Squeezed Light Simulator: Quantum Noise Below the Vacuum Limit

simulator intermediate ~10 min
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ΔX = 0.25 — noise reduced to 50% of vacuum

At 6 dB squeezing, the noise in the squeezed quadrature is reduced to half the vacuum level (factor of 2), while the anti-squeezed quadrature increases by a factor of 2. The Heisenberg uncertainty relation ΔX·ΔP ≥ ¼ is saturated.

Formula

r = r_dB / (20 log₁₀ e) ≈ r_dB / 8.686
ΔX = ½ e^{-r}, ΔP = ½ e^{+r}
ΔX · ΔP = ¼ (minimum uncertainty state)

Quantum Noise and the Vacuum

Even in complete darkness, the electromagnetic field fluctuates — these vacuum fluctuations set a fundamental noise floor called the standard quantum limit. For coherent laser light, intensity and phase noise are equal and symmetric, forming a circular noise distribution in phase space. Squeezing breaks this symmetry, compressing noise in one direction while stretching it in the perpendicular direction.

Phase-Space Ellipse

In the Wigner function representation, a coherent state appears as a circular Gaussian blob displaced from the origin. Squeezing deforms this circle into an ellipse: the minor axis represents the reduced-noise quadrature, and the major axis the amplified-noise quadrature. The area of the ellipse is preserved by the Heisenberg uncertainty principle — you cannot reduce total noise, only redistribute it.

Generating Squeezed Light

Optical parametric amplifiers (OPAs) are the workhorse for producing squeezed light. A nonlinear crystal pumped by a strong laser correlates photon pairs, reducing fluctuations in one quadrature. Modern OPAs in bow-tie cavities routinely achieve 10-15 dB of squeezing. Four-wave mixing in atomic vapors and optomechanical systems offer alternative approaches.

LIGO and Beyond

The most dramatic application of squeezed light is in gravitational wave detection. Since 2019, both LIGO detectors inject squeezed vacuum to reduce shot noise, effectively increasing their range by ~15%. Future detectors plan frequency-dependent squeezing using filter cavities to reduce both shot noise (high frequency) and radiation pressure noise (low frequency) simultaneously.

FAQ

What is squeezed light?

Squeezed light is a quantum state where the noise in one quadrature (amplitude or phase) is reduced below the vacuum fluctuation level, while the conjugate quadrature noise increases to satisfy the Heisenberg uncertainty principle. It is produced using optical parametric amplifiers or four-wave mixing.

How is squeezing measured in decibels?

Squeezing is measured as the noise reduction in dB relative to the shot-noise level: dB = -10 log₁₀(variance_squeezed / variance_vacuum). 3 dB means noise reduced by half; 10 dB means noise reduced to 10% of vacuum. The current record exceeds 15 dB.

How is squeezed light used in LIGO?

LIGO injects squeezed vacuum into the dark port of its interferometer to reduce shot noise at high frequencies. Since 2019, approximately 3 dB of squeezing has been routinely used, increasing the detection rate of gravitational wave events by roughly 50%.

What is the Heisenberg uncertainty relation for light?

For the two quadratures X and P of the electromagnetic field, ΔX · ΔP ≥ ¼. A coherent state saturates this with equal noise in both (ΔX = ΔP = ½). Squeezing redistributes the noise: one quadrature goes below ½ while the other goes above, keeping the product at the minimum ¼.

Sources

Embed

<iframe src="https://homo-deus.com/lab/quantum-optics/squeezed-light/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub