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arXiv:2406.14435 · SciPost Physics

The superconducting clock-circuit: Improving the coherence of Josephson radiation beyond the thermodynamic uncertainty relation

David Scheer, Jonas Völler, Fabian Hassler

Published Nov 21, 2024• 1 citation
arXivHTMLPDF

Abstract

In the field of superconducting electronics, the on-chip generation of AC radiation is essential for further advancements. Although a Josephson junction can emit AC radiation from a purely DC voltage bias, the coherence of this radiation is significantly limited by Johnson-Nyquist noise. We relate this limitation to the thermodynamic uncertainty relation (TUR) in the field of stochastic thermodynamics. Recent findings indicate that the thermodynamic uncertainty relation can be broken by a classical pendulum clock. We demonstrate how the violation of the TUR can be used as a design principle for radiation sources by showing that a superconducting clock circuit emits coherent AC radiation from a DC bias.

DOI
10.21468/scipostphys.17.5.140

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In the field of superconducting electronics, the on-chip generation of AC radiation is essential for further advancements. Although a Josephson junction can emit AC radiation from a purely DC voltage bias, the coherence of this radiation is significantly limited by Johnson-Nyquist noise. We relate this limitation to the thermodynamic uncertainty relation (TUR) in the field of stochastic thermodynamics. Recent findings indicate that the thermodynamic uncertainty relation can be broken by a classical pendulum clock. We demonstrate how the violation of the TUR can be used as a design principle for radiation sources by showing that a superconducting clock circuit emits coherent AC radiation from a DC bias.
A resistively shunted Josephson junction with a DC-bias exhibits Josephson oscillations that link voltage and frequency through fundamental constants. These oscillations can synchronize their frequency to an external microwave signal achieving the metrological precision that underlies the modern Josephson voltage standard. Its electromagnetic dual, the phase-slip junction, exhibits Bloch oscillations that connect current to frequency in an analogous way. A current standard based on synchronized Bloch oscillations could close the quantum metrology triangle, providing a consistent test of the underlying fundamental relations between voltage, current, and resistance. The experimental realization, however, remains challenging, as external microwave lines introduce parasitic capacitances that can destroy the high-impedance environment required for Bloch oscillations. This work explores the use of on-chip synchronization to stabilize both Josephson and Bloch oscillations without the need for an external microwave drive. We review the theoretical framework of the synchronization between two coupled oscillators and the dynamics of superconducting circuits with a focus on quantum metrology. Building on this, we analyze a recent experiment on the mutual synchronization of Bloch oscillations in a pair of ultrasmall Josephson junctions. Our model in terms of correlated phase-slip junctions realized in the ground state of the device shows good agreement with the experimental results, confirming synchronized Bloch oscillations. At larger currents, nonadiabatic transitions wash out the coherence of the Bloch oscillations and therefore the synchronization features. Motivated by these findings, we propose an alternative circuit setup where the Bloch oscillations in a single phase-slip junction are stabilized by synchronization to on-chip Josephson oscillations. We study the back-action of the Bloch oscillations on the Josephson oscillations and identify a parameter regime in which it is minimized, rendering the latter an effectively rigid driving signal. Moreover, we find that the small remaining back-action further enhances the thermal stability of the synchronized Bloch oscillations compared to the externally driven case. Without a back-action mechanism, the coherence of Josephson oscillations is severely limited by thermal fluctuations. We relate this limitation to the thermodynamic uncertainty relation (TUR) in the field of stochastic thermodynamics. Recent findings show, that the TUR can be broken by a classical pendulum clock. We propose a circuit that mimics the dynamics of a pendulum clock as a flexible on-chip microwave source for high impedance environments. Due to an internal synchronization, the clock circuit emits coherent radiation beyond the limits of the TUR. Finally, we explore the use of symmetry breaking drives as a resource for nonreciprocal transport in superconducting circuits. We demonstrate that a biharmonic microwave signal applied to a conventional Josephson junction induces an ideal supercurrent diode effect with a tunable direction.
A Josephson junction (JJ) has been under intensive study ever since 1960's. Yet even in the present era of building quantum information processing devices based on many JJs, open questions regarding a single junction remain unsolved, such as quantum phase transitions, coupling of the JJ to an environment and improving coherence of a superconducting qubit. Here we design and build an engineered on-chip reservoir that acts as an efficient bolometer for detecting the Josephson radiation under non-equilibrium (biased) conditions. The bolometer converts ac Josephson current at microwave frequencies, up to about 100 100\,100GHz, into a measurable dc temperature rise. The present experiment demonstrates an efficient, wide-band, thermal detection scheme of microwave photons and provides a sensitive detector of Josephson dynamics beyond the standard conductance measurements. Using a circuit model, we capture both the current-voltage characteristics and the measured power quantitatively.
Superconducting electronic devices have reemerged as contenders for both classical and quantum computing due to their fast operation speeds, low dissipation, and long coherence times. An ultimate demonstration of coherence is lasing. We use one of the fundamental aspects of superconductivity, the ac Josephson effect, to demonstrate a laser made from a Josephson junction strongly coupled to a multimode superconducting cavity. A dc voltage bias applied across the junction provides a source of microwave photons, and the circuit's nonlinearity allows for efficient down-conversion of higher-order Josephson frequencies to the cavity's fundamental mode. The simple fabrication and operation allows for easy integration with a range of quantum devices, allowing for efficient on-chip generation of coherent microwave photons at low temperatures.
In this talk, I will start by briefly introducing the Josephson-junction, which is the non-linear circuit element used to engineer the artificial atoms. Then I will discuss two qualitatively different methods using this non-linear element for generating entangled photon pairs in superconducting circuits. One approach builds on parametric down-conversion of a coherent ac drive (see fig. 1)[2] while the other relies on the ac Josephson effect, requiring only a dc voltage bias (see fig. 2) [3]. Finally, I will discuss a few recent experimental implementations [4-8].
Existing concepts of reversible superconducting circuits as well as demonstrated adiabatic circuits require three-phase bias/clock signals generated by room temperature sources. A while ago, we suggested that a multi-phase bias/clock could be provided by a local Josephson junction-based generator. The generator looks like a long annular Josephson junction, only composed of discreet elements - junctions and inductors, and closed into a ring via a flux pump to inject any required number of vortices into the ring. A steady motion of the vortices forced by a uniformly distributed dc bias current applied to the ring is accompanied by a nearly harmonic ac currents flowing via the Josephson junctions (JJs) connected in series with small inductors. These ac currents serve as multi-phase bias/clock for nSQUID-based circuitry. To verify this concept and compare the dissipated energy with kBTln2 threshold, we developed a ring composed of 256 unshunted JJs with 20 μA target critical current, Ic. We investigated the behavior of the ring oscillator at each vortex count from 0 to 256. The measured critical current of the ring with vortices was about 0.1 μA per one JJ, which can be explained by unavoidable nonuniformity of the ring components and the influence of fluxes frozen near the ring. The corresponding energy dissipation, about 10kBT per passage of one vortex through one JJ, should be reduced further for prospective experiments with reversible circuits. However, obtained I-V characteristics could be of interest for scientists working with long Josephson junctions. Superiority of the fabrication process used in this work is demonstrated by the obtained about 200 times reduction of Icof the ring with vortices with respect to a single comprising JJ, much larger than in any previously described case.