Electrometry Using Coherent Exchange Oscillations in a Singlet-Triplet-Qubit (1208.2023v5)

Abstract: Two level systems that can be reliably controlled and measured hold promise in both metrology and as qubits for quantum information science (QIS). When prepared in a superposition of two states and allowed to evolve freely, the state of the system precesses with a frequency proportional to the splitting between the states. In QIS,this precession forms the basis for universal control of the qubit,and in metrology the frequency of the precession provides a sensitive measurement of the splitting. However, on a timescale of the coherence time, $T_2$, the qubit loses its quantum information due to interactions with its noisy environment, causing qubit oscillations to decay and setting a limit on the fidelity of quantum control and the precision of qubit-based measurements. Understanding how the qubit couples to its environment and the dynamics of the noise in the environment are therefore key to effective QIS experiments and metrology. Here we show measurements of the level splitting and dephasing due to voltage noise of a GaAs singlet-triplet qubit during exchange oscillations. Using free evolution and Hahn echo experiments we probe the low frequency and high frequency environmental fluctuations, respectively. The measured fluctuations at high frequencies are small, allowing the qubit to be used as a charge sensor with a sensitivity of $2 \times 10^{-8} e/\sqrt{\mathrm{Hz}}$, two orders of magnitude better than the quantum limit for an RF single electron transistor (RF-SET). We find that the dephasing is due to non-Markovian voltage fluctuations in both regimes and exhibits an unexpected temperature dependence. Based on these measurements we provide recommendations for improving $T_2$ in future experiments, allowing for higher fidelity operations and improved charge sensitivity.

• The paper reveals non-Markovian voltage noise as a key factor driving dephasing during exchange oscillations in singlet-triplet qubits.
• The paper demonstrates that temperature variations significantly affect coherence times, with improved performance observed at lower temperatures.
• The paper establishes that singlet-triplet qubits exhibit exceptional charge sensing, outperforming RF-SETs by up to two orders of magnitude.

Overview of Electrometry Using Coherent Exchange Oscillations in a Singlet-Triplet Qubit

This paper provides an in-depth analysis of the dephasing mechanisms affecting singlet-triplet ($S$-$T_0$) qubits in GaAs quantum dots. These qubits, which hold promise for applications in quantum information science and metrology, are subject to environmental noise that impacts their coherence and operational fidelity. The paper focuses primarily on voltage noise as a source of dephasing during exchange oscillations, which are critical for the $S$-$T_0$ qubits' functionality.

The researchers conducted meticulous experiments to characterize the level splitting due to exchange interactions and its consequent dephasing caused by voltage noise. They revealed several crucial findings:

1. Non-Markovian Noise Behavior: The voltage fluctuations impacting the qubits are non-Markovian, persisting unexpectedly at high frequencies. This non-Markovian nature indicates that noise is not white and varies with frequency, presenting a Gaussian decay in free induction decay (FID) experiments.
2. Temperature Dependencies: There is a notable temperature dependence of noise impact on qubit coherence, with both $T_2^*$ (FID) and $T_2^{echo}$ (Hahn echo) showing various temperature sensitivities. The $T_2^{echo}$, in particular, exhibited strong improvement with lower temperatures, suggesting a significant role of temperature in qubit dephasing dynamics.
3. Charge Sensing Capabilities: By analyzing the exchange oscillations, the paper demonstrates that the $S$-$T_0$ qubit serves as an highly sensitive charge sensor. The charge sensitivity achieved is two orders of magnitude greater than what is typically attained with RF single-electron transistors (RF-SETs), which is attributed to both the coherence properties and the inherent designs of the qubit operation.
4. High-Frequency Noise Spectrum Analysis: Hahn echo experiments provided insights into the high-frequency part of the noise spectrum. The coherence times ($T_2^{echo}$) reported suggest the existence of a colored noise spectrum, which transitions towards Markovian characteristics at higher temperatures.

The implications of these findings are manifold. Practically, the enhancement of qubit coherence via temperature regulation and advanced pulse sequences (e.g., CPMG and UDD) could significantly improve quantum gate fidelities. This is especially pertinent for two-qubit operations which heavily rely on exchange interactions. Theoretically, the insights into the non-Markovian nature of the environmental noise could prompt revisions in the modeling of noise effects on quantum systems. The promising sensitivity of the qubit as a charge sensor also opens up new avenues for its application in precision measurement and metrology.

Looking forward, advancing refrigeration techniques to achieve lower operational temperatures could further boost the coherence times by making the noise spectrum even more non-Markovian. Exploring larger qubit systems and experimenting with multiple entangled qubits could yield collective benefits in sensitivity and operational precision, enhancing the qubit's utility in quantum information applications.

This comprehensive analysis serves as an important contribution to the ongoing efforts in improving the performance and reliability of quantum dot-based qubits, positioning them as valuable tools for both quantum computing and high-precision metrology.