Exploring a New Regime for Processing Optical Qubits: Squeezing and Unsqueezing Single Photons

We implement the squeezing operation as a genuine quantum gate, deterministically and reversibly acting “online” upon an input state no longer restricted to the set of Gaussian states. More specifically, by applying an efficient and robust squeezing operation for the first time to non-Gaussian states, we demonstrate a two-way conversion between a particlelike single-photon state and a wavelike superposition of coherent states. Our squeezing gate is reliable enough to preserve the negativities of the corresponding Wigner functions. This demonstration represents an important and necessary step towards hybridizing discrete and continuous quantum protocols.

Figure 1

Experimental setup. BS($T$), beam splitter with transmittance $T$ determining the degree of squeezing; OPO, optical parametric oscillator; SC, separating cavity; FC, filter cavity; APD, avalanche photo diode; HD, homodyne detector; LO, optical local oscillator; EOM, electro-optic modulator; CC, classical channel; R, reflectivity. An optical delay line of about 12 m, traveling in free space, is used to match the propagation times of the two signals, one of which gets converted to an electrical signal and back, while the other one remains optical throughout.

Figure 2

Experimental quantum states for the conversion from particle to wave. The leftmost column shows the input single-photon state, while the other three columns show the output states for a squeezing parameter $\gamma$ of 0.26, 0.37, and 0.67, from left to right. (a) Quadrature distributions over a period. (b) Wigner functions. (c) Photon number distributions and photon number representation of density matrices. The minimum value of $-0.22$ for the input Wigner function becomes, respectively, $-0.15$, $-0.12$, and $-0.06$, after the conversion.

Figure 3

Experimental quantum states for the conversion from wave to particle. The left column shows the input coherent-state superposition, while the right column shows the output state for a squeezing parameter $\gamma$ of $-0.26$. (a) Quadrature distributions over a period. (b) Wigner functions. (c) Photon number distributions and photon number representation of density matrices. The minimum value of $-0.16$ for the input Wigner function becomes $-0.10$ after the conversion.