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Maximal Fidelity Isolines of a Pulsed-Driven Qubit: Pulse Shape Effects
A.M. Khallaf, O.M. Frege and S.S. Hassan

The transient quantum fidelity, F(τ), for a pulsed driven non-dissipative qubit is investigated in cases of different pulse shapes, namely, rectangular, triangular, sin2– and 𝑛-Gaussian pulses. Specifically, for the qubit initially in the coherent state |θ, φ⟩, we search, graphically and analytically, for the contours (isolines) of the maximum fidelity in the respected planes: (θ, φ)-, (θ, τ)- and (φ, τ)-planes. In the (θ, φ)-plane closed isolines are identified for all four pulse shapes. In the (θ, τ)-and (φ, τ)-planes the isolines are periodic open curves in cases of rectangular, triangular and sin2 pulses, while for Gaussian pulses the maximum fidelity occurs for negative τ, in addition to open/closed isolines for τ > 0. The temporal behaviour of the maximum average fidelity over the (θ, φ) parameters is a sinusoidal, non-sinusoidal, monotonic or non-monotonic, depending on the pulse shape. The case of moving atom in a cavity is investigated and compared with the above pulsed-driven cases.

Keywords: Qubit, Laser pulses, Fidelity and its average