Decoherence of two entangled spin qubits coupled to an interacting sparse nuclear spin bath: Application to nitrogen vacancy centers

Abstract

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 |Ψ and |Φ 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 van easily obtain information about non-Gaussianity of environmental noise affecting the qubits from the comparison of dephasing of |Ψ and |Φ Bell states. Numerical results are obtained for two nitrogen vacancy centers interacting with a bath of 13 C nuclei of natural concentration, for which we obtain that Gaussian description of correlated part of environmental noise starts to hold for centers separated by about 3 nm. arXiv:1806.06845v2 [cond-mat.mes-hall]

Measure of qubit-environment entanglement for pure dephasing evolutions

“…The assumptions of a lack of interactions and correlations between constituents of the environment are reasonable for many qubits which undergo pure dephasing as their dominating decoherence mechanism. For example, for a qubit defined on a nitrogen-vacancy center interacting with an environment of carbon nuclear spins, the decoherence occurs on much shorter timescales than in nuclear dynamics [56,57]. The system is therefore effectively described by a Hamiltonian of the form (2) with an environment of noninteracting spin qubits (spinful carbon isotopes have spin-1/2 nuclei).…”

The dynamical-decoupling-based spatiotemporal noise spectroscopy

“…(assuming l c is an even number). According to (44), if the dimension of ( ) V 1 is greater than the revival period of Fourier coefficients (i.e. l c +1>l 0 ), the lth and (l 0 +l)th rows of the matrix are identical (or are very similar, when (N 0 +1)/γ is not an integer).…”

“…This means that, in total, we had to generate 10×18=180 unique slopes. Then we computed the matrices -U 1 and -(˜) ( ) V m 1 (for m=1, 3) according to equations (43) and (44). Finally, we made use of the formula (42) to obtain the values of the reconstructed spectral density, which are presented in figure 6.…”

“…Using multiple entangled qubit to enhance the precision of spectroscopy of perfectly correlated noises was discussed in [41]. However, quantitative investigations of more general forms of crosscorrelations of multiple classical [37,42] and quantum noises [38,[42][43][44] (the term 'quantum noise' indicates a case when the interaction between the environment and qubits requires full quantum mechanical treatment as it cannot be approximated with an exposition to effective external stochastic process), have been subject to closer investigation only quite recently. Such investigations are currently of high importance for ongoing and nearfuture development of multi-qubit quantum registers for various applications.…”

Spatial noise correlations in a Si/SiGe two-qubit device from Bell state coherences

“…In addition, QEC schemes exist that can deal with short-range correlations in the noise [6]. Spatial noise correlations have therefore been studied extensively, both theoretically [7][8][9][10][11][12][13][14] and experimentally [11,15,16].…”