Uniaxial Dynamical Decoupling for an Open Quantum System

Dynamical decoupling (DD) is an active and effective method for suppressing decoherence of a quantum system from its environment. In contrast to the nominal biaxial DD, this work presents a uniaxial decoupling protocol that requires a significantly reduced number of pulses and a much lower bias field satisfying the “magic” condition. We show this uniaxial DD protocol works effectively in a number of model systems of practical interest, e.g., a spinor atomic Bose-Einstein condensate in stray magnetic fields (classical noise), or an electron spin coupled to nuclear spins (quantum noise) in a semiconductor quantum dot. It requires only half the number of control pulses and a 10–100 times lower bias field for decoupling as normally employed in the above mentioned illustrative examples, and the overall efficacy is robust against rotation errors of the control pulses. The uniaxial DD protocol we propose shines new light on coherent controls in quantum computing and quantum information processing, quantum metrology, and low field nuclear magnetic resonance.

Figure 1

The schematic illustration for one cycle of the Uni-DD $[Y{U}_{\tau }Y{U}_{\tau }]$ on the Bloch sphere. (I) A spin or qubit precesses around the total field composed of a large (longitudinal) bias and a small stochastic field for a duration $\tau$ (blue solid lines), (II) rotated by a hard $Y$ pulse (red dashed lines), (III) precesses around the total field for another $\tau$, (IV) and rotated by a second $Y$ pulse. The green solid line denotes the initial spin or qubit state.

Figure 2

Suppressing classical noise with Uni-DD in a spinor atomic BEC for $\tau =0.05$. (a) The evolution of the spin average under Uni-DD cycles for an initial CSS in the worst case at $\omega -{\omega }_m=-2$ (magenta squares), $-1$ (blue circles), 0 (red solid line), 1 (blue dashed line), and 2 (magenta dotted line). The magic condition requires ${\omega }_m=2\pi /\tau \approx 126$. The FE results are presented for easier comparisons. The horizontal green dashed line denotes how the characteristic time $T_{0.9}$, where $j/J=0.9$, is extracted. (b) Dependence of the enhanced coherence time on the Larmor frequency (or the bias field). A peak occurs at the magic condition ${\omega }_m\tau =2\pi$. (c) Same as (a) except for the squeezing parameter ${\xi }^2$ with an initial SSS. The horizontal green dashed line is for $T_{0.05}$ where ${\xi }^2=0.05$. (d) Same as (b) except for $T_{0.05}$ with an initial SSS.

Figure 3

Suppression of quantum noise by the Uni-DD in a GaAs QD for $\tau =0.05$. (a) The evolution of fidelity under Uni-DD cycles in the worst case for $\omega -{\omega }_m=-2$ (magenta squares), $-1$ (blue circles), 0 (red solid line), 1 (blue dashed line), and 2 (magenta dotted line). The FE (black dashed line), Hahn echo (black dash-dotted line), and PDD (black dotted line) results are also presented for comparisons. The horizontal green dashed line denotes how the characteristic time $T_{0.9}$ is extracted. (b) Dependence of the prolonged coherence time on the Larmor frequency (or the bias field), exhibiting a peak at the magic condition ${\omega }_m\tau =2\pi$.

Figure 4

Robustness of the Uni-DD against rotation angle errors for $[Y{U}_{\tau }Y{U}_{\tau }]$ with $ϵ=3\%$ (black dotted line with triangles), 1% (blue dotted line with circles), 0% (red dotted line) and for $[\overline{Y}{U}_{\tau }Y{U}_{\tau }]$ with $ϵ=3\%$ (black solid line with triangles), 1% (blue solid line with circles), 0% (red solid line, coinciding with the red dotted line). The FE results are also presented for comparisons.