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Here, a protocol for robust preparation of an atomic concatenated Greenberger-Horne-Zeilinger (C-GHZ) state via shortcuts to adiabaticity (STA) is proposed. The devices for implementing the protocol consist of atoms, cavities, and the optical fibers, which are feasible with current technology. The atoms are trapped in the separated cavities allowing individual control over each atom with classical fields. STA helps to design Rabi frequencies of classical fields so that the atoms can be driven from the initial states to the target states. The numerical simulations show that the protocol holds robustness against atomic spontaneous emissions and photonic leakages. Thus, the protocol may be realized by experiments in the near future.been proposed to prepare the GHZ states with different systems. For example, Zheng [21] has proposed a protocol to generate GHZ states with atoms. Wu et al. [23] have used the superconducting qubits to generate GHZ states.The protocols [21][22][23] for preparing the GHZ states mentioned above focus on the GHZ states encoded in the physical qubits directly. Recently, Fröwis and Dür [24,25] have suggested a new type of entangled states named concatenated Greenberger-Horne-Zeilinger (C-GHZ) states, which are the GHZ-like states encoded in the qubits formed by the traditional GHZ states. More specifically, the C-GHZ states can be written as DenotationState of system Denotation State of system |ψ 1 | 0, 0, 0, 0 |0 | ψ 2 | 0, 2, 0, 0 |0 |ψ 3 | 0, 1, 0, 0 |1 11l | ψ 4 | 0, 1, 0, 0 |1 f 11 |ψ 5 | 0, 1, 0, 0 |1 0l | ψ 6 | 0, 1, 1, 1 |0 |ψ 7 | 1, 0, 0, 0 |0 | ψ 8 | 1, 1, 0, 0 |0 |ψ 9 | 1, 1, 0, 0 |1 11l | ψ 10 | 1, 2, 0, 0 |1 f 11 |ψ 11 | 1, 1, 0, 0 |1 0l | ψ 12 | 2, 0, 0, 0 |0 |ψ 13 | 3, 1, 0, 0 |0

We present a scheme to implement a orbital state quantum cloning machine assisted by quantum Zeno dynamics. By constructing shortcuts to adiabatic passage with transitionless quantum driving, we can complete this scheme effectively and quickly in one step. The effects of decoherence, including spontaneous emission and the decay of the cavity, are also discussed. The numerical simulation results show that high fidelity can be obtained and the feasibility analysis indicates that this can also be realized in experiments.

By controlling the parameters of the system, the effective interaction between different atoms is achieved in different cavities. Based on the interaction, scheme to generate three-atom Greenberger–Horne–Zeilinger (GHZ) is proposed in coupled cavities. Spontaneous emission of excited states and decay of cavity modes can be suppressed efficiently. In addition, the scheme is robust against the variation of hopping rate between cavities.