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Physical Review B

Observation of quantum stochastic synchronization in a dissipative quantum system

G. M. Xue, Ming Gong, Huikai Xu, W. Y. Liu, Hui Deng, Ye Tian, Haifeng Yu, Yang Yu, Dongning Zheng, Shaoyang Zhao, Siyuan Han

Published Dec 3, 2014• 11 citations
Publisher

Abstract

We report the observation of quantum stochastic synchronization (QSS) in a dissipative quantum system---a moderately damped current-biased Josephson junction. We show that when the junction is biased subcritically by a combination of a constant current and a small sinusoidal modulation signal, forced phase synchronization between the otherwise random, incoherent quantum tunneling and the signal may arise as a consequence of the interplay between quantum fluctuation and the weak periodic drive. It is found that optimal synchronization occurs at a signal frequency ${f}_{\text{QSS}}$ that is comparable to the quantum tunneling rate. We also find a phenomenon called ``modulation induced suppression of quantum noise'': for signal frequency well below ${f}_{\text{QSS}},$ the power spectral density of escape time distribution of the junction could be reduced substantially from the floor level of the unmodulated system. Furthermore, we demonstrate that the application of a small signal with proper phase can suppress the average tunneling rate and enhance the stability of the metastable system. Our experimental results agree well with the numerical calculations without the use of adjustable parameters.

DOI
10.1103/physrevb.90.224505

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We report the observation of quantum stochastic synchronization (QSS) in a dissipative quantum system---a moderately damped current-biased Josephson junction. We show that when the junction is biased subcritically by a combination of a constant current and a small sinusoidal modulation signal, forced phase synchronization between the otherwise random, incoherent quantum tunneling and the signal may arise as a consequence of the interplay between quantum fluctuation and the weak periodic drive. It is found that optimal synchronization occurs at a signal frequency fQSS{f}_{\text{QSS}}fQSS​ that is comparable to the quantum tunneling rate. We also find a phenomenon called ``modulation induced suppression of quantum noise'': for signal frequency well below fQSS,{f}_{\text{QSS}},fQSS​, the power spectral density of escape time distribution of the junction could be reduced substantially from the floor level of the unmodulated system. Furthermore, we demonstrate that the application of a small signal with proper phase can suppress the average tunneling rate and enhance the stability of the metastable system. Our experimental results agree well with the numerical calculations without the use of adjustable parameters.
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A new phase diffusive regime in a current biased Josephson junction is theoretically explored which originates from embedding the junction in a circuit environment with anomalous dissipation. This is realized by placing parallel to the junction a resistor in series with a capacitor such that electromagnetic fluctuations effectively couple also to the charge of the junction. This leads to rich Josephson dynamics, in particular for the switching of the junction out of a zero voltage state. Modelled as the escape process of a fictitious phase-particle out of a metastable well, a detailed study reveals that anomalous dissipation has a strong impact at low temperatures when quantum tunneling dominates against thermal activation. As a manifestation, a regime is found, where for realistic circuit parameters the quantum escape process is substantially enhanced, followed by a short voltage pulse and re-trapping with high probability. This class of circuits may be leveraged for detecting microwave photons or dissipative quantum annealing processes. In addition, the analysis provides a general framework for engineering dissipative dynamics in nonlinear systems using anomalous environments.
We theoretically investigate the escape rate occurring via quantum tunneling in a system affected by tailored dissipation. Specifically, we study the environmental assisted quantum tunneling of the superconducting phase in a current-biased Josephson junction. We consider Ohmic resistors inducing dissipation both in the phase and in the charge of the quantum circuit. We find that the charge dissipation leads to an enhancement of the quantum escape rate. This effect appears already in the low Ohmic regime and also occurs in the presence of phase dissipation that favors localization. Inserting realistic circuit parameters, we address the question of its experimental observability and discuss suitable parameter spaces for the observation of the enhanced rate.
We generalize the phenomenon of forced stochastic synchronization into the quantum domain within the framework of a paradigmatic spin‐boson model (tunneling charge, or flipping spin 1/2 coupled to an environment) which is driven by an external periodic rectangular field. The overdamped regime of dissipative quantum tunneling is studied. Thermal noise assisted synchronization of a very high quality is shown to occur in a broad range of temperatures, driving strengths and frequencies, if the external driving frequency exceeds the zero‐temperature limit of dissipative tunneling rate, the dissipation strength exceeds a critical value, and the driving is sufficiently strong. A simple criterion for such stochastic synchronization is established. Both the similarities and the profound differences with the akin phenomenon of quantum stochastic resonance are outlined.
We analyze the effect of dissipation and low-frequency current noise on quantum coherence in a current-biased Josephson junction that has low damping. Developing a stochastic Bloch equation for the reduced density matrix of the system, we determine the resonance response of the system to a weak external microwave current drive. We characterize the response by finding the spectroscopic coherence time T2∗{T}_{2}^{*}T2∗​ as a function of the energy relaxation time T1{T}_{1}T1​ and the current noise power spectral density. For current noise with a constant spectral density up to a frequency ${f}_{c}⪢{(2\ensuremath{\pi}{T}_{1})}^{\ensuremath{-}1}$, we find that the resonance broadening is proportional to the noise spectral density, while for ${f}_{c}⪡{(2\ensuremath{\pi}{T}_{1})}^{\ensuremath{-}1}$, the broadening is proportional to the rms current noise. We compare our results to microwave spectroscopy data on $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{2}$ Nb and Al tunnel junctions at milli-Kelvin temperatures and find good agreement between the measured response spectra and our model simulations.
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on a Josephson phase escape for switching from the superconducting (the zero-voltage) state to a resistive one. Above the crossover temperature Tcr{T}_{cr}Tcr​ the thermal fluctuations of the Josephson phase induce such a switching, and as T<TcrT<{T}_{cr}T<Tcr​ the regime of the MQT occurs. In the absence of two-level systems (TLSs) a magnetic field applied parallel to the junction plane results in a smooth reduction of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$, where $\mathrm{\ensuremath{\Phi}}$ is an applied magnetic flux. As the TLSs are present in Josephson junctions we obtain a resonant enhancement of the MQT. This phenomenon manifests itself by a narrow peak in the dependence of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$ occurring in the intermediate range of $\mathrm{\ensuremath{\Phi}}$, i.e., $0<\mathrm{\ensuremath{\Phi}}<{\ensuremath{\phi}}_{0}$ (${\ensuremath{\phi}}_{0}$ is the magnetic flux quantum). We explain this effect quantitatively by a strong resonant suppression of the potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.