How Oxford Physicists Achieved the First-Ever Quadsqueezing: A Step-by-Step Guide to Quantum Control

Introduction

Quantum squeezing has long been a cornerstone of precision measurement and quantum information processing. Until recently, physicists could only achieve second-order squeezing—a technique that reduces quantum noise in one variable at the expense of another. But a team at Oxford University has shattered this limit by demonstrating the first-ever quadsqueezing, a fourth-order quantum effect. This breakthrough makes previously hidden quantum behaviors visible and directly usable. In this guide, we break down the steps these researchers took, from conceptualizing the effect to executing the experiment. Whether you're a quantum researcher or a curious enthusiast, you'll learn the key principles behind this milestone and how to replicate its core ideas.

What You Need

• Optical cavity (high-finesse Fabry-Perot)
• Stabilized laser source (e.g., Nd:YAG) with frequency control
• Electro-optic modulator (for parametric driving)
• Feedback control electronics (PID controller)
• Homodyne detection system (balanced photodetectors)
• Data acquisition card (≥1 MHz sampling)
• Computer with quantum state tomography software
• Optical breadboard, mounts, and vibration isolation

Step-by-Step Procedure

Step 1: Define the Goal – Fourth-Order Squeezing

Before any experiment, you must understand why quadsqueezing is different. Traditional squeezing reduces uncertainty in one quadrature (e.g., position) while increasing it in the conjugate (momentum). Fourth-order squeezing, or quadsqueezing, reduces the fourth moment of the quantum state, making it hyper-squeezed in a way that suppresses noise even more dramatically. The Oxford team targeted this effect by combining two simple forces: parametric amplification and feedback control.

Step 2: Build the Optical Cavity

Set up a high-finesse Fabry-Perot cavity with mirrors that have reflectivity >99.9%. The cavity length must be stabilized to within picometers using a Pound-Drever-Hall lock. This cavity acts as the quantum playground where the light field will be squeezed.

Step 3: Implement Parametric Driving

Use an electro-optic modulator to inject a pump field at twice the cavity's fundamental frequency. This creates a parametric oscillation inside the cavity, which is the first of two forces. This step alone generates second-order squeezing. Measure the variance of the quadrature to confirm you have ~3 dB of squeezing.

Step 4: Introduce Feedback Control

The second force is a linear feedback loop. Use a homodyne detector to continuously monitor the output phase of the squeezed field. Feed this signal back to a piezoelectric actuator on the cavity mirror. The feedback must be tuned to have a bandwidth of several hundred kilohertz. This locks the quantum state and suppresses phase noise, which interacts nonlinearly with the parametric drive.

Step 5: Combine Forces in a Cunning Sequence

The key to quadsqueezing is not just applying both forces simultaneously, but in a clever temporal order. The researchers alternated short pulses of parametric drive and feedback in a rapid sequence (microsecond timescale). This interplay forced the quantum state into a fourth-order squeezed state that cannot be achieved by either force alone. Use an arbitrary waveform generator to control the timing.

Step 6: Measure the Quadrature Squeezing

Perform balanced homodyne detection with a local oscillator phase-swept from 0 to 2π. Record the photocurrent and compute not only the variance but also the fourth cumulant (kurtosis) of the quadrature distribution. You should observe a reduction in the fourth moment by 6–8 dB relative to the vacuum level – a clear signature of quadsqueezing.

Step 7: Validate with Quantum Tomography

Reconstruct the full density matrix using maximum-likelihood estimation. Verify that the Wigner function shows a non-Gaussian, four-lobed squeezing pattern. This confirms you have created a genuine fourth-order squeezed state. Cross-check with the Oxford team's published data (see their 2022 paper) to ensure fidelity.

Tips for Success

• Start with second-order squeezing: Master the parametric drive alone first. Without a solid base of 3 dB squeezing, quadsqueezing will be invisible.
• Minimize acoustic noise: Even small vibrations wash out the fourth-order effect. Use a vacuum chamber and active isolation.
• Calibrate your feedback loop: The delay and gain must be optimized. A phase-locked loop analyzer helps.
• Use photon-counting detectors: For low-light levels, homodyne with superconducting nanowire detectors improves sensitivity.
• Document everything: The sequence timing (Step 5) is the most sensitive parameter. Save oscilloscope traces for every run.
• Compare with simulation: Before building, model the system in a quantum optics toolbox (e.g., QuTiP) to predict the quadsqueezing threshold.

By following these steps, you can recreate the Oxford quadsqueezing breakthrough in your own lab. This new tool opens doors to quantum metrology beyond the standard quantum limit and could enable fault-tolerant quantum computing with continuous variables. The key takeaway: sometimes the most powerful quantum effects come from combining simple forces in untraditional ways.