In this review, our primary goal was to tell in a clear and understandable way what is meant by quantum measurement in GW detectors. It was conceived as a comprehensive introduction to the quantum noise calculation techniques that are employed currently for the development of advanced interferometric detectors. The target audience are the young researchers, students and postdocs, who have just started their way in this field and need a guide that provides a step-by-step tutorial into the techniques and covers all the current achievements in the field. At the same time, we tried to make this manuscript interesting to all our colleagues from the GW community and, perhaps, from other branches of physics, who might be interested in getting themselves familiar with this area, not necessarily close to their own research field.

However, the reality is crude and such a lofty ambition is always a pot of gold at the end of the rainbow. Thus, we could not claim this review to be a complete and comprehensive description of the field of quantum measurement. We present here a pretty detailed analysis of the quantum noise features in the first and second generation of GW interferometers, contemplating the techniques considered robust and established. However, many hot topics, related to the planned third generation of GW interferometers [44, 125, 80] remained uncovered. Here are only some of them: (i) xylophone configurations [78], (ii) multiple-carrier detectors [130, 129], (iii) negative optical inertia [89], (iv) intracavity detection schemes [18, 17, 84, 86, 52], etc. It is our determined intention to enjoy the great advantages of the format of living reviews and include those topics in future revisions of this review.

We would like to conclude our review by pointing out how the new swiftly-developing areas of modern science and technology, not directly related to GW astronomy and detector science, turn out to be deeply rooted in the quantum measurement theory developed by the GW community. It is amazing how sinuous the ways of scientific progress are. The history of how GW detection and quantum-measurement theory developed and interwove might serve as an example thereof. Indeed, from the very first steps towards the experimental observation of GWs made by Weber in the early 1960s [165, 166], it was realized that the extreme weakness of interaction between the ripples of space-time and matter appeals for unprecedentedly precise measurement. And almost at the same time, Braginsky realized that the expected amplitude of the GW-induced oscillations of the bar detector signal mode would be on the order of the zero point oscillations of this mode, as predicted by quantum mechanics; that is, in order to observe GWs, one has to treat a detector quantum-mechanically and as a consequence there will be a quantum back action, setting a limitation on the achievable sensitivity, the SQL [16].

This serendipity had a powerful impact on the quantum measurement theory development, for it set an objective to contrive some ways to overcome this limitation. For decades up to this point, it was a purely theoretical discipline having little in common with experimental science, and, fancy that, become a vital necessity for GW astronomy. And again, for several decades, GW detection has been perhaps the only field where the results of quantum measurement theory were applied, mainly in the struggle with quantum noise, considered as a hindrance towards the noble goal of the detection of GWs. And only recently, the same optomechanical interaction, begetting quantum noise and the SQL in the interferometric GW detectors, has aroused a keen interest among wide circles of researchers studying the quantum behavior of macroscopic objects and testing the very foundations of quantum mechanics in the macroscopic world [91, 10].

All the techniques and concepts developed in the GW community turn out to be highly sought by this new field [45]. Such methods, initially developed for future GW detectors, as back-action evasion via properly constructed cross correlation between the measurement and back-action noise sources [162, 159, 158, 160, 161, 51, 53], find a use in the optomechanical experiments with micro- and nanoscale mechanical oscillators [46, 114, 108, 105, 106, 170, 62]. It turns out that GW detectors themselves fit extremely well for testing the fundamental principles of quantum mechanics just for the record low values of the noise, having non-quantum origin, that owes to the ingenuity, patience and dedication by an entire generation of experimental physicists [131]. The very fact that the mechanical differential mode of the km-scale LIGO detector has been cooled down to without any special arrangement, just by modifying the standard feedback kernel of the actuators to provide a virtual rigidity, shifting the 10-kg suspended mirrors oscillation frequency from to , where the GW detector is most sensitive [2], tells its own tale. Noteworthy also is the experiment on cooling a several-ton AURIGA bar detector mechanical oscillation mode to [153]. In principle, some dedicated efforts might yield even cooling to ground state of these definitely macroscopic oscillators [54, 107].

One might foresee even more striking, really quantum phenomena, to be demonstrated experimentally by future GW detectors, whose sensitivity will be governed by quantum noise and not limited by the SQL. It is possible, e.g., to prepare the mechanical degree of freedom of the interferometer in a close-to-pure squeezed quantum state [114], entangle the differential and common motion of the kg-scale mirrors in the EPR-like fashion [56, 115], or even prepare it in a highly non-classical Schrödinger-cat state [135, 88].

Living Rev. Relativity 15, (2012), 5
http://www.livingreviews.org/lrr-2012-5 |
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