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 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.
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 study of quantum many-body spin physics in realistic solid-state platforms has been a long-standing goal in quantum and condensed-matter physics. We demonstrate separate steps required to reach this goal using nitrogen-vacancy (NV) centers in diamond. First, standard (TEM) electron irradiation is used for the enhancement of N to NV conversion efficiencies by over an order-of-magnitude. Second, robust pulsed and continuous dynamical decoupling (DD) techniques enable the preservation of arbitrary states of the ensemble. These combined efforts could lead to the desired interaction-dominated regime. Finally, we simulate the effects of continuous and pulsed microwave (MW) control on the resulting NV-NV many body dynamics in a realistic spin-bath environment. We emphasize that dominant interaction sources could be identified and decoupled by the application of proper pulse sequences, and the modification of such sequences could lead to the creation engineered interaction Hamiltonians. Such interaction Hamiltonians could pave the way toward the creation of non-classical states, e.g. spin-squeezed states, which were not yet demonstrated in the solid-state, and could eventually lead to magnetic sensing beyond the standard quantum limit (SQL).
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.
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 effects and DD microwave pulses are used to increase the transverse coherence time 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.