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Scientific Reports

Rapid population transfer of a two-level system by a polychromatic driving field

Dongxiao Li, Xiao‐Qiang Shao

Published Jun 21, 2019• 11 citations
Publisher

Abstract

We propose a simple exact analytical solution for a model consisting of a two-level system and a polychromatic driving field. It helps us to realize a rapid complete population transfer from the ground state to the excited state, and the system can be stable at the excited state for an extremely long time. A combination of the mechanism and the Rydberg atoms successfully prepares the Bell state and multipartite W state, and the experimental feasibility is discussed via the current experimental parameters. Finally, the simple exact analytical solution is generalized into a three-level system, which leads to a significant enhancement of the robustness against dissipation.

DOI
10.1038/s41598-019-45558-5

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Rapid population transfer of a two-level system by a polychromatically driving field

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We propose a simple exact analytical solution for a model consisting of a two-level system and a polychromatic driving field. It helps us to realize a rapid complete population transfer from the ground state to the excited state, and the system can be stable at the excited state for an extremely long time. A combination of the mechanism and the Rydberg atoms successfully prepares the Bell state and multipartite W state, and the experimental feasibility is discussed via the current experimental parameters. Finally, the simple exact analytical solution is generalized into a three-level system, which leads to a significant enhancement of the robustness against dissipation.
We propose a simple exact analytical solution for a model consisting of a two-level system and a polychromatically driving field. It helps us to realize a rapid complete population transfer from the ground state to the excited state, and the system can be stable at the excited state for an extremely long time. A combination of the mechanism and the Rydberg atoms successfully prepares the Bell state and multipartite WWW state, and the experimental feasibility is discussed via the current experimental parameters. Finally, the simple exact analytical solution is generalized into a three-level system, which leads to a significant enhancement of the robustness against dissipation.
Analytically exact solutions of a driven two-level system are extremely important in many areas of physics [E. Barnes and S. Das Sarma, Phys. Rev. Lett. 109, 060401 (2012)]. Here we present a simple method of synchronous and asynchronous combined modulations to generate such exact solutions, and apply several of the simplest solutions to perform the coherent control of quantum states. The interesting physical phenomena, such as the arbitrary population transfers between the different and/or asymptotic stationary states and the controlled coherent population oscillation, are achieved analytically and numerically. Simplification of the exact solutions and the modulated fields renders the control strategies more transparent and the qubit manipulation more convenient in experiments.
The effect of radiative decay and collisional damping on the delayed-field population transfer in the three-level system is investigated. The simple analytical steady-state solution of the three-level system, interacting with two intense delayed laser pulses in the dressed-state frame, is obtained and analyzed. The radiative relaxation transfers the system to the ``trapped state,'' which is shown to be stable relative to both radiative decay and collisional damping. The effect of an additional level \ensuremath{\Vert}m〉, situated close to the final level \ensuremath{\Vert}3〉, on the population-transfer process is considered. The field-induced relaxation rate from intermediate level \ensuremath{\Vert}2〉 to level \ensuremath{\Vert}3〉 is shown to be a very easily controllable parameter of the field intensities and their relative delay. This result leads to selective population transfer to the desired level and may prevent leaking out of the three-level system. Theoretical analysis corresponds entirely to recent experimental data [U. Gaubatz et al., J. Chem. Phys. 92, 1 (1990); 92, 5363 (1990)].
An automated and robust method for adiabatic population transfer and the preparation of an arbitrary quantum superposition state in atomic system using the oscillating dark states (ODS) is presented. Quantum state of a three-level ΛΛΛ configuration atomic system oscillates periodically between two ground levels, when two pairs of classical detuning laser fields driving the system into the ODS under evolving adiabatic conditions. The decoherence of the ODS evolution is greatly suppressed, and the oscillation is very stable, therefore adiabatic population transfer and the preparation of an arbitrary quantum superposition state of atomic system can be completed accurately and conveniently.
For a two-level system, it is believed that a far-off-resonant driving cannot help coherent population transfer between two states. In this work, we propose a scheme to implement the coherent transfer with far-off-resonant driving. The scheme works well with both constant driving and Gaussian driving. The total time to finish population transfer is also minimized by optimizing the detuning and coupling constants. We find that the scheme is sensitive to spontaneous emission much more than dephasing. It might find potential applications in X-ray quantum optics and population transfer in Rydberg atoms as well.
In the previous paper on this topic it was shown how, for a pulse of arbitrary shape and duration, the drive frequency can be analytically optimized to maximize the amplitude of the population oscillations between the selected two levels in a general many level quantum system. It was shown how the standard Rabi theory can be extended beyond the simple two-level systems. Now, in order to achieve the quickest and as complete as possible population transfer between two pre-selected levels, driving pulse should be tailored so that it produces only a single half-oscillation of the population. In this paper, this second (and final) step towards the controlled population transfer using modified (i.e. many level system) Rabi oscillations is discussed. The results presented herein can be regarded as an extension of the standard πππ-pulse theory - also strictly valid only in the two level systems - to the coherently driven population oscillations in general many level systems.