Month: March 2011

Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath | Phys. Rev. A 83, 032303 (2011)

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Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath

Ashok Ajoy1,2,3,*, Gonzalo A. Álvarez1,†, and Dieter Suter1,‡

1Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany

2Birla Institute of Technology and Science, Pilani, Zuarinagar, Goa 403726, India

3NMR Research Centre, Indian Institute of Science, Bangalore 560012, India

Received 29 November 2010; published 8 March 2011

Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where, for instance, it is employed in multiparameter estimation. While a sequence of equidistant control pulses [the Carr-Purcell-Meiboom-Gill (CPMG) sequence] has been ubiquitously used for decoupling, Uhrig recently proposed that a nonequidistant pulse sequence [the Uhrig dynamic decoupling (UDD) sequence] may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system qubits are 13C nuclear spins and the environment consists of a 1H nuclear spin bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs better than any nonequidistant DD sequence in the presence of this kind of environmental noise.

©2011 American Physical Society

via Phys. Rev. A 83, 032303 (2011): Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath.

Experimental (symbols) and simulated (line) decay rates of the 13C magnetization for different UDD orders (blue circles) compared with decay rates achieved with the CPMG sequence (red rhombus). The same number of pulses during a time window t are applied by scaling the cycle time as τc = 110.4N μs.
Experimental (symbols) and simulated (line) decay rates of the 13C magnetization for different UDD orders (blue circles) compared with decay rates achieved with the CPMG sequence (red rhombus). The same number of pulses during a time window t are applied by scaling the cycle time as τc = 110.4N μs.
Comparison of filter functions |FN (ω, τM )| for different UDD orders: (a) UDD4 with M = 1 (dotted line) and M = 12 (solid line),even UDD orders N with M = 1 (b) and M = 48/N (c), and (d) CPMG=UDD2 with M = 1 (dotted line) and M = 24 (solid line). ω0 is defined in terms of the cycle time of the CPMG sequence, ω=2π/τ_CPMG. Blue circles (a), red rhombuses (d) and empty circles in (b) are the coefficients of the Fourier expansion of fN (t′, ∞). They are modulated by the shape of the filter function |FN(ω,τcf)|, shown in panel (b) and rep- resented by blue and red dotted lines in panels (a) and (d), where τ_CPMG=2τ and τ_UDDN =Nτ.
Comparison of filter functions |FN (ω, τM )| for different UDD orders: (a) UDD4 with M = 1 (dotted line) and M = 12 (solid line),even UDD orders N with M = 1 (b) and M = 48/N (c), and (d) CPMG=UDD2 with M = 1 (dotted line) and M = 24 (solid line). ω0 is defined in terms of the cycle time of the CPMG sequence, ω=2π/τ_CPMG. Blue circles (a), red rhombuses (d) and empty circles in (b) are the coefficients of the Fourier expansion of fN (t′, ∞). They are modulated by the shape of the filter function |FN(ω,τcf)|, shown in panel (b) and rep- resented by blue and red dotted lines in panels (a) and (d), where τ_CPMG=2τ and τ_UDDN =Nτ.
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