We theoretically investigate high-order harmonic generation and attosecond pulses by numerically solving the three-dimensional time-dependent Schrödinger equation from a helium ion in a two-color laser field, which is synthesized by adding a 1600-nm laser pulse to a multicycle 800-nm laser pulse. The numerical results show that the short quantum path selection and broadband continuum spectra are achieved by adjusting the relative phase between two laser pulses, and isolated attosecond pulses can be generated successfully. Compared with the case of He + ions from the 1s ground state, the emission efficiency of the continuous harmonics and the intensity of the isolated attosecond pulse are enhanced approximately thirteen orders of magnitude by preparing He + ions in a coherent superposition of the states 1s and 2s. Furthermore, the bandwidth of the continuum spectrum is further broadened by increasing the intensity of the 1600-nm laser pulse, and an intense 38-as isolated pulse with a bandwidth of 109 eV is straightforwardly obtained.
Using a GHZ-class state as a quantum channel, we investigate the remote preparation of a qubit state and that of an entangled state in noisy environments. By analytically solving the master equation in Lindblad form, we first obtain the time evolution of the GHZ-class quantum channel. Then the influence of the noises on the process of remote state preparation is considered through analytical derivation of the fidelity and numerical calculations of the corresponding average fidelity. Our results show that the fidelity depends on the noise type, the state to be remotely prepared, the GHZ-class state and the decoherence rate. Moreover, it is found that no matter whether the qubit state or the entangled state is to be remotely prepared, the maximally entangled quantum channel has a relatively stronger ability to resist the influence of noises. Besides, the effect of the bit-phase flip noise on the average fidelity is relatively stronger than that of the bit flip noise or phase flip noise.
Using a GHZ-class state as quantum channel, we investigate the joint remote preparation of a qubit state in Pauli noise environments. By analytically solving the master equation in Lindblad form, we calculate the time evolution of the GHZ-class channel under different noisy conditions and then obtain the fidelity of the joint remote state preparation (JRSP) process and the corresponding average fidelity. We find that the fidelity depends on the noise type, the GHZ-class state, the initial state to be remotely prepared, and the Pauli decoherence rate. We also find that how two senders share the polar angle information of initial state plays an important role in the fidelity, and information sharing reduces the ability to resist the influence of Pauli noises in our JRSP protocol. Furthermore, how the two senders share the phase information affects the intensity of the bit-phase flip noise and the bit flip noise acting on the average fidelity. Besides, the fidelity of our JRSP protocol achieved via the maximally entangled channel is larger than that achieved via the partially entangled channel.
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