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Tunable passive squeezing of squeezed light through unbalanced double homodyne detection

This paper demonstrates that unbalanced double homodyne detection can actively manipulate and characterize quantum states by using the beamsplitter's reflectivity as a tunable parameter to perform effective squeezing or anti-squeezing transformations on the measured Husimi Q function.

Original authors: Niels Tripier-Mondancin, David Barral, Ganaël Roeland, Raúl Leonardo Rincon Celis, Yann Bouchereau, Nicolas Treps

Published 2026-01-26

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CC BY 4.0

Original authors: Niels Tripier-Mondancin, David Barral, Ganaël Roeland, Raúl Leonardo Rincon Celis, Yann Bouchereau, Nicolas Treps

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 take a perfect photograph of a tiny, invisible, wiggly object made of light. In the world of quantum physics, this object is a "quantum state," and to understand it, scientists usually need to take many different pictures from different angles and then use a computer to reconstruct the 3D shape. This process, called "tomography," is like trying to figure out what a statue looks like by only looking at its shadow from one side at a time; it takes a long time and requires complex math to put the pieces together.

This paper introduces a clever new trick that changes how we take these pictures. Instead of just being a passive camera that records what's there, the scientists made their camera an active participant that can reshape the object while it is taking the picture.

Here is the breakdown of their discovery using simple analogies:

1. The Standard Camera (Balanced Detection)

Normally, scientists use a tool called "double homodyne detection." Think of this as a special camera that splits a beam of light in half and takes two photos at once: one showing the light's "height" (amplitude) and one showing its "speed" (phase).

The Problem: Because of the laws of quantum physics (specifically the Heisenberg uncertainty principle), you can't measure both perfectly at the same time without adding some "static" or "noise" to the image.
The Result: This standard setup gives you a blurry map (called the Husimi Q function) of the light. It's a good map, but it's just a snapshot of what the light looks like naturally.

2. The Magic Lens (Unbalanced Detection)

The authors asked: What if we didn't split the light beam exactly in half?
Imagine you have a pair of sunglasses that you can tilt. If you tilt them just right, they don't just darken the view; they stretch the image horizontally or vertically.

The Trick: The team built a setup where they intentionally split the light beam unevenly (using a special "unbalanced" splitter).
The Effect: By changing how much light goes one way versus the other (tuning a knob called "reflectivity"), the camera itself acts like a stretching lens.
- If you tilt the knob one way, the camera stretches the "height" of the light wave and squishes the "speed."
- If you tilt it the other way, it does the opposite.
- If you find the perfect middle spot, the stretching cancels out the light's natural squishiness, making the wiggly light look like a calm, round ball (a "thermal state").

3. The "On-the-Fly" Transformation

The most exciting part of this paper is that the scientists didn't need to build a separate machine to stretch or squeeze the light before taking the picture.

Old Way: Build a machine to squeeze the light $\rightarrow$ Send it to the camera $\rightarrow$ Take a picture.
New Way: Send the light to the camera $\rightarrow$ The camera squeezes it itself while taking the picture.

The camera is no longer just a passive observer; it is a reconfigurable quantum processor. By simply turning a dial on the splitter, they can instantly change the "shape" of the quantum state they are measuring.

4. What They Actually Did

The team tested this with a machine that generates "squeezed vacuum" light (a state where the light is already squished in one direction).

They set their camera to split the light evenly and took a picture. It confirmed the light was squished.
Then, they turned the dial to make the split uneven.
The Result: The picture they took showed the light being squished even more in one direction, or being stretched out until it looked round and calm.
They proved mathematically and experimentally that the picture they got was exactly what you would expect if you had squeezed the light with a separate machine first.

Summary

In short, this paper shows that by slightly breaking the symmetry of a standard light-measuring tool, you can turn that tool into a tunable shaper. You can stretch, squeeze, or flatten the quantum state of light inside the detector itself. This allows scientists to see different "versions" of a quantum state instantly, without needing extra equipment to manipulate the light before measuring it. It turns a simple camera into a versatile, shape-shifting tool for exploring the quantum world.

Technical Summary: Tunable Passive Squeezing of Squeezed Light through Unbalanced Double Homodyne Detection

Problem Statement
Full characterization of quantum states of light is a central task in quantum optics. While standard homodyne detection allows for the measurement of electromagnetic field quadratures, reconstructing complex quantum states (e.g., via the Wigner function) from single-quadrature measurements often requires extensive data acquisition and sophisticated post-processing algorithms. Double homodyne detection (DHD) offers a more direct alternative by simultaneously measuring orthogonal quadratures to sample the Husimi Q quasi-probability distribution. However, the conventional paradigm treats the measurement apparatus as a passive observer, strictly separated from state generation and manipulation. This paper addresses the challenge of integrating state manipulation directly into the measurement process to enable "on-line" processing without complex optical setups.

Methodology
The authors propose and experimentally realize a technique where the measurement apparatus itself performs an effective squeezing transformation on the input state. The core mechanism involves intentionally unbalancing the input beamsplitter ( $BS^*$ ) in a DHD setup.

Theoretical Framework: In a standard DHD, a signal state $\hat{\rho}_s$ is split by a beamsplitter with reflectivity $R$ and measured by two phase-locked homodyne detectors. The Positive Operator-Valued Measure (POVM) for an unbalanced DHD corresponds to projectors on squeezed displaced states. The probability distribution measured is not the Q function of the original state, but rather the Q function of the state after undergoing an effective squeezing transformation $\hat{S}(-\xi)$ , where the squeezing parameter $\xi = \ln(r/t)$ is determined by the reflection ( $r$ ) and transmission ( $t$ ) coefficients of the input beamsplitter ( $R=r^2$ ).
Experimental Implementation: To overcome the difficulty of mechanically changing beamsplitter coefficients, the authors employ a robust, polarization-encoded optical scheme.
- A polarizing beamsplitter (PBS) replaces the standard input beamsplitter.
- A half-wave plate (HWP) in the signal path controls the unbalancing by tuning the ratio of power transmitted (horizontal polarization) versus reflected (vertical polarization).
- A circularly polarized local oscillator (LO) naturally provides the required $\pi/2$ phase shift between the two detection arms, simplifying the phase-locking requirements.
- The source is a synchronously pumped optical parametric oscillator (SPOPO) generating a multimode squeezed vacuum state. The LO is shaped to match the first spectral eigenmode of the cavity.
- Data acquisition involves a "hold-and-measure" sequence to lock the LO-signal phase, followed by the collection of homodyne traces which are processed to reconstruct the Q function.

Key Contributions

Demonstration of Active Measurement: The paper presents the first experimental realization of a measurement device that acts as an active optical element. By tuning the beamsplitter reflectivity $R$ , the DHD system performs a controllable squeezing or anti-squeezing transformation on the state being measured.
Tunable Phase-Space Deformation: The authors demonstrate that the measurement outcome directly samples the Q function of the input state as if it had been acted upon by a squeezing operator. The strength and orientation of this transformation are continuously tunable via the reflectivity $R$ .
Experimental Validation: Using a polarization-encoded setup, the team successfully characterized a squeezed vacuum state, observing the controlled deformation of its phase-space distribution.

Results

Balanced vs. Unbalanced: With a balanced DHD ( $R=0.5$ ), the system reconstructs the original squeezed vacuum state, yielding raw squeezing and anti-squeezing levels of -1.25 dB and 2.6 dB, respectively.
Controlled Transformation: By varying $R$ $R$ , the authors observed distinct regimes:
- For $R > 0.5$ , the state is further squeezed in the amplitude quadrature ( $q$ ).
- For $R < 0.5$ , the state is squeezed in the phase quadrature ( $p$ ).
- Crucially, at a specific reflectivity ( $R \approx 0.39$ ), the unbalancing exactly counteracts the intrinsic squeezing of the input state. This results in a measured Q function resembling a thermal state (where both quadrature variances are equal), effectively "unsqueezing" the input.
Theoretical Agreement: The experimental data for the squeezing and anti-squeezing parameters of the reconstructed Q functions across six different reflectivity values showed strong agreement with the theoretical model derived from the POVM formalism. Minor deviations were attributed to experimental stability limits over the extended measurement time.

Significance
The paper claims that unbalanced double homodyne detection serves as a versatile tool that blurs the line between measurement and manipulation. By transforming the detector into a reconfigurable quantum processor, the technique allows for:

Simultaneous Characterization and Manipulation: The ability to reshape a state's phase-space distribution "on-line" during the measurement process.
Enhanced Metrology and Certification: The potential to dynamically reshape states to better estimate parameters encoded in squeezing amplitude or phase, or to tailor states to maximize fidelity for certifying high-order non-Gaussian features.
Resource Efficiency: The technique offers a robust, resource-efficient alternative to complex quantum-state reconstruction, avoiding the need for separate, complex optical elements to perform squeezing transformations before detection.

The authors conclude that this approach establishes unbalanced DHD as a practical addition to the quantum optics toolkit, enabling the controlled deformation of quantum states directly within the detection apparatus.