By using transitionless quantum driving algorithm (TQDA), we present an efficient scheme for the shortcuts to the holonomic quantum computation (HQC). It works in decoherence-free subspace (DFS) and the adiabatic process can be speeded up in the shortest possible time. More interestingly, we give a physical implementation for our shortcuts to HQC with nitrogen-vacancy centers in diamonds dispersively coupled to a whispering-gallery mode microsphere cavity. It can be efficiently realized by controlling appropriately the frequencies of the external laser pulses. Also, our scheme has good scalability with more qubits. Different from previous works, we first use TQDA to realize a universal HQC in DFS, including not only two noncommuting accelerated single-qubit holonomic gates but also a accelerated two-qubit holonomic controlled-phase gate, which provides the necessary shortcuts for the complete set of gates required for universal quantum computation. Moreover, our experimentally realizable shortcuts require only two-body interactions, not four-body ones, and they work in the dispersive regime, which relax greatly the difficulty of their physical implementation in experiment. Our numerical calculations show that the present scheme is robust against decoherence with current experimental parameters.The decoherence-free subspace (DFS) [29-31] of a quantum system can protect the fragile quantum information against collective noises as the system undergoes a unitary evolution in its DFS. It has been demonstrated that DFS can be implemented experimentally with different physical systems [32][33][34]. In 2005, Wu et al [35] presented a theoretic scheme by combining the HQC and DFS to perform universal QC. By making the dark states of the Hamiltonian of a quantum system adiabatically evolve along a closed cyclic loop, one can acquire a Berry phase or quantum holonomy. In 2006, Zhang et al [36] and Cen et al [37] gave two schemes for HQC with DFS in trapped ions. In 2009, Oreshkov et al [38] introduced a scheme for fault-tolerant HQC on stabilizer codes. The adiabatic evolution for HQC requires a long run time. To eliminate this dilemma, Berry[39] came up with a transitionless quantum driving algorithm (TQDA), which is also outlined in slightly different manner by Demirplak and Rice [40, 41], to speed up the adiabatic quantum gates when the eigenstates of a time-dependent Hamiltonian are non-degenerate in 2009. Later, this transitionless algorithm has been gained widespread attention in both theory and experiment [42-47]. In 2010, Chen et al [42] used the TQDA to speed up adiabatic passage techniques in two-level and three-level atoms extending to the short-time domain their robustness with respect to parameter variations. In 2012, Bason et al [46] experimentally implemented the optimal high-fidelity transitionless superadiabatic protocol on Bose-Einstein condensates in optical lattices. In 2013, Zhang et al [47] implemented the acceleration of quantum adiabatic passages on the electron spin of a single NV center in diamond....

Three-level quantum systems, which possess some unique characteristics beyond two-level ones, such as electromagnetically induced transparency, coherent trapping, and Raman scatting, play important roles in solid-state quantum information processing. Here, we introduce an approach to implement the physically feasible threelevel transitionless quantum driving with multiple Schrödinger dynamics (MSDs). It can be used to control accurately population transfer and entanglement generation for three-level quantum systems in a nonadiabatic way. Moreover, we propose an experimentally realizable hybrid architecture, based on two nitrogen-vacancycenter ensembles coupled to a transmission line resonator, to realize our transitionless scheme which requires fewer physical resources and simple procedures, and it is more robust against environmental noises and control parameter variations than conventional adiabatic passage techniques. All these features inspire the further application of MSDs on robust quantum information processing in experiment.

We propose a scheme to generate spatially dependent four-wave mixing (FWM) in an asymmetric semiconductor three-coupled-quantum-well nanostructure. By adjusting the detuning of the control field, one can effectively manipulate the FWM output field. Specifically, the vortex phase of the FWM field can be modulated. The detailed explanations based on the dispersion relation are given, which are in good agreement with our results. Furthermore, we perform the interference between the FWM field and the same-frequency Gaussian beam. Our results show that the interference patterns can also be modulated via the detuning of the control field, which may provide a way to observe helical phase modulation via the intensity measurement. This work may be useful for investigating the nonlinear optical phenomena based on orbital angular momentum light.

Orbital angular momentum (OAM) is an important property of vortex light, which provides a valuable tool to manipulate the light-matter interaction in the study of classical and quantum optics. Here we propose a scheme to generate vortex light fields via four-wave mixing (FWM) in asymmetric semiconductor quantum wells. By tailoring the probe-field and control-field detunings, we can effectively manipulate the helical phase and intensity of the FWM field. Particularly, when probe field and control field have identical detuning, we find that both the absorption and phase twist of the generated FWM field are significantly suppressed. Consequently, the highly efficient vortex FWM is realized, where the maximum conversion efficiency reaches around 50%. Our study provides a tool to transfer vortex wavefronts from input to output fields in an efficient way, which may find potential applications in solid-state quantum optics and quantum information processing.

With a perturbative treatment based on the Keldysh Green's function technique, we study the resonant enhancement of nonlinear interaction effects in a four-mode optomechanical ring. In such a system, we identify five distinct types of resonant scattering between unperturbed polariton modes, induced by the nonlinear optomechanical interaction. By computing the cavity density of states and optomechanical induced transparency signal, we find that the largest nonlinear effects are induced by a decay process involving the two phonon-like polaritons. In contrast to the conventional twomode optomechanical system, our proposed system can exhibit prominent nonlinear features even in the regime when the single-photon coupling is much smaller than the cavity damping.