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arXiv:quant-ph/0510001

Quantum kinetics of refocusing

Leonid P. Pryadko, Pinaki Sengupta

Published Sep 30, 2005• 0 citations
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Abstract

We consider quantum kinetics of an open quantum system in the presence of periodic fields designed to suppress the internal evolution and shield the system from generic low-frequency environment (refocusing or dynamical decoupling in application to multi-qubit systems). Assuming that the refocusing has order K, that is, for frozen environment the cumulant expansion of the evolution operator over the period tau begins with the term ~tau^(K+1), we trace the associated cancellations in the kernel of the quantum kinetic equation in the Floquet formalism and characterize the remaining decoherence processes.

DOI
10.48550/arxiv.quant-ph/0510001

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We consider quantum kinetics of an open quantum system in the presence of periodic fields designed to suppress the internal evolution and shield the system from generic low-frequency environment (refocusing or dynamical decoupling in application to multi-qubit systems). Assuming that the refocusing has order K, that is, for frozen environment the cumulant expansion of the evolution operator over the period tau begins with the term ~tau^(K+1), we trace the associated cancellations in the kernel of the quantum kinetic equation in the Floquet formalism and characterize the remaining decoherence processes.
We consider quantum kinetics of an open quantum system in the presence of periodic fields designed to suppress the internal evolution and shield the system from a generic low-frequency environment (refocusing or dynamical decoupling in an application to multiqubit systems). Assuming that the refocusing has order KKK, that is, for a frozen environment the cumulant expansion of the evolution operator over the period $\ensuremath{\tau}$ begins with the term $\ensuremath{\sim}{\ensuremath{\tau}}^{K+1}$, we trace the associated cancellations in the kernel of the quantum kinetic equation in the Floquet formalism and characterize the remaining decoherence processes.
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'' $\ensuremath{\pi}$ pulse. To second order in the pulse duration, we characterize a symmetric pulse shape by three parameters, two of which can be made 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 a controlled Jaynes-Cummings Hamiltonian. When errors are cancelled to second order, numerical simulations show excellent qubit fidelity with strongly suppressed oscillator heating.
Refocusing, or dynamical decoupling, is a coherent control technique where the internal dynamics of a quantum system is effectively averaged out by an application of specially designed driving fields. The method has originated in nuclear magnetic resonance, but it was independently discovered in atomic physics as a ``coherent destruction of tunneling''. Present work deals with the analysis of the performance of ``soft'' refocusing pulses and pulse sequences in protecting the coherence of a qubit system coupled to a quantum oscillator.
We consider the effect of broadband decoherence on the performance of refocusing sequences, having in mind applications of dynamical decoupling in concatenation with quantum error correcting codes as the first stage of coherence protection. Specifically, we construct cumulant expansions of effective decoherence operators for a qubit driven by a pulse of a generic symmetric shape and for several sequences of $\ensuremath{\pi}$ and $\ensuremath{\pi}/2$ pulses. While, in general, the performance of soft pulses in decoupling sequences in the presence of Markovian decoherence is worse than that of the ideal $\ensuremath{\delta}$ pulses, it can be substantially improved by shaping.
An irreversible time evolution of a quantum system interacting with a surrounding environment is described by a quantum master equation. When an external field is applied to a quantum system, a non-Markovian master equation is derived in a rigorous way, where the relaxation terms in the quantum master equation include the effect of the external field that is ignored in the conventional treatment. It is shown that when the external field is a sequence of phase-modulation π-pulses, the decoherence of the quantum system can be suppressed. In particular, when the pulse separation is sufficiently short in comparison with the correlation time of the environmental system, dynamical decoupling takes place. To see the effect of the phase-modulation π-pulses, the time evolution of qubit entanglement is investigated in detail.