Quantum sensing using squeezed light states to enhance measurement precision beyond standard limits.Quantum squeezed light sensing exploits a special property of light called squeezing, where the quantum noise in one observable (e.g., phase) is reduced below the standard quantum limit at the expense of increased noise in its conjugate observable (e.g., amplitude). This allows measurements to exceed the shot-noise limit, which is the usual precision floor set by the particle nature of light. Squeezed light is now a standard tool in gravitational-wave detectors and is being developed for microscopy and other precision measurements.
The concept of squeezed light was first proposed in the 1970s, and the first experimental demonstrations were achieved in the mid-1980s. The first practical application was in the LIGO gravitational-wave detector, which began using squeezed light in 2019.
In a squeezed state, the uncertainty in one quadrature of the electromagnetic field is reduced, while the uncertainty in the orthogonal quadrature is correspondingly increased, preserving the Heisenberg uncertainty principle. By aligning the squeezed quadrature with the signal of interest, the measurement noise is reduced. This is achieved by passing light through a nonlinear optical crystal, where a strong pump beam generates pairs of correlated photons, leading to a reduction of noise in one phase.
Squeezed light is used in gravitational-wave observatories like LIGO and Virgo to enhance sensitivity, and in quantum microscopy to image delicate biological samples with less photodamage.
The first gravitational-wave detection in 2015 was made without squeezed light, but subsequent upgrades that included it have doubled the detector's sensitivity.
| squeezing | variable | squeezing parameter (magnitude) — squeezing parameter |
| n̄ | variable | mean photon number — mean photon number |
| ln | operator | natural logarithm function — natural logarithm |
| \Delta \theta | variable | Uncertainty in the estimated parameter — parameter uncertainty |
| N | variable | Number of independent probes or particles — particle number |
| \ge | operator | Indicates a lower bound — greater than or equal |
| ⟨N⟩ | variable | mean particle number — particle number |
| r | variable | squeeze parameter — squeeze parameter |
| \hat{t} | variable | Defect density (average number of topological defects per unit volume) — defect density per cubic metre |
| \tau_Q | variable | Quench time (characteristic time over which the system is driven through the critical point) — time second |
| \nu | constant | Correlation length critical exponent of the equilibrium phase transition — critical exponent nu = varies |
| z | constant | Dynamic critical exponent relating relaxation time to correlation length — dynamic critical exponent z = varies |
| n | variable | density (or control parameter) — number density per metre cubed |
| R | variable | measured indicator (response) |
| arg max | operator | argument of the maximum: value of n that maximizes the expression — argmax operator |
| d log R / d log n | operator | logarithmic derivative of R with respect to n, measuring relative sensitivity — logarithmic derivative |









