Squeezed gravitons from superradiant axion fields around rotating black holes

We propose, in ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>3</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> )-dimensional spacetimes, a novel astrophysical source of squeezed graviton states, due to superradiant axionic clouds surrounding rotating (Kerr-type) black holes (BHs). The microscopic origin of these axions is diverse, ranging from the Kalb-Ramond (model-independent) axions and compactification axions in string theory, to contorted geometries exemplified by a totally antisymmetric component of torsion in Einstein-Cartan theory. The axion fields couple to chiral gauge and gravitational Chern-Simons (CS) anomaly terms in the effective gravitational actions. In the presence of a Kerr BH background, such axions lead, upon acquiring a mass, to superradiance and the production of pairs of entangled gravitons in a squeezed state. The specific microscopic origin of the axions is not important, provided they are massive. We explain, by means of simplified but representative examples, how this multimode squeezed-graviton state can be studied via an Autonne-Takagi decomposition, used in quantum optics. In the effective action it is shown that squeezing effects associated with conventional general relativity (GR) dominate, by many orders of magnitude, the corresponding effects due to the CS gravitational anomaly terms. For a sufficiently long lifetime of the axionic cloud of the BH, we find that significant squeezing (quantified through the average number of gravitons with respect to the appropriate vacuum) can be produced from the GR effects. Our approach also allows for an imposition of phenomenological upper bounds on axion-cloud lifetimes, due to the nonobservation of squeezed graviton states in current interferometers. In addition, it is demonstrated explicitly that the structure of the entangled states (when the latter are expressed in a left-right polarization basis) depends highly on whether GR or the anomalous CS effects produce the entanglement.