| Abstrakt: |
We study numerically the effects of spontaneous emission from the upper state in a single two-level atom (qubit) driven by a field of constant amplitude and frequency varying linearly in time, crossing the atomic resonance, the Landau-Zener model, using a discontinuous jump quantum trajectory formalism. A single trajectory describes the pure state atomic evolution during the sweep of the field frequency across the atomic transition. Each jump returns the atom to its ground state, but the behavior of reexcitation depends on the time the jump occurred: before, near, or after the resonance, as a result of the nonstationary nature of the Landau-Zener model. The evolution of the Bloch vector during a single trajectory is unitary (a pure state preserves the trace), but shows the stochastic nature of the particular qubit history. The ensemble average, which agrees with the Bloch equations, shows that spontaneous emission causes both the shrinking of the Bloch vector shortly after crossing the resonance and its recovery for longer times. The quantum jump approach allows a simple calculation of the distribution of emissions per sweep. Its mean agrees with the integrated emission rate, the variance increases with the field strength and decay rate, and the zero-jump value of the distribution gives the fraction of trajectories without a jump. [ABSTRACT FROM AUTHOR] |
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