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THE DETECTION OF GRAVITATIONAL WAVES




Interview given to Science News of the MSU Faculty of Physics by the Moscow University research group taking part in the international scientific collaboration. The Moscow group is the generally recognized leader in the field of quantum measurements for laser detectors of gravitational waves, and continues working actively in this area. I.A. Bilenko, S.P. Vyatchanin, M.L. Gorodetsky, V.P. Mitrofanov, L.G. Prokhorov, S.E. Strighin, F.Ya. Khalili, scientists from the Department of Physics of Oscillations at Moscow State University, are members of the research group.

February 11, 2016 at a press conference in Washington, scientists announced about the detection of gravitational waves the existence of which even 100 years ago, Albert Einstein predicted. Researchers of the Faculty of Physics of Moscow State University have been actively involved in this major scientific discovery. Until recently, the research group was headed by Corresponding Member of the Russian Academy of Sciences Vladimir Borisovich Braginsky — the world-famous scientist, one of the pioneers of gravitational wave research. Besides Professor V.B. Braginsky, the research group includes professors of the chair of physics of oscillations I.A. Bilenko, M.L. Gorodetsky, V.P. Mitrofanov, F.Ya. Khalili, S.P. Vyatchanin associate professor C.E. Strigin and assistant L.G. Prokhorov. They are co-authors of the scientific discovery. An invaluable contribution to the research was made by the students, graduate students and technical staff of the chair. The team members answer at SN editorial questions:

SN: Please tell us about the essence of the discovery that so excited not only the scientific world, but many people far from gravity. The gravitational waves were detected on September 14, 2015 at 9:51 UTC by both of the twin Laser Interferometer Gravitational-wave Observatory (LIGO) detectors, located in Livingston, Louisiana, and Hanford, Washington, USA. The LIGO Observatories are funded by the National Science Foundation (NSF), and were conceived, built, and are operated by Caltech and MIT. LIGO research is carried out by the LIGO Scientific Collaboration (LSC), a group of more than 1000 scientists from universities around the United States and in 14 other countries, including Russia, which is represented by two research groups: from Lomonosov Moscow State University (Moscow ) and the Institute of Applied Physics of the Russian Academy of Sciences ( Nizhny Novgorod). Notice of registration of gravitational waves has been published in the journal Physical Review Letters 116, 061102 (2016).

Based on these signals, scientists have concluded that the detected gravitational waves were produced during the final fraction of a second of the merger of two black holes to produce a single, more massive spinning black hole. This collision of two black holes had been predicted but never observed. Merging black holes have masses of 29 and 36 times the mass of the Sun. They moved on the final stage of the merger at about half the speed of light, as happened 1.3 billion years ago, the event itself. For a split second about 3 times the mass of the sun was converted into gravitational waves. By looking at the time of arrival of the signals— the detector in Livingston recorded the event 7 milliseconds before the detector in Hanford—scientists can say that the source was located in the Southern Hemisphere. On Earth, they have caused oscillations in the relative pairs of test masses separated by 4 kilometers with an amplitude of about 10–19 m . This is an extremely small change in the distance between the test masses and was recorded by interferometric gravitational wave detectors of the LIGO.

The discovery of gravitational waves is of great importance for modern science. A new era begins: the scientists can not only see but also hear the distant universe that will help solve many mysteries of the Universe.

SN: What are gravitational waves?

In 1915, Albert Einstein suggested that General Relativity (GR) , in which the gravity is interpreted as the curvature of space-time. As a simple analogy, consider a rubber film stretched over a horizontal hoop. If you start on the tape small balls, they will move in a straight line. This is analogous to the flat space. If one puts the massive apple in the center of the hoop, it will break» bend» a smooth film surface. If you then start the film by small balls, then they will move not in a straight line and an arc on «curve» line. I stress that this is not an explanation, but only a rough analogy. General relativity, Einstein received a decision from the equations corresponding to the gravitational waves (GW). However, it was clear that it is unlikely to detect them because of the extreme weakness of the gravitational interaction. Figuratively speaking, the GW — is flying pieces of space-time curvature. Recall that James Maxwell’s equations predict electromagnetic waves were obtained in 1864, and they were found experimentally by Heinrich Hertz only twenty years later (in 1885). The ability to transfer information with them (radio) has been demonstrated by Alexander Popov, another 20 years later (1905). Therefore, the detection of much weaker gravitational waves just a hundred years (!) after the formulation of general relativity can be regarded as a wonderful gift to Albert Einstein.

Hertz’s experiment on the detection of electromagnetic waves suspected presence of the emitter and receiver in the laboratory. But such a scheme as the transmitter — receiver can not be used for gravitational waves — again because of their weakness. Therefore, all that remains for us - hope for the registration of the GW from the cosmological catastrophes: supernova explosions, mergers of black holes, neutron stars, and so forth. By the way, in 1993, R. Hulse and J. Taylor won the Nobel Prize for the discovery of GW analyzing the speed of rotation of a double star, which is well described in the framework of general relativity as a loss of energy by radiation of GW. But it should be emphasized, it was only an indirect confirmation of GW, the waves themselves have not yet been registered.

It is now run improved antenna of the second generation: Advanced LIGO. This is the most complex and unique engineering structures. Suffice it to say that they will measure the displacement of the two mirrors (test mass) at a distance of 4 km, with incredible accuracy — about 10–19 m. To illustrate this, let us recall a well-known example: if the Earth is reduced to the size of an orange, the orange is reduced by the same factor, we get the size of an atom. If, however, reduce the number of times an atom, we have reduced the Earth, get the size of 10–19 m.

Interestingly, this corresponds exactly to the quantum limits for continuous measurement called standard quantum limit (SQL). Thus, if the Advanced LIGO will reach SQL (and perhaps even surpass it) that we get the quantum device! And very macroscopic — 4 km.

SN: 100 years passed from the time the prediction of the existence of gravitational waves to detect them. What can you tell us about the history of the search for gravitational waves?

The first attempt at an experimental detection of gravitational waves was made about 50 years after the prediction of their existence of Albert Einstein. The problem is that the gravitational waves generated even by the universal scale catastrophes cause very little response on Earth. The American physicist Joseph Weber has carried out the first experiment on the detection of gravitational waves. The detector he used is a 1.5 ton aluminum cylinder with piezoelectric transducers, registering cylinder deformation under the influence of a gravitational wave. In 1969 he announced the discovery of gravitational waves. Professor V.B. Braginsky was the first who have created the gravitational wave detector in the Faculty of physics. He checked and did not confirm the results of Weber’s detection of signals of gravitational waves. Science Newsletter № 1 / 2016 But while Weber’s attempt was unsuccessful, it marked the beginning of research on the creation of gravitational wave detectors. First it was the Weber -type detectors, but more advanced. The key point is to achieve the maximum quality factor for the mechanical oscillation modes of the cylinder — the detector, as well as its cooling, allowing significantly reduce thermal noise. It was experimentally demonstrated that materials such as sapphire and silicon, allows to obtain better mechanical Q- value than aluminum. However, a more sensitive detector of this type in various laboratories around the world has not led to the detection of gravitational waves. At the same time, V.B. Braginsky began to develop a theory of quantum measurements. He formulated the concept of the standard quantum limit of sensitivity and quantum non-demolition measurements and together with his colleagues applied the theory of quantum measurements to analyze the sensitivity of gravitational wave detectors. In 80-ies of XX century, the California Institute of Technology and the Massachusetts Institute of Technology in the United States have started creating laser interferometric gravitational wave detectors with the distance between the test masses, first 10 meters, then 40 meters. Later the modern detectors of gravitational waves LIGO with the length of arms of 4 km have been created. Since the signal of gravitational waves is proportional to the distance between the test masses, the transition to the interferometric detectors with long base has allowed to significantly increase their sensitivity. V. B. Braginsky together with his research group was directly involved in the work on the creation of interferometric detectors. Full-scale first-generation detectors, the creation of which began in 1992, failed to detect gravitational waves. Only more sophisticated Advanced LIGO detectors have detected gravitational waves generated by the merger of two black holes.

Later it became clear that such a simple system - a dielectric cylinder with a reflective coating, gives rise to a wide zoo of different basic quantum, thermodynamic and other excess noises. There are more than a dozen of types. In particular, it was found that the strongest noise of the mirrors is not the Brownian noise of the test mass but the noise of a thin dielectric multilayer reflective coating. In analysis and optimization of the coating, we were also seriously engaged.

SN: Please tell us a few words about LIGO detectors design.

The core of laser detector of gravitational waves is a Michelson interferometer: the laser beam is divided into two perpendicular beams that are reflected from the mirrors located at a distance of 4 km from the beam splitter, and fall back to a photodetector. Signal at its output dependent on the phase difference in the rays which, in turn, depends on the difference of passed paths. In order to increase the phase shift each arm is equipped with additional mirrors forming a Fabry-Perot cavities: we can say that the rays 300 times run over 4 kilometers in every direction before get into the photodetector. The frequencies that LIGO detectors can detect ranging from 10 Hz to several kilohertz (coincidentally exactly such frequencies perceived by a human ear). It is necessary to measure very small vibrations of the mirrors in this frequencies range, so a major problem in the design of the detector is to reduce all kinds of noise that can mask the desired signal or simulate it. Noises have different nature; we will mention only some of them. Fluctuations in the Earth’s surface caused by seismic and anthropogenic factors many orders of magnitude greater than the magnitude to be measured, so mirrors are hung on a complex, multi-stage filter to suppress these fluctuations. The light rays propagate inside the pipe where a high vacuum is maintained. Since light is a quantum phenomenon and consists of individual particles — photons, there is a special kind of fluctuations — the photon shot noise. It can be shown that, to minimize its effects is necessary to increase the intensity of light in the interferometer. Therefore, in the second generation detectors, which are used now, the laser sources power ranges from 15 to 100 watts, and the effective power stored inside the interferometer, due to accumulation in the resonators and use of so-called recycling of light, reaches one megawatt! The most important factor limiting the sensitivity is a Brownian noise — the result of the thermal motion of atoms and molecules. To reduce it monolithic quartz suspension of the mirrors having a large mechanical quality factor was developed. In general, the detector is an extremely complex device, which utilizes unique components, including a specially created for it in various laboratories around the world. Suffice it to say that the coating of mirrors is such a perfect one that from each million photons incident on them only one get lost, position adjustment of mirrors and other optical elements provided by over 5,000 tracking systems, and to process the incoming information (order of 1 terabyte per day) – several supercomputers and global distributed computing network are used.

SN: Please tell us about the participation in the project of scientists of the Faculty of Physics of Moscow State University.

From the outset, the main efforts of the team members were sent to the study of the conditions to achieve maximum sensitivity of gravitational wave detectors, determination of fundamental quantum and thermodynamic sensitivity constraints for the development of new measurement methods. Theoretical and experimental studies of Russian scientists were embodied in creating a new generation of detectors allowed to directly observe gravitational waves from merging black holes. Among the specific achievements of the research group of the Faculty of Physics are the following.

Fused silica test masses, they are also a mirror of the interferometer were suspended by steel wires in the first generation of detectors. Such suspensions are not allowed to reach the minimum loss of energy for their own modes of elastic vibrations and oscillations of its center of mass. According to the fluctuation-dissipation theorem, it is necessary to reduce thermal noise of the test masses. In addition, an additional excess noise is also extremely undesirable. The monolithic suspension of the fused silica test mass was developed in the V.B. Braginsky group. It was experimentally demonstrated that the decay time of the pendulum oscillation of the silica test mass is about 5 years, which corresponds to the quality factor of 1.8 x 108. Quasimonolithic suspension of the test masses in the detectors of Advanced LIGO — is a sophisticated 4-stage design, but it all started with simple models studied in the laboratory of the chair of physics of oscillations.

Another source of noise in gravitational antenna is vibration of mirrors’ surface. For a long time since the preliminary estimates of antenna sensitivity it was suggested that the only and main source of this vibration is Brownian noise of the probe masses on which reflective multiple layers are coated. To decrease the contribution of these fluctuations at lower frequencies of gravitational signal significantly one can manufacture probe masses from high-quality material, having maximal possible quality factor of acoustical oscillations. That is why, it was planned for the Advanced LIGO antenna to change fused silica, that was used before, to high purity leucosapphire (Al2O3). The development of these mirrors was under way, when we in our group decided to look for other physical processes which can lead to appearance of additional vibrations of surfaces. Rigorous calculations from the first principles revealed, that one of mechanisms associated with thermodynamic fluctuations of temperature in a volume of the sapphire crystal (thermoelastic noise), leads to much stronger fluctuations on the surface than Brownian ones not only for sapphire but also for fused silica. This work had an effect of bomb explosion, and the project had to be repainted on the move, returning to the silica mirrors.

Another problem, the solution of which we have worked in recent years, is associated with electrostatic charges, which are always present in the fused silica test masses. Their source is any contact of the test mass with other objects, desorption of gases, cosmic rays and so forth. The charges interact with the surrounding test mass bodies and electric fields, creating additional fluctuation effect. Important factors of reduction of the noise associated with electrostatic charges are to reduce their number and increase in the relaxation time of the charge distribution. In our experiments, it reached 3 years. In the summer of 2015, L.G. Prokhorov together with American colleagues investigated the charges behavior of test masses of LIGO detector in Hanford. They had set the optimum mode of operation of electrostatic actuators used to adjust the position of the test masses — the interferometer mirrors.

One of the important achievements of the group is the effect of parametric oscillatory instability predicted by V.B. Braginsky in 2001. In order to increase the sensitivity in the schemes of gravitational-wave interferometers Advanced LIGO is expected to reduce the mechanical noise of the mirrors and to increase the power circulating in the arms of the interferometer up to a value of W = 830 kW. However, large values of circulating power with low mechanical losses in the mirrors may result in undesirable nonlinear effect of parametric oscillatory instability.

Parametric interaction between two optical modes of Fabry-Perot resonator (pump and Stokes modes) and a mechanical oscillator (the oscillations of the mirrors) leads to the appearance of parametric instability. The existence of small oscillations in Stokes optical mode produces the ponderomotive force acting on a movable mirror at the difference frequency, which resonantly excites mechanical vibrations. On the other hand, small mechanical vibrations of the mirrors due to the Doppler effect lead to the appearance of the reflected waves with matching frequencies, one of which excites resonance vibrations in the optical Stokes mode. It is obvious that by increasing the pump power, these mechanisms will result in additional transfer of the energy. In accordance with the ratios of the Manley-Rowe, the energy from the pump wave will be transferred to the Stokes optical and mechanical modes. This effect can be viewed as introducing negative damping, so when a certain threshold of the pump power is reached the parametric instability will arise. Because of the asymmetry of the distribution of optical modes relative to the pump mode the effect of the simultaneous stimulation of anti-Stokes mode does not completely suppress the effect of parametric instability. In 2015, the effect of parametric oscillatory instability was observed experimentally in the gravitational-wave detector Advanced LIGO, fully confirming all the theoretical calculations of the group.

SN: Are there any fundamental limitations of the sensitivity of gravitational wave detectors?

The history of gravitational-wave astronomy from the very beginning was closely associated with development of methods of macroscopic quantum measurements. Sensitivity of the first solid-state bar detectors of gravitational waves (late 60s – early 70s) was about 100 attometers. In the next 20 years, it has been improved by about two orders of magnitude, to about 1 attometer. This value was already not so far away from zero-point quantum fluctuations of mechanical modes of the bar detectors, with the amplitudes of about 0.01 attometer for the typical late detectors.

The need for further increase the sensitivity by at least several orders of magnitude was already evident at that time, which triggered interest to exploration of quantum limitations in macroscopic mechanical measurements and to development of methods of circumventing these limitations. In 1968 V.B. Braginsky pointed out at so-called Standard Quantum Limit (SQL) of the precision in mechanical position measurements accuracy. The SQL is a direct consequence of the Heisenberg uncertainty relation. In the particular case of the harmonic oscillator it is equal to the amplitude of its zero-point oscillations. Search of methods of bypassing this limit resulted in the publication of two pioneering works, where two ideologically similar, but different in implementation measurement schemes allowing to overcome the SQL were proposed. The first one was authored by V.B. Braginsky and his colleagues and the second one — by one of the future founders of the LIGO project Kip Thorne and his colleagues.

These early works did receive any direct experimental continuation due to technological limitations of that time and also due to the fact that development of gravitational wave detectors went the other way. In early 80s designing and in the 90s — construction of the laser interferometric detectors begun. These devices have about the same accuracy of the of mechanical displacement measurement that the best bar detectors. However, their sensitivity to gravitational waves is much better simply due to their sheer size — kilometers compared with meters of the bar detectors. For example, the displacement sensitivity of the Advanced LIGO gravitational- wave detectors is currently a few times worse than the SQL (which is approximately equal to 0.05 attometers). However, their sensitivity to the gravitational waves exceeds the one of the best bar detectors by several orders of magnitude.

The design sensitivity of the Advanced LIGO, which should be reached in a few years, virtually equal to the SQL. The next iterations of the Advanced LIGO, as well as other future detectors have to surpass this limit. The only alternative to this is further increase of the lengths of the interferometer arms up to tens of kilometers; prospects for this are doubtful due to the financial limitations.

Development of methods of quantum measurements for the laser interferometers started in the MSu group in the early 90s. Now, of two main options of overcoming the SQL in laser interferometers, the first one, so-called quantum speed meter, was proposed by the MSU group and the second one, the interferometer with additional filter cavities, was developed with active participation the MSU group.

At present, Moscow State University Group is a recognized leader in the field of quantum measurements for laser detectors of gravitational waves and continues to actively work in this area.