State transfer based on classical nonseparability

We present a state-transfer protocol that is mathematically equivalent to quantum teleportation but uses classical nonseparability instead of quantum entanglement. In our implementation we take advantage of nonseparability among three parties: orbital angular momentum (OAM), polarization, and the radial degrees of freedom of a beam of light. We demonstrate the transfer of arbitrary OAM states, in the subspace spanned by any two OAM states, to the polarization of the same beam.

Figure 1

Three examples of classical nonseparability. The left panel represents a beam for which the radial and orbital angular momentum ($l=3$) degrees of freedom are nonseparable. The middle panel shows a beam for which the orbital angular momentum ($l=1$) and polarization are nonseparable. The panel on the right represents a beam for which radial and polarization degrees of freedom are nonseparable.

Figure 2

Transfer of an arbitrary OAM state to a polarization. The intensity is encoded in the brightness, the phase in the color. The OAM information can be read from the phase profile. For simplicity we have depicted a pure OAM superposition of $|\pm 3\rangle$. (Top) The initial beam: OAM is separable from the other two DoFs and the polarization and radial DoFs are maximally nonseparable. (Bottom, right) After projection on a maximally nonseparable state of OAM and radial, we end up with a polarization state that carries the same information as the initial OAM state. The intensity of each of polarization gives information about the amplitude of each of the two OAM components, and the phase between the two polarizations, $H$ and $V$, is the same as the phase between the two OAM components. (Bottom, left) The two angles $\xi$ and $\eta$ are half of the spherical angles on the Poincarè sphere, respectively.

Figure 3

The setup to implement the state transfer from OAM to the polarization DoF; the beam emerging from a single-mode fiber is collimated and shined onto a spatial light modulator (SLM1). The beam emerging from the SLM1 has two rings with identical azimuthal phase profiles (OAM states). Using a polarizer and a small half-wave plate (Bell-state synthesizer), orthogonal polarizations are introduced onto the two rings. To implement projection onto a radial-OAM maximally nonseparable state, we divide the surface of SLM2 into two parts. The beam is first shined onto one half of SLM2, where we have impressed a phase screen that has two rings with opposite OAM values. Then we use a half-wave plate to rotate the polarization of the beam 90 deg and then shine the light on the second half of SLM2. This combination allows us to perform polarization-insensitive projections onto the radial-OAM maximally nonseparable state. To complete the projection we use a pinhole to separate the projected light and then use different combinations of a quarter-wave plate and a polarizer to measure the Stokes parameters.

Figure 4

Fidelity of state transfer for different states. All OAM states are in the subspace spanned by $l=\pm 10$. The three last states are mixed states. For brevity of notation, we have shown the un-normalized states.