Introduction
High-fidelity single-shot readout of qubits is a critical component for building fault-tolerant quantum computers and scalable quantum networks. The nitrogen-vacancy (NV) center in diamond has emerged as a promising platform for these applications due to its unique properties, including long coherence times and optical addressability. Current methods for single-shot readout often rely on the resonance fluorescence method, which involves optically exciting the NV center and measuring the emitted fluorescence to determine the spin state. However, this method suffers from limitations imposed by spin-flip processes during the optical cycling transition. These processes interrupt the optical cycling, reducing the readout fidelity and hindering the achievement of high-fidelity single-shot readout crucial for surpassing the fault-tolerance threshold. The challenge lies in the fact that spin-flip processes introduce errors, making it difficult to reliably determine the spin state. These spin-flip errors significantly limit the achievable fidelity of single-shot readout, especially when aiming to exceed the fault-tolerant threshold required for robust quantum computation and communication. Previous attempts to overcome this limitation have focused on improving the optical collection efficiency by using microstructures like solid-state immersion lenses or high-quality nanocavities. While these methods have shown some success, they remain technically challenging and can introduce unwanted strain and defects, negatively affecting the spin and optical properties of the NV centers. The present research explores an alternative approach to enhance the readout fidelity by utilizing spin-to-charge conversion (SCC). This method offers the advantage of circumventing the limitations of the resonance fluorescence technique by directly converting the spin state into a charge state, which is then measured with high fidelity. By doing so, the method avoids the spin-flip errors associated with the optical cycling transition, paving the way for significantly improved readout fidelity.
Literature Review
The resonance fluorescence method has been widely used for single-shot readout in various solid-state spin systems including quantum dots, rare-earth ions, silicon-vacancy centers, and nitrogen-vacancy (NV) centers in diamond. This method relies on spin-selective excitation of an optical cycling transition, inferring the spin state from the collected fluorescence photon counts. However, spin non-conservation processes limit the readout window and introduce spin-flip errors, hindering the attainment of high-fidelity single-shot readout. To mitigate these errors, research efforts have explored the use of optical structures such as solid-state immersion lenses to enhance fluorescence collection efficiency. High-quality nanocavities offer the potential for significant enhancement of the photon emission rate, but their practical implementation remains challenging due to fabrication complexities, precise emitter placement, and frequency tuning. Furthermore, fabrication processes can introduce strain and defects, degrading the spin and optical properties. Existing techniques, such as spin-to-charge conversion using non-resonant excitation, have demonstrated some improvement in readout efficiency, but the present study aims to enhance this approach.
Methodology
This research introduces a novel method for single-shot readout of the NV center electron spin by combining spin-selective excitation with a photoionization process. The key concept is to convert the spin state into a charge state on demand before significant spin-flip relaxation occurs. This conversion is achieved by using near-infrared (NIR) light in conjunction with a spin-selective excitation of the NV center's optical transition. The charge state, characterized by its stability under optical illumination, is then measured with near-unity fidelity. The success of this method hinges on maximizing the ratio of the ionization rate (Γion) to the spin-flip rate (Γflip). Experiments were performed on a bulk NV center embedded within a solid immersion lens at a cryogenic temperature of 8 K. The measurement scheme utilized the cycling transition Eγ (connecting excited and ground states with ms = 0) and the E1,2 transitions (connecting states with ms = ±1). The solid immersion lens introduced non-axial strain, resulting in a significantly faster spin-flip rate (0.75 ± 0.02 MHz) than previously reported values for low-strain NV centers. Under selective excitation of Eγ, the |0⟩ spin state was pumped to the excited state and then ionized to the NV0 charge state using a 1064 nm NIR laser. Conversely, the |±1⟩ states remained in the NV− charge state. This deterministic SCC differs from previous work utilizing non-resonant excitation. The charge state readout was characterized by measuring the correlation between consecutive readouts. The high correlation demonstrated a unity readout fidelity for the NV0 state and 99.92 ± 0.03% for the NV− state. The small imperfection in NV− readout was attributed to the charge state lifetime (400.7 ± 9.7 ms). The ionization rate was investigated by varying the NIR laser power, revealing a linear relationship and providing an estimate for the ionization coefficient. To improve the readout fidelity, a correction scheme using an auxiliary level (ms = -1) was implemented. By transferring the leakage population from |0⟩ to the auxiliary state back to |0⟩ via a microwave pulse, the conversion efficiency of |0⟩ to NV0 was increased, achieving an average single-shot readout fidelity of 95.4 ± 0.2%. This was compared to the resonance fluorescence method, which yielded a much lower fidelity (79.6 ± 0.8%) due to the faster spin-flip rate. The final fidelity improvements were analyzed based on the ratio of ionization rate to spin-flip rate. Simulations predicted that for lower spin-flip rates and higher NIR power, fidelities exceeding 99.9% could be achieved.
Key Findings
This research achieved a significant advancement in single-shot readout fidelity of NV center electron spins. The key findings are:
1. **Development of a novel spin-to-charge conversion (SCC) method:** This method uses near-infrared (NIR) light to ionize the NV center's excited state, converting the spin state into a charge state that is measured with high fidelity. This circumvents the limitations of resonance fluorescence readout caused by spin-flip processes.
2. **High single-shot readout fidelity:** The researchers achieved an average single-shot readout fidelity of 95.4 ± 0.2% for the NV center electron spin, surpassing the fidelity of the conventional resonance fluorescence method (79.6 ± 0.8%) under the same experimental conditions characterized by high strain resulting in fast spin-flip processes.
3. **Charge state readout fidelity:** A near-unity fidelity of 99.96 ± 0.02% was demonstrated for the charge state readout, which is a crucial step in the SCC method.
4. **Linear relationship between ionization rate and NIR power:** The ionization rate was shown to be linearly dependent on the NIR laser power, offering a direct and controllable way to enhance the conversion efficiency of spin to charge.
5. **Auxiliary level correction scheme:** The introduction of an auxiliary level and a corresponding microwave pulse significantly improved the readout fidelity by recovering the population that leaked to the auxiliary level, thus improving the overall conversion efficiency.
6. **Potential for exceeding the fault-tolerant threshold:** Simulations showed that with improved NIR power and potentially lower spin-flip rates, the SCC method has the potential to achieve a single-shot readout fidelity exceeding 99.9%, meeting the requirements for fault-tolerant quantum computation and networks. This demonstrates a significant leap in the fidelity of single-shot readout of NV electron spins, paving the way for their utilization in fault-tolerant quantum computing and networks.
Discussion
The results presented in this study significantly advance the field of quantum computing by demonstrating a high-fidelity single-shot readout method for NV centers. The achievement of a 95.4% fidelity in the presence of high strain and fast spin-flip rates is a substantial improvement over previous methods. This surpasses the performance of conventional resonance fluorescence, which is limited by the intrinsic spin-flip processes. The success of this method lies in its ability to circumvent the limitations of the resonance fluorescence approach by directly converting the spin state to a charge state, which can be measured with near-unity fidelity. The key innovation lies in the effective suppression of spin-flip errors by carefully balancing the ionization rate and the spin-flip rate. The direct correlation between the NIR power and the ionization rate further provides a convenient way to control and optimize the SCC process. The additional correction scheme using the auxiliary level further enhanced the fidelity by addressing population leakage issues. The implications are significant for the development of fault-tolerant quantum computers and scalable quantum networks. The potential to achieve fidelities exceeding 99.9% highlights the scalability and robustness of this method. The technique's simplicity, using only an additional NIR beam without complex cavity engineering, adds to its practicality. Furthermore, the presented method opens avenues for integrated optoelectronic devices and high-efficiency quantum sensing.
Conclusion
This research successfully demonstrated a near-infrared (NIR)-assisted spin-to-charge conversion (SCC) method for single-shot readout of electron spins in NV centers with a fidelity of 95.4%. This method overcomes limitations of conventional resonance fluorescence by converting the spin state into a more reliably measurable charge state. The method's efficiency is directly controllable via NIR power, and simulations suggest it could surpass the fault-tolerant threshold with further improvements. Future research should focus on enhancing NIR power and exploring NV centers with inherently lower spin-flip rates to fully realize the method's potential for applications in fault-tolerant quantum computation and integrated optoelectronic devices.
Limitations
The main limitation of the current SCC method is the relatively low ionization rate compared to the spin-flip rate. Although an auxiliary level correction scheme improved the fidelity, the maximum fidelity achieved is still below the fault-tolerant threshold. While simulations suggest exceeding the threshold is possible with higher NIR power and lower intrinsic spin-flip rates, practical limitations in laser power and achieving lower spin-flip rates in the NV center remain challenges for future research. The study focused on bulk NV centers; the applicability of the SCC method to other systems, such as NV centers in nanodiamonds, requires further investigation.
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