Generation of Large Coherent-State Superpositions in Free-Space Optical Pulses

TL;DR

This work addresses the challenge of producing non-Gaussian resources for universal continuous-variable quantum computation by generating large-amplitude squeezed coherent-state superpositions (SCSS) in free-space optical pulses. It uses heralded mixing of Fock states $|1\rangle$ and $|2\rangle$ on a tunable beam splitter, with homodyne heralding and a quantum memory cavity enabling temporal multiplexing, achieving an odd SCSS with amplitude $|\alpha| = 2.47$ and squeezing parameter $z = 0.56$ and fidelity $F = 0.53^{+0.01}_{-0.06}$ to the target $\hat{S}(z)(|\alpha\rangle - |-\alpha\rangle)$. The Wigner function of the generated state displays three negative regions, and the experiment demonstrates the viability of iterative breeding protocols toward optical GKP states, with a generation rate around a few hertz that can be increased with detector upgrades and real-time processing. This work thus advances scalable, fault-tolerant photonic architectures by providing a large, non-Gaussian resource in free-space settings and outlining practical routes to higher-rate GKP-state generation.

Abstract

The generation of non-Gaussian quantum states is a key requirement for universal continuous-variable quantum information processing. We report the experimental generation of large-amplitude squeezed coherent-state superpositions (squeezed cat states) on free-space optical pulses, reaching an amplitude of $α= 2.47$, which, to our knowledge, exceeds all previously reported values. Our protocol relies on the controlled mixing of the Fock states $|1\rangle$ and $|2\rangle$ through a tunable beam splitter, followed by heralding via homodyne detection. The resulting state displays three well-resolved negative regions in its Wigner function and achieves a fidelity of $0.53$ with the target state $\propto \hat{S}(z)(|α\rangle - |-α\rangle)$, with $α= 2.47$ and squeezing parameter $z = 0.56$. These results constitute a significant milestone for temporal breeding protocols and for the iterative generation of optical GKP states, opening new perspectives for scalable and fault-tolerant photonic quantum architectures.

Figures (10)

• Figure 1: Fock states $|1\rangle$ and $|2\rangle$ enter the two input ports of a beam splitter with amplitude reflectivity $r$ and transmissivity $t$, and a homodyne measurement is performed on one output port.
• Figure 2: Fidelity between the state $|\psi\rangle_{X=0}$ and the closest SCSS $\hat{S}(z)(|\alpha\rangle - |-\alpha\rangle)$ as a function of $R=r^2$ (blue). The corresponding cat-state amplitude $\alpha$ is shown in orange.
• Figure 3: Simulated fidelity with the closest SCSS $\hat{S}(z)(|\alpha\rangle - |-\alpha\rangle)$ as a function of $R=r^2$ (blue), and corresponding amplitude $\alpha$ (orange).
• Figure 4: Simplified schematic of the experimental setup, showing the main building-blocks: the resource state source, the QMC and the homodyne detection.
• Figure 5: Diagram of the different steps of one experimental cycle : (a) heralding of a $p$-polarized single photon, half-wave plate operation by the PC. (b) The single photon is stored inside the QMC. (c) A $p$-polarized $|2\rangle_p$ is heralded and the PC apply a $\delta$ retardance to the $|2\rangle_p|1\rangle_s$ state. (d) A quadrature measurement is performed on the output path. If the result is $X=0$, the state in the QMC is the targeted state.