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Laser Physics Letters

Accelerating quantum information transfer in a three-level system via a specified intermediate Hamiltonian

Chun-Rong Huang, Ye‐Hong Chen

Published Oct 23, 2024• 0 citations
Publisher

Abstract

Abstract We propose a general approach to speed up quantum adiabatic processes for fast quantum information transfer in a three-level system. In the approach, by using an intermediate Hamiltonian which is assumed to be formed by the original Hamiltonian H 0 ( t ) and its counterdiabatic driving Hamiltonian H cd ( t ) with a simple linear relationship, we design exact dynamics following the eigenstates of the intermediate Hamiltonian to speed up the desired population processes. We apply the present approach to a three-level system to show that by suitably choosing the parameters, not only the population processes could be sped up, but also the existence of the undesired off-diagonal terms, the populations of the intermediate states, and even the shapes of the pulses would be controllable in the speeding up scheme.

DOI
10.1088/1612-202x/ad724e

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Abstract We propose a general approach to speed up quantum adiabatic processes for fast quantum information transfer in a three-level system. In the approach, by using an intermediate Hamiltonian which is assumed to be formed by the original Hamiltonian H 0 ( t ) and its counterdiabatic driving Hamiltonian H cd ( t ) with a simple linear relationship, we design exact dynamics following the eigenstates of the intermediate Hamiltonian to speed up the desired population processes. We apply the present approach to a three-level system to show that by suitably choosing the parameters, not only the population processes could be sped up, but also the existence of the undesired off-diagonal terms, the populations of the intermediate states, and even the shapes of the pulses would be controllable in the speeding up scheme.
We propose a scheme to speed up adiabatic passage by using Lyapunov control theory. This is a good choice to solve the problem that may emerge in Berry's transitionless quantum driving [M. V. Berry, J. Phys. A 42, 365303 (2009)]. That is, the extra couplings in the counterdiabatic driving Hamiltonian can be avoided by choosing the available control Hamiltonian in an actual physical system. As examples, we shorten the evolution time of adiabatic population transfer in a three-level system and the entanglement generation in a cavity quantum electrodynamics system. Moreover, the occupation of an intermediate state can be sharply suppressed by properly choosing the control Hamiltonian in the three-level system. The scheme can also be generalized to a complex system where the exact expressions of adiabatic eigenstates are difficult to obtain.
Shortcuts to adiabaticity in various quantum systems have attracted much attention with their wide applications in quantum information processing and quantum control. In this paper, we concentrate on a stimulated Raman shortcut-to-adiabatic passage in quantum three-level systems. To implement counterdiabatic driving but without additional coupling, we first reduce the quantum three-level systems to effective two-level problems at large intermediate-level detuning, or on resonance, apply counterdiabatic driving along with the unitary transformation and eventually modify the pump and Stokes pulses for achieving fast and high-fidelity population transfer. The required laser intensity and stability against parameter variation are further discussed, to demonstrate the advantage of shortcuts to adiabaticity.
We present a general approach to speed up the adiabatic process without adding the traditional counterdiabatic driving Hamiltonian. The strategy is to design an easy-to-get intermediate Hamiltonian to connect the original Hamiltonian and final transitionless Hamiltonian. With a final transitionless Hamiltonian, the same target can be achieved as in the adiabatic process governed by the original Hamiltonian, but in a shorter time. We apply the present approach to a three-level system and the result shows that the final transitionless Hamiltonian usually has the same structure as the original Hamiltonian but with different time-dependent coefficients, allowing speedup to be achieved in a much easier way compared to previous methods.
We develop new pulse schemes to significantly speed up adiabatic state transfer protocols. Our general strategy involves adding corrections to an initial control Hamiltonian that harness nonadiabatic transitions. These corrections define a set of dressed states that the system follows exactly during the state transfer. We apply this approach to stimulated Raman adiabatic passage protocols and show that a suitable choice of dressed states allows one to design fast protocols that do not require additional couplings, while simultaneously minimizing the occupancy of the "intermediate" level.
We propose an efficient method to construct shortcuts to adiabaticity through designing a substitute Hamiltonian to try to avoid the defect in which the speed-up protocols' Hamiltonian may involve terms which are difficult to realize in practice. We show that as long as the counterdiabatic coupling terms---even only some of them---have been nullified by the additional Hamiltonian, the corresponding shortcuts to the adiabatic process could be constructed and the adiabatic process would be sped up. As an application example, we apply this method to the popular Landau-Zener model for the realization of fast population inversion. The results show that in both Hermitian and non-Hermitian systems, we can design different additional Hamiltonians to replace the traditional counterdiabatic driving Hamiltonian to speed up the process. This method provides many choices for designing additional terms of the Hamiltonian such that one can choose a realizable model in practice.
The difficulty in combining high fidelity with fast operation times and robustness against sources of noise is the central challenge of most quantum control problems, with immediate implications for the realization of quantum devices. We theoretically propose a protocol, based on the widespread stimulated Raman adiabatic passage technique, which achieves these objectives for quantum state transfers in generic three-level systems. Our protocol realizes accelerated adiabatic following through the application of additional control fields on the optical excitations. These act along frequency sidebands of the principal adiabatic pulses, dynamically counteracting undesired transitions. The scheme facilitates experimental control, not requiring new hardly-accessible resources. We show numerically that the method is efficient in a very wide set of control parameters, bringing the timescales closer to the quantum speed limit, also in the presence of environmental disturbance. These results hold for complete population transfers and for many applications, e.g., for realizing quantum gates, both for optical and microwave implementations. Furthermore, extensions to adiabatic passage problems in more-level systems are straightforward.