סמינר בחומר מעובה: Quantum coherent control for complete population inversion in multi-level systems

Abstract:

Quantum control science plays a central role in quantum dynamical systems, providing powerful tools to describe their evolution in terms of quantum states and control operations based on their symmetries. Multi-level quantum control is considered to be the most suited approach for a variety of applications in quantum information research, as it exponentially reduces the resources required in the quantum computation process. However, the usefulness and popularity of multi-level systems was and still is limited by a dearth of theoretical methods for understanding and controlling their dynamics leading researchers to commonly limit their use to two-levels to preserve simplicity.

In my talk, I will share with you our recent research that involves quantum control of multi-level dynamics based on a well-known isomorphism between the SO(4) group and SU(2)xSU(2) dynamical groups. Specifically, I will focus on the dynamics of four-level systems and will show the evolution of such systems can be written in an analytical close-form description using two uncoupled Bloch spheres with two distinct frequencies, the generalization of the single Rabi frequency in a two-state dynamics. Such analysis helped to uncover a method for population inversion in these systems, coined the Pythagorean coupling dynamics where, the coupling coefficients are found to be linked to fundamental number theory, whereas complete population transfer occurs if and only if the ratios between coupling coefficients exactly match a set of Pythagorean triples, which are the set of three integer numbers satisfying the equation  . Also, I will share with you the first experimental realization of the Pythagorean coupling using a superconducting Josephson phase qudit excited by a single multi-tone excitation. Last, I will present our recent advance, where we introduced a novel method for translating multi-state control problems to two-state systems. The method, coined by us the quantum retrograde canon, provides a new framework for importing the knowledge, tools and intuition related to two-state systems, into multi-state research and will allow deepening our understanding of multi-state dynamics.

מארגן הסמינר: פרופ' אלכסנדר גרבר