[论文解读] Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator

Guillaume Beaulieu, Fabrizio Minganti+5 more|arXiv (Cornell University)|Oct 20, 2023

Quantum Information and Cryptography被引用 4

一句话总结

本研究首次在两光子驱动的超导Kerr共振腔中实验观测到一阶与二阶耗散相变（DPTs）。通过设计参数驱动的非线性腔，作者观测到一阶DPT中的相共存与滞后现象，以及二阶DPT中的自发对称性破缺与临界慢化，该结果通过量子轨迹监测与Liouvillian谱分析得到验证，展示了在超导电路中对非平衡临界性的调控能力。

ABSTRACT

In open quantum systems, first- and second-order dissipative phase transitions (DPTs) can emerge in the thermodynamic limit from the competition between unitary evolution, driving terms, and dissipation. The order of a DPT is defined by the continuity properties of the steady state. Until now, second-order DPTs have predominantly been investigated theoretically, while first-order DPTs have been observed in key experiments based on the theory of the single-photon driven Kerr resonator. We present here the first comprehensive experimental and theoretical analysis of both first and second-order DPTs in a two-photon (i.e., parametrically) driven Kerr superconducting resonator. Firstly, we characterize the steady state and its main features at the second- and first-order critical points: squeezing below vacuum and coexistence of two phases with different photon numbers, respectively. Then, by continuously monitoring the system along quantum trajectories, we study the non-equilibrium dynamics across the critical points. We witness the hysteresis cycles associated with the first-order DPT and the spontaneous symmetry breaking due to the second-order DPT. Applying the spectral theory of the Liouvillian superoperator, we develop efficient procedures to quantify the critical slowing down associated with the timescales of these processes. When scaling towards the thermodynamic limit, these timescales span five orders of magnitude. Our results corroborate the predictions derived using the Liouvillian theory of DPTs. This work stands as a compelling example of engineering and controlling of criticality in superconducting circuits. It marks a significant advancement in the use of two-photon driven Kerr resonators for criticality-enhanced quantum information applications.

研究动机与目标

• 在两光子驱动的超导Kerr共振腔中，实验观测并表征一阶与二阶耗散相变（DPTs）。
• 利用连续量子轨迹监测，研究临界点附近的非平衡动力学。
• 通过Liouvillian超算符的谱理论量化临界慢化。
• 利用可扩展的超导电路平台，验证开放量子系统中DPT理论预测的正确性。
• 展示临界性的工程化调控，为量子信息与增强传感等潜在应用提供支持。

提出的方法

• 采用$λ/4$平面波导共振腔，通过电容耦合至传输线以收集信号，并通过SQUID终端调节共振频率与Kerr非线性度。
• 在约两倍腔频率的相干泵浦信号作用下，实现两光子驱动，从而实现参数激发。
• 采用混频检测连续监测系统沿量子轨迹的演化，实现对非平衡动力学的观测。
• 对Liouvillian超算符进行谱分析，提取最小的非零本征值，量化临界慢化的时间尺度。
• 对Lindblad主方程进行数值与解析建模，模拟稳态特性与关联函数。
• 将测量的量子轨迹与理论预测进行对比，提取Liouvillian能隙并确认临界行为。

实验结果

研究问题

• RQ1 能否在两光子驱动的Kerr共振腔中实验观测到一阶与二阶耗散相变？
• RQ2 临界点附近的非平衡动力学，包括滞后与自发对称性破缺，如何表现？
• RQ3 Liouvillian谱在表征开放量子系统中临界慢化方面起什么作用？
• RQ4 此类系统中弛豫与退相干的时间尺度在趋于热力学极限时如何演化？
• RQ5 量子轨迹监测在多大程度上能揭示耗散相变的潜在临界行为？

主要发现

• 实验观测到一阶DPT，其特征为相共存、亚稳态与滞后现象，由量子轨迹监测确认。
• 观测到二阶DPT，表现为自发对称性破缺，体现为非零序参量的出现与临界涨落。
• 通过量子轨迹分析，实验提取了二阶DPT（λ_SSB）与一阶DPT（λ_1st）对应的Liouvillian谱能隙，证实理论预测。
• 临界慢化通过关联函数的指数衰减得到量化，当趋近热力学极限时，时间尺度跨越五个数量级。
• 在二阶临界点，稳态下系统表现出低于真空的压缩，表明存在强量子关联。
• 测量的量子轨迹与Liouvillian谱理论之间的一致性，验证了开放量子系统中DPT理论框架的正确性。