Generation of a Superposition of Odd Photon Number States for Quantum Information Networks

We report on the experimental observation of quantum-network-compatible light described by a nonpositive Wigner function. The state is generated by photon subtraction from a squeezed vacuum state produced by a continuous wave optical parametric amplifier. Ideally, the state is a coherent superposition of odd photon number states, closely resembling a superposition of weak coherent states $|\alpha ⟩-|-\alpha ⟩$. In the limit of low squeezing the state is basically a single photon state. Light is generated with about 10 000 and more events per second in a nearly perfect spatial mode with a Fourier-limited frequency bandwidth which matches well atomic quantum memory requirements. The generated state of light is an excellent input state for testing quantum memories, quantum repeaters, and linear optics quantum computers.

Figure 1

Experimental setup: SHG, second harmonic generator; OI, optical isolator (to prevent scattered LO light from entering the OPO); $\lambda /2$, half-wave plate; PBS, “magic” beam splitter; PZT, piezomounted mirror; HD, homodyne detector; IF, interference filter; APD, avalanche photodiode. The inset shows the squeezing spectrum obtained from a Fourier analysis of the raw data. The blue curve is the best fit of the theoretical spectrum. The fitted parameters (OPO gain 2.3, and total efficiency ${\eta }_t=0.56$) match well the experimentally estimated values.

Figure 2

Part of a typical trace obtained after application of the temporal mode function (shown in the inset) to each of the 20 000 raw data segments. Each segment of raw data is multiplied by the mode function and integrated, producing one (phase, quadrature) point for the trace. The phase of the LO has been scanned at roughly $1\pi /\mathrm{s}$. The temporal mode function is shifted with respect to the APD click due to the delay in electronics.

Figure 3

Panels (a) and (b) show the density matrices and Wigner functions (including a top-down contour plot) reconstructed from experimental data. (a) The OPO gain 1.8, (b) gain 2.3. The presented plots are averages of 50 separate states, each reconstructed from a 20 000 points quadrature trace as explained in the text and corrected for the 85% detector efficiency. (c) State calculated from full multimode theory with the same temporal mode function and the same overall propagation efficiency $\eta =0.64$ as for the experimental state (b). (d) State calculated with perfect efficiency $\eta =1$.