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Optical noise correlations and beating the standard quantum limit in LIGO-II

Alessandra Buonanno, Yanbei Chen

Published Oct 4, 2000• 2 citations
OpenAlex

Abstract

The uncertainty principle, applied naively to the test masses of a laser interferometer gravitational wave detector, produces a standard quantum limit (SQL) on the interferometer's sensitivity. It has long been thought that beating this SQL would require a radical redesign of interferometers. We show that no redesign is needed at all. LIGO-II interferometers, as currently planned, can beat the SQL by as much as a factor two over a bandwidth \\Delta f \\sim f, if their thermal noise can be pushed low enough. This is due to quantum correlations between photon shot noise and radiation pressure noise, produced by the LIGO-II signal-recycling mirror.

Related papers

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•Jan 1, 2013•14 citations
The uncertainty principle, applied naively to the test masses of a laser interferometer gravitational wave detector, produces a standard quantum limit (SQL) on the interferometer's sensitivity. It has long been thought that beating this SQL would require a radical redesign of interferometers. We show that no redesign is needed at all. LIGO-II interferometers, as currently planned, can beat the SQL by as much as a factor two over a bandwidth \Delta f \sim f, if their thermal noise can be pushed low enough. This is due to quantum correlations between photon shot noise and radiation pressure noise, produced by the LIGO-II signal-recycling mirror.
It has long been thought that the sensitivity of laser interferometric gravitational-wave detectors is limited by the free-mass standard quantum limit, unless radical redesigns of the interferometers or modifications of their input or output optics are introduced. Within a fully quantum-mechanical approach we show that in a second-generation interferometer composed of arm cavities and a signal recycling cavity, e.g., the LIGO-II configuration, (i) quantum shot noise and quantum radiation-pressure-fluctuation noise are dynamically correlated, (ii) the noise curve exhibits two resonant dips, (iii) the standard quantum limit can be beaten by a factor of 2, over a frequency range $\ensuremath{\Delta}f/f\ensuremath{\sim}1,$ but at the price of increasing noise at lower frequencies.
In the sensitivity of laser interferometer gravitational-wave detectors, there exists the standard quantum limit (SQL), derived from Heisenberg's uncertainty relation. The SQL can be overcome using the quantum correlation between shot noise and radiation-pressure noise. One of the methods to overcome SQL, signal recycling, is considered so far only in a recombined-type interferometer such as Advanced-LIGO, LCGT, and GEO600. In this paper, we investigated quantum noise and signal recycling in a differential-type interferometer. We also applied it to a real detector and compared the sensivity with a recombined type.
Abstract The measurement of minuscule forces and displacements with ever greater precision is inhibited by the Heisenberg uncertainty principle, which imposes a limit to the precision with which the position of an object can be measured continuously, known as the standard quantum limit1–4. When light is used as the probe, the standard quantum limit arises from the balance between the uncertainties of the photon radiation pressure applied to the object and of the photon number in the photoelectric detection. The only way to surpass the standard quantum limit is by introducing correlations between the position/momentum uncertainty of the object and the photon number/phase uncertainty of the light that it reflects5. Here we confirm experimentally the theoretical prediction5 that this type of quantum correlation is naturally produced in the Laser Interferometer Gravitational-wave Observatory (LIGO). We characterize and compare noise spectra taken without squeezing and with squeezed vacuum states injected at varying quadrature angles. After subtracting classical noise, our measurements show that the quantum mechanical uncertainties in the phases of the 200-kilowatt laser beams and in the positions of the 40-kilogram mirrors of the Advanced LIGO detectors yield a joint quantum uncertainty that is a factor of 1.4 (3 decibels) below the standard quantum limit. We anticipate that the use of quantum correlations will improve not only the observation of gravitational waves, but also more broadly future quantum noise-limited measurements.
The Heisenberg uncertainty principle dictates that the position and momentum of an object cannot be simultaneously measured with arbitrary precision, giving rise to an apparent limitation known as the standard quantum limit (SQL). Gravitational-wave detectors use photons to continuously measure the positions of freely falling mirrors and so are affected by the SQL. We investigated the performance of the Laser Interferometer Gravitational-Wave Observatory (LIGO) after the experimental realization of frequency-dependent squeezing designed to surpass the SQL. For the LIGO Livingston detector, we found that the upgrade reduces quantum noise below the SQL by a maximum of three decibels between 35 and 75 hertz while achieving a broadband sensitivity improvement, increasing the overall detector sensitivity during astrophysical observations.
Quantum fluctuations in the phase and amplitude quadratures of light set limitations on the sensitivity of modern optical instruments. The sensitivity of the interferometric gravitational-wave detectors, such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), is limited by quantum shot noise, quantum radiation pressure noise, and a set of classical noises. We show how the quantum properties of light can be used to distinguish these noises using correlation techniques. Particularly, in the first part of the paper we show estimations of the coating thermal noise and gas phase noise, hidden below the quantum shot noise in the Advanced LIGO sensitivity curve. We also make projections on the observatory sensitivity during the next science runs. In the second part of the paper we discuss the correlation technique that reveals the quantum radiation pressure noise from the background of classical noises and shot noise. We apply this technique to the Advanced LIGO data, collected during the first science run, and experimentally estimate the quantum correlations and quantum radiation pressure noise in the interferometer.
Direct detection of gravitational waves will require earth based detectors to measure strains of the order 10−21, at frequencies of 100 Hz, a sensitivity that has been accomplished with the initial generation of LIGO interferometric gravitational wave detectors. A new generation of detectors currently under construction is designed improve on the sensitivity of the initial detectors by about a factor of 10. The quantum nature of light will limit the sensitivity of these Advanced LIGO interferometers at most frequencies; new approaches to reducing the quantum noise will be needed to improve the sensitivity further. This quantum noise originates from the vacuum fluctuations that enter the unused port of the interferometer and interfere with the laser light. Vacuum fluctuations have the minimum noise allowed by Heisenberg’s uncertainty principle, ∆X1∆X2 ≥ 1, where the two quadratures X1 and X2 are non-commuting observables responsible for the two forms of quantum noise, shot noise and radiation pressure noise. By replacing the vacuum fluctuations entering the interferometer with squeezed states, which have lower noise in one quadrature than the vacuum state, we have reduced the shot noise of a LIGO interferometer. The sensitivity to gravitational waves measured during this experiment represents the best sensitivity achieved to date at frequencies above 200 Hz, and possibly the first time that squeezing has been measured in an interferometer at frequencies below 700 Hz. The possibility that injection of squeezed states could introduce environmental noise couplings that would degrade the crucial but fragile low frequency sensitivity of a LIGO interferometer has been a major concern in planning to implement squeezing as part of baseline interferometer operations. These results demonstrate that squeezing is compatible with the low frequency sensitivity of a full scale gravitational wave interferometer. We also investigated the limits to the level of squeezing observed, including optical losses and fluctuations of the squeezing angle. The lessons learned should allow for responsible planning to implement squeezing in Advanced LIGO, either as an alternative to high power operation or an early upgrade to improve the sensitivity. This thesis is available at DSpace@MIT and has LIGO document number P1300006. Thesis Supervisor: Nergis Mavalvala Title: Professor of Physics