# Energy absorption in gate controlled quantum dots

#### Abstract

Energy absorption in quantum dots is investigated. We have calculated energy absorption without using any phenomenological parameters, such as correlation time. We have considered absorption in a correlated system of quantum dots in the presence of charging effects, when energy of the dot and effective tunneling rate on and off the dot depend on the electron charge in the dot. We developed theory of energy absorption in the presence of a.c. electromagnetic field in a quantum dot. Quantum dot has been considered as a system with two discrete energy levels. We have neglected effects of natural line width, and aimed at finding absorption due to intrinsic properties of electrons in quantum dots and their interactions with surrounding structure. We observed that once the natural line width is neglected, in absence of interactions with some other system with continuous spectra, two discrete levels in the presence of a.c. perturbation will sustain Rabi oscillations, but no absorption of energy will take place. We have chosen electrons in contacts to a lateral quantum dot as a system with continuous spectrum that interacts with electrons of discrete spectra in a quantum dot. We demonstrated that tunneling on and off the dot results in energy absorption. We have calculated electron density matrix and absorption of energy in a small quantum dot, in which one-electron energy scale exceeds that of charging effects. We developed general theory of such absorption and constructed a procedure, which leads to susceptibility vanishing at zero frequency, without appealing to the so-called high temperature approximation, which is often used in textbooks. We have shown that quantum transitions resulting in absorption in conditions close to resonance between frequency of excitations and spin splitting of levels are not transitions between discrete levels of the dot, but transitions between one state in a dot and a state in a contact. The other discrete level in the dot becomes a virtual state in absorption process. We demonstrated that quantum kinetic equation for electron in a dot contains important additional term proportional to escape rate, which is linear in a.c. magnetic field, and linear in tunneling rate. In the presence of charging effects, we have considered both resonant absorption of energy and relaxational mechanism of absorption. We demonstrated that at large frequencies if a.c. excitation position of peaks of absorption differ from positions of peaks of conductance through a charged quantum dot. We derived the system of quantum kinetic equations for components of density matrix of the charged dot coupled to contacts. Our treatment differs from all previous considerations by the presence of terms that are linear in both excitation perturbation and in tunneling rate. Similar terms will arise in kinetic (master equations) in cases when intrinsic line width of levels is caused by processes other than tunneling to contacts, e.g., by coupling to vibrations of molecules in absorption of light by molecules. We described the effects of gate voltage on absorption for both resonant and relaxational mechanism. Relaxational mechanism at small frequencies can dominate absorption of energy away from the Coulomb blockade conductance peak. In the Coulomb blockade valley, relaxational absorption can exhibit features of motional narrowing phenomena. We considered effects analogous to motional narrowing in the context of resonant mechanism of absorption of energy in a charged quantum dot. We demonstrated that despite absorption can be inverse proportional to tunneling rate, charging effects suppress motional narrowing.

#### Degree

Ph.D.

#### Advisors

Lyanda-Geller, Purdue University.

#### Subject Area

Nanoscience|Quantum physics|Condensed matter physics

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