Quantum mechanics governs the dynamics of microscopic and mesoscopic systems. One of the most intriguing aspects of quantum dynamics is the adiabatic geometric evolution. It allows for manipulation of the state of a quantum system by slowly varying the system's parameters along a contour in parameter space. Robustness of this technique motivated proposals of, e.g., geometric manipulations (gates) of quantum bits for quantum computing or geometric pumping of charge for setting the standard of current. It should also be noted that the statistical phase of identical particles (e.g., anyons), an element in the very foundations of quantum mechanics, is related to adiabatic dynamics (exchange of particles) as well.
The aim of this project is to assess the role of geometric manipulations in quantum solid-state devices for future ICT applications and in metrological applications under realistic conditions. Since all realistic solid-state devices suffer from dissipation due to their coupling to uncontrolled environment with many degrees of freedom it is crucial to understand how the geometric effects are modified and whether they are still useful. Also, since infinitely slow manipulations are impractical in solid-state devices, it is very important to explore the very concept of adiabatic limit, separating adiabatic and non-adiabatic regimes of evolution.
The influence of dissipation may be twofold. On one hand it is natural to expect the dissipation to suppress the effects related to quantum coherence. On the other hand dissipation may force the system into the instantaneous ground state and, therefore, enhance the precision of the adiabatic approximation. We expect, thus, that, unlike in majority of quantum phenomena, dissipation can sometimes stabilize the geometric phases and play a positive role in rendering them of practical importance. We also expect that experimental studies of adiabatic quantum evolution will shed a new light on the very nature of the dissipative environment typical for solid-state devices.
The main objectives of the project are:
a) To arrive at full theoretical understanding of how dissipation modifies geometric effects in various solid-state systems. Specifically, we study Josephson circuits, quantum dots, and nanowires.
b) To establish the existence of and measure geometric dissipative effects experimentally in Josephson circuits and in circuit-QED systems both via direct observation of Berry phases and via charge pumping measurements.
c) To investigate both experimentally and theoretically regimes where either dissipation or topological properties stabilize geometric effects.
d) To consider theoretically influence of dissipation and interactions on pumping of charge and spin in quantum dots and nanowires.
We will regard our project as successful if convincing experimental and theoretical results allow us to unambiguously determine the usefulness of geometric devices in future ICT applications (we, of course, hope for a positive answer). Experimental success will be measured by two criteria: 1) the ability to overcome the dissipation and reach precision of geometric manipulations similar to, e.g., that in quantum optics; 2) the ability to clearly identify and characterize the dissipative corrections to the geometric phases or pumped charge. Theoretical success will be measured by (i) the ability to explain experimental data to a good precision; (ii) the ability to quantify the degree to which dissipation affects geometrical effects (and undermine their observability); (iii) the ability to identify systems and regimes where presence of dissipation does not prohibit geometric manipulations.