An Alternate Scheme to Mode-Lock Quantum Phase Slips.

Bastien Dassonneville, José Aumentado

David B. Haviland

Jaw-Shen Tsai

Hans Christiansen, Jens Paaske

It is well known from classical physics that weakly coupled self-sustained oscillators may spontaneously lock their phases. Just like classical synchronization is known to break down due to noise induced phase slips, we show here how the synchronization of continuous variable quantum systems breaks down by proliferation of quantum phase slips. Within a Keldysh path integral formulation of limit cycles, we analyze the phase dynamics and show how, in spite of strong phase correlations, quantum phase slips degrade the actual phase locking. This approach also allows us to address non-Markovian effects on the synchronization of limit cycles, which we illustrate explicitly for superconducting resonators coupled via a voltage biased double quantum dot.

Yanfu Yang, Qian Xiang, Qun Zhang +4 more

We propose a joint estimation scheme for fast, accurate, and robust frequency offset (FO) estimation along with phase estimation based on modified adaptive Kalman filter (MAKF). The scheme consists of three key modules: extend Kalman filter (EKF), lock detector, and FO cycle slip recovery. The EKF module estimates time-varying phase induced by both FO and laser phase noise. The lock detector module makes decision between acquisition mode and tracking mode and consequently sets the EKF tuning parameter in an adaptive manner. The third module can detect possible cycle slip in the case of large FO and make proper correction. Based on the simulation and experimental results, the proposed MAKF has shown excellent estimation performance featuring high accuracy, fast convergence, as well as the capability of cycle slip recovery.

Aleksandr E. Svetogorov, D. M. Basko

We study coherent quantum phase slips in a Josephson junction chain, including two types of quenched disorder: random spatial modulation of the junction areas and random induced background charges. Usually, the quantum phase-slip amplitude is sensitive to the normal-mode structure of superconducting phase oscillations in the ring (Mooij-Sch\"on modes, which are all localized by the area disorder). However, we show that the modes' contribution to the disorder-induced phase-slip action fluctuations is small, and the fluctuations of the action on different junctions are mainly determined by the local junction parameters. We study the statistics of the total quantum phase-slip amplitude on the chain and show that it can be non-Gaussian for not sufficiently long chains.