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Physical Review Letters

Experimental Demonstration of a Classical Analog to Quantum Noise Cancellation for Use in Gravitational Wave Detection

Conor M Mow-Lowry, Benjamin Sheard, M. Gray, David E. McClelland, S. E. Whitcomb

Published Apr 23, 2004• 32 citations
Publisher

Abstract

We present results that are a classical analog to quantum noise cancellation. It is possible to breach the standard quantum limit in an interferometer by the use of squeezing to correlate orthogonal quadratures of quantum noise, causing their effects on the resulting sensitivity to cancel. A laser beam incident on a Fabry-Perot cavity was imprinted with classical, correlated noise in the same quadratures that cause shot noise and radiation pressure noise. Couplings between these quadratures due to a movable mirror, sensitive to radiation pressure, cause the excess classical noise to cancel. This cancellation was shown to improve the signal to noise ratio of an injected signal by approximately a factor of 10.

DOI
10.1103/physrevlett.92.161102

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We present results that are a classical analog to quantum noise cancellation. It is possible to breach the standard quantum limit in an interferometer by the use of squeezing to correlate orthogonal quadratures of quantum noise, causing their effects on the resulting sensitivity to cancel. A laser beam incident on a Fabry-Perot cavity was imprinted with classical, correlated noise in the same quadratures that cause shot noise and radiation pressure noise. Couplings between these quadratures due to a movable mirror, sensitive to radiation pressure, cause the excess classical noise to cancel. This cancellation was shown to improve the signal to noise ratio of an injected signal by approximately a factor of 10.
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.
Quantum radiation pressure noise has never been experimentally demonstrated, though it has been predicted for more than thirty years. It is, however, expected to limit the low-frequency sensitivity of second generation gravitational-wave interferometers. We have demonstrated classical radiation-pressure-induced correlations between two optical beams sent into the same high-finesse cavity with a moving mirror. Our two-beam scheme can be used to retrieve quantum noise embedded in an overwhelming classical noise, and has applications both in high-sensitivity measurements and in quantum optics.
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.
We have developed an experiment of ultrasensitive interferometric measurement of small displacements based on a high-finesse Fabry-Perot cavity. We have observed the internal thermal noise of mirrors and fully characterized their acoustics modes with a sensitivity of 3 × 10 −20 m/Hz 1/2 . This unique sensitivity is a step towards the first observation of the radiation pressure effects and the resulting standard quantum limit in interferometric measurements. Our experiment may become a powerful facility to test quantum noise reduction schemes such as the use of squeezed light or quantum locking of mirrors. As a first result, we present the observation of a cancellation of radiation pressure effects in our cavity. This back-action noise cancellation was first proposed within the framework of gravitational-wave detection with dual resonators, and may drastically improve the sensitivity of such measurements.
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.
We have developed an experiment of ultrasensitive interferometric measurement of small displacements based on a high-finesse Fabry-Perot cavity. We describe recent progress in our experimental setup in order to reach a sensitivity better than 10-20 m/√Hz. This unique sensitivity is a step towards the first observation of radiation pressure effects and the resulting standard quantum limit in interferometric measurements. Our experiment may become a powerful facility to test quantum noise reduction schemes, and we already report the first experimental demonstration of a back-action noise cancellation. Using a classical radiation-pressure noise to mimic the quantum noise of light, we have observed a drastic improvement of sensitivity either in position or force measurements.