Macroscopic Single-Qubit Operation for Coherent Photons

Polarisation is described by an $SU(2)$ wavefunction due to macroscopic coherence of photons emitted from a ubiquitous laser source, and thus, a laser pulse is expected to behave as a macroscopic quantum bit (qubit), i.e., a qubit realised by a macroscopic number of photons. Here, we show that an arbitrary single-qubit operation can be carried out for such a macroscopic qubit by employing optical modulators, together with standard optical plates, in a computer-controlled fibre-optic configuration. We named the device as a Poincar\'e rotator, which allows a dynamic control over a polarisation state by executing an arbitrary amount of rotations on the Poincar\'e sphere. The Poincar\'e rotator works as an arbitrary $SU(2)$ operator in a Lie group, by combining a $U(1)$ operation to change the phase and another $U(1)$ operation to change the amplitude of the wavefunction. We have realised various polarisation states, such as $4 \times 4=16$, $8 \times 8=64$, and $10 \times 10=100$ distinguishable states on the sphere. As a locus of the realised polarisation states on the sphere, we have successfully drawn the molecular structure of Buckminsterfullerene (C$_{60}$) and the coastline of the earth.