Towards optimized suppression of dephasing in systems subject to pulse timing constraints

Abstract

We investigate the effectiveness of different dynamical decoupling protocols for storage of a single qubit in the presence of a purely dephasing bosonic bath, with emphasis on comparing quantum coherence preservation under uniform vs. non-uniform delay times between pulses. In the limit of instantaneous bit-flip pulses, this is accomplished by establishing a new representation of the controlled qubit evolution, where the resulting decoherence behaviour is directly expressed in terms of the free evolution. Simple analytical expressions are given to approximate the long-and short-term coherence behaviour for both ohmic and supra-ohmic environments. We focus on systems with physical constraints on achievable time delays, with emphasis on pure dephasing of excitonic qubits in quantum dots. Our analysis shows that little advantage of high-level decoupling schemes based on concatenated or optimal design is to be expected if operational constraints prevent pulses to be applied sufficiently fast. In such constrained scenarios, we demonstrate how simple modifications of repeated periodic echo protocols can offer significantly improved coherence preservation in realistic parameter regimes.

Robust dynamical decoupling

“…One non-ideal property of real control pulses is their finite duration, which implies a minimum achievable cycle time. The effects introduced by finite pulse lengths have been considered in different theoretical works [45,81,82]. These works predict that high order CDD or UDD sequences in general lose their advantages when the delays between the pulses or the duration of the pulses themselves are strongly constrained.…”

“…Ideally, each level of concatenation improves the decoupling performance and the tolerance to pulse imperfections; in practice, higher order sequences do not always perform better. It has been theoretically predicted [45,81,82] and later observed experimentally that the finite duration of the pulses and constrained delays between pulses result in the existence of optimal levels of concatenation [54,55].…”

“…Clearly, this procedure is limited by finite field strengths and associated pulse durations. Within these limitations, the goal remains to find those sequences that provide the best possible decoupling performance [45,54,55,67,[81][82][83][84]. Furthermore, the pulses do not only have finite lengths, they also do not implement perfect rotations.…”

Time-invariant discord in dynamically decoupled systems

“…In order to express the controlled decoherence function Γ n (t) in terms of its uncontrolled counterpart Γ 0 (t), we simply relate |y n (ωt)| 2 to |y 0 (ωt)| 2 using iteration to find the following exact expression [6]:…”

“…DD techniques for open quantum systems are among the most successful methods to subdue decoherence. Specifically, "bang bang" periodic dynamical decoupling (PDD) schemes can be exploited to prolong coherence times and restore monotonically decaying correlations in quantum systems which are undergoing decoherence [6,7].…”