Speeding up maximum population transfer in periodically driven multi-level quantum systems

Abstract

A fast and robust approach to controlling the quantum state of a multi-level quantum system is investigated using a twofrequency time-varying potential. A comparison with other related approaches in the context of a two-level system is also presented, showing similar times and fidelities. As a concrete example, we study the problem of a particle in a box with a periodically oscillating infinite square-well potential, from which we obtain results that can be applied to systems with periodically oscillating boundary conditions. We show that the transition between the ground and first excited state is about 20 times faster than the one performed using a single frequency, both with fidelity of 99.97%. The transition time is about 3.5 times the minimum allowed by quantum mechanics. A test of the robustness of the approach is presented, concluding that, counter-intuitively, it is not only faster but also easier to tune up two frequencies than one. This robustness makes the approach suitable for real applications.

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

“…For example, as mentioned earlier, they arise naturally in inverse scattering problems [242], where the presence of measured scatted data nonlocal boundary conditions are typical, and advanced data-based methodologies, such as deep learning schemes [215], may be required. Other substantial sources are provided by open driven systems, and in particular driven quantum systems [50,158,[243][244][245], including those for Floquet engineering [246], quantum information control with quantum computing applications [247], as well as various nonlinear problems such as those described by Rabi's models, providing, among other things, new perspectives on the entanglement via the von Neumann entropy [248,249]. It is envisaged that in dealing with such systems, communication complexity will play a progressively growing role.…”

Complete Population Transfer of Maximally Entangled States in $2^{2N}$-level Systems via Pythagorean Triples Coupling

“…Due to the difficulty of synthesis and analysis of CPT schemes increases in multi-state systems, multi-state control problems are usually reduced to two-state ones [17][18][19][20][21]. Several approaches have been also proposed for CPTs in multi-level systems [22][23][24][25][26][27]. Recently, the dynamics of four level atomic system has been explored from a geometrical point of view, revealing that one can obtain CPTs in the lab frame if and only if some constraints on the couplings are obeyed [28].…”