We investigate the gravitational Aharonov-Bohm effect by placing a quantum system in free fall around a gravitating body, e.g., a satellite orbiting the Earth. Since the system is in free fall, by the equivalence principle, the quantum system is local in flat, gravity free space-time---it is screened from the gravitational field. For a slightly elliptical orbit, the gravitational potential will change with time. This leads to the energy levels of the quantum system developing sidebands which is the signature for this version of the Aharonov-Bohm effect. This contrasts with the normal signature of the Aharonov-Bohm effect of shifting of interference fringes. 

Gravitational Aharonov-Bohm effect

Laser frequency noise is a dominant noise background for the detection of gravitational waves using long-baseline optical interferometry. Amelioration of this noise requires near simultaneous strain measurements on more than one interferometer baseline, necessitating, for example, more than two satellites for a space-based detector or two interferometer arms for a ground-based detector. We describe a new detection strategy based on recent advances in optical atomic clocks and atom interferometry which can operate at long baselines and which is immune to laser frequency noise. Laser frequency noise is suppressed because the signal arises strictly from the light propagation time between two ensembles of atoms. This new class of sensor allows sensitive gravitational wave detection with only a single baseline. This approach also has practical applications in, for example, the development of ultrasensitive gravimeters and gravity gradiometers.

A New Method for Gravitational Wave Detection with Atomic Sensors

Going Down the Tube Two pillars of modern physics are quantum mechanics and general relativity. So far, both have remained apart with no quantum mechanical description of gravity available. Van Zoest et al. (p. 1540; see the Perspective by Nussenzveig and Barata) present work with a macroscopic quantum mechanical system—a Bose-Einstein condensate (BEC) of rubidium atoms in which the cloud of atoms is cooled into a collective quantum state—in microgravity. By dropping the BEC down a 146-meter-long drop chamber and monitoring the expansion of the quantum gas under these microgravity conditions, the authors provide a proof-of-principle demonstration of a technique that can probe the boundary of quantum mechanics and general relativity and perhaps offer the opportunity to reconcile the two experimentally. Studies of atomic quantum states in free-fall conditions may provide ways to test predictions of general relativity. Albert Einstein’s insight that it is impossible to distinguish a local experiment in a “freely falling elevator” from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.

Bose-Einstein Condensation in Microgravity

On August 22, 2014, the satellites GSAT-0201 and GSAT-0202 of the European GNSS Galileo were unintentionally launched into eccentric orbits. Unexpectedly, this has become a fortunate scientific opportunity since the onboard hydrogen masers allow for a sensitive test of the redshift predicted by the theory of general relativity. In the present Letter, we describe an analysis of approximately three years of data from these satellites including three different clocks. For one of these, we determine the test parameter quantifying a potential violation of the combined effects of the gravitational redshift and the relativistic Doppler shift. The uncertainty of our result is reduced by more than a factor 4 as compared to the values of Gravity Probe A obtained in 1976.

pdf/test-of-the-gravitational-redshift-with-galileo-satellites-22bxhjxdhd.pdf

Test of the Gravitational Redshift with Galileo Satellites in an Eccentric OrbitenTest of the Gravitational Redshift with Galileo Satellites in an Eccentric Orbit

The Aharonov-Bohm effect is a quantum mechanical phenomenon that demonstrates how potentials can have observable effects even when the classical fields associated with those potentials are absent. Initially proposed for electromagnetic interactions, this effect has been experimentally confirmed and extensively studied over the years. More recently, the effect has been observed in the context of gravitational interactions using atom interferometry. Additionally, recent predictions suggest that temporal variations in the phase of an electron wave function will induce modulation sidebands in the energy levels of an atomic clock, solely driven by a time-varying scalar gravitational potential [1]. In this study, we consider the atomic clock as a two-level system undergoing continuous Rabi oscillations between the electron's ground and excited state. We assume the photons driving the transition are precisely frequency-stabilized to match the transition, enabling accurate clock comparisons. Our analysis takes into account, that when an atom transitions from its ground state to an excited state, it absorbs energy, increasing its mass according to the mass-energy equivalence principle. Due to the mass difference between the two energy levels, we predict that an atomic clock in an eccentric orbit will exhibit a constant frequency shift relative to a ground clock corresponding to the orbit's average gravitational redshift, with additional modulation sidebands due to the time-varying gravitational potential. 

Scalar gravitational Aharonov–Bohm effect: Generalization of the gravitational redshift

The flight model of the laser cooled cesium atomic clock, PHARAO, has been qualified for operation in space. The clock has passed the vibration, thermal and electromagnetic compatibility tests required to fly in low Earth orbit (400 km). On ground, the clock realized a typical frequency stability of 3.0x10-13 t-1/2 with an estimated accuracy of 2.3x10-15. Frequency comparisons with the SYRTE primary frequency standard FOM agree within their stated accuracies. Because PHARAO is optimized for the longer interaction times possible in microgravity, we expect a frequency stability of 1.1x10-13 t-1/2 and a frequency accuracy of 1.1x10-16 for operation in space. The clock has been delivered to the European Space Agency for the assembly of the ACES payload and is scheduled to be launched into space in 2021.

Qualification and frequency accuracy of the space based primary frequency standard PHARAO

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Qualification and frequency accuracy of the space based primary frequency standard PHARAO