Nonvanishing effect of detuning errors in dynamical-decoupling-based quantum sensing experiments
J. E. Lang, Trisha Madhavan, Jean‐Philippe Tetienne, David A. Broadway, Liam T. Hall, Tokuyuki Teraji, T. S. Monteiro, Alastair D. Stacey, Lloyd C. L. Hollenberg
Characteristic dips appear in the coherence traces of a probe qubit when dynamical decoupling (DD) is applied in synchrony with the precession of target nuclear spins, forming the basis for nanoscale nuclear magnetic resonance (NMR). The frequency of the microwave control pulses is chosen to match the qubit transition but this can be detuned from resonance by experimental errors, hyperfine coupling intrinsic to the qubit, or inhomogeneous broadening. The detuning acts as an additional static field which is generally assumed to be completely removed in Hahn echo and DD experiments. Here we demonstrate that this is not the case in the presence of finite pulse-durations, where a detuning can drastically alter the coherence response of the probe qubit, with important implications for sensing applications. Using the electronic spin associated with a nitrogen-vacancy center in diamond as a test qubit system, we analytically and experimentally study the qubit coherence response under CPMG and XY8 dynamical decoupling control schemes in the presence of finite pulse-durations and static detunings. Most striking is the splitting of the NMR resonance under CPMG, whereas under XY8 the amplitude of the NMR signal is modulated. Our work shows that the detuning error must not be neglected when extracting data from quantum sensor coherence traces.
Characteristic dips appear in the coherence traces of a probe qubit when dynamical decoupling (DD) is applied in synchrony with the precession of target nuclear spins, forming the basis for nanoscale nuclear magnetic resonance (NMR). The frequency of the microwave control pulses is chosen to match the qubit transition but this can be detuned from resonance by experimental errors, hyperfine coupling intrinsic to the qubit, or inhomogeneous broadening. The detuning acts as an additional static field which is generally assumed to be completely removed in Hahn echo and DD experiments. Here we demonstrate that this is not the case in the presence of finite pulse-durations, where a detuning can drastically alter the coherence response of the probe qubit, with important implications for sensing applications. Using the electronic spin associated with a nitrogen-vacancy center in diamond as a test qubit system, we analytically and experimentally study the qubit coherence response under CPMG and XY8 dynamical decoupling control schemes in the presence of finite pulse-durations and static detunings. Most striking is the splitting of the NMR resonance under CPMG, whereas under XY8 the amplitude of the NMR signal is modulated. Our work shows that the detuning error must not be neglected when extracting data from quantum sensor coherence traces.
Nuclear magnetic resonance (NMR) schemes can be applied to micron-, and nanometer-sized samples by the aid of quantum sensors such as nitrogen vacancy (NV) color centers in diamond. These minute devices allow for magnetometry of nuclear spin ensembles with high spatial and frequency resolution at ambient conditions, thus having a clear impact in different areas such as chemistry, biology, medicine, and material sciences. In practice, NV quantum sensors are driven by microwave (MW) control fields with a twofold objective: On the one hand, MW fields bridge the energy gap between NV and nearby nuclei which enables a coherent and selective coupling among them while, on the other hand, MW fields remove environmental noise on the NV leading to enhanced interrogation time. In this work we review distinct MW radiation patterns, or dynamical decoupling techniques, for nanoscale NMR applications.
Dynamical decoupling multipulse sequences can be applied to solid-state spins for sensing weak oscillating fields from nearby single nuclear spins. By periodically reversing the probing system's evolution, other noises are counteracted and filtered out over the total evolution. However, the technique is subject to intricate interactions resulting in additional resonant responses, which can be misinterpreted with the actual signal intended to be measured. We experimentally characterize three of these effects present in single nitrogen-vacancy centers in diamond, where we also develop a numerical simulation model without rotating-wave approximation, showing robust correlation to the experimental data. Regarding centers with the N 15 nitrogen isotope, we observe that a small misalignment in the bias magnetic field causes the precession of the nitrogen nuclear spin to be sensed by the electronic spin of the center. Another studied case of ambiguous resonances comes from the coupling with lattice C 13 nuclei, where we use the echo modulation frequencies to obtain the interaction Hamiltonian and then utilize the latter to simulate multipulse sequences. Finally, we also measure and simulate the effects from the free evolution of the quantum system during finite pulse durations. Due to the large data volume and the strong dependence of these ambiguous resonances with specific experimental parameters, we provide a simulations data set with a user-friendly graphical interface, where users can compare simulations with their own experimental data for spectral disambiguation. Although focused on nitrogen-vacancy centers and dynamical decoupling sequences, these results and the developed model can potentially be applied to other solid-state spins and quantum sensing techniques.
Quantum sensors based on the electron spin states of nitrogen vacancy centers in diamond have found wide application in magnetometry and nuclear spin magnetic resonance measurements. Previously, we have theoretically and experimentally investigated the effect of finite pulse width on quantum sensing for synchronous alternating-current (AC) magnetic fields to dynamical decoupling sequences [T. Ishikawa et al., Phys. Rev. Appl. 10, 054059 (2018)]. However, many biological and condensed-matter systems exhibit fluctuating AC fields over time, and thus, our model needs modifications because of additional non-ideal conditions in practical measurements. Here, we investigate the effects of finite pulse width of multiple-pulse decoupling sequences on quantum sensing for asynchronous AC magnetic fields. For this purpose, we use a spin ensemble of nitrogen vacancy centers in an isotopically purified diamond film. We reveal through experiments that the finite-width pulse causes shifts in AC magnetometry signals in a free-precession-time plot. In addition, our results indicate that the finite-width pulse affects the amplitude of magnetometry signals, implying that the finite-pulse-width effect should be taken into account for realizing accurate measurement of the frequency and amplitude of asynchronous AC magnetic fields.
Nanoscale sensing experiments based on defects in diamond are at the forefront of quantum-technology research. Nanoscale NMR and MRI employ microwave pulses to decouple the quantum sensor from sources of decoherence, and to enhance weak signals from a single nuclear spin. Here finite pulse duration has been largely considered a source of experimental error, but the authors see it differently: A quantum model shows that seemingly spurious signals due to nonzero pulse width are predictable, allowing experimental protocols for either their full suppression, or their exploitation to increase resolution.
Spin systems in solid state materials are promising qubit candidates for quantum information in particular as quantum memories or for quantum sensing. A major prerequisite here is the coherence of spin phase oscillations. In this work, we show a control sequence which, by applying RF pulses of variable detuning, allows to increase the visibility of spin phase oscillations. We experimentally demonstrate the scheme on single NV centers in diamond and analytically describe how the NV electron spin phase oscillations behave in the presence of classical noise models. We hereby introduce detuning as the enabling factor that modulates the filter function of the sequence, in order to achieve a visibility of the Ramsey fringes comparable to or longer than the Hahn-echo T2 time and an improved sensitivity to DC magnetic fields in various experimental settings.
Spin ensembles show increasing promise for highly efficient quantum sensing and quantum technologies. However, protecting their coherent properties remains a significant challenge. Dynamical decoupling (DD) typically employs a sequence of fast pulses that aim to reduce the effect of unwanted system-environment interactions. However, the performance of the DD sequences typically suffers in spin ensembles, e.g., due to amplitude and frequency inhomogeneities and control errors. In this work, we compare the performance of an extensive number of DD protocols for coherence protection and quantum sensing in an ensemble of negatively charged NV centers under ambient conditions. We identify the optimal approach that uses rapid adiabatic passage pulses, which are robust to amplitude and frequency inhomogeneity, in combination with the variation of their phases. We experimentally demonstrate an improved signal contrast and an order-of-magnitude increase in memory time with the optimal sequence compared to the widely used XY8 with standard rectangular pulses. We also apply our approach for improved sensing of a weak oscillating field. While our particular demonstration is with NV centers in diamond, the optimized protocol is generally applicable to other spin ensembles and to systems with high amplitude and/or frequency inhomogeneities.