Robust Preparation of Atomic Concatenated Greenberger–Horne–Zeilinger States via Shortcuts to Adiabaticity

Abstract

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

Manipulation of phonon states in ion traps by shortcuts to adiabaticity

“…This process can be realized by adding counteradiabatic driving, which is one of the types of shortcuts to adiabaticity (STA) [19,[37][38][39][40]. Previously, some theoretical work on realizing STA based on basis vector transformation has been studied in systems such as atoms and NV centers in diamond [41][42][43]. However, it is difficult to implement counteradiabatic driving in real experiments when Hamiltonian is included in the creation and annihilation operators.…”