Abstract
Here we demonstrate how the standard, temporal-only, dynamical-decoupling-based noise spectroscopy method can be extended to also encompass the spatial degree of freedom. This spatiotemporal spectroscopy utilizes a system of multiple qubits arranged in a line that are undergoing pure dephasing due to environmental noise. When the qubits are driven by appropriately coordinated sequences of π pulses the multi-qubit register becomes decoupled from all components of the noise, except for those characterized by frequencies and wavelengths specified by the pulse sequences. This allows for employment of the procedure for reconstruction of the two-dimensional spectral density that quantifies the power distribution among spatial and temporal harmonic components of the noise.
Highlights
Single qubits have been successfully used to characterize the frequency spectrum of environmental fluctuations affecting their coherence [1, 2]
There we develop the supporting methods that allow to deal with expected difficulties that would not be an issue for the temporal-only variant of spectroscopy, but here can make or break the whole method
In order to overcome these imperfections of this type of filter, so that an accurate spatiotemporal spectroscopy can be carried out, one has to implement a generalized version of the procedure for data acquisition and analysis, that was originally developed for single-qubit spectrometers in [63]
Summary
Single qubits have been successfully used to characterize the frequency spectrum of environmental fluctuations affecting their coherence [1, 2]. The key element is the ability to filter particular noise frequencies together with the wavevectors (or wavelengths) of spatial fluctuations; in our setup it is achieved with coordination of pulse timings between qubits that is specific to given spatial configuration of the register While this design of spatiotemporal frequency filter is broadly applicable to all noise fields, the detailed scheme for extracting the data on the spectral density from the multi-qubit coherence measurements that we present here works for stationary and spatially uniform fields having Gaussian statistics (i.e., fields completely specified by their average value and the auto-correlation).
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