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High-fidelity fast and robust coherent population transfer is a major challenge in coherent quantum control. At present, all coherent population transfer approaches are based on a well-known adiabatic condition. In this work, we demonstrate that a more strict adiabatic condition can markedly improve the performance of the coherent population transfer approach. Based on this, we propose a coherent population transfer approach, which just needs only one control parameter and depends on the eigenvalues of the systems. Comparing to other approaches, we numerically demonstrate that our approach can provide a more robustness coherent population transfer without affecting the fidelity and speed. Moreover, this approach may be generalized to complex quantum systems where the exact expressions of eigenstates are difficult to obtain or the parameters of systems are difficult to simultaneously drive. In short, our idea provides a way to further improve the performance of coherent population transfer approaches.

The non-Abelian geometric phases appear only in a degenerate subspace and the most familiar model with such a subspace is the $N$-pod system. Here we propose an alternative system to realize a non-Abelian gauge structure. We demonstrate that a three-level system with a triangular form can have two degenerate eigenstates which can induce non-Abelian geometric phases, and notably they are the lowest eigenstates of the system. As an application of the degenerate subspace, we propose an experimentally feasible scheme to realize a universal set of quantum gates based on the adiabatic non-Abelian geometric phases. To shorten the evolution time constrained by the adiabatic condition, the shortcut to adiabaticity is adopted to speed up the adiabatic geometric quantum gates. The combination of the intrinsic geometric characteristic and shortcut to adiabaticity makes the quantum operations fast and robust against certain control errors.

Realization of the highly efficient $\ensuremath{\pi}$ and $\ensuremath{\pi}/2$ pulses is crucial in an atom interferometry. Here we propose a scheme to realize these operations based on an intrinsically fault-tolerant geometric phase and stimulated Raman shortcuts to the adiabatic passage. The scheme is fast due to the shortcuts to adiabaticity and is robust based on the geometric phase. In the presence of various noises, we show that the fringe contrast of the proposed interferometer is higher than that of the resonant Raman pulse and the stimulated Raman adiabatic passage. Furthermore, the scheme is demonstrated to be especially suitable for applications that require a large space-time area enclosed by interfering wave packets.

Coherent stimulated Raman adiabatic passages (STIRAP) based on a dark state have many applications in diverse quantum systems. In the case of large single-photon detuning in three-level $\ensuremath{\Lambda}$ systems, one of the bright states almost does not involve the excited state and then acts as the dark state. In this paper, we report the experimental observation of STIRAP based on the dark state, as well as b-STIRAP based on the above bright state, with the same transfer efficiency in a three-level $\ensuremath{\Lambda}$ cold atomic ensemble. Moreover, both STIRAP and b-STIRAP are found to be immune to the time-varying ac Stark shift. As for a typical example to manipulate a superposition state, we realize an inverse operation on an initial superposition state, which cannot be achieved efficiently for STIRAP based on only the dark state. Our observed double STIRAP thus provides a feasible and robust manner to manipulate quantum states.

Implementing nonadiabatic holonomic quantum computation in decoherence-free subspaces may consolidate the advantages of both strategies and thus leads to suppression of both local and collective noises. In a recent paper, Xu et al. [Phys. Rev. Lett. 109, 170501 (2012)] proposed an interesting implementation of such a scheme; however, four-body interaction, which is hard to achieve in a realistic system, is required there. In this paper we propose a simplified scheme to implement such single-qubit and two-qubit logical operations by utilizing only two-body interactions, which is much easier to realize in a trapped ion system.

In a three-level $\ensuremath{\Lambda}$ atomic system coupled by a symmetrical bichromatic laser field, a weak probe laser field shows multiple absorption peaks in the case of cold atoms. As for hot atomic vapors, we experimentally observe double symmetrical electromagnetically induced transparency windows instead of multiple absorption peaks. This abnormal spectrum is due to the Doppler averaging. The electromagnetically induced transparency windows observed here are useful for obtaining slow photons at different frequencies.

We propose a theoretical scheme to realize a rotation-sensing interferometer with spin-orbit coupled atoms. The sensitivity of this interferometer is dependent on the atomic mass ${m}^{\ensuremath{-}\ensuremath{\alpha}}$ with a factor $\ensuremath{\alpha}\ensuremath{\geqslant}1$. Thus, the sensitivity can be improved by about one order of magnitude when we choose Li instead of Rb. Furthermore, compared to the standard Raman interferometer, the response to high-frequency, time-dependent rotation can be improved through the continuous coupling between spin and orbital freedoms of the atoms.

We show that a non-Abelian gauge potential in two nearly degenerated dressed states may be induced by two laser beams interacting with a three-level $\ensuremath{\Lambda}$ atomic system. We demonstrate that the populations of the atomic states at the end of a composed path formed by two closed loops are dependent on the order of those two loops, showing an unambiguous signature of the non-Abelian geometric phase. Through numerical calculations, we show that the non-Abelian feature of the geometric phases can be tested under realistic conditions.