|Type||International scientific collaboration|
|Purpose||Gravitational wave detection|
|CNRS (France), INFN (Italy), NIKHEF (Netherlands), POLGRAW (Poland), RMKI (Hungary) and Spain|
|Jo van den Brand|
|Affiliations||LVC (LIGO Scientific Collaboration and Virgo Collaboration)|
|About ten million euros per year|
|More than 320 people contribute to the Virgo experiment|
The Virgo interferometer is a large interferometer designed to detect gravitational waves predicted by the general theory of relativity. Virgo is a Michelson interferometer that is isolated from external disturbances: its mirrors and instrumentation are suspended and its laser beam operates in a vacuum. The instrument's two arms are three kilometres long and located in Santo Stefano a Macerata, near the city of Pisa, Italy.
Interferometry is a family of techniques in which waves, usually electromagnetic waves, are superimposed, causing the phenomenon of interference, which is used to extract information. Interferometry is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy, quantum mechanics, nuclear and particle physics, plasma physics, remote sensing, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, and optometry.
Gravitational waves are disturbances in the curvature (fabric) of spacetime, generated by accelerated masses, that propagate as waves outward from their source at the speed of light. They were proposed by Henri Poincaré in 1905 and subsequently predicted in 1916 by Albert Einstein on the basis of his general theory of relativity. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that physical interactions propagate instantaneously – showing one of the ways the methods of classical physics are unable to explain phenomena associated with relativity.
General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.
Virgo is part of a scientific collaboration of laboratories from six countries: Italy and France (the two countries behind the project), the Netherlands, Poland, Hungary and Spain. Other interferometers similar to Virgo have the same goal of detecting gravitational waves, including the two LIGO interferometers in the United States (at the Hanford Site and in Livingston, Louisiana). Since 2007, Virgo and LIGO have agreed to share and jointly analyze the data recorded by their detectors and to jointly publish their results.Because the interferometric detectors are not directional (they survey the whole sky) and they are looking for signals which are weak, infrequent, one-time events, simultaneous detection of a gravitational wave in multiple instruments is necessary to confirm the signal validity and to deduce the angular direction of its source.
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Two large observatories were built in the United States with the aim of detecting gravitational waves by laser interferometry. These can detect a change in the 4 km mirror spacing of less than a ten-thousandth the charge diameter of a proton.
The Hanford Site is a decommissioned nuclear production complex operated by the United States federal government on the Columbia River in Benton County in the U.S. state of Washington. The site has been known by many names, including Hanford Project, Hanford Works, Hanford Engineer Works and Hanford Nuclear Reservation. Established in 1943 as part of the Manhattan Project in Hanford, south-central Washington, the site was home to the B Reactor, the first full-scale plutonium production reactor in the world. Plutonium manufactured at the site was used in the first nuclear bomb, tested at the Trinity site, and in Fat Man, the bomb detonated over Nagasaki, Japan.
Livingston is the parish seat of Livingston Parish, Louisiana, United States. The population was 1,769 at the 2010 census.
The interferometer is named for the Virgo Cluster of about 1,500 galaxies in the Virgo constellation, about 50 million light-years from Earth. As no terrestrial source of gravitational wave is powerful enough to produce a detectable signal, Virgo must observe the Universe. The more sensitive the detector, the further it can see gravitational waves, which then increases the number of potential sources. This is relevant as the violent phenomena Virgo is potentially sensitive to (coalescence of a compact binary system, neutron stars or black holes; supernova explosion; etc.) are rare: the more galaxies Virgo is surveying, the larger the probability of a detection.
The Virgo Cluster is a cluster of galaxies whose center is 53.8 ± 0.3 Mly away in the constellation Virgo. Comprising approximately 1300 member galaxies, the cluster forms the heart of the larger Virgo Supercluster, of which the Local Group is a member. The Local Group actually experiences the mass of the Virgo Supercluster as the Virgocentric flow. It is estimated that the Virgo Cluster's mass is 1.2×1015M☉ out to 8 degrees of the cluster's center or a radius of about 2.2 Mpc.
A galaxy is a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter. The word galaxy is derived from the Greek galaxias (γαλαξίας), literally "milky", a reference to the Milky Way. Galaxies range in size from dwarfs with just a few hundred million stars to giants with one hundred trillion stars, each orbiting its galaxy's center of mass.
Virgo is one of the constellations of the zodiac. Its name is Latin for virgin, and its symbol is ♍. Lying between Leo to the west and Libra to the east, it is the second-largest constellation in the sky and the largest constellation in the zodiac. It can be easily found through its brightest star, Spica.
The Virgo project was approved in 1993 by the French CNRS and in 1994 by the Italian INFN, the two institutes at the origin of the experiment. The construction of the detector started in 1996 in the Cascina site near Pisa, Italy.
The Istituto Nazionale di Fisica Nucleare is the coordinating institution for nuclear, particle and astroparticle physics in Italy.
Cascina is a comune (municipality) in the Province of Pisa in the Italian region Tuscany, located about 60 kilometres (37 mi) west of Florence and about 13 kilometres (8 mi) southeast of Pisa.
Pisa is a city and comune in Tuscany, central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for its leaning tower, the city of over 91,104 residents contains more than 20 other historic churches, several medieval palaces, and various bridges across the Arno. Much of the city's architecture was financed from its history as one of the Italian maritime republics.
In December 2000,CNRS and INFN created the European Gravitational Observatory (EGO consortium), later joined by the Netherlands, Poland, Hungary and Spain. EGO is responsible for the Virgo site, in charge of the construction, the maintenance and the operation of the detector, as well as of its upgrades. The goal of EGO is also to promote research and studies about gravitation in Europe. By December 2015, 19 laboratories plus EGO were members of the Virgo collaboration.
The European Gravitational Observatory or EGO is located in the countryside near Pisa, in the hamlet of Santo Stefano a Macerata in the comune of Cascina. In order to ensure the long term scientific exploitation of the Virgo interferometric antenna for gravitational waves detection as well as to foster European collaboration in this upcoming field, the Virgo funding institutions have created a consortium called EGO.
The Netherlands is a country located mainly in Northwestern Europe. The European portion of the Netherlands consists of twelve separate provinces that border Germany to the east, Belgium to the south, and the North Sea to the northwest, with maritime borders in the North Sea with Belgium, Germany and the United Kingdom. Together with three island territories in the Caribbean Sea—Bonaire, Sint Eustatius and Saba— it forms a constituent country of the Kingdom of the Netherlands. The official language is Dutch, but a secondary official language in the province of Friesland is West Frisian.
Poland, officially the Republic of Poland, is a country located in Central Europe. It is divided into 16 administrative subdivisions, covering an area of 312,696 square kilometres (120,733 sq mi), and has a largely temperate seasonal climate. With a population of approximately 38.5 million people, Poland is the sixth most populous member state of the European Union. Poland's capital and largest metropolis is Warsaw. Other major cities include Kraków, Łódź, Wrocław, Poznań, Gdańsk, and Szczecin.
In the 2000s, the "initial" Virgo detector was built, commissioned and operated. The instrument reached its design sensitivity to gravitational wave signals. This long-term endeavour allowed the technical choices made to build Virgo to be validated; it also showed that giant interferometers are promising devices to detect gravitational waves in a wide frequency band.However, the initial Virgo detector was not sensitive enough to achieve such a detection. Therefore, it was decommissioned from 2011 in order to be replaced by the "advanced" Virgo detector which aims at increasing its sensitivity by a factor of 10. The advanced Virgo detector benefits from the experience gained on the initial detector and from technological advances since it was made.
The construction of the initial Virgo detector was completed in June 2003and several data taking periods followed between 2007 and 2011. Some of these runs were done in coincidence with the two LIGO detectors. Then a long upgrade to the second generation detector, called Advanced Virgo, started; its aim is to reach a sensitivity one order of magnitude better than the initial Virgo detector, allowing it to probe a volume of the Universe 1,000 times larger, making detections of gravitational waves more likely.
Advanced Virgo started commissioning in 2016, joining the two advanced LIGO detectors ("aLIGO") for a first "engineering" observing period in May and June 2017.On 14 August 2017, LIGO and Virgo detected a signal, GW170814, which was reported on 27 September 2017. It was the first binary black hole merger detected by both LIGO and Virgo.
The first goal of Virgo is to directly observe gravitational waves, a straightforward prediction of Albert Einstein's general relativity.The study over three decades of the binary pulsar 1913+16, whose discovery was awarded the 1993 Nobel Prize in Physics, led to indirect evidence of the existence of gravitational waves. The observed evolution over time of this binary pulsar's orbital period is in excellent agreement with the hypothesis that the system is losing energy by emitting gravitational waves. The rotation motion is accelerating (its period, reported in 2004 to be 7.75 hours, is decreasing by 76.5 microseconds per year) and the two compact stars get closer by about three meters each year. They should coalesce in about 300 million years. But only the very last moments preceding that particular cosmic collision will generate gravitational waves strong enough to be visible in a detector like Virgo. This theoretical scenario for the evolution of Binary Pulsar B1913+16 would be confirmed by a direct detection of gravitational waves from a similar system, the main goal of giant interferometric detectors like Virgo and LIGO.
On the longer term, after accomplishing the primary goal of discovering gravitational waves, Virgo aims at being part of the birth of a new branch of astronomy by observing the Universe with a different and complementary perspective than current telescopes and detectors. Information brought by gravitational waves will be added to those provided by the study of the electromagnetic spectrum (microwaves, radio waves, infrared, the visible spectrum, ultraviolet, X-rays and gamma rays), of cosmic rays and of neutrinos. In order to correlate a gravitational wave detection with visible and localized events in the sky, the LIGO and Virgo collaborations have signed bilateral agreements with many teams operating telescopes to quickly inform (on the timescale of a few days or a few hours) these partners that a potential gravitational wave signal has been observed. These alerts must be sent before knowing whether the signal is real or not, because the source (if it is real) may only remain visible during a short amount of time.
In general relativity, a gravitational wave is a space-time perturbation which propagates at the speed of light. It then curves slightly the space-time, which changes locally the light path. Mathematically speaking, if is the amplitude (assumed to be small) of the incoming gravitational wave and the length of the optical cavity in which the light is in circulation, the change of the optical path due to the gravitational wave is given by the formula:
with being a geometrical factor which depends on the relative orientation between the cavity and the direction of propagation of the incoming gravitational wave.
To start with, Virgo is a Michelson interferometer whose mirrors are suspended. A laser is divided into two beams by a beam splitter tilted by 45 degrees. The two beams propagate in the two perpendicular arms of the interferometer, are reflected by mirrors located at the end of the arms and recombine on the beam splitter, generating interferences which are detected by a photodiode. An incoming gravitational wave changes the optical path of the laser beams in the arms, which then changes the interference pattern recorded by the photodiode.
The signal induced by a potential gravitational wave is thus "embedded" in the light intensity variations detected at the interferometer output.Yet, several external causes—globally denoted as noises—changes the interference pattern perpetually and significantly. Should nothing be done to remove or mitigate them, the expected physical signals would be buried in noise and would then remain undetectable. The design of detectors like Virgo and LIGO thus requires a detailed inventory of all noise sources which could impact the measurement, allowing a strong and continuing effort to reduce them as much as possible. During the data taking periods, dedicated software monitors in real time the noise levels in the interferometer, and deep studies are carried out to identify the loudest noises and mitigate them. Each period during which a detector is found to be "too noisy" is excluded from the data analysis: these dead times need to be reduced as much as possible.
A detector like Virgo is characterized by its sensitivity, a figure of merit providing information about the tiniest signal the instrument could detect—the smaller the value of the sensitivity, the better the detector. The sensitivity varies with frequency as each noise has its own frequency range. For instance, it is foreseen that the sensitivity of the advanced Virgo detector be ultimately limited by:
Virgo is a wide band detector whose sensitivity ranges from a few Hz up to 10 kHz. Mathematically speaking, its sensitivity is characterized by its power spectrum which is computed in real time using the data recorded by the detector. The curve opposite shows an example of a Virgo amplitude spectrum density (the square root of the power spectrum) from 2011, plotted using log-log scale.
Using an interferometer rather than a single optical cavity allows one to enhance significantly the sensitivity of the detector to gravitational waves. changes by a quantity , the perpendicular optical path of same length changes by (same magnitude but opposite sign). And the interference at the output port of a Michelson interferometer depends on the difference of length between the two arms: the measured effect is hence amplified by a factor 2 with respect to a simple cavity.Indeed, in this configuration based on an interference measurement, the contributions from some experimental noises are strongly reduced: instead of being proportional to the length of the single cavity, they depend in that case on the length difference between the arms (so equal arm length cancels the noise). In addition, the interferometer configuration benefits from the differential effect induced by a gravitational wave in the plane transverse to its direction of propagation: when the length of an optical path
Then, one has to "freeze" the various mirrors of the interferometer: when they move, the optical cavity length changes and so does the interference signal read at the instrument output port. The mirror positions relative to a reference and their alignment are monitored accurately in real timewith a precision better than the tenth of a nanometre for the lengths; at the level of a few nanoradians for the angles. The more sensitive the detector, the narrower its optimal working point.
Reaching that working point from an initial configuration in which the various mirrors are moving freely is a control system challenge.In a first step, each mirror is controlled locally to damp its residual motion; then, an automated sequence of steps, usually long and complex, allows one to make the transition between a series of independent local controls to a unique global control steering the interferometer as a whole. Once this working point is reached, it is simpler to keep it as error signals read in real time provide a measurement of the deviation between the actual state of the interferometer and its optimal condition. From the measured differences, mechanical corrections are applied on the various mirrors to bring the system closer to its best working point.
The optimal working point of an interferometric detector of gravitational waves is slightly detuned from the "dark fringe", a configuration in which the two laser beams recombined on the beam splitter interfere in a destructive way: almost no light is detected at the output port. Calculations show that the detector sensitivity scales as , where is the arm cavity length and the laser power on the beam splitter. To improve it, these two quantities must be increased.
Seen from the air, the Virgo detector has a characteristic "L" shape with its two 3-km long perpendicular arms. The arm "tunnels" house vacuum pipes with a 120 cm diameter in which the laser beams are travelling under ultra-high vacuum. To increase the interaction between the light and an incoming gravitational wave, a Fabry-Perot optical cavity is installed in each arm as well as a mirror called "recycling mirror" at the instrument entrance, between the laser source and the beam splitter.
Virgo is sensitive to gravitational waves in a wide frequency range, from 10 Hz to 10,000 Hz. The main components of the detector are the following:
The initial Virgo detector recorded scientific data from 2007 to 2011 during four science runs.There was a shut-down of a few months in 2010 to allow for a major upgrade of the Virgo suspension system: the original suspension steel wires were replaced by glass fibers in order to reduce the thermal noise. After several months of data taking with this final configuration, the initial Virgo detector was shut down in September 2011 to begin the installation of Advanced Virgo.
The Advanced Virgo aims to be 10 times more sensitive than the initial Virgo. mm in diameter, with a weight of 40 kg), and their optical performances have been improved. The critical optical elements used to control the interferometer are under vacuum on suspended benches. A system of adaptive optics was to be installed to correct the mirror aberrations in-situ. In the final Advanced Virgo configuration, the laser power will be 200 W.According to the Advanced Virgo Technical Design Report VIR–0128A–12 of 2012, advanced Virgo keeps the same vacuum infrastructure as Virgo, with four additional cryotraps located at both ends of both three-kilometre-long arms to trap residual particles coming from the mirror towers, but the remainder of the interferometer has been significantly upgraded. The new mirrors are larger (350
A milestone for the Advanced Virgo was reached in 2017 with the installation of the new detector. A first joint science run with LIGO, in the second half of 2017, started following a commissioning period of a few months.
The first detection of gravitational waves by Virgo is known as GW170814, which was announced on 27 September 2017 in a G7 science meeting conference in Turin, Italy.
Just few days later, GW170817 was detected by the LIGO and Virgo on 17 August 2017. The GW was produced by the last minutes of two neutron stars spiralling closer to each other and finally merging, and is the first GW observation which has been confirmed by non-gravitational means.
The full design sensitivity of the Advanced Virgo should be achieved in 2018.
The Laser Interferometer Space Antenna (LISA) is a European Space Agency mission designed to detect and accurately measure gravitational waves—tiny ripples in the fabric of space-time—from astronomical sources. LISA would be the first dedicated space-based gravitational wave detector. It aims to measure gravitational waves directly by using laser interferometry. The LISA concept has a constellation of three spacecraft, arranged in an equilateral triangle with sides 2.5 million km long, flying along an Earth-like heliocentric orbit. The distance between the satellites is precisely monitored to detect a passing gravitational wave.
The Michelson interferometer is a common configuration for optical interferometry and was invented by Albert Abraham Michelson. Using a beam splitter, a light source is split into two arms. Each of those light beams is reflected back toward the beamsplitter which then combines their amplitudes using the superposition principle. The resulting interference pattern that is not directed back toward the source is typically directed to some type of photoelectric detector or camera. For different applications of the interferometer, the two light paths can be with different lengths or incorporate optical elements or even materials under test.
The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer. A beam of light is split and the two beams are made to follow the same path but in opposite directions. On return to the point of entry the two light beams are allowed to exit the ring and undergo interference. The relative phases of the two exiting beams, and thus the position of the interference fringes, are shifted according to the angular velocity of the apparatus. In other words, when the interferometer is at rest with respect to a nonrotating frame, the light takes the same amount of time to traverse the ring in either direction. However, when the interferometer system is spun, one beam of light has a longer path to travel than the other in order to complete one circuit of the mechanical frame, and so takes longer, resulting in a phase difference between the two beams. This arrangement is also called a Sagnac interferometer. Georges Sagnac set up this experiment to prove the existence of the aether that Einstein's theory of special relativity had discarded.
GEO600 is a gravitational wave detector located near Sarstedt in the South of Hanover, Germany. It is designed and operated by scientists from the Max Planck Institute for Gravitational Physics, Max Planck Institute of Quantum Optics and the Leibniz Universität Hannover, along with University of Glasgow, University of Birmingham and Cardiff University in the United Kingdom, and is funded by the Max Planck Society and the Science and Technology Facilities Council (STFC). GEO600 is part of a worldwide network of gravitational wave detectors. This instrument, and its sister interferometric detectors, when operational, are some of the most sensitive gravitational wave detectors ever designed. They are designed to detect relative changes in distance of the order of 10−21, about the size of a single atom compared to the distance from the Sun to the Earth. GEO600 is capable of detecting gravitational waves in the frequency range 50 Hz to 1.5 kHz. Construction on the project began in 1995.
The Kamioka Gravitational Wave Detector (KAGRA), formerly the Large Scale Cryogenic Gravitational Wave Telescope (LCGT), is a project of the gravitational wave studies group at the Institute for Cosmic Ray Research (ICRR) of the University of Tokyo. It aims to be the world's first major gravitational wave observatory that is built underground, and the first major detector to use cryogenic mirrors. It will also be the first major gravitational wave observatory in Asia.
A gravitational-wave observatory is any device designed to measure gravitational waves, tiny distortions of spacetime that were first predicted by Einstein in 1916. Gravitational waves are perturbations in the theoretical curvature of spacetime caused by accelerated masses. The existence of gravitational radiation is a specific prediction of general relativity, but is a feature of all theories of gravity that obey special relativity. Since the 1960s, gravitational-wave detectors have been built and constantly improved. The present-day generation of resonant mass antennas and laser interferometers has reached the necessary sensitivity to detect gravitational waves from sources in the Milky Way. Gravitational-wave observatories are the primary tool of gravitational-wave astronomy.
Gravitational-wave astronomy is an emerging branch of observational astronomy which aims to use gravitational waves to collect observational data about objects such as neutron stars and black holes, events such as supernovae, and processes including those of the early universe shortly after the Big Bang.
The Australian International Gravitational Observatory (AIGO) is a research facility located near Gingin, north of Perth in Western Australia. It is part of a worldwide effort to directly detect gravitational waves. Note that these are a major prediction of the general theory of relativity and are not to be confused with gravity waves, a phenomenon studied in fluid mechanics.
An interferometric gravitational-wave detector is a gravitational wave detector that uses laser interferometry to detect the influence of gravitational waves on light that is moving back and forth between test masses.
Carlton "Carl" Morris Caves is an American physicist. He is currently Professor Emeritus and Distinguished Professor in Physics and Astronomy at the University of New Mexico. Caves works in the areas of physics of information; information, entropy, and complexity; quantum information theory; quantum chaos, quantum optics; the theory of non-classical light; the theory of quantum noise; and the quantum theory of measurement.
Einstein Telescope (ET) or Einstein Observatory, is a proposed third-generation ground-based gravitational wave detector, currently under study by some institutions in the European Union. It will be able to test Einstein's general theory of relativity in strong field conditions and realize precision gravitational wave astronomy.
David Reitze is an American laser physicist who is Professor of Physics at the University of Florida and served as the scientific spokesman of the Laser Interferometer Gravitational-Wave Observatory (LIGO) experiment in 2007-2011. In August 2011, he took a leave of absence from the University of Florida to be the Executive Director of LIGO, stationed at the California Institute of Technology, Pasadena, California. He obtained his BA in 1983 from Northwestern University, his PhD in Physics from the University of Texas at Austin in 1990, and had positions at Bell Communications Research and Lawrence Livermore National Laboratory, before taking his faculty position at the University of Florida. He is a Fellow of the American Physical Society and The Optical Society.
Allegro was a ground-based, cryogenic resonant Weber bar, gravitational-wave detector run by Warren Johnson, et al. at Louisiana State University in Baton Rouge, Louisiana. The detector was commissioned in the early 90's, and was decommissioned in 2008.
INDIGO, or IndIGO is a consortium of Indian gravitational-wave physicists. This is an initiative to set up advanced experimental facilities for a multi-institutional observatory project in gravitational-wave astronomy located near Aundha Nagnath, Hingoli District, Maharashtra.
The International Pulsar Timing Array (IPTA) is a multi-institutional, multi-telescope collaboration, comprising the European Pulsar Timing Array (EPTA), the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), and the Parkes Pulsar Timing Array (PPTA). The goal of the IPTA is to detect gravitational waves using an array of approximately 30 pulsars. This goal is shared by each of the participating institutions, but they have all recognized that their goal will be achieved more quickly in collaboration, and by combining their respective resources.
A common-path interferometer is a class of interferometers in which the reference beam and sample beams travel along the same path. Examples include the Sagnac interferometer, Zernike phase-contrast interferometer, and the point diffraction interferometer. A common-path interferometer is generally more robust to environmental vibrations than a "double-path interferometer" such as the Michelson interferometer or the Mach–Zehnder interferometer. Although travelling along the same path, the reference and sample beams may travel along opposite directions, or they may travel along the same direction but with the same or different polarization.
The first direct observation of gravitational waves was made on 14 September 2015 and was announced by the LIGO and Virgo collaborations on 11 February 2016. Previously, gravitational waves had only been inferred indirectly, via their effect on the timing of pulsars in binary star systems. The waveform, detected by both LIGO observatories, matched the predictions of general relativity for a gravitational wave emanating from the inward spiral and merger of a pair of black holes of around 36 and 29 solar masses and the subsequent "ringdown" of the single resulting black hole. The signal was named GW150914. It was also the first observation of a binary black hole merger, demonstrating both the existence of binary stellar-mass black hole systems and the fact that such mergers could occur within the current age of the universe.
In quantum physics, light is in a squeezed state, if its electric field strength Ԑ for some phases has a quantum uncertainty smaller than that of a coherent state. The term squeezing thus refers to a reduced quantum uncertainty. To obey Heisenberg's uncertainty relation, a squeezed state must also have phases at which the electric field uncertainty is anti-squeezed, i.e. larger than that of a coherent state.