Causality violation in the Glauber theory of photodetection

Michel De Haan

Michel De Haan

L I Plimak, Stig Stenholm, W P Schleich

A formal implementation of the concepts of mesoscopic electromagnetic interaction and of the propagating wave in quantum electrodynamics beyond the rotating wave approximation is discussed. Used as a guide, these concepts lead to a natural resolution of a long-standing controversy: causality violations in the Glauber–Kelley–Kleiner photodetection theory. The Glauber–Kelley–Kleiner definition of the time-normal operator ordering must be amended without the rotating wave approximation, which eliminates all causality problems.

Peter W. Milonni, Daniel F. V. James, H. Fearn

The theory of photodetection and quantum-optical coherence is formulated in the Heisenberg picture and in such a way that the causal propagation of fields at the velocity of light is manifest. Objections to the standard theory, based on a putative violation of causality, are shown to be unfounded, as is the notion that normal ordering is essential for the elimination of an infinite contribution from the vacuum field. In a similar vein we revisit the Fermi two-atom problem and explicitly demonstrate the causal nature of the interaction without invoking simplifying approximations that have recently been called into question.

Nadia Koliopoulou, Charis Anastopoulos, Ntina Savvidou

The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential relativistic principles of locality, causality, and Lorentz covariance, and are therefore inadequate for quantum field theoretic settings. While most existing work focuses on scalar fields, realistic particles possess spin, polarization, and internal degrees of freedom that introduce new conceptual and operational challenges. To this end, we employ the Quantum Temporal Probabilities (QTP) framework for relativistic measurements to describe electromagnetic, Dirac, and internally structured scalar fields. Our results include probabilities for the time-of-arrival that take spin/polarization into account, generalized photodetection formulas beyond Glauber's theory, an unambiguous derivation of the particle oscillation formula together with its limitations, and a first-principles analysis of relativistic qudits.

Jeffrey H. Shapiro

In semiclassical theory, light is a classical electromagnetic wave and the fundamental source of photodetection noise is the shot effect arising from the discreteness of the electron charge. In quantum theory, light is a quantum-mechanical entity and the fundamental source of photodetection noise comes from measuring the photon-flux operator. The Glauber coherent states are Gaussian quantum states which represent classical electromagnetic radiation. Quantum photodetection of these states yields statistics that are indistinguishable from the corresponding Poisson point-process results of semiclassical photodetection. Optical parametric interactions, however, can be used to produce other Gaussian quantum states, states whose photodetection behavior cannot be characterized semiclassically. A unified analytical framework is presented for Gaussian-state photodetection that includes the full panoply of nonclassical effects that have been produced via parametric interactions.