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Annales de Physique

Can photon noise be reduced ?

Serge Reynaud, A. Heidmann

Published Jan 1, 1985• 4 citations
Publisher

Abstract

The sensitivity of the interferometric methods for detection of gravitational waves is limited at the moment by photon noise. This noise can theoretically be reduced by entering in one input part of the interferometer a field in a particular quantum state, the so called squeezed state. A wide variety of non-linear processes, such as the degenerate four wave mixing, can realize the transformation of coherent states of the field into squeezed states. We show that the photon noise reduction is very sensitive to the spatial and temporal coherence properties of the squeezed field, and that photon noise is not appreciably reduced with incoherent sources of squeezed field.

DOI
10.1051/anphys:01985001003022700

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The sensitivity of the interferometric methods for detection of gravitational waves is limited at the moment by photon noise. This noise can theoretically be reduced by entering in one input part of the interferometer a field in a particular quantum state, the so called squeezed state. A wide variety of non-linear processes, such as the degenerate four wave mixing, can realize the transformation of coherent states of the field into squeezed states. We show that the photon noise reduction is very sensitive to the spatial and temporal coherence properties of the squeezed field, and that photon noise is not appreciably reduced with incoherent sources of squeezed field.
The interferometers now being developed to detect gravitational waves work by measuring the relative positions of widely separated masses. Two fundamental sources of quantum-mechanical noise determine the sensitivity of such an interferometer: (i) fluctuations in number of output photons (photon-counting error) and (ii) fluctuations in radiation pressure on the masses (radiation-pressure error). Because of the low power of available continuous-wave lasers, the sensitivity of currently planned interferometers will be limited by photon-counting error. This paper presents an analysis of the two types of quantum-mechanical noise, and it proposes a new technique---the "squeezed-state" technique---that allows one to decrease the photon-counting error while increasing the radiation-pressure error, or vice versa. The key requirement of the squeezed-state technique is that the state of the light entering the interferometer's normally unused input port must be not the vacuum, as in a standard interferometer, but rather a "squeezed state"---a state whose uncertainties in the two quadrature phases are unequal. Squeezed states can be generated by a variety of nonlinear optical processes, including degenerate parametric amplification.
The search for gravitational radiation has driven important improvements in a variety of technologies for detecting very weak forces. These improvements have renewed the interest for the problem of quantum noise reduction. The use of squeezed fields was considered by Caves' and Bondurant and Shapiro2, who showed that a squeezed state interferometer requires substantially fewer photons than does a conventional (coherent-state) interferometer to reach the standard quantum limit. This note reanalyzes the problem, pointing out the importance of the coherence properties of the squeezed fields for the evaluation of photon noise reduction3.
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, [Delta]X1 [Delta]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.
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
A fundamental noise source limiting the measurement sensitivity of interferometric gravitational wave (GW) observatories is the light's quantum noise. While the sensitivity of the first observatory generation was limited by the shot noise at Fourier frequencies above several hundred hertz, the future observatory generations are expected to be limited by quantum noise also in their low-frequency detection band. Squeezed states of the light field allow for improving the sensitivity at all quantum-noise-limited frequencies. Recently, a squeezing-reduced shot noise of the GW observatory GEO 600 was demonstrated. Based on this success, the Einstein Telescope design study proposes squeezed-light injection to reduce shot noise as well as quantum radiation pressure noise by a factor of ten in power, i.e. by 10 dB. This contribution summarizes the current state of the art in the field of squeezed-light generation for gravitational wave astronomy and the prospects for the intermediate future.
We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so-called “dark port case,” when the beam splitter is oriented close to 90° to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (“dark port”). For this case it had been suggested that signal amplification is possible without concurrent noise amplification [R. Barak and Y. Ben-Aryeh, J. Opt. Soc. Am. B 25 , 361 (2008)]. We show that by injection of a squeezed vacuum state into the second input port, counting noise is reduced for large values of the squeezing factor, however the signal is not amplified. Signal strength only depends on the intensity of the laser beam.