Experimental Generation of Squeezed Cat States with an Operation Allowing Iterative Growth

We present what is, to our knowledge, the first implementation of a “cat breeding” operation, which allows an iterative growth of cat states. We thus report the experimental generation of a squeezed cat state from two single photon Fock states, which can be seen as cat states with zero amplitude. These Fock states are mixed on a symmetrical beam splitter, and the generation is heralded by a homodyne measurement in one of the two output arms. The output state has a fidelity of 61% with an even squeezed cat state of amplitude $\alpha =1.63$. This hybrid operation opens up new prospects in quantum optics, as the protocol depicted here can be iterated in order to produce new kinds of mesoscopic states.

Figure 1

Setup for the generation of an even squeezed cat state.

Figure 2

Experimental setup for the generation of squeezed cat states. (a) Setup for the generation of the two single photon Fock states $|1⟩$ and the local oscillator (LO). SHG: second harmonic generation, OPA: optical parametric amplifier, F: spectral filter, SPCM: single photon counting module. (b) The breeding operation involved in the left figure. HD: homodyne detection, BB: breeding beam splitter. The phase stabilization is performed with piezo mounted mirrors, symbolized by prisms at variable insertions in the figure.

Figure 3

(Top row) 2D histograms of the experimental distributions of quadrature points. (Bottom row) Theoretical probability distributions of the homodyne points. Both are plotted for a relative phase between the two homodyne detections of (a) 90°, (b) 120°, (c) 150°, and (d) 180°. $x_0$: points measured by HD0, $x_1$: points measured by HD1.

Figure 4

Reconstructed Wigner function of the produced state, with 77% detection efficiency correction. (Inset left) Wigner function (7) obtained with the model (3) of imperfections ($\sigma =1.02$ and $\delta =1.17$). (Inset right) Wigner function of the expected state (squeezed CS of amplitude $\alpha =1.63$ and squeezed by a factor of $s=1.52$).