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Journal of Theoretical and Computational Chemistry

PERFECT POPULATION TRANSFER IN PULSE-DRIVEN QUANTUM CHAINS

Xin Chen, Yaoxiong Wang, Yunjian Ge, Junhui Shi, HERSCHEL A. RABITZ, Feng Shuang

Published Oct 1, 2010• 1 citation
Publisher

Abstract

The quantum dynamics of a pulse-driven finite-dimensional quantum chain with only nearest-neighbor coupling is studied. We extend the concept of Rabi oscillations from two-level quantum systems to the multi-level quantum chains. The time-dependent quantum dynamics and solutions producing perfect population transfer are obtained for up to five-level quantum chains. The Gröbner basis analysis technique is used to generalize the results and get all analytical solutions for perfect population transfer. Explicit formulas for the solutions up to nine levels are presented. These results could be used to design control strategies for general finite-dimensional quantum systems.

DOI
10.1142/s0219633610006031

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State-selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules, or quantum dots is the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision metrology, and quantum computing. Rabi oscillations are one of the simplest, yet potentially quite useful mechanisms for achieving such manipulation. Rabi theory establishes that in the two-level systems resonant drive leads to the periodic and complete population oscillations between the two system levels. In this paper an analytic optimization algorithm for producing Rabi-like oscillations in the general discrete many-level quantum system is presented.
Abstract The Demkov-Kunike (DK) model, characterized by a hyperbolic tangent detuning and a hyperbolic secant coupling, serves as a universal framework for describing driven quantum systems. However, existing research has primarily focused on two-level systems, some gaps still persist in extending the model to three-level configurations to achieve coherent population transfer (CPT). This study constructs exact solutions for both two- and three-level DK models via a canonical transformation, providing a basis for the quantitative analysis of population transfer, and achieves effective regulation of CPT via a finite-time adiabatic driving mechanism under specific parameter constraints. Furthermore, we analyze the impact of pulse truncation—a common experimental constraint—as well as environmental dissipation on quantum state evolution. The results show that the proposed scheme achieves rapid, high-fidelity coherent population transfer not only under ideal conditions, but also in the presence of realistic pulse truncation and even when decoherence induced by system-environment coupling is included. This work achieves CPT in the three-level DK model, offering a promising approach for advancing quantum state control in practical applications.
We consider the optimal control problem of transferring population between states of a quantum system where the coupling proceeds only via intermediate states that are subject to decay. We pose the question whether it is generally possible to carry out this transfer. For a single intermediate decaying state, we recover the stimulated Raman adiabatic passage process, which we identify as the global optimum in the limit of infinite control time. We also present analytical solutions for the case of transfer that has to proceed via two consecutive intermediate decaying states. We show that in this case, for finite power the optimal control does not approach perfect state transfer even in the infinite time limit. We generalize our findings to characterize the topologies of paths that can be achieved by coherent control under the assumption of finite power. If two or more consecutive states in an NNN-level chain are subject to decay, complete population transfer with finite-power controls is not possible.
Quantum communication through spin chains has been extensively investigated. In this scenario, state transfer through linearly arranged spins connected by uniform nearest-neighbor couplings qualifies as a natural choice, with minimal control requirements. However, quantum states usually cannot be perfectly transferred through a uniformly coupled chain due to the dispersion of the chain. Here, we propose an effective quantum control technique to realize almost exact state transfer (AEST) in a quantum spin chain. The strategy is to add a leakage elimination operator Hamiltonian to the evolution, which implements a sequence of pulse control acting on a perfect state transfer subspace. By using the one-component Feshbach PQ partitioning technique, we obtain the conditions over the required pulses. AEST through a spin chain can then be obtained under a suitable pulse intensity and duration.