Resonant quantum dynamics of neutral spin-1 particles in a magnetic guide

We investigate the resonant quantum motion of spin-1 particles in a magnetic guide. A symmetry analysis is undertaken in order to reveal the complex symmetry properties of the system which lead to a twofold degeneracy in the energy-level spectrum. Lifetimes and energies of the resonance states are computed by employing the complex scaling method. By analyzing several hundreds of resonances we are able to make conclusions about the global properties of the resonance spectrum. The effect of an Ioffe field which is applied parallel to the guide is also discussed. We observe a global increase of the lifetimes with increasing Ioffe-field strength. For certain parameter regimes we find the ground-state resonance to exhibit a longer lifetime than the energetically neighbored excited states. The latter could have interesting implications on the time evolution of trapped ultracold atomic ensembles. Applications of our results to calculate the resonance energies andlifetimes of the trapped alkali-metal atoms ${}^7\mathrm{Li}$ and ${}^{87}\mathrm{Rb}$ are outlined.

Figure 1

(Color online) Resonance energies and decay widths in the absence of an Ioffe field. The red lines connect resonances which belong to the same $m$ manifold. The left-hand side of the pattern is defined by the energetically lowest resonances of the individual $m$ manifolds.

Figure 2

(Color online) Resonance distribution for three different values of the Ioffe field parameter $\gamma$. Compared to the $\gamma =0$ case the pattern is significantly altered. The formally degenerate states are now energetically separated with the splitting being determined by the Ioffe-field parameter $\gamma$. The higher the modulus of $m$, the smaller the energetic splitting becomes. High-$m$ states are less affected by the Ioffe field. (The positive values, shown underneath the negative values, are represented by dashed lines.)

Figure 3

(Color online) Decay width of the ground-state resonance for selected values of the scaled Ioffe-field strength $\gamma$. Apparently the Ioffe field has a stabilizing effect on the trapped states.

Figure 4

(Color online) Decay width of the ground-state resonance plotted against the ${\Lambda }_z$ eigenvalue $m$ for $\gamma =0$. An exponential decrease of the decay width is observed if $m$ is increased. A corresponding fit (red line) yields $\Gamma \approx 0.490e^{-0.575\mid m\mid }$.

Figure 5

(Color online) Resonance energies vs ${\Lambda }_z$ eigenvalue $m$. The minimal resonance energy in the different $m$ subspaces increases approximately linearly with $\mid m\mid$. For $\gamma =0$ the global ground state is located in the $m=0$ subspace whereas for $\gamma =4$ it is found in the $m=-1$ subspace.

Figure 6

(Color online) The unitary transformation (28) rotates the spin vector into the direction of the local magnetic field. The field vector thereby constitutes a local quantization axis.