Soft-pulse dynamical decoupling in a cavity

Abstract

Dynamical decoupling is a coherent control technique where the intrinsic and extrinsic couplings of a quantum system are effectively averaged out by application of specially designed driving fields (refocusing pulse sequences). This entails pumping energy into the system, which can be especially dangerous when it has sharp spectral features like a cavity mode close to resonance. In this work we show that such an effect can be avoided with properly constructed refocusing sequences. To this end we construct the average Hamiltonian expansion for the system evolution operator associated with a single ``soft'' pi-pulse. To second order in the pulse duration, we characterize a symmetric pulse shape by three parameters, two of which can be turned to zero by shaping. We express the effective Hamiltonians for several pulse sequences in terms of these parameters, and use the results to analyze the structure of error operators for controlled Jaynes-Cummings Hamiltonian. When errors are cancelled to second order, numerical simulations show excellent qubit fidelity with strongly-suppressed oscillator heating.Comment: 9pages, 5eps figure

Soft-pulse dynamical decoupling with Markovian decoherence

“…1(a),(b)] was analayzed in Refs. [21,35]. General conclusion is that a carefully-designed sequence with the period τ ≡ 2π/Ω provides an excellent decoherence protection as long as the adiabaticity condition Ω ω c is satisfied.…”

“…When this is done, only the effective, DD-renormalized coupling to such modes matters. Nonequilibrium effects like mode heating do not occur as long as this renormalized coupling is small compared to either the width of the spectral peak or the corresponding frequency bias [35].…”

“…1(b)]; the corresponding modes have to be included in the Hamil-tonian of the system and the controlled dynamics reanalyzed [35]. Compared to qubits-only systems, presence of oscillators in H S can generate some additional terms in the Magnus expansion of the unitary evolution operator U (τ ) for the closed system which requires more careful sequence design.…”

“…The functions of the doubled angle are specifically due to the Markovian decoherence operators; they were not present in the analysis of Hamiltonian dynamics in Refs. 35,52. For the symmetric pulse shape,…”

“…. Dynamical decoupling can be very effective in preserving coherence in the presence of (a) featureless lowfrequency bath [21] and also (b) sharp resonances [35]. In this work we consider the effect of Markovian noise (c) on DD of a single qubit.…”