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arXiv:2307.14567 · New Journal of Physics

A quantum ticking self-oscillator using delayed feedback

Yanan Liu, William J. Munro, Jason Twamley

Published Nov 29, 2023• 0 citations
arXivHTMLPDF

Abstract

Abstract Self-sustained oscillators (SSOs) is a commonly used method to generate classical clock signals and SSOs using delayed feedback have been developed commercially which possess ultra-low phase noise and drift. Research into the development of quantum self-oscillation, where one can also have a periodic and regular output tick, that can be used to control quantum and classical devices has received much interest and quantum SSOs so far studied suffer from phase diffusion which leads to the smearing out of the quantum oscillator over the entire limit cycle in phase space seriously degrading the system’s ability to perform as a self-oscillation. In this paper, we explore quantum versions of time-delayed SSOs, which has the potentials to develop a ticking quantum clock. We first design a linear quantum SSO which exhibits perfect oscillation without phase diffusion. We then explore a nonlinear delayed quantum SSO but find it exhibits dephasing similar to previously studied non-delayed systems.

DOI
10.1088/1367-2630/ad1072

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Abstract Self-sustained oscillators (SSOs) is a commonly used method to generate classical clock signals and SSOs using delayed feedback have been developed commercially which possess ultra-low phase noise and drift. Research into the development of quantum self-oscillation, where one can also have a periodic and regular output tick, that can be used to control quantum and classical devices has received much interest and quantum SSOs so far studied suffer from phase diffusion which leads to the smearing out of the quantum oscillator over the entire limit cycle in phase space seriously degrading the system’s ability to perform as a self-oscillation. In this paper, we explore quantum versions of time-delayed SSOs, which has the potentials to develop a ticking quantum clock. We first design a linear quantum SSO which exhibits perfect oscillation without phase diffusion. We then explore a nonlinear delayed quantum SSO but find it exhibits dephasing similar to previously studied non-delayed systems.
A driven linear oscillator and a feedback mechanism are two necessary elements of any classical periodic clock. Here, we introduce a fully quantum clock using a driven oscillator in the quantum regime and coherent quantum feedback. We show that if we treat the model semiclassically, this system supports limit cycles, or self-sustained oscillations, as needed for a periodic clock. We then analyze the noise of the system quantum mechanically and prove that the accuracy of this clock is higher compared with the clock implemented with the classical measurement feedback. We experimentally implement the model using two superconducting cavities with incorporated Josephson junctions and microwave circulators for the realization of the quantum feedback. We confirm the appearance of the limit cycle and study the clock accuracy both in frequency and time domains. Under specific conditions of noisy driving, we observe that the clock oscillations are more coherent than the drive, pointing towards the implementation of a quantum autonomous clock.
Atomic frequency standards have achieved steadily increasing precision over the past seventy years, enabled in part by feedback mechanisms that stabilise their output. In parallel, the timekeeping capabilities of quantum systems have been explored within the recently developed ticking-clock framework, which models clocks as dynamical systems producing a stochastic sequence of ticks. However, a theoretical description that unifies these perspectives and incorporates feedback into autonomous quantum clocks has been lacking. We introduce a framework for feedback-controlled clockworks in which classical information extracted from the tick sequence is used to influence the subsequent dynamics of the clock. We show that such feedback preserves the core structural features of self-timing and clockwork independence that characterise autonomous ticking clocks. We further identify the signal-to-noise ratio S\mathfrak{S}S as the fundamental figure of merit for assessing the performance of feedback-controlled clocks. Applying our framework to two representative architectures, we prove that classical clockworks cannot surpass the optimal signal-to-noise ratio achievable without feedback. In contrast, for quantum clockworks we present numerical evidence that feedback can provide a genuine and robust performance enhancement, improving the maximal attainable signal-to-noise ratio. We provide additional numerical evidence, suggesting that the magnitude of the improvement strongly depends on the amount and type of the stored, classical information. These results establish feedback as a potentially essential ingredient in pushing the fundamental limits of timekeeping in the quantum regime.
Classical self-sustained oscillators, which generate periodic motion without periodic external forcing, are ubiquitous in science and technology. The realization of nonclassical self-oscillators is an important goal of quantum physics. We here present the experimental implementation of a quantum van der Pol oscillator, a paradigmatic autonomous quantum driven-dissipative system with nonlinear damping, using a single trapped atom. We demonstrate the existence of a quantum limit cycle in phase space in the absence of a drive and the occurrence of quantum synchronization when the nonlinear oscillator is externally driven. We additionally show that synchronization can be enhanced with the help of squeezing perpendicular to the direction of the drive and, counterintuitively, linear dissipation. We also observe the bifurcation to a bistable phase-space distribution for large squeezing. Our results pave the way for the exploration of self-sustained quantum oscillators and their application to quantum technology.
Resonators driven to self-oscillation by active feedback play an important role in technology. The laser is an example of such a device. Generally, the feedback that sustains self-oscillation is contaminated with amplifier noise, which leads to phase diffusion. Here we show that under suitable conditions phase noise from the feedback amplifier can be evaded, allowing one to track the resonator's phase in a quantum nondemolition manner. In particular, we consider a resonator with a Kerr nonlinearity. The output of the resonator is fed into a linear amplifier, phase shifted, fed through an amplitude limiter, and then fed back into the resonator. Stable operation is achieved, even on portions of the resonance curve for which the resonator would exhibit optical bistability under open-loop conditions. By operating the system at a point on the resonance curve for which the slope of the phase versus frequency is infinite, the long-term phase stability of the oscillator becomes insensitive to the amplifier's output noise. In addition, the amplifier's input-port noise can be evaded by making the coupling between the resonator and the amplifier sufficiently weak.
Creating precise timing devices at ultra-short time scales is not just an important technological challenge, but confronts us with foundational questions about timekeeping's ultimate precision limits. Research on clocks has either focused on long-term stability using an oscillator stabilized by a level transition, limiting precision at short timescales, or on making individual stochastic ticks as precise as possible. Here, we prove the viability of a conceptually different avenue: the autonomous self-correction of consecutive ticks by quantum correlations. This provides a new paradigm that integrates the advantages and insights from quantum transport theory to operate clocks at ultra-short timescales. We fully solve a model of coupled quantum systems and show how the emergent Pauli exclusion principle correlates the clock at the quantum level yielding an exponential advantage in precision. We furthermore demonstrate through simulations with realistic imperfections that this remarkable gain in precision remains stable providing a roadmap for implementation with contemporary quantum technologies.