Figure 4: Towards spin-projective measurement with a single detected photon.
From: Macroscopic rotation of photon polarization induced by a single spin
(a) Principle of projective quantum-non-demolition measurement with a single detected photon, provided the two output polarization states are orthogonal (that is, ‹Ψ⇓|Ψ⇑›=0, with |Ψ⇑› and |Ψ⇓› the polarization states associated to the spin states |⇑› and |⇓>, respectively). In this experiment, a half-wave plate (λ/2) and a quarter wave-plate (λ/4) are used to perform unitary transformations mapping states |Ψ⇑› and |Ψ⇓> into states |H> and |V›. The latter are then distinguished using a polarizing beam-splitter (PBS) and single-photon counters (SPCs). (b) Minimal value of |‹Ψ⇓|Ψ⇑›| achievable for a given set of device parameters C and κ1 /κ (analytic calculations, see Supplementary Note 3): the ideal configuration ‹Ψ⇓|Ψ⇑›=0 can be obtained for a large range of parameters, represented by the white area. The parameters of the current device are represented by a white circle at κ1/κ=0.4 and C=0.2. (c) Maximal value of the mode reflectivity Rm achievable under the condition that ‹Ψ⇓|Ψ⇑›=0. The white circles indicate two sets of parameters (κ1/κ=0.66, C=0.3) and (κ1/κ=0.9, C=2.5). Increasing mode reflectivities are obtained when the device is further optimized. The hatched region corresponds to parameters for which the orthogonality condition can not be achieved.
