⚛️ quantum physics

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

This paper reports the experimental generation of large-amplitude squeezed coherent-state superpositions (squeezed cat states) on free-space optical pulses with an amplitude of $\alpha=2.47$ , achieving a record-breaking size and a fidelity of 0.53 through a protocol involving Fock state mixing and homodyne heralding, which represents a significant milestone for scalable fault-tolerant photonic quantum architectures.

Original authors: Lucas Caron, Hector Simon, Hugo Basset, Romaric Journet, Rosa Tualle-Brouri

Published 2026-01-15

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CC BY 4.0

Original authors: Lucas Caron, Hector Simon, Hugo Basset, Romaric Journet, Rosa Tualle-Brouri

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to build a computer that uses light instead of electricity. To make this computer powerful enough to solve the world's hardest problems, it needs to handle a very specific, tricky type of information. In the world of light, this information comes in the form of "quantum states."

Most of the time, light behaves in a smooth, predictable way (like a calm lake). But to build a truly powerful quantum computer, scientists need to create "non-Gaussian" states—think of these as light waves that have been twisted into complex, jagged shapes, like a stormy sea with distinct peaks and valleys. One of the most important shapes they need is called a "cat state."

The "Cat" Analogy

In quantum physics, a "cat state" is named after Schrödinger's famous thought experiment. It's a state where light is in two different conditions at the same time—like a cat that is both alive and dead simultaneously. In this experiment, the scientists created a "superposition" where a pulse of light is in two places at once: a bright pulse and a dark pulse, existing together.

The goal of this paper is to make these "cat states" bigger and more complex than ever before.

The Challenge: Making the Cat Bigger

Previously, scientists could only make these cat states very small (like a kitten). If you want to build a scalable quantum computer, you need a "big cat" (a large-amplitude state). The bigger the cat, the more useful it is for complex calculations.

The team at the Institut d'Optique in France managed to create a "cat state" with an amplitude of 2.47. To put this in perspective, this is the largest "cat" ever created in free space (light traveling through the air, not trapped in a chip). It's like going from a kitten to a full-grown lion in a single leap.

How They Did It: The "Mixing Bowl" Recipe

The scientists used a clever recipe involving two main ingredients:

Single Photons: Tiny packets of light (one photon).
Double Photons: Two packets of light stuck together (two photons).

Here is the step-by-step process, using a kitchen analogy:

The Ingredients: They generated a single photon and a two-photon packet.
The Mixing Bowl (Beam Splitter): They sent these two packets into a special "mixing bowl" (a tunable beam splitter). This device is like a magical fork in the road that splits and mixes the light paths. By adjusting the bowl just right, they could mix the single photon and the two-photon packet together in a precise way.
The "Herald" (The Bell): This is the most critical part. They didn't just mix them and hope for the best. They set up a detector on one side of the mixing bowl. When this detector "rang a bell" (detected a specific signal), it told them: "Success! The mixing worked perfectly on the other side."
- This is called heralding. It's like baking a cake and having a sensor tell you, "The cake is done," so you know the other side of the kitchen has the perfect cake ready to eat.
The Quantum Memory (The Freezer): Because the "bell" takes a tiny fraction of a second to ring, and the mixing happens incredibly fast, they had to catch the result and hold it. They used a "Quantum Memory Cavity" (a room with mirrors that bounce light back and forth) to store the light pulse for a brief moment (about 200 nanoseconds) while they prepared to measure it.

The Result: A Stormy Sea

When they finally looked at the light they created, they used a special imaging technique (called a Wigner function) to see its shape.

The Goal: They wanted to see three distinct "negative" valleys in the shape of the light. In quantum physics, seeing these negative valleys is the "smoking gun" proof that the light is behaving in a truly quantum, non-classical way.
The Outcome: Their "big cat" showed three clear, well-resolved negative regions. This confirmed they had successfully created a large, complex quantum state.

They achieved a "fidelity" (a measure of how close their result was to the perfect theoretical target) of 0.53. While this might sound like a test score, in the world of creating these complex states, it is a significant milestone, proving the method works.

Why This Matters (According to the Paper)

The paper states that this achievement is a major step toward a specific type of quantum computing architecture called GKP states (Gottesman-Kitaev-Preskill).

Think of GKP states as the "error-correcting code" for light-based computers. They are the safety net that allows the computer to fix mistakes automatically.
By creating these large "cat states" and showing they can be mixed and stored, the team has demonstrated the essential building blocks needed to eventually build these error-correcting codes.

Summary

In simple terms, these scientists built a machine that takes tiny bits of light, mixes them in a precise way, and uses a "bell" to signal when they have successfully created a giant, complex quantum shape. This shape is bigger than anything made before and looks exactly like the "stormy sea" pattern required to build the next generation of fault-tolerant quantum computers. They didn't just make a small ripple; they made a wave.

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

Problem and Context
The generation of non-Gaussian quantum states is a fundamental requirement for universal continuous-variable (CV) quantum information processing. While photonic platforms offer advantages such as room-temperature operation and modularity, fully unlocking their potential for fault-tolerant quantum computing requires the encoding of qubits in Gottesman–Kitaev–Preskill (GKP) states. These states enable universal computation using only Gaussian operations. Although recent progress has been made in on-chip generation and free-space production of increasingly complex non-Gaussian states (such as squeezed cat states), a significant gap remained in the amplitude of coherent-state superpositions (CSS) generated in free-space optical pulses. Previous free-space experiments had not exceeded an amplitude of $\alpha \approx 1.9$ .

Methodology
The authors report an experimental protocol for generating large-amplitude squeezed coherent-state superpositions (SCSS), also known as squeezed cat states, using free-space optical pulses. The core of the protocol involves the controlled mixing of Fock states $|1\rangle$ and $|2\rangle$ on a tunable beam splitter, followed by heralding via homodyne detection.

The experimental setup utilizes a mode-locked Ti:Sapphire laser (850 nm, 76 MHz) to drive a two-stage nonlinear process:

Resource Generation: A blue pump beam (425 nm) drives an optical parametric amplifier (OPA) to generate a two-mode squeezed vacuum (TMSV) state.
Heralding: One mode of the TMSV is filtered and detected by avalanche photodiodes (APDs). A single click heralds a single-photon Fock state ( $|1\rangle$ ), while simultaneous clicks herald a two-photon Fock state ( $|2\rangle$ ).
Quantum Memory Cavity (QMC): The other mode of the TMSV is directed into a low-loss optical cavity. A heralded single-photon state is stored in the QMC while the system waits for the heralding of a two-photon state.
Controlled Mixing: The stored $|1\rangle$ and the incoming $|2\rangle$ (carrying orthogonal polarizations) are mixed using a Pockels cell (PC) and a polarizing beam splitter (PBS). This assembly acts as a tunable beam splitter with reflectivity $R$ controlled by the PC-induced retardance $\delta$ .
Heralding Measurement: A homodyne detector (76% efficiency) performs a measurement on one output port. The state is post-selected based on a measurement outcome of $X=0$ (where $\hat{X} = (\hat{a} + \hat{a}^\dagger)/\sqrt{2}$ ).

To accommodate the bandwidth limitations of the homodyne detector (2 MHz) relative to the laser repetition rate (76 MHz), the generated state is stored in the QMC for approximately 195 ns (15 round trips) before extraction and characterization. Quantum state tomography (QST) is performed using a maximum-likelihood algorithm on a dataset of 16,339 quadrature measurements.

Key Contributions and Results
The primary contribution of this work is the experimental generation of free-space optical coherent-state superpositions with an amplitude of $\alpha = 2.47$ , which the authors state exceeds all previously reported values for free-space systems.

State Characterization: The reconstructed Wigner function of the generated state displays three well-resolved negative regions, a signature of strong non-Gaussianity.
Fidelity: The experimentally generated state achieves a fidelity of $F = 0.53^{+0.01}_{-0.06}$ with the target squeezed cat state defined as $\hat{S}(z)(|\alpha\rangle - |-\alpha\rangle)$ , with $\alpha = 2.47$ and a squeezing parameter $z = 0.56$ (corresponding to 4.82 dB of squeezing).
Optimization: Theoretical modeling indicated that the optimal beam splitter reflectivity for maximizing fidelity under realistic loss conditions is $R \approx 0.72$ . The experiment utilized a PC retardance of $\delta \approx 2.03$ rad to achieve this condition.
Generation Rate: The generation rate for the high-amplitude odd cat state is approximately 3.1 Hz. The authors note that increasing the storage time of the first photon allows for higher rates (e.g., 4.25 Hz) at the cost of reduced state fidelity due to storage losses.
Even Cat States: The protocol also produces even cat states when a single-photon state is heralded instead of a two-photon state, achieving a fidelity of $\sim 0.58$ with an even cat state of $\alpha = 1.71$ at a rate of $\sim 1$ kHz.

Significance
The authors position this result as a significant milestone for "temporal breeding protocols." By demonstrating the generation of large-amplitude SCSS in a free-space architecture with temporal multiplexing capabilities, the work lays the groundwork for the iterative generation of optical GKP states. The successful implementation of the necessary components for a two-step large-SCSS breeding protocol is presented as a step toward scalable and fault-tolerant photonic quantum architectures. The paper concludes that while technical improvements (such as replacing APDs with superconducting nanowire single-photon detectors and implementing real-time analysis) could further enhance performance, the current demonstration validates the feasibility of generating high-complexity non-Gaussian states required for advanced quantum information processing.