A test of the equivalence principle(s) for quantum superpositions

Abstract

We propose a simple experimental test of the quantum equivalence principle introduced by Zych and Brukner [arXiv:1502.00971], which generalises the Einstein equivalence principle to superpositions of internal energy states. We consider a harmonically-trapped spin-1 2 atom in the presence of both gravity and an external magnetic field and show that when the external magnetic field is suddenly switched off, various violations of the equivalence principle would manifest as otherwise forbidden transitions. Performing such an experiment would put bounds on the various phenomenological violating parameters. We further demonstrate that the classical weak equivalence principle can be tested by suddenly putting the apparatus into free fall, effectively 'switching off' gravity.Classical equivalence principles.-At least since the days of Galileo and Newton, it has been known that acceleration under gravity is independent of an object's mass [1,2]. This peculiarity has led to the proposition of gravitational equivalence principles which, if broken, represent a departure from our current understanding of gravity. The weak equivalence principle (WEP) states that all objects, starting with the same position and velocity, and subject only to a gravitational field will follow the same trajectory, irrespective of the object's constituents or properties [3]. Mathematically, this statement translates to the inertial prescription of mass being equal to the gravitational prescription. Early tests of the WEP consisted of dropping similar objects of differing mass or measuring the period of pendulums [4]. These have now been superseded by extremely accurate torsion balance experiments [4-6], whose null results place limits as stringent as one part in 10 13 on WEP violation. Hoping to detect violations at very low mass scales, free-fall experiments have been performed with systems as light as individual neutrons, finding no deviation from equivalence [7][8][9][10].The mass-energy relation of special relativity [11], E = mc 2 , dictates that internal energy of a system must contribute to its mass; different internal energy states correspond to different effective masses for the system:2 , where the index k = {R, I, G} denotes quantities corresponding to the rest, inertial, and gravitational masses respectively and m ext is the mass of the system when the internal energy is at its lowest. The 'rest' internal energy E int R is derived from the Hamiltonian that generates internal dynamics in the absence of external motion. By explicitly labelling the inertial and gravitational contributions, we examine the possibility that they differ from each other. The gravitational effects of the mass-energy equivalence can be measured in the weak-field limit-where a Newtonian description is mostly satisfactory-avoiding the need for the complete machinery of general relativity. An example is the gravitational redshift observed in the seminal Pound-Rebka experiment, which can be calculated by coupling the effective massm = hν/c 2 to a * felix.pollock@mo...

Equivalence principle for quantum systems: dephasing and phase shift of free-falling particles

“…In order to obtain a QFT where inertial and gravitational mass differ, we have to start with a field-gravity coupling that is incompatible with General Relativity. Consider for example the Lagrangian, 15) where η µν is the Minkowski metric, λ is the gravitational coupling constant (proportional to the gravitational constant G) and U(x) a scalar field that describes the field coupling to gravity. Eq.…”

How Does Interference Fall?

“…Proposals for tests on board the international space station have been put forward which, if performed, are expected to surpass the best classical tests by a factor of 100 [11]. Finally, tests of the uniquely quantum mechanical equivalence principle for superpositions have also been proposed [12].…”

“…Proposals for tests on board the international space station have been put forward which, if performed, are expected to surpass the best classical tests by a factor of 100 [11]. Finally, tests of the uniquely quantum mechanical equivalence principle for superpositions have also been proposed [12].In this article, we study how single-and double-slit interference patterns fall due to gravity. Initially, we ignore the lowest order relativistic effects introduced by internal degrees of freedom and find (unsurprisingly) that the interference patterns fall just as classical objects do; in other words, the universality of free fall holds for spatially delocalised quantum systems.…”

Interesting Examples of Violation of the Classical Equivalence Principle but Not of the Weak One

“…We point out that [52][53][54][55] may be helpful for those interested in investigations similar in a sense to those dealt with in the present work.…”