We consider pure dephasing of Bell states of electron spin qubits interacting with a sparse bath of nuclear spins. Using the newly developed two-qubit generalization of cluster-correlation expansion method, we calculate the spin-echo decay of $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ and $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$ states for various interqubit distances. Comparing the results with calculations in which dephasing of each qubit is treated independently, we identify signatures of influence of common part of the bath on the two qubits. At large interqubit distances, this common part consists of many nuclei weakly coupled to both qubits, so that decoherence caused by it can be modeled by considering multiple uncorrelated sources of noise (clusters of nuclei), each of them weakly affecting the qubits. Consequently, the resulting genuinely two-qubit contribution to decoherence can be described as being caused by classical Gaussian noise. On the other hand, for small interqubit distances the common part of the environment contains clusters of spins that are strongly coupled to both qubits, and their contribution to two-qubit dephasing has visibly non-Gaussian character. We show that one can easily obtain information about non-Gaussianity of environmental noise affecting the qubits from the comparison of dephasing of $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ and $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$ Bell states. Numerical results are obtained for two nitrogen vacancy centers interacting with a bath of $^{13}\mathrm{C}$ nuclei of natural concentration, for which we obtain that Gaussian description of a correlated part of environmental noise starts to hold for centers separated by about 3 nm.We consider pure dephasing of Bell states of electron spin qubits interacting with a sparse bath of nuclear spins. Using the newly developed two-qubit generalization of cluster-correlation expansion method, we calculate the spin-echo decay of $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ and $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$ states for various interqubit distances. Comparing the results with calculations in which dephasing of each qubit is treated independently, we identify signatures of influence of common part of the bath on the two qubits. At large interqubit distances, this common part consists of many nuclei weakly coupled to both qubits, so that decoherence caused by it can be modeled by considering multiple uncorrelated sources of noise (clusters of nuclei), each of them weakly affecting the qubits. Consequently, the resulting genuinely two-qubit contribution to decoherence can be described as being caused by classical Gaussian noise. On the other hand, for small interqubit distances the common part of the environment contains clusters of spins that are strongly coupled to both qubits, and their contribution to two-qubit dephasing has visibly non-Gaussian character. We show that one can easily obtain information about non-Gaussianity of environmental noise affecting the qubits from the comparison of dephasing of $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ and $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$ Bell states. Numerical results are obtained for two nitrogen vacancy centers interacting with a bath of $^{13}\mathrm{C}$ nuclei of natural concentration, for which we obtain that Gaussian description of a correlated part of environmental noise starts to hold for centers separated by about 3 nm.

arXiv:1806.06845Physical review. B./Physical review. BOct 5, 201832 citations

Distinguishing Quantum and Classical Baths via Correlation Measurements

Fink, Thomas, Hendrik Bluhm

Investigations of quantum mechanical effects in macroscopic systems are of great interest to shed light onto the question where and how the transition to the classical world appears. It is also of practical relevance to determine if a bath dephasing a qubit can be described classically or requires a quantum mechanical treatment. We propose a measurement scheme to detect quantum backaction via correlation measurements to answer this question for a bath coupled to a single qubit. The presence of backaction leads to a dependence of correlations of subsequent initialization-evolution-readout cycles on how the qubit is manipulated in between. We compute the autocorrelation function for both an instructive spin model and the realistic case of an electron spin coupled to a bath of $10^6$ nuclear spins, as found in gated GaAs quantum dots, and show that backaction from the qubit onto the nuclear spin bath should be detectable even in such a large system.Investigations of quantum mechanical effects in macroscopic systems are of great interest to shed light onto the question where and how the transition to the classical world appears. It is also of practical relevance to determine if a bath dephasing a qubit can be described classically or requires a quantum mechanical treatment. We propose a measurement scheme to detect quantum backaction via correlation measurements to answer this question for a bath coupled to a single qubit. The presence of backaction leads to a dependence of correlations of subsequent initialization-evolution-readout cycles on how the qubit is manipulated in between. We compute the autocorrelation function for both an instructive spin model and the realistic case of an electron spin coupled to a bath of $10^6$ nuclear spins, as found in gated GaAs quantum dots, and show that backaction from the qubit onto the nuclear spin bath should be detectable even in such a large system.

arXiv:1402.0235Feb 2, 20142 citations

Characterization of Qubit Dephasing

Florian Förster, G. Petersen, Stephan Manus +5 more

Jan 1, 20140 citations

^{13}\mathrm{C}

nuclei of natural concentration, for which we obtain that Gaussian description of a correlated part of environmental noise starts to hold for centers separated by about 3 nm.

10^6

nuclear spins, as found in gated GaAs quantum dots, and show that backaction from the qubit onto the nuclear spin bath should be detectable even in such a large system.