Towards MIGO, the matter-wave interferometric gravitational-wave observatory, and the intersection of quantum mechanics with general relativity

Abstract

A dynamical, non-Euclidean spacetime geometry in general relativity theory implies the possibility of gravitational radiation. Here we explore novel methods of detecting such radiation from astrophysical sources by means of matter-wave interferometers (MIGOs), using atomic beams emanating from supersonic atomic sources that are further cooled and collimated by means of optical molasses. While the sensitivities of such MIGOs compare favorably with LIGO and LISA, the sizes of MIGOs can be orders of magnitude smaller, and their bandwidths wider. Using a pedagogical approach, we place this problem into the broader context of problems at the intersection of quantum mechanics with general relativity.worldline. If spacetime were strictly flat (as shown in figure 2(a)), these two straight and parallel worldlines would never meet. However, like the great circles on a sphere, or geodesics on a pseudosphere, in curved spacetimes these lines can either converge, or diverge from each other, respectively, depending on the sign of the components of the Riemann curvature tensor. An observer fixed on O would see the object P either come towards him, or go away from him, and would interpret this motion as being due to an effective 'tidal' force acting on P (see Chapter 1 of [4] for a description of this). In figure 2(b) we have drawn the specific case where components of the local Riemann curvature tensor are negative, and the worldlines diverge from one another. Since both the observer and the object are simply following their own worldlines-which are geodesics in the absence of all other forces on both the observer and the object-the equivalence principle still holds, and consequently this force is proportional to the mass of the object. The resulting motion of P as observed by O is therefore independent of the mass, composition, or thermodynamic state of the test object at P, and herein lies the geometrical meaning of the equivalence principle. Moreover, when the local Riemann curvature tensor between O and P can be approximated as a constant, this force, like the action of the Moon's gravity on the tides, increases linearly with the distance between O and P (see figure 2(b)), and indeed, the use of the name 'tidal' for this effective force comes from the tidal force on the oceans by the Moon's gravitational field.It is important to note that while the worldline illustrations in figure 2 are a visualization of geometry, and its connection to gravity and gravitational tidal forces, they are only a convenience, and do not represent any frame that can be achieved physically. As drawn, the perspectives are that of an Observer who is removed from the spacetime, and standing outside of it looking in. This is unphysical. Every experimental measurement is made through an experimental apparatus-which may be as simple a device as a pair eyes used to see the motion of an object P a small distance away-that is, by necessity, a physical object. As such, the apparatus must lie along a worldline in the spacetime of the universe, and cannot be...

Gravitational Wave Detection with Atom Interferometry

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Atomic gravitational wave interferometric sensor

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On the interaction of mesoscopic quantum systems with gravity

“…Finally, we note some further ideas which have led to proposed candidates for a measurable interaction between quantum mechanics and GR: (i) the interaction of Rydberg atoms with gravitational fields [36], (ii) an atomic analogue of the LIGO interference experiment labeled the 'Matter-wave Interferometric Gravitational-wave Observatory' (MIGO), in which quantum interference between atoms replaces the classical interference between light rays [37] (this proposition has been criticized recently in [38]), and (iii) the identification of the dark energy in the universe with the quantum fluctuations as determined in noise measurements in Josephson junctions [39].…”