Extension of the Morris-Shore transformation to arbitrary time-dependent driving fields

TL;DR

This paper extends the Morris-Shore transformation to handle arbitrary time-dependent external fields in quantum systems, enabling new control techniques like adiabatic passage and superposition state generation.

Contribution

It introduces a generalized time-dependent Morris-Shore transformation that relaxes previous restrictions on field profiles, broadening its applicability in quantum control.

Findings

Demonstrates population transfer between MS states with different field time profiles

Shows generation of superposition states via adiabatic techniques

Analyzes adiabatic and double-adiabatic limits in the generalized framework

Abstract

The treatment of time-dependent dynamics of quantum systems involving multiple states poses considerable technical challenges. One of the most efficient approaches in treating such systems is the Morris-Shore (MS) transformation which decomposes the multistate dynamics to a set of independent systems of simpler interaction pattern and uncoupled spectator states. The standard MS transformation imposes restrictions on the time dependence of the external fields addressing the states, as it requires that both Rabi frequencies have the same time profile. In this work we treat the case of the time-dependent MS transformation, which opens prospects for a variety of physically interesting processes wherein the fields may have different time dependences. We explore the adiabatic and the double-adiabatic limit, in which we demonstrate population transfer between the MS states that results in population transfer from one set of states onto another. We demonstrate the generation of superposition states between the MS states by the techniques of half adiabatic passage and fractional stimulated Raman adiabatic passage, which translate to superpositions of all the states of the involved levels.