The decoherence of a spin‐1/2 particle (qubit) interacting with a nuclear spin bath in quantum dots has been studied using an isotropic Heisenberg model. An effective magnetic field (a feature of unitary evolution) and an effective temperature (a non‐unitary feature) describe the effective dynamics of the qubit. The decoherence time scale is calculated as a function of the nuclear bath spin distribution and the nuclear polarizations in various spin channels. The averaged auto correlation function of the qubit spin, averaged over all possible initial states of the qubit, depends on the nuclear spin distribution, but is insensitive to the nuclear polarizations.
We consider the spin echo decay of a nitrogen-vacancy center spin qubit, based on
m=0 and
m=1 levels of the
S=1 ground state spin manifold of the center, in presence of finite dynamic nuclear polarization of the nuclear environment. We show that the signal acquires a nontrivially time-dependent phase shift in presence of such polarization. In Gaussian approximation to calculation of dephasing this phase shift is absent when the NV center is prepared in a superposition of
m=1 and
m=−1 states, i.e. when the qubit couples to the spin environment in a way analogous to that of spin-
1/2. For nuclear environment devoid of spins strongly coupled to the qubit, the phase shift can be quite well described in Gaussian approximation, which makes it clear that it is related to a linear response function of the environment affected by an evolving qubit. Consequently, its observation signifies the presence of back-action of the qubit on the environment, and it thus excludes the possibility of physically well-motivated treatment of environment as a source of external classical noise affecting the qubit. Furthermore, when exact coherence dynamics is well described by weak coupling approximation, for qubit based on
m=0 and
m=1 levels observation of dependence of modulus of echo signal on nuclear polarization signifies non-Gaussian character of environmental influence. The same conclusion follows from observation of nonzero phase shift of spin echo signal of a qubit based on
m=±1 levels.
Molecular spins offer promise in emerging quantum technologies such as quantum sensing and computing. At low temperatures, nuclear spin-spin interactions affect electron spin coherence lifetimes through pure dephasing. Nuclear-spin noise can originate from spin pairs within a molecule itself, pairs in a surrounding environment system, or pairs in which one spin is on the molecule and the other in the environment. Improving coherence times requires detailed knowledge of the dominant sources of dephasing. Here, we analyze the decoherence behavior of two molecular qubit candidates with various ligands and in different nuclear-spin containing solvents. We apply an electronic-structure enhanced, non-Markovian perturbative theoretical method to connect experimentally comparable dephasing times to individual spin pairs. This analysis allows the development of a computational workflow to strategically improve coherence lifetimes in spin systems where decoherence is dominated by spin-spin dephasing.
The dynamics of a spin-
1∕2 particle coupled to a nuclear spin bath through an isotropic Heisenberg interaction is studied as a model for the spin decoherence in quantum dots. The time-dependent polarization of the central spin is calculated as a function of the bath-spin distribution and the polarizations of the initial bath state. For short times, the polarization of the central spin shows a Gaussian decay, and at later times it is revived displaying nonmonotonic time dependence. The decoherence time scale depends on moments of the bath-spin distribuition, and also on the polarization strengths in various bath-spin channels. The bath polarizations have a tendency to increase the decoherence time scale. The effective dynamics of the central spin polarization is shown to be described by a master equation with non-Markovian features.
Molecular spins are promising candidates for quantum information science, leveraging coherent electronic spin states for quantum sensing and computation. However, the practical application of these systems is hindered by electronic spin decoherence, driven by interactions with nuclear spins in the molecule and the surrounding environment at low temperatures. Predicting dephasing dynamics remains a formidable challenge due to the complexity of the spin bath. In this work, we develop a non-Markovian time-convolutionless master equation to treat an electronic spin coupled to a nuclear-spin bath. By relating ab initio electronic structure parameters directly to the decoherence dynamics, we provide a framework that accounts for pure dephasing in the low-temperature limit. We apply this method to a series of molecular qubit candidates and demonstrate good agreement with experimental relaxation trends. This approach offers a computationally efficient path for the prediction of low-temperature decoherence trends in molecular spin systems.
We consider the spin-echo dynamics of a nitrogen-vacancy (NV)-center qubit based on the
S=1 ground-state spin manifold, caused by a dynamically polarized nuclear environment. We show that the echo signal acquires then a nontrivially time-dependent phase shift. This effect should be observable for polarization $\ensuremath{\approx}0.5$ of nuclei within $\ensuremath{\sim}1$ nm from the qubit, and for the NV center initialized in a superposition of
m=0 and either
m=1 or $m=\ensuremath{-}1$ states. This phase shift is much smaller when the NV center is prepared in a superposition of
m=1 and $m=\ensuremath{-}1$ states, i.e., when the qubit couples to the spin environment in a way analogous to that of spin-
1/2. For a nuclear environment devoid of spins strongly coupled to the qubit, the phase shift is well described within Gaussian approximation, which provides an explanation for the dependence of the shift magnitude on the choice of states on which the qubit is based, and makes it clear that its presence is related to the linear response of the environment perturbed by an evolving qubit. Consequently, its observation signifies the presence of an environment-mediated self-interaction of the qubit and, hence, it invalidates the notion that the nuclear environment acts as a source of external noise driving the qubit. We also show how a careful comparison of the echo signal from qubits based on
m=0,1 and $m=\ifmmode\pm\else\textpm\fi{}1$ manifolds can distinguish between effectively Gaussian and non-Gaussian environments.