Spin-orbit states of neutron wave packets

We propose a method to prepare an entangled spin-orbit state between the spin and the orbital angular momenta of a neutron wave packet. This spin-orbit state is created by passing neutrons through the center of a quadrupole magnetic field, which provides a coupling between the spin and orbital degrees of freedom. A Ramsey-fringe-type measurement is suggested as a means of verifying the spin-orbit correlations.

Figure 1

The probabilities for each of the $\ell =0,1,-1$ and $n_r=0,1$ states when a neutron wave packet with no OAM ($n_{r_i}={\ell }_i=0$) passes through a spiral phase plate with a topological charge $q$.

Figure 2

The coefficients $C_{n_r,\ell ,s}$ of the spin-orbit state for $n_r=0$ and $n_r=1$ as a function of $r_c/{\sigma }_{\perp }$. The input state is $n_{r_i}={\ell }_i=0$. The vertical line at $r_c/{\sigma }_{\perp }=1.82$ corresponds to the point of maximum concurrence for the $n_r=0$ subspace (see Fig. 3). Strong quadrupole fields correspond to $r_c\to 0$ while no quadrupole corresponds to $r_c\to \infty$.

Figure 3

Concurrence (on the left) of the spin-orbit state for the filtered $\eta =0,1,2$ subspaces, and the probability (on the right) of the given $\eta =0,1,2$ subspaces. The vertical line at $r_c/{\sigma }_{\perp }=1.82$ corresponds to the point of maximum concurrence for the $\eta =0$ subspace.

Figure 4

Concurrence of the spin-orbit state obtained by tracing the radial subspace. The vertical line at $r_c/{\sigma }_{\perp }=1.82$ corresponds to the point of maximum mixed state concurrence of 0.97. The concurrence does not go to 1 because the traced state is not pure.

Figure 5

The top figure is the setup for the spin-orbit Ramsey fringe experiment. The arrows on the magnets depict the quadrupole geometry. The bottom figure is the integrated intensity at the output for the spin-up and spin-down neutrons as a function of spin precession $\beta$ inside the solenoid. The rotation of the second quadrupole is set to $\theta =\pi$. An identical plot can be obtained when $\beta =\pi$ and the quadrupole rotation is varied. This variation of the intensity is an indication of the correlations between the spin and OAM. The phase induced by the spin rotation can be compensated by the rotation of the quadrupole.