Multichannel scattering resonance of one-dimensional ultracold spinor bosons

So far, the interaction of ultracold atoms can only be tuned within one particular scattering channel near a resonance, where the spinor structure of atomic isotopes is destroyed due to the typically large magnetic field. In this work, we propose a scheme to realize multichannel scattering resonance (MCSR) of ultracold bosons in one-dimension while still keeping their spinor structure. The MCSR refers to a simultaneous scattering resonance among all different scattering channels, including those breaking SU(2) and SO(2) spin-rotation symmetries. Essential ingredients for MCSR include the three-dimensional interactions, the confinement potential, and a spin-flipping field. Near MCSR a many-body spinor system exhibits exotic spin-density distributions and pair correlations, which are significantly different from those near a single-channel resonance.

Figure 1

Schematic plots of virtual scattering processes involving higher excited modes (a) without or (b and (c) with rf field. $u_{11}$, $u_{10}$, and $u_{1,-1}$ are renormalized through the processes in (a), (b), and (c), respectively.

Figure 2

Multichannel scattering resonances with tunable $a_1$ and fixed $a_0=a_{-1}=a_{\perp }/4$ [24]. $\Omega$ is scaled by ${\omega }_{\perp }$, and $u_{11}$ and $u_{10}$ are scaled by $2/\left(m{\omega }_{\perp }\right)$. (a) Resonance position ${\Omega }_{\mathrm{res}}$ as a function of $a_{\perp }/a_1$. $u_{11}$ and $u_{10}$ as functions of (b1) and (b2) $\Omega$ at fixed $a_{\perp }/a_1=1.6$ and (c1) and (c2) $a_{\perp }/a_1$ at fixed $\Omega =0.1{\omega }_{\perp }$, corresponding to the blue vertical and horizontal arrows in (a), respectively. For comparison, CIR predictions [17] are shown by dashed lines.

Figure 3

Virtual bound-state energies $E_Q$ (shifted by $E_{th})$ as a function of (a) $\Omega$ at fixed $a_{\perp }/a_1=1.6$ and (b) $a_{\perp }/a_1$ at fixed $\Omega =0.1{\omega }_{\perp }$. Here (a) and (b) follow the vertical and horizontal arrows in Fig. 2, respectively. $E_Q$ and $\Omega$ are scaled by ${\omega }_{\perp }$.

Figure 4

(a1) Diagonal and (a2) off-diagonal matrix elements of $u$ as a function of $a_{\perp }/a_1$ at fixed $\Omega =0.1{\omega }_{\perp }$. The other parameters, $a_0=a_{-1}=a_{\perp }/4$, are the same as those in Fig. 2. Insets show magnified plots of $u$-matrix elements except for $u_{11}$ and $u_{10}$. (b) Resonance widths $W_{MN}$ defined in Eq. (21). $u$ elements and $W_{MN}$ are both scaled by $2/\left(m{\omega }_{\perp }\right)$.

Figure 5

(left) Spin densities [in units of $1/a_T$, $a_T={\left(m{\omega }_T\right)}^{-1/2}]$ and (right) correlation functions (in units of $1/a_T^2)$ for four trapped bosons in 1D. $z$ is in units of $a_T$. The parameters $(u_{11}/\left(a_T{\omega }_T\right),u_{10}/\left(a_T{\omega }_T\right),\Omega /{\omega }_T)$, are (a1) and (b1) $(12,0,0)$, (a2) and (b2) $(12,0,1)$, (a3) and (b3) $(12,2\sqrt{2},1)$, and (a4) and (b4) $(12,4\sqrt{2},1)$. For comparison, gray curves in (a1) and (b1) show the case with identical fermions (see text), and (a2)–(a4) show the density distribution of noninteracting bosons.