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IEEE journal on multiscale and multiphysics computational techniques

Dressed Atom Fields and Dressed States in Waveguide Quantum Electrodynamics

Aiyin Y. Liu, Weng Cho Chew

Published Jan 1, 2017• 13 citations
Publisher

Abstract

The fully quantized problem of a dipole atom coupled to transverse electric fields is solved for both simple harmonic and two-level atoms in a general lossless electromagnetic environment. The method employed is a direct factorization of the Hamiltonian in terms of coupled excitations of atom and fields. Time evolution of the system is considered with emphasis on the effect of an atom-photon bound state. The rectangular waveguide is used as an example to illustrate the predicted behavior.

DOI
10.1109/jmmct.2017.2698341

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The fully quantized problem of a dipole atom coupled to transverse electric fields is solved for both simple harmonic and two-level atoms in a general lossless electromagnetic environment. The method employed is a direct factorization of the Hamiltonian in terms of coupled excitations of atom and fields. Time evolution of the system is considered with emphasis on the effect of an atom-photon bound state. The rectangular waveguide is used as an example to illustrate the predicted behavior.
In this thesis, a framework for cavity and waveguide quantum electrodynamic (CQED, and WQED, respectively) problems is presented. The essence of this framework is to use the dyadic Green's function (DGF) to obtain the local density of states (LDOS) and radiative shift of a two-level system (TLS) embedded in an arbitrary electromagnetic continuum. The dressed states of the system are also found using a method of direct diagonalization of operators. The physics and essential features of the dressed states are related to the DGF. The dynamics of the system are solved in connection with the resolvent formalism of quantum scattering theory. The work presented here represent the first attempts in this important topic of study. This thesis accomplishes the full solution of the problem of a two-level atom coupled to arbitrary lossless electromagnetic environments. The cases of transmission line, hollow rectangular waveguide and free space are considered. At the same time, an attempt to gather much of the required background for this highly interdisciplinary topic is made, in particular, the quantization of an arbitrary lossless waveguide is presented in detail, which to the best of our knowledge, has not appeared in the literature. More detailed investigations will follow in a Ph.D. dissertation.
We investigate the dynamics of an arbitrary atomic system (n-level atom or many n-level atoms) interacting with a resonant quantized mode of an electromagnetic field in a lossless cavity. Initially, the field is taken in a coherent state with a large average photon number. If the initial atomic state is chosen as an eigenstate of the atomic Hamiltonian in the classical field limit (semiclassical eigenstates), then the evolution of the system wave function is approximately factorized into the field and atomic parts. Explicit analytical expressions are given for the factorized wave functions. The time evolution of an arbitrary initial atomic state can be fully described in terms of factorized states. As examples, we discuss trapping states, and collapses and revivals of the atomic energy.
Quantum mechanical treatment of light inside dielectric media is important to understand the behavior of an optical system. In this paper, a two-level atom embedded in a rectangular waveguide surrounded by a perfect electric conductor is considered. Spontaneous emission, propagation, and detection of a photon are described by the second quantization formalism. The quantized modes for light are divided into two types: photonic propagating modes and localized modes with exponential decay along the direction of waveguide. Though spontaneous emission depends on all possible modes including the localized modes, detection far from the source only depends on the propagating modes. This discrepancy of dynamical behaviors gives two different decay rates along space and time in the correlation function of the photon detection.
The coupling of two or more quantum mechanical states representing two different quantum mechanical systems leads to a new class of quantum mechanical states called entangled states. In this case, a two level atom, coupled to a single mode quantized electromagnetic field, results in the dressed state. The Dressed State is an example of Entangled States. This state exhibits a quantum correlation between the two entities, atom and field. The interaction energy of the atom and the quantized field can be written, in the dipolar interaction case, in the same way as in the semi classical theory. The emission of a photon by an atom creates an electromagnetic field that can act with the atom itself. An atom in the excited state, in the absence of a field, decays exponentially with time. This is Wigner Weisskopf model for spontaneous emission.