Relativistic Particle Motion and Quantum Optics in a Weak Gravitational Field

Abstract: The possibility of long-baseline quantum experiments in space makes it necessary to better understand the time evolution of relativistic quantum particles in a weakly varying gravitational field. We explain why conventional treatments by traditional quantum optics and atomic physics based on quantum mechanics may become inadequate when faced with issues related to locality, simultaneity, signaling, causality, etc. Quantum field theory is needed. Adding the effects of gravitation, we are led to Quantum Field Theory in Curved Spacetime (QFTCST). This well-established theory should serve as the canonical reference theory to a large class of proposed space experiments testing the foundations of gravitation and quantum theory, and the basic notions of quantum information theory in relativistic settings. This is the first in a series of papers treating near-term quantum optics and matter waves experiments in space from the perspective of QFTCST. We analyze the quantum motion of photons and of scalar massive particles using QFTCST with application to interferometer experiments. Our main result is that, for photons, the weak gravitational field is to leading order completely equivalent to an inhomogeneous dielectric, thus allowing for a description of quantum optics experiments in curved space using familiar notions from the theory of optical media. We also discuss interference experiments that probe first-order quantum coherence, the importance of a covariant particle detection theory, and the relevance of time of arrival measurements. For massive particles with internal structure, we identify a novel gravity-induced phase shift that originates from the different gravitational masses attributed to the excited internal states. This phase shift can in principle be measured in space experiments.