Control of electron spin decoherence caused by electron–nuclear spin dynamics in a quantum dot

Abstract

Control of electron spin decoherence in contact with a mesoscopic bath of many interacting nuclear spins in an InAs quantum dot is studied by solving the coupled quantum dynamics. The nuclear spin bath, because of its bifurcated evolution predicated on the electron spin up or down state, measures the which-state information of the electron spin and hence diminishes its coherence. The many-body dynamics of nuclear spin bath is solved with a pair-correlation approximation. In the relevant timescale, nuclear pair-wise flip-flops, as elementary excitations in the mesoscopic bath, can be mapped into the precession of non-interacting pseudo-spins. Such mapping provides a geometrical picture for understanding the decoherence and for devising control schemes. A close examination of nuclear bath dynamics reveals a wealth of phenomena and new possibilities of controlling the electron spin decoherence. For example, when the electron spin is flipped by a π-pulse at τ , its coherence will partially recover at √ 2τ as a consequence of quantum disentanglement from the mesoscopic bath. In contrast to the re-focusing of inhomogeneously broadened phases by conventional spin-echoes, the disentanglement is realized through shepherding quantum evolution of the bath state via control of the quantum object. A concatenated construction of pulse sequences can eliminate the decoherence with arbitrary accuracy, with the nuclear-nuclear spin interaction strength acting as the controlling small parameter.

Comparison of dynamical decoupling protocols for a nitrogen-vacancy center in diamond

“…Many methods have been developed in the field of magnetic resonance, [81][82][83][84] and recently in the field of quantum information processing. 4,25,59,60,[85][86][87][88][89][90][91][92][93][94][95] In this work, we treat the spin bath of P1 centers in a mean-field manner, approximating it as a classical noise field acting on the NV center spin. This treatment is justified because the coupling between the bath spins is of long-range character, and its magnitude is of the same order as the coupling of a bath spin to the central spin.…”

“…If the couplings between the bath spins are much smaller than the coupling between a single bath spin and the central spin, then the bath dynamics is conditioned on the state of the central spin, and the resulting correlations in the bath play a major role. 60,87,[89][90][91]95 The noise field B(t), which is Gaussian, Markovian, and stationary, is represented by an Ornstein-Uhlenbeck (O-U) process 97 with the correlation function,…”

Protection of quantum systems by nested dynamical decoupling

“…They increase exponentially with the DD order. Even though the exponentially increasing number of control pulses does yield significant improvement of precision (through reduction of the coefficient in front of the power of time T N+1 ) [11,35,36], implementation of CDD to high orders is challenging in experiments since errors are inevitably introduced in each control pulse.…”

Hyperfine interaction induced dephasing of coupled spin qubits in semiconductor double quantum dots

“…For a single spin in a QD, this approach is valid when the evolution time t is shorter than the inverse of the typical spread of nuclear spin Knight shifts, 28 i.e., t ≪ N Ψ /A. 32,77,78 Thus in this short-time limit, the exact shape of the electron's wavefunction is irrelevant. On the other hand, when t ≫ N Ψ /A α , this wavefunction shape has to be taken into account.…”