Quantum squeezing reduces uncertainty in one observable at the expense of another.Quantum squeezing is a technique that redistributes the uncertainty inherent in quantum measurements, reducing fluctuations in one observable (like the phase of a light wave) while increasing them in a conjugate observable (like its amplitude). This does not violate the Heisenberg uncertainty principle—it simply 'squeezes' the uncertainty into a direction where it causes less harm for a particular measurement. The result is a quantum state with noise below the standard quantum limit in the chosen variable.
The concept was first proposed by Carlton Caves in 1981, who showed that injecting squeezed light into an interferometer could beat the standard quantum limit. Experimental demonstrations followed in the late 1980s, and the technique was fully integrated into gravitational-wave detectors by the 2010s.
For light, squeezing is typically achieved by sending a laser beam through a nonlinear optical crystal, where one photon can split into two lower-energy photons that are quantum-correlated. These correlated photons produce a state where the noise in one quadrature (e.g., phase) is suppressed below the vacuum level, at the cost of increased noise in the other quadrature (amplitude). The squeezed light is then used as a probe in interferometers, where the reduced phase noise directly translates to better sensitivity in detecting tiny displacements, such as those caused by passing gravitational waves.
Squeezed light is currently used in the LIGO and Virgo gravitational-wave observatories to enhance their sensitivity, allowing them to detect more distant and weaker cosmic events. It is also being explored for quantum-enhanced microscopy and atomic clocks.
In 2023, researchers squeezed magnons—collective spin excitations—in a macroscopic iron sphere, achieving a quantum state with noise below the standard limit in a solid object visible to the naked eye.
| \Delta X | variable | Change in a physical quantity — physical quantity change |
| \theta | variable | Angle variable — angle radian |
| \theta_0 | variable | Reference angle offset — angle radian |
| \propto | operator | Indicates the left side scales with the right side — proportionality |
| \cos | operator | Computes the cosine of an angle — cosine function |
| z | variable | Input vector to be projected — vector |
| p | variable | Projected vector on the simplex — vector |
| proj | operator | Finds the closest point in the simplex to the input vector — projection operator |
| argmin | operator | Returns the value that minimizes the expression — argmin operator |
| ‖·‖ | operator | Computes the square root of the sum of squares — euclidean norm |
| x | variable | input point — input variable |
| x' | variable | another input point — input variable |
| σ | variable | signal amplitude — amplitude |
| ℓ | variable | length scale — length scale |
| exp | operator | raises e to the given power — exponential function |
| k_{qJ} | variable | Quantum Jeans wavenumber — wavenumber reciprocal metre |
| m | variable | Particle mass — mass kilogram |
| \rho | variable | Mass density — mass density kilogram per cubic metre |
| G | constant | Universal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \hbar | constant | Planck constant divided by 2π — reduced planck constant = 1.054571817e-34 joule second |
| σ_χA | variable | scattering cross section of particle χ with nucleus A — cross section square metre |
| σ_χB | variable | scattering cross section of particle χ with nucleus B — cross section square metre |
| μ_χA | variable | reduced mass of particle χ and nucleus A — reduced mass kilogram |
| μ_χB | variable | reduced mass of particle χ and nucleus B — reduced mass kilogram |
| ρ | variable | density operator of the first quantum state — density operator |
| σ | variable | density operator of the second quantum state — density operator |
| tr | operator | sums diagonal elements of an operator in any basis — trace operator |
| log | operator | takes the operator logarithm, defined via spectral decomposition — matrix logarithm |
