Conditional production of superpositions of coherent states with inefficient photon detection

It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude $(\alpha >2)$ and high fidelity $(F>0.99)$. In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.

Figure 1

A schematic of the non-deterministic CSS-amplification process. See the text for details.

Figure 2

The success probabilities of the CSS-amplifying process in Fig. 1 for the input fields of two identical odd CSSs (solid line), two identical even CSSs (dashed line), and even and odd CSSs (dotted line).

Figure 3

The fidelity between an odd CSS and squeezed single photon. The odd CSS is extremely well approximated by the squeezed single photon for a small coherent amplitude, $\alpha ⩽1.2$.

Figure 4

(a) The maximum fidelity obtained in our scheme vs the coherent amplitude. (b) The number of iterations which gives the maximum fidelity vs the coherent amplitude.