PHOTONICS INSIGHTS
quantum correlations
ends of the arms, mirrors reflect the beams back toward the beam splitter. The returning beams recombine at the interferometer output, producing interference. The output power depends on the difference in the arms’ lengths. A passing gravitational wave induces a differential change in the arm lengths, altering the interference condition and causing a measurable power variation at the detector output. The challenge in these measurements lies in reducing every possible source of noise that could mask the tiny variations caused by gravitational waves( of the order of 10-19 m over 3 km). Over the past 10 years since the first detection, more than 300 gravitational wave events have been measured from merging compact objects, especially binary black hole systems. This new form of astronomy has already unveiled a new cosmos: previously unobserved binary black hole systems and a new population of more massive black holes. They have also enabled new measurements of the universe’ s expansion rate, contributing to a major scientific debate that may lead to a crisis in modern cosmology. Over the next decade, gravitational waves will provide even more insight into cosmology, nuclear physics, and astrophysics— and may even offer clues to a quantum theory of gravity, the holy grail of theoretical physics. To push this scientific program forward, detectors must increase their sensitivity more and more. This is a challenging task, as lowering the noise level becomes increasingly difficult when approaching the fundamental limits of the instruments. The main limiting factor is quantum noise, which constrains the detector sensitivity across much of its frequency band( 10 Hz to a few kHz). In a semi-classical view, quantum noise arises because light consists of photons. The photon arrival rate in a laser beam follows a Poissonian distribution, meaning the power on a photodiode fluctuates around a mean value. This results in the so-called“ shot noise,” which limits the precision with which changes in the interferometer’ s output power can be measured. Reducing shot noise can be achieved by increasing the laser power, as fluctuations scale more slowly than the photon flux. This strategy has been employed and additional power enhancements are planned in upcoming instrument upgrades. Nonetheless, it presents two notable limitations: on one hand, it
Figure 2. Timeline of experimentally achieved squeezed-light levels since the first demonstration in 1985, showing steady improvements in noise reduction over time. From wikipedia: https:// commons. wikimedia. org / wiki / File: Squeezed-light-timeline. svg increases radiation pressure, a random force arising from fluctuations in the arrival times of photons on the interferometer’ s test masses( i. e., the mirrors), which causes random motion of the mirrors masking the effect of gravitational waves. Moreover, elevated laser power induces thermal effects that deform the interferometer mirrors, introducing optical aberrations which substantially degrade sensitivity and may compromise detector operation. But light is not just particles; it is also a wave. When we apply quantum mechanics to light, by quantizing the electromagnetic field, we get a different and powerful view of quantum noise. This insight came from the physicist Carlton Caves in the 1980s. While investigating how laser radiation pressure affected detectors, Caves developed a fully quantum picture of quantum noise in the interferometer and realized that it actually comes from the vacuum fluctuations [ 2 ]. Such fluctuations, also known as " zero-point fluctuations " allow virtual particles( like photons) to be created and destroyed temporarily, due to Heisenberg’ s uncertainty principle. They are also responsible for laser spontaneous emission, the Lamb shift, and the Casimir effect( a force between two metal plates in vacuum). In a fully quantum picture, laser light can be described by a coherent state. Such a state is characterized by the fact that its phase and its amplitude( which are two canonically conjugate variables) have the minimum possible uncertainty allowed by the Heisenberg principle. This laser state can be represented in the phase – amplitude plane as a circle displaced from the origin by an amount corresponding to the laser’ s amplitude. A vacuum state is also a coherent state, a state with minimum uncertainty, with zero amplitude and its representation in the phase-amplitude plane is a circle cantered in the origin( See Fig. 3 left panel). The key point to keep in mind is that laser and vacuum are much alike when it comes to considering their fluctuations; the only difference is that these fluctuations occur around a given amplitude for the laser and around zero
56 www. photoniques. com I Photoniques 134