Squeezed gravitational waves: when quantum optics meets black holes ✦
Gluon and graviton radiation from scattering on strong-field shock waves is described by effective Lipatov vertices; the gravitational vertex is proportional to a bilinear combination of the gluon vertex. It is shown that the n-gluon emission spectrum is given by a generalized squeezed coherent state of the Susskind–Glogower type (gSG). The double copy ensures that multi-graviton emission is also described by a gSG state. Analysis of the physical parameter region reveals that for nearly minimum-uncertainty configurations, extremely large squeezing parameters (~ln of the average graviton number) are achievable. Consequently, quantum noise in the gravitational-wave spectrum is amplified above the sensitivity of existing and planned detectors, paving the way to detecting quantum gravity effects in strong-field processes.
Context
Directly observing the quantum nature of gravity is one of the major unsolved challenges. Gravitational waves, predicted by Albert Einstein and first detected by LIGO detectors, carry information about collisions of black holes and neutron stars, but their quantum structure remains invisible: metric fluctuations are on the Planck scale, ∼10⁻³⁵ m. Yet, back in the day, Stephen Hawking and others pointed out that if gravitational radiation is in a squeezed state, quantum noise could be greatly amplified. This new study exploits an unexpected link — the double copy between quantum chromodynamics and gravity — to show that in strong fields during near-light-speed collisions, squeezed graviton states indeed form.
Methods
The key idea rests on the double-copy concept, linking scattering amplitudes in gauge theories and gravity. The authors considered the scattering of gravitational shockwaves (Aichelburg–Sexl metric) in the Regge limit, where the exchange of "reggeized" gravitons dominates. The emission is described by effective Lipatov vertices, and the gravitational vertex is proportional to a bilinear combination of QCD gluon vertices. Multi-particle production is modeled as the iteration of t-channel processes (a "horizontal ladder"), leading to a negative binomial distribution (NBD) for the number of gravitons. Then the NBD is transformed into a generalized Susskind–Glogower coherent state (GCS), which in the Fock basis is a superposition of states with definite particle numbers and specific weights. This state, like the coherent states introduced in quantum optics by Roy Glauber, possesses phase coherence but additionally exhibits quadrature squeezing.
Results
Analyzing the properties of the GCS state showed that its squeezing parameter ξ depends on the average graviton number ¯n and parameter r (analogous to the number of correlated sources). For realistic gravitational waves detected by LIGO, ¯n ∼ 4·10³⁶. Using the uncertainty principle, the authors derived that maximum squeezing reaches |ξ| ∼ ½ ln(4¯n) ≈ 42. This means an exponential amplification of quantum noise: from ∼10⁻³⁵ m to ∼10⁻¹⁷ m, which exceeds the sensitivity threshold of current detectors (around 10⁻¹⁹ m/√Hz). However, the state can remain arbitrarily close to the minimum uncertainty product: the deviation δ∼1/(32r) can be made negligible for r>1. Thus, the regime of strong squeezing and nearly minimal uncertainty is simultaneously attainable.
Implications
If gravitational radiation is indeed a GCS-squeezed state, this radically changes the approach to searching for quantum effects in gravity. Quantum noise ceases to be elusive and could be detected by analyzing data from existing gravitational-wave antennas. Moreover, the connection to QCD allows methods for describing nonequilibrium glasma (a high-density gluon system) to be applied to gravitational waves, opening new perspectives for understanding thermalization and decoherence in strong fields.
Future development
Further studies must confirm that the double copy holds at the level of multi-particle amplitudes and compute the parameter r from first principles. Of particular interest is the search for sub-Poissonian statistics of graviton "clicks" — a clear indicator of quantum nature — which could manifest in correlations between detectors analogous to Hanbury Brown–Twiss correlations in optics. It is also important to study the effects of finite signal duration and non-Planckian corrections.
Impact
The results impact a wide range of fields: from gravitational-wave phenomenology and quantum field theory to the physics of ultrarelativistic heavy-ion collisions and precision quantum metrology.
Next steps
Immediate next steps include computing two-graviton correlation functions in the shockwave formalism and developing methods to search for nonclassical statistics in data from LIGO, Virgo, and the future LISA detector.
Key open problems
The work connects several fundamental problems: detecting quantum gravity, the black hole information loss (since squeezing could affect the entropy of radiation), thermalization in nonequilibrium quantum systems, and the potential to observe individual gravitons.
🎯 If the quantum noise in gravitational waves could be converted into sound, squeezing would transform it from the squeak of a mosquito wing into the roar of a jet engine — that's how huge the amplification is.
Key numbers
- Average graviton occupation for LIGO events: 4·10³⁶
- Achieved squeezing parameter: ~42
- Quantum noise amplification (from 10⁻³⁵ m to): ~10⁻¹⁷ m
- LIGO sensitivity threshold: ~10⁻¹⁹ m
- Deviation from minimum uncertainty: ~1/(32r)