Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum

We have created heralded coherent-state superpositions (CSSs) by subtracting up to three photons from a pulse of squeezed vacuum light. To produce such CSSs at a sufficient rate, we used our high-efficiency photon-number-resolving transition edge sensor to detect the subtracted photons. This experiment is enabled by and utilizes the full photon-number-resolving capabilities of this detector. The CSS produced by three-photon subtraction had a mean-photon number of $2.{75}_{-0.24}^{+0.06}$ and a fidelity of $0.{59}_{-0.14}^{+0.04}$ with an ideal CSS. This confirms that subtracting more photons results in higher-amplitude CSSs.

Figure 1

Scheme for optical CSS creation. An up-converted laser pulse enters an optical parametric amplifier (OPA) to create a squeezed vacuum state in section (A). After spectral filtering, this state is sent to a weakly reflecting beam splitter R in (B). Reflected photons that are detected herald a CSS emerging from R into (C). Its quadratures are measured by homodyne detection in (C).

Figure 2

Maximum-likelihood estimate of an odd CSS generated by one-photon subtraction from a squeezed vacuum. The graph shows the unitless Wigner function value $W(q,p)$ as a function of the unitless quadratures of the electromagnetic field.

Figure 3

Wigner functions of the maximum-likelihood estimates of even CSS created by two-photon subtraction and heralded with (a) one transition edge sensor and (b) two multiplexed APDs.

Figure 4

Maximum-likelihood estimate of an odd CSS after the subtraction of three photons from a squeezed vacuum. The reconstructed state has a fidelity of $F=0.{592}_{-0.142}^{+0.036}$ with a CSS of amplitude $\left|\alpha \right|=1.{76}_{-0.19}^{+0.02}$. Inset, Wigner function of an ideal odd CSS with $\left|\alpha \right|=1.76$.