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arXiv:2008.09027 · New Journal of Physics

Coherence protection and decay mechanism in qubit ensembles under concatenated continuous driving

Guoqing Wang, Yi-Xiang Liu, Paola Cappellaro

Published Dec 1, 2020• 34 citations

Abstract

Abstract Dense ensembles of spin qubits are valuable for quantum applications, even though their coherence protection remains challenging. Continuous dynamical decoupling can protect ensemble qubits from noise while allowing gate operations, but it is hindered by the additional noise introduced by the driving. Concatenated continuous driving (CCD) techniques can, in principle, mitigate this problem. Here we provide deeper insights into the dynamics under CCD, based on Floquet theory, that lead to optimized state protection by adjusting driving parameters in the CCD scheme to induce mode evolution control. We experimentally demonstrate the improved control by simultaneously addressing a dense nitrogen-vacancy (NV) ensemble with 1010 spins. We achieve an experimental 15-fold improvement in coherence time for an arbitrary, unknown state, and a 500-fold improvement for an arbitrary, known state, corresponding to driving the sidebands and the center band of the resulting Mollow triplet, respectively. We can achieve such coherence time gains by optimizing the driving parameters to take into account the noise affecting our system. By extending the generalized Bloch equation approach to the CCD scenario, we identify the noise sources that dominate the decay mechanisms in NV ensembles, confirm our model by experimental results, and identify the driving strengths yielding optimal coherence. Our results can be directly used to optimize qubit coherence protection under continuous driving and bath driving, and enable applications in robust pulse design and quantum sensing.

DOI: 10.1088/1367-2630/abd2e5

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Abstract Dense ensembles of spin qubits are valuable for quantum applications, even though their coherence protection remains challenging. Continuous dynamical decoupling can protect ensemble qubits from noise while allowing gate operations, but it is hindered by the additional noise introduced by the driving. Concatenated continuous driving (CCD) techniques can, in principle, mitigate this problem. Here we provide deeper insights into the dynamics under CCD, based on Floquet theory, that lead to optimized state protection by adjusting driving parameters in the CCD scheme to induce mode evolution control. We experimentally demonstrate the improved control by simultaneously addressing a dense nitrogen-vacancy (NV) ensemble with 1010 spins. We achieve an experimental 15-fold improvement in coherence time for an arbitrary, unknown state, and a 500-fold improvement for an arbitrary, known state, corresponding to driving the sidebands and the center band of the resulting Mollow triplet, respectively. We can achieve such coherence time gains by optimizing the driving parameters to take into account the noise affecting our system. By extending the generalized Bloch equation approach to the CCD scenario, we identify the noise sources that dominate the decay mechanisms in NV ensembles, confirm our model by experimental results, and identify the driving strengths yielding optimal coherence. Our results can be directly used to optimize qubit coherence protection under continuous driving and bath driving, and enable applications in robust pulse design and quantum sensing.

The coherence times achieved with continuous dynamical decoupling techniques are often limited by fluctuations in the driving amplitude. In this work, we use time-dependent phase-modulated continuous driving to increase the robustness against such fluctuations in a dense ensemble of nitrogen-vacancy centers in diamond. Considering realistic experimental errors in the system, we identify the optimal modulation strength and demonstrate an improvement of an order of magnitude in the spin preservation of arbitrary states over conventional single continuous driving. The phase-modulated driving exhibits results comparable to those found with previously examined amplitude-modulated techniques and is expected to outperform them in experimental systems having higher phase accuracy. The proposed technique could open new avenues for quantum information processing and many-body physics in systems dominated by high-frequency spin-bath noise, for which pulsed dynamical decoupling is less effective.

The loss of coherence is one of the main obstacles for the implementation of quantum information processing. The efficiency of dynamical decoupling schemes, which have been introduced to address this problem, is limited itself by the fluctuations in the driving fields which will themselves introduce noise. We address this challenge by introducing the concept of concatenated continuous dynamical decoupling, which can overcome not only external magnetic noise but also noise due to fluctuations in driving fields. We show theoretically that this approach can achieve relaxation limited coherence times, and demonstrate experimentally that already the most basic implementation of this concept yields an order of magnitude improvement to the decoherence time for the electron spin of nitrogen vacancy centers in diamond. The proposed scheme can be applied to a wide variety of other physical systems, including trapped atoms and ions and quantum dots, and may be combined with other quantum technologies challenges such as quantum sensing and quantum information processing.

Hole spins in silicon quantum dots are a promising platform for quantum computing due to their strong intrinsic spin-orbit coupling (SOC), which enables fast, all-electrical control. However, this coupling also increases their susceptibility to charge noise, thereby limiting coherence times. Moreover, holes in silicon are also affected by hyperfine interactions with residual nuclear spins in the silicon substrate, introducing a non-negligible source of low-frequency noise. Here, we implement a phase-modulated concatenated continuous driving (CCD) technique for hole spin qubits to suppress low-frequency noise through microwave phase modulation. This approach stabilizes Rabi oscillations and extends the oscillation decay time compared to the conventional method. Furthermore, by defining a qubit in the CCD frame, we achieve coherent control while simultaneously protecting the qubit from noise, confirming coherence protection during gate operations. These results demonstrate a viable route toward noise-robust hole spin qubits.

Exchange-based two-qubit gates in semiconductor spin qubits are sensitive to low-frequency detuning noise and control errors. Here, we extend concatenated continuous driving (CCD), implemented by phase modulation of a global microwave drive, to exchange-based SWAP and

\sqrt{\mathrm{SWAP}}

operations between double-dressed spin qubits and investigate its effectiveness for protecting two-qubit gates. We find that CCD retains strong protection against quasistatic common-mode detuning errors while substantially improving robustness against Rabi-frequency errors and qubit-to-qubit Rabi-frequency mismatch compared with conventional continuous dressing. By contrast, the gate fidelity is impacted by differential detuning errors. By modeling partially correlated quasistatic detuning noise, we further show that the noise-averaged gate fidelity depends strongly on the spatial correlation of the qubit-frequency fluctuations, with positive correlations enhancing CCD protection by suppressing the differential-noise component. These results identify the symmetry and spatial correlation of qubit-frequency noise as key factors governing continuous-drive protection in coupled spin-qubit systems.

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.

The rate of coherence loss is lower for a qubit under the Rabi drive than a freely evolving qubit

T_{2}^{\rm{Rabi}}>T_{2}^*

. Building on this principle, concatenated continuous driving (CCD) keeps the qubit under continuous drive to suppress noise and manipulate dressed states by either phase or amplitude modulation. In this work, we propose a variant of CCD which simultaneously modulates both the amplitude and phase of the driving field to generate a circularly polarized field in the rotating frame of the carrier frequency. This circular-modulated CCD(CMCCD) cancels the counter-rotating term in the second rotating frame, eliminating a systematic pulse-area error that arises from an imperfect rotating wave approximation for fast gates. Numerical simulations demonstrate that the proposed CMCCD achieves higher gate fidelity than conventional CCD schemes. We further implement and compare different CCD protocols using an electron spin-qubit in an isotopically purified

^{28}

Si-MOS quantum dot and evaluate its robustness by applying static detuning and Rabi frequency errors. The robustness is significantly improved compared with the standard Rabi drive, showing the effectiveness of this scheme for qubit arrays with variation in qubit frequency, coupling to the Rabi drive, and low-frequency noise. The proposed scheme can be applied to various physical systems, including trapped atoms, cold atoms, superconducting qubits, and NV centers.