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A scheme for arbitrary quantum state engineering (QSE) in three-state systemsis proposed. Firstly, starting from a set of complete orthogonal time-dependentbasis with undetermined coefficients, a time-dependent Hamiltonian is derivedvia Counterdiabatic driving for the purpose of guiding the system to attain anarbitrary target state at a predefined time. Then, on request of the assumedtarget states, two single-mode driving protocols and a multi-mode drivingprotocol are proposed as examples to discuss the validity of the QSE scheme.The result of comparison between single-mode driving and multi-mode drivingshows that multi-mode driving seems to have a wider rang of applicationprospect because it can drive the system to an arbitrary target state from anarbitrary initial state also at a predefined time even without the use ofmicrowave fields for the transition between the two ground states. Moreover,for the purpose of discussion in the scheme's feasibility in practice, apolynomial ansatz as the simplest exampleis used to fix the pulses. The resultshows that the pulses designed to implement the protocols are not hard to berealized in practice. At the end, QSE in higher-dimensional systems is alsodiscussed in brief as a generalization example of the scheme.

Arbitrary quantum state engineering in three-state systems via Counterdiabatic driving