Milestones in a Continuing Tale of Big and Small : Large Magnitude Squeezed Light at 100 Hz, and a Squeezed 4km Gravitational-wave Detector
[Sheon Chua is the recipient of the 2013 GWIC (Gravitational Wave International Committee) Thesis Prize for his PhD thesis “Quantum Enhancement of a 4km Laser Interferometer Gravitational-Wave Detector” (PDF). -- 2Physics.com]
Author: Sheon Chua
Currently at: Laboratoire Kastler Brossel, University of Pierre and Marie Curie (UPMC), Paris, France.
PhD research performed at: Centre for Gravitational Physics, Australian National University (ANU), Canberra, Australia.
Gravitational-wave sources of astronomical size from our Universe. Gravitational-wave displacement signals expected at one thousandth of the diameter of a single proton. Interferometric instruments with kilometre-long arms. Light ‘squeezed’ on the quantum scale.
The construction and implementation of second-generation laser-interferometric gravitational-wave detectors  are rapidly progressing , forming a detector network expected to be online over the next few years. These amazing instruments will use state-of-the-art isolation systems, optics, and hundred watt input lasers, and have kilometre-scale arms. For these detectors, the effect of a passing gravitational wave causes a relative displacement change between the interferometer arm end mirrors, which is encoded in the relative phase of the light beams propagating in the arms . The relative displacement sensitivities will be of order of 10-19 m in the 10 Hz to 10 kHz Fourier frequency band, achieved after monumental efforts in research and development across many fields of physics and engineering.
However, even after these impressive technological efforts, there remain fundamental noise sources that limit measurement sensitivity that arise from the underlying physics of the instrument itself. One such noise source is the quantum nature of light , that comes from a non-zero commutation relationship between a light beam’s phase (ϕ) and amplitude (A) . The Heisenberg Uncertainty Principle for this specific pair of quantities is given by ∆ϕ ∆A ≥ 1. Figure 1(a) shows this relation diagrammatically as a noise ‘ball’. As the gravitational-wave signal is encoded in the relative phase, with quantum phase noise Δϕ present we reach a signal-to-noise level where we can no longer distinguish a passing gravitational wave in the measurement. Therefore, the quantum noise of light is a limitation to achievable sensitivity.
However, the Heisenberg Uncertainty Principle relation is multiplicative. This means that one of the uncertainties can be below the quantum level, or ‘squeezed’, if the other uncertainty is above the level, or ‘antisqueezed’. This is illustrated in Figure 1(b), where the overall uncertainty is the same, but the individual uncertainties have been ‘rearranged’. The amount of squeezing has units of decibels [dB], referenced to the unsqueezed quantum noise level amplitude, given by [dB]=20 log10[(anti)squeezed noise / unsqueezed noise].
Figure 1 (a) Quantum noise ‘ball’, showing the even distribution of uncertainty between the two quantities amplitude (A) and phase (ϕ). (b) Squeezed noise, where the uncertainty in one quantity is less than quantum noise, while the other uncertainty is greater than quantum noise.
As an example, if we have 6 dB of squeezing, we mean that the noise is squeezed to about half the value of the quantum noise level, or that the noise is reduced by a factor of 2. It follows that if we inject squeezed light into an interferometer so that it results in the phase uncertainty being reduced, the measurement sensitivity limited by quantum phase noise will be improved.
The tale of squeezed light for enhancing gravitational-wave detectors is now three decades young, with theoretical proposals for injecting squeezed light into interferometers published in the early 1980s , a few years before first experimental measurement of squeezing  took place. Since then, there has been a steady advancement in techniques and technologies to generate squeezed light within the 10 Hz to 10 kHz detection band [8-10], as well as to implement squeezed light with interferometers [11-14]. The GEO600 detector is now routinely using squeezed light, with ever-increasing timescales and duty cycles .
Figure 2: First measurement of greater than 10 dB squeezing across the audio gravitational-wave detection band, with 11.6 dB from 200 Hz and above. The degradation of squeezing level below 100 Hz is due to remaining residual classical noise entering the squeezing detector. Adapted from , and includes resolution bandwidth and window information.
The first milestone recently added to this story is the measurement of greater than 10 dB squeezing across the 10 Hz – 10 kHz frequency band . This measurement was achieved by a team at the Australian National University, with valuable input from the Albert Einstein Institute. Figure 2 shows the result, with a maximum of 11.6 dB measured at 100 Hz and above. This was achieved after a detailed study characterizing and minimizing classical noise sources that impacted the squeezing measurement. This result represents the current record for squeezing in the 10 Hz – 10 kHz band, and further demonstrates the availability of large squeezing magnitude applicable for gravitational-wave detector enhancement.
The second milestone recently achieved is realising a squeezed 4 km interferometric gravitational-wave detector . This was an experiment completed on the Enhanced LIGO 4 km interferometer in Washington State USA, performed by scientists from across the LIGO Scientific Collaboration, with LIGO Hanford Observatory, LIGO Massachusetts Institute of Technology, Australian National University and the Albert Einstein Institute being the lead institutions.
Figure 3: Enhanced LIGO interferometer with squeezing. (a) The Reference trace shows the displacement sensitivity of the interferometer without squeezing being injected, while the Squeezing trace shows the interferometer with squeezing injected. (b) Squeezing enhancement in LIGO’s most sensitive frequency band, at a lesser level due to significant contributions from noise sources other than quantum noise. Adapted from .
Figure 3(a) shows the interferometer displacement sensitivity curve with and without squeezed light. Up to 2.15 dB of squeezing enhancement is measured in the quantum noise limited regime (above 150 Hz). This is in line with the expected experiment parameters. Furthermore, as shown in Figure 3(b), in the most sensitive band between 150 Hz and 300 Hz, there is enhancement gained by squeezing. This result confirmed the compatibility of squeezing at lower detection frequencies where future gravitational-wave detectors will have their best sensitivity.
Squeezed light is a tool that is now available for, and being used for enhancing interferometric gravitational-wave detectors . Third generation detector designs, such as the Einstein Telescope , have squeezed light injection as part of baseline technology. To realise maximum benefit from squeezed light injection, further improvements and refinements are needed, such as for improved parameters for squeezing injection and for minimizing adverse impacts on future detectors with more stringent requirements. This development work continues on as I write. It is safe to say that there are many more milestones to come in this continuing tale of big and small.
This article is a ‘synopsis’ of the squeezed light story and the two milestone results. For an in-depth review of squeezed light, squeezed light technologies and injection experiments up to 2013 (including both of these recent milestones), a Topical Review article is to be published soon . I also recommend the LIGO Magazine, Issue 3 , which is focussed on squeezed light.
 Advanced LIGO website: www.advancedligo.mit.edu ; Advanced Virgo website: wwwcascina.virgo.infn.it/advirgo ; KAGRA website: gwcenter.icrr.u-tokyo.ac.jp/en/; GEO600 website: www.geo600.org
 For example: www.advancedligo.mit.edu/adligo_news.html .
 For an expanded introduction to interferometric gravitational-wave detector measurement, I recommend this short video: www.youtube.com/watch?v=RzZgFKoIfQI .
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 Einstein Telescope: www.et-gw.eu .
 S. Chua et al, "Quantum Squeezed Light for Advanced Gravitational-wave Detectors". Classical and Quantum Gravity Topical Review, accepted for publication (2014).
 LIGO Magazine, Issue 3: www.ligo.org/magazine/LIGO-magazine-issue-3.pdf .