How Does Interference Fall?

Abstract

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...

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

“…Version A is compatible with the results of Ref. [25], where it was shown that two-slit interference patterns fall like particles in a homogeneous gravitational field.…”

“…This statement of the EP also implies that wave function dispersion is the same for a free and a free-falling particle of the same type, which is a non-trivial prediction that is in principle testable. Version A is compatible with the results of [25], where it was shown that two-slit interference patterns fall like particles in a homogeneous gravitational field.…”

Puzzling out the mass-superselection rule

“…The result also offers an interpretation of the Newtonian theory of particles with dynamical masses in terms of low-energy relativistic particles with dynamical internal degrees of freedom. Our results are relevant to the growing body of works studying relativistic effects in low-energy quantum systems [12][13][14][15][16][17][18][19], and clarify why MSR does not invalidate the analyses, contrary to some arguments [20].…”

“…Independently of its interpretation, the regime of lowenergy particles with dynamical mass-energy has its own symmetry and phenomenology, and can be studied fully in its own right. It has already allowed exploring proper time effects in unstable [9] and interfering quantum particles [12,[14][15][16]42], it was used to assess the limits to the notion of an ideal clock [19,43] and to the notion of time [30], and to study the role of mass-energy equivalence in atom-light interactions [17,44]. The approach has further enabled a quantum formulation of the EEP for composite particles [18] and can shed light on the role of proper time in quantum-to-classical transition [13,[45][46][47].…”

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.…”