Off-shell quantum fields and measurement theory

Daniel Bar

Kazuya Okamura

In this study, we develop quantum measurement theory for quantum systems described by C∗-algebras. This is the first step to establish measurement theory for interacting quantum fields with off-shell momenta. Unlike quantum mechanics (i.e., quantum systems with finite degrees of freedom), measurement theory for quantum fields is still in development because of the difficulty of quantum fields that are typical quantum systems with infinite degrees of freedom. Furthermore, the mathematical theory of quantum measurement is formulated in the von Neumann algebraic setting in previous studies. In the paper, we aim to extend the applicable area of quantum measurement theory to quantum systems described by C∗-algebras from a mathematical viewpoint, referring to the sector theory that is related to symmetry and based on the theory of integral decomposition of states. In particular, we define central subspaces of the dual space of a C∗-algebra and use them to define instruments. This attempt makes the connection between measurement theory and sector theory explicit and enables us to understand the macroscopic nature and the physical meaning of measurement.

Ramesh V. Pai, Jamshid Moradi Kurdestany, K. Sheshadri +1 more

We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri et al. [Phys. Rev. Lett. 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.

B. DeFacio

Mahi R. Singh, Patrick D. Persaud

We have developed a theory for the two-photon fluorescence in nanohybrids made of an ensemble of metallic nanorod shells and an ensemble of quantum emitters. A metallic nanorod shell is made of a metallic rod and dielectric shell. We consider that the quantum emitters are four-level quantum systems. When a probe laser light falls on the metallic nanorod shells, the surface plasmon polariton electric field is produced at the interface between the metallic nanorod and dielectric shell. This electric field, along with the probe field, induces dipoles in the quantum emitters and nanorod shells. These dipoles interact with each other via the dipole–dipole interaction. The two-photon fluorescence has been calculated by using the quantum density matrix method in the presence of the dipole–dipole interaction (coupling). Analytical expressions of the two-photon fluorescence have been derived in the presence of the dipole–dipole interaction. We showed that that the two-photon process is made of two terms. The first term is the two-photon process due to the two probe field photons. On other the hand, the second term is made of one DDI field photon and one probe field photon. It is found that the surface plasmon polariton resonance energy is not resonant with the exciton energy, the two-photon fluorescence spectrum splits from one peak to three peaks. The splitting in the spectrum is due to the presence of the dressed states created in the system due to the strong dipole–dipole interaction. We also compared our theory with the experimental data of the metallic nanohybrid system made of metallic nanorod shells and quantum emitters (T790 molecules) and found a good agreement between the theory and the experiments.