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 These have now been superseded by extremely accurate torsion balance experiments [4-6], whose null results place limits as stringent as one part in 10 13 on WEP violation.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...

We study how single-and double-slit interference patterns fall in the presence of gravity. First, we demonstrate that universality of free fall still holds in this case, i.e., interference patterns fall just like classical objects. Next, we explore lowest order relativistic effects in the Newtonian regime by employing a recent quantum formalism which treats mass as an operator. This leads to interactions between nondegenerate internal degrees of freedom (like spin in an external magnetic field) and external degrees of freedom (like position). Based on these effects, we present an unusual phenomenon, in which a falling double slit interference pattern periodically decoheres and recoheres. The oscillations in the visibility of this interference occur due to correlations built up between spin and position. Finally, we connect the interference visibility revivals with non-Markovian quantum dynamics. * patrick.james.orlando@gmail.com † felix.pollock@monash.edu ‡ kavan.modi@monash.edu 1 arXiv:1610.02141v1 [quant-ph] Oct 2016Since the days of Galileo and Newton, it has been known that acceleration under the influence of gravity is independent of an object's mass [1,2]. This peculiarity has led to the proposition of various gravitational equivalence principles which, if broken, represent a departure from our current understanding of the theory of gravity. Einstein's theory of general relativity is fundamentally classical, describing gravity on large length scales in terms of curvature of the underlying spacetime metric. Although it is possible to formulate quantum field theories on a static curved metric, it remains unclear how existing theory should be modified to describe gravity on the quantum mechanical scale [3]. Whilst the work we present here does not attempt to quantise gravity, it demonstrates that there is much insight to be gained from exploring non-relativistic quantum mechanics in weak-field gravity.In the weak-field limit, a Newtonian description of gravity provides a satisfactory approximation and is, advantageously, compatible with the Hamiltonian formulation of quantum mechanics; however, its disadvantage lies in the concealment of relativistic effects, such as gravitational time dilation and the gravitational redshift of photons. Fortunately, one need not utilise the complete machinery of general relativity to take these effects into account. In fact, lowest order relativistic effects can be introduced by simply considering the mass contributions of different energy states, as given by the mass-energy relation E = mc 2 of special relativity [4]. This is true even in the case of internal energy and becomes particularly interesting for quantum systems, whose internal energy can exist in superposition. Recent work by Zych and Brukner [5] treats this by promoting mass to an operator, the purpose of which is to account for the effective mass of quantised internal energy. In addition to introducing lowest order relativistic effects, this construction provides a new quantum mechanical generalisatio...

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