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Frontiers in Photonics

A Hahn-Ramsey scheme for dynamical decoupling of single solid-state qubits

Nikola Sadzak, Alexander Carmele, Claudia Widmann, Christoph Erwin Nebel, Andreas Knorr, Oliver J. Benson

Published Nov 29, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.3389/fphot.2022.932944

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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 systems in solid state materials are promising qubit candidates for quantum information or 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 spin phase oscillation visibility and to perform DC magnetometry as well. 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 T2T_2T2​ time and an improved sensitivity to DC magnetic fields in various experimental settings.
In this work, we optimize a dynamical decoupling (DD) protocol to improve the spin coherence properties of a dense ensemble of nitrogen-vacancy (NV) centers in diamond. Using liquid nitrogen-based cooling and DD microwave pulses, we increase the transverse coherence time T2 from ∼ 0.7 ms up to ∼ 30 ms. We extend previous work of single-axis (Carr-Purcell-Meiboom-Gill) DD towards the preservation of arbitrary spin states. After performing a detailed analysis of pulse and detuning errors, we compare the performance of various DD protocols. We identify that the concatenated XY8 pulse sequences serves as the optimal control scheme for preserving an arbitrary spin state. Finally, we use the concatenated sequences to demonstrate an immediate improvement of the AC magnetic sensitivity up to a factor of two at 250 kHz. For future work, similar protocols may be used to increase coherence times up to NV-NV interaction time scales, a major step toward the creation of quantum collective NV spin states.
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.
We demonstrate significant improvements of the spin coherence time of a dense ensemble of nitrogen-vacancy (NV) centers in diamond through optimized dynamical decoupling (DD). Cooling the sample down to 77 K suppresses longitudinal spin relaxation T1{T}_{1}T1​ effects and DD microwave pulses are used to increase the transverse coherence time T2{T}_{2}T2​ from $\ensuremath{\sim}0.7\phantom{\rule{0.28em}{0ex}}\mathrm{ms}$ up to $\ensuremath{\sim}30\phantom{\rule{0.28em}{0ex}}\mathrm{ms}$. We extend previous work of single-axis (Carr-Purcell-Meiboom-Gill) DD towards the preservation of arbitrary spin states. Following a theoretical and experimental characterization of pulse and detuning errors, we compare the performance of various DD protocols. We identify that the optimal control scheme for preserving an arbitrary spin state is a recursive protocol, the concatenated version of the XY8 pulse sequence. The improved spin coherence might have an immediate impact on improvements of the sensitivities of ac magnetometry. Moreover, the protocol can be used on denser diamond samples to increase coherence times up to NV-NV interaction time scales, a major step towards the creation of quantum collective NV spin states.
The extension of the spin coherence times is a crucial issue for quantum information and quantum sensing. In solid state systems, suppressing noises with various techniques have been demonstrated. On the other hand, an electrical control for suppression is important toward individual controls of on-chip quantum information devices. Here we show the electrical control for extension of the spin coherence times of 40 nm-deep ion-implanted single nitrogen vacancy center spins in diamond by suppressing magnetic noises. We applied 120 V DC across two contacts spaced by 10 micrometers. The spin coherence times, estimated from a free-induction-decay and a Hahn-echo decay, were increased up to about 10 times (reaching 10 microseconds) and 1.4 times (reaching 150 microseconds), respectively. From the quantitative analysis, the dominant decoherence source depending on the applied static electric field was elucidated. The electrical control for extension can deliver a sensitivity enhancement to the DC sensing of temperature, pressure and electric (but not magnetic) fields, opening a new technique in solid-state quantum information devices.
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.