Cavity‐Photon‐Induced High‐Order Transitions between Ground States of Quantum Dots

Abstract

We show that quantum electromagnetic transitions to high orders are essential to describe the time-dependent path of a nanoscale electron system in a Coulomb blockage regime when coupled to external leads and placed in a three-dimensional rectangular photon cavity. The electronic system consists of two quantum dots embedded asymmetrically in a short quantum wire. The two lowest in energy spin degenerate electron states are mostly localized in each dot with only a tiny probability in the other dot. In the presence of the leads we identify a slow high order transition between the ground states of the two quantum dots. The Fourier power spectrum for photon-photon correlations in the steady state shows a Fano-type of a resonance for the frequency of the slow transition. Full account is taken of the geometry of the multi-level electronic system, and the electron-electron Coulomb interactions together with the para-and diamagnetic electron-photon interactions are treated with step wise exact numerical diagonalization and truncation of appropriate many-body Fock spaces. The matrix elements for all interactions are computed analytically or numerically exactly.

Self-induction and magnetic effects in electron transport through a photon cavity

“…2 for the two linear polarizations. The quantized vector potential for the two polarizations for the cavity photon field is expressed as [30,31]…”

“…For an easier comparison of the electron-photon interaction used in other models we use the vector potential (4) and the field operators for the electrons to rewrite the Hamiltonian for the electron-photon interactions as [30]…”

“…where d i is the annihilation operator for an electron in the single-particle state labeled by i, and d † i is the corresponding creation operator. The definition of the coupling matrices (in the z = 0 plane) [30] in terms of the wavefunctions of the original single-electron basis {|a } is…”

“…Earlier, we have shown that high order transitions can be important when describing the approach of systems to a steady state in which otherwise low order forbidden transitions play a role [30]. This has lead us to the questions: What about the higher order electric and magnetic terms of the para-and diamagnetic electron-photon interactions?…”

Generalized Master Equation Approach to Time-Dependent Many-Body Transport

“…This is a small correction in most cases but may be important when studying high order transitions or nonperturbational effects caused by the photon field. This has led us to discover a very slow high order transition between the ground states of two slightly dissimilar quantum dots [ 115 ].…”