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arXiv:1604.07891 · The European Physical Journal B

Optimal state transfer of a single dissipative two-level system

Hamza Jirari, Ning Wu

Published Apr 1, 2016• 3 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2016-60523-y

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We discuss a general formalism to optimize quasi-adiabatic state-transfer protocols, where high fidelity is achieved by maintaining the system in a dark subspace protected from the dominant dissipative channels. We cast the residual fidelity loss, induced by a combination of dissipation and non-adiabatic transitions, in the form of a classical action where the time-dependent control parameters act as coordinates. This allows us to apply the least action principle, yielding the fidelity upper-bound and the corresponding optimal transfer time. As an application, we analyze a system of two qubits subject to weak relaxation and dephasing, interacting through a strongly dissipative quantum bus. In this case, our formalism, we obtain a full characterization of the optimal state-transfer fidelity.
We describe the dynamics of tripartite state mapping and entanglement transfer from qubit-like radiation states to two-level atoms via optical cavity modes. When the entangled radiation is carried to the cavities by single-mode fibers, optimal pure and mixed state transfer is predicted for perfect mirror transmittance, and entanglement sudden death (and birth) is demonstrated for Werner input states. The general case of multi-mode fiber coupling is also discussed. The dynamics is finally investigated under various dissipative effects.
Adiabatic rapid passage (ARP) is extensively used to achieve efficient transfer or inversion of populations in quantum systems. Landau and Zener accurately estimated the transfer probability of ARP for a closed system and showed that this probability improved with higher drive amplitude. Recently, we found that, in open quantum systems, applying a strong drive can give rise to significant drive-induced dissipation (DID). Here, we investigate the effect of DID on the performance of ARP that is implemented using a linearly chirped pulse on a two-level system. From the Landau-Zener formula, the population transfer was known to be enhanced with increasing drive amplitude. However, here we show that, beyond a threshold value of the drive amplitude, the transfer probability is reduced because of the detrimental effect of DID. We show that the competition between the two processes results in an optimal behavior of the population transfer. We also propose a phenomenological model that helps explain such nonmonotonic behavior of the transfer. Using this model, we estimate the optimum time at which the maximum population transfer occurs. We extend the analysis for rectangular as well as Gaussian pulse profiles and conclude that a Gaussian pulse outperforms a rectangular pulse.