We study the quantum field evolution in a temporal imaging system, including the vacuum noise due to finite time aperture. We show how the gravitational wave detector signal can be transmitted to a higher frequency.
Optical temporal imaging is a technique of stretching or compressing an optical waveform in time, while fully preserving its temporal structure [1]. The key element of a temporal imaging system is a time lens, introducing a quadratic in time phase modulation into the signal field, which may be based, for example, on the sum-frequency generation (SFG). A quantum treatment of the time lens becomes important in some special cases, in particular when the information on some physical process is conveyed by single photons or by squeezed light [2,3].
Using the space-time analogy, we compare the performance of quantum temporal imaging with its classical counterpart. We consider a temporal imaging scheme, based on the sum-frequency generation time lens, but our results can be applied to other temporal imaging schemes such as, for instance, four-wave mixing. Extending the theory presented in our previous publications, in this paper we take into account the finite time aperture of the imaging system, characterized by its pupil function. Using the quantum theory, we obtain a unitary transformation of the quantum field from the input to the output of the imaging scheme and identify the contribution of the vacuum fluctuations missing in the classical theory. This contribution plays a key role in the quantum temporal imaging of nonclassical temporal waveforms, characterized by nonclassical fluctuations of the electromagnetic field. As an example, we consider quantum temporal imaging of broadband squeezed light and formulate the criteria for conservation of its squeezing properties at the output of the system.
A century after Einstein's formulation of general relativity, the detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) made the first direct detection of gravitational waves. This historic achievement was the culmination of a world-wide effort and decades of instrument research. While sufficient for this monumental discovery, the current generation of gravitational-wave detectors represent the least sensitive devices necessary for the task; improved detectors will be required to fully exploit this new window on the Universe. In this paper, we review the application of squeezed vacuum states of light to gravitational-wave detectors as a way to reduce quantum noise, which currently limits their performance in much of the detection band.
Since 2015, the gravitational-wave detectors LIGO and Virgo have opened a new window on the universe, detecting hundreds of signals and launching a new era of astronomy with profound impact on relativity, astrophysics, and cosmology. To listen deeper into the cosmos, detectors must become increasingly sensitive. One of the main limitations is quantum noise, ultimately arising from vacuum fluctuations entering the instrument. By “squeezing” this vacuum, i.e. manipulating its noise properties, LIGO and Virgo have already extended their reach by up to 65%, revealing events that would otherwise remain hidden. This article provides an overview of squeezing techniques for gravitational-wave detectors, from their origins to the most recent advances.
Among the revolutionary predictions of Einstein’s theory of general relativity is the existence of gravitational waves, which are perturbations in the fabric of spacetime that travel at the speed of light. The first indirect evidence pointing to their existence came from the observation of the Hulse-Taylor pulsar in 1974[4]. More recently, gravitational wave observatories like the Laser Interferometer Gravitational-wave Observatory (LIGO) and Virgo have been built with the purpose of detecting gravitational waves (GW) directly, providing not only further evidence in support of general relativity, but also a whole new way of viewing the cosmos. The strain produced by a passing gravitational wave (namely, the relative change in the length of the matter a gravitational wave passes through) is so small that the best sensitivity achieved by the detectors has not produced a positive detection as of today. With a clear understanding that there should be gravitational waves, scientists are working on improving the sensitivity of the detectors to increase the likelihood of a detection. One of the main sources of noise for the next generation gravitational wave detectors, such as advanced LIGO, is shot noise. Shot noise dominates the noise spectrum above a few hundred Hz. This noise is due to uncertainties in quantum statistics, according to the generalized uncertainty principle. There are two ways to reduce the shot noise. The first way is to increase the intensity of the