Figure 1

Schematic diagram of a photon-number quantum-nondemolition detector based on a cross-Kerr optical nonlinearity [12]. The two inputs are a Fock state $\mid n_a⟩$ (with $n_a=0$, 1,… in the signal mode $a$ and a coherent state with real amplitude ${\alpha }_c$ in the probe mode $c$. The presence of photons in mode $a$ causes a phase shift on the coherent state $\mid {\alpha }_c⟩$ directly proportional to $n_a$ which can be determined with a momentum quadrature measurement.Reuse & Permissions

Figure 2

Schematic diagram of a polarization-preserving photon-number quantum-nondemolition detector based on a pair of identical cross-Kerr optical nonlinearities. The signal mode is a Fock state with an unknown polarization, which is resolved into orthogonal polarization states by a polarizing beam splitter. The phase shift applied to the probe mode is proportional to $n_a$, independent of the polarization of the signal mode.Reuse & Permissions

Figure 3

Schematic diagram of the interaction between a four-level $\mathcal{N}$ atom and a nearly resonant three-frequency electromagnetic field. We note that the annihilation of a photon of frequency ${\omega }_k$ is represented by the complex number ${\Omega }_k$.Reuse & Permissions

Figure 4

Plot of the minimum number of NV-diamond color centers needed to generate the phase shift ${\theta }_{\max }$ for three different values of the error probability $P_{\text{error}}$ in the case $n_a=1$. We have chosen $⟨n_b⟩=10⟨n_c⟩$, requiring a minimum detuning ${\nu }_{c\min }∕{\gamma }_2=1.1$.Reuse & Permissions