Aspects of entanglement with background electric and magnetic fields in quantum field theoretic systems

Abstract

This thesis investigates the impact of the background magnetic field on correlations or entanglement between pairs created by the background electric field in quantum field theoretic systems in the Minkowski, the primordial inflationary de Sitter and the Rindler spacetimes. These analyses might provide insight into the relativistic entanglement in the early inflationary universe scenario, where such background fields might exist due to primordial fluctuations, and in the near-horizon of non-extremal black holes, which are often endowed with background electromagnetic fields due to the accretion of plasma onto them. In the beginning, with a brief introduction to relativistic quantum field theory in curved spacetimes, a review of relevant spacetimes and quantum field phenomenon in these spacetimes is provided. After that, we reviewed the Schwinger effect and different measures to quantify correlations or entanglement. In the first objective of this thesis, we begin with the simplest scenario in which we consider two complex scalar fields, not necessarily of the same rest masses, coupled to the constant background electric and mag¬netic fields in the (3 + 1)-dimensional Minkowski spacetime and subsequently investigate a few measures quantifying the correlations between the created Schwinger pairs. Since the background magnetic field itself cannot cause the decay of the Minkowski vacuum, our chief motivation here is to investigate the interplay between the effects due to the electric and magnetic fields. We first compute the entanglement entropy for the vacuum state of a single scalar field. Next, we consider some maximally entangled states for the two-scalar field system and compute the logarithmic negativity and the mutual information corresponding to different particle-antiparticle excitations. In the second objective, we consider Dirac fermions in the cosmological de Sitter spacetime in the presence of background electric and magnetic fields of constant strength. We investigate the violation of the Bell inequality and the mutual information. This scenario has two sources of particle creation: the background electric field and the time-dependent gravitational field. The orthonormal Dirac mode functions are obtained, and the relevant in-out squeezed state expansions in terms of the Bogoliubov coefficients are found. We focus on two scenarios here: 1. a strong electric field limit, 2. a heavy mass limit (with respect to the Hubble constant). Using the squeezed state expansion, we demonstrate the Bell violations for the vacuum and some maximally entangled initial states. Our chief aim thus far is to investigate the role of the background magnetic field strength in the Bell violation. Qualitative differences in this regard for different maximally entangled initial states are shown. Further extension of these results to the one parameter family of de Sitter a-vacua is also discussed. Our next natural aim is to investigate the correlations between the fermionic pairs created in the Rindler spacetime in the presence of background electric and magnetic fields of constant strength. By solving the Dirac equation in closed form in each wedge, the orthonormal local in and out modes are obtained. Next, we construct the global modes from the local ones, which are analytic in both wedges. We further quantize the field, and by comparing the local and global modes, field quantizations and the Bogoliubov transformations are obtained. Using them, the squeezed state expansion of the global vacuum in terms of local states is acquired, and accordingly, the spectra of created particles are found. This scenario also has two sources of particle creation: the Schwinger and the Unruh effects. Our chief aim is to investigate the role of the strength of the background electric and magnetic fields on the spectra of created particles. Next, we discuss some possible implications of this result in the context of quantum entanglement by computing the Bell inequality and the logarithmic negativity for the global vacuum. Finally, we summarise the results discussed in the aforementioned main studies of the thesis. We also mention some future directions that might help in gaining a deeper understanding of correlations between pairs created in the presence of background fields.