of the dimer threshold. Dashed line: asymptotic law from Eq. (10).

Figure 2

Rescaled relative binding energy of the pure confinement-induced trimer as a function of the small parameter ${(a_{\perp }/a_{1\mathrm{D}})}^2$ in the vicinity of the dimer threshold. Solid line: spectrum of the excited state of Eq. (4). Dashed line: analytical result of Eq. (18).

Figure 3

Solid line: trimer spectrum in the waveguide as a function of the external magnetic field obtained for the ratio $a_{\perp }/\epsilon =20$ in the case of the FR at $B_0\sim -11.7$ G for cesium atoms; dashed line: energy of one dimer and one atom at rest in the waveguide; crosses: 3D Efimov spectrum; dotted lines: thresholds of the three-body continuum without the waveguide ($E=0$) and with the waveguide ($E=2\hslash \omega$). Plot (a): zoom for the details of the spectrum near the three-body continuum at $E=2\hslash \omega$; plot (b): lower part of the spectrum. The parameter $\epsilon$ is the van der Waals length (see text).