Filtration and extraction of quantum states from classical inputs

We propose using a nonlinear Mach-Zehnder interferometer (NMZI) to efficiently prepare photonic quantum states from a classical input. We first analytically investigate the simple NMZI that can filtrate a single-photon state from weak coherent state by preferentially blocking a two-photon component. As a generalization, we show that the cascaded NMZI can deterministically extract an arbitrary quantum state from a strong coherent state. Finally, we numerically demonstrate that the cascaded NMZI can be very efficient in both the input power and the level of cascade. The protocol of quantum state preparation with the NMZI can be extended to various systems of bosonic modes.

Figure 1

(a) Schematic of the arbitrary quantum state filtration and extraction from the coherent state input. (b) The configuration for QSF of a single photon from coherent-state input $|\alpha \rangle$ using the simple NMZI (consisting of a Mach-Zehnder interferometer, a Kerr medium, and a phase shifter). (c) Three processes for two-photon output of path A for weak coherent input. (d) The probabilities of $n$-photons' output of path A against the phase difference between two arms $\varphi$ with $\phi =0.1$ and $\alpha =0.1$. (e) The second-order correlation function $\left(g^{\left(2\right)}\right)$ of light output of path A against $\varphi$ for various $\phi$'s with $\alpha =0.1$. The solid and dashed lines are obtained by the exact numerical and approximated analytical solutions, respectively.

Figure 2

Cascaded NMZI. (a) The basic element consists of a BS $\left(\theta \right)$ followed by a linear phase shifter $\left(\varphi \right)$ and a Kerr medium $\left(\phi \right)$ in the upper path. (b) Schematic of the element for cascaded NMZI. (c) Fidelity of the single-photon extraction increases with the number of cascade elements $N$. The parameters are optimized numerically under the constraint $P_{n\ge 2}<0.01$ with $\phi =0.1$. (d) Fidelity of a Fock state extraction $\left(n=1\text{–}3\right)$ increase with ${\left|\alpha \right|}^2$ for cascaded NMZI with $N=40$. The results are obtained by optimizing the parameters of each unit under the constraint that $1-P_0-P_n\le 0.01$.

Figure 3

QSE for $|{\psi }_{\mathrm{target}}\rangle =\left(\right|0\rangle +|1\rangle )/\sqrt{2}$. (a) The probability of $|0\rangle$ and $|1\rangle$, (b) the fidelity $\left(F\right)$ and purity $\left(Q\right)$ of the output. The results are obtained by optimizing the parameters of a chain of $N=20$ units under the constraint that $1-P_0-P_1\le 0.01$.