Quantum state engineering via coherent-state superpositions in traveling optical fields

We propose two experimental schemes for producing coherent-state superpositions which approximate different nonclassical states conditionally in traveling optical fields. Although these setups are constructed of a small number of linear optical elements and homodyne measurements, they can be used to generate various photon number superpositions in which the number of constituent states can be higher than the number of measurements in the schemes. We determine numerically the parameters to achieve maximal fidelity of the preparation for a large variety of nonclassical states, such as amplitude squeezed states, binomial states, squeezed cat states, and various photon number superpositions. The proposed setups can generate these states with high fidelities and with success probabilities that can be sufficient for practical applications.

Figure 1

Experimental scheme for generating superpositions of coherent states on a straight line or on a lattice.

Figure 2

Experimental scheme with two homodyne measurements for generating superpositions of coherent states on a straight line or on a lattice.

Figure 3

The minimized misfit between the approximating coherent-state superposition and the original squeezed vacuum state as a function of the number of constituent states $N$ in the superposition for different values of the real squeezing parameter $r$.

Figure 4

The average misfit ${\varepsilon }_{\text{avg}}$ as a function of the overall probability $P$ for the cat state ${\left|2.5,0\right.〉}_{\mathrm{SC}}$ approximated along a line in the scheme presented in Fig. 1.