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.
Highlights
A fast and robust approach to controlling the quantum state of a multi-level quantum system is investigated using a twofrequency time-varying potential
Researchers have shown, using an analytical exacta approach, that it is possible to control the transition between two predefined states by a particular time-dependent wall motion of this system[6], which extended the results obtained by Lenz et al.[7] for a different system
As an illustration of this procedure, we offer the transition from the ground state to the first excited state in a infinite square-well potential
Summary
We turn to our primary objective: achieve fast maximum population transfer. To do so, we make use of a system movement which is the superposition of two periodic movements, one to drive the system to the desired state and another to bring back the population from higher levels. Both transitions have a fidelity of 99.97%, and so they are comparable. This comes from the fact that the use of two frequencies allows us to use larger amplitudes, which have a wider spectrum of resonance frequencies
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