Nonlinearly driven Landau-Zener transition with telegraph noise

Abstract

We study Landau-Zener like dynamics of a qubit influenced by transverse random telegraph noise. The telegraph noise is characterized by its coupling strength, $v$ and switching rate, $\gamma$. The qubit energy levels are driven nonlinearly in time, $\propto \sign(t)|t|^ν$, and we derive the transition probability in the limit of sufficiently fast noise, for arbitrary exponent $\nu$. The longitudinal coherence after transition depends strongly on $\nu$, and there exists a critical ${\nu }_c$ with qualitative difference between $\nu <{\nu }_c$ and $\nu >{\nu }_c$. When $\nu <{\nu }_c$ the end state is always fully incoherent with equal population of both quantum levels, even for arbitrarily weak noise. For $\nu >{\nu }_c$ the system keeps some coherence depending on the strength of the noise, and in the limit of weak noise no transition takes place. For fast noise ${\nu }_c=1/2$, while for slow noise ${\nu }_c<1/2$ and it depends on $\gamma$. We also discuss transverse coherence, which is relevant when the qubit has a nonzero minimum energy gap. The qualitative dependency on $\nu$ is the same for transverse as for longitudinal coherence. The state after transition does in general depend on $\gamma$. For fixed $v$, increasing $\gamma$ decreases the final state coherence when $\nu <1$ and increase the final state coherence when $\nu >1$. Only the conventional linear driving is independent of $\gamma$.

arXiv comment7 pages, 5 figures

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• Non-Markovian dynamics of single- and two-qubit systems interacting with Gaussian and non-Gaussian fluctuating transverse environments
• Temperature can enhance coherent oscillations at a Landau-Zener transition
• Interplay of charge noise and coupling to phonons in adiabatic electron transfer between quantum dots
• Suppression of the Landau-Zener transition probability by a weak classical noise
• Landau-Zener-Stueckelberg physics with a singular continuum of states
• Landau-Zener transition driven by a slow noise
• Theory of nonlinear microwave absorption by interacting two-level systems
• Noisy Demkov-Kunike model