Passive On-Chip Superconducting Circulator Using a Ring of Tunnel Junctions

Clemens Müller, Shengwei Guan, Nicolas Vogt, Jared H. Cole, and Thomas M. Stace

Phys. Rev. Lett. 120, 213602 – Published 25 May 2018

Abstract

We present the design of a passive, on-chip microwave circulator based on a ring of superconducting tunnel junctions. We investigate two distinct physical realizations, based on Josephson junctions (JJs) or quantum phase slip elements (QPS), with microwave ports coupled either capacitively (JJ) or inductively (QPS) to the ring structure. A constant bias applied to the center of the ring provides an effective symmetry breaking field, and no microwave or rf bias is required. We show that this design offers high isolation, robustness against fabrication imperfections and bias fluctuations, and a bandwidth in excess of 500 MHz for realistic device parameters.

Received 12 October 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.213602

Physics Subject Headings (PhySH)

Aharonov-Bohm effect Aharonov-Casher effect Phase slips Quantum information with solid state qubits Superconducting quantum optics

Tunnel junctions

Atomic, Molecular & OpticalQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Clemens Müller^1,2,*, Shengwei Guan¹, Nicolas Vogt³, Jared H. Cole³, and Thomas M. Stace¹

¹ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland 4072, Australia
²Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
³Chemical and Quantum Physics, School of Science, RMIT University, Melbourne, Victoria 3001, Australia

^*c.muller2@uq.edu.au

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Issue

Vol. 120, Iss. 21 — 25 May 2018

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Images

Figure 1
Center: Schematic representation of the circulator, consisting of three ports connected via coupling elements to the numbered nodes of the ring to the coordinate $n_{j}$ associated with node $j$ . A central ring bias $X$ is conjugate to $n_{j}$ . Nodes of the ring are mutually coupled by tunneling elements with tunneling energy $E_{T}^{(k)}$ and “mass” $m_{T}^{(k)}$ . Notionally, the tunneling elements are identical. Differences lead to imperfect operation. Left: The QPS implementation of the scheme using flux tunneling and capacitive bias. Here $n_{j} \to ϕ_{j} / Φ_{0}$ are coupled inductively to the external lines, $E_{T}^{(k)} \to E_{S}^{(k)}$ is the phase slip energy, $m_{T}^{(k)} = L_{S}^{(a)}$ is the QPS inductance, and $X \to Q_{x} / (2 e)$ is the linked charge. Right: The JJ implementation of the scheme relying on charge tunneling and inductive bias. Then $n_{j} \to q_{j} / (2 e)$ is coupled capacitively to the external lines, $E_{T}^{(k)} \to E_{J}^{(k)}$ is the Josephson energy, $m_{T}^{(k)} = C_{J}^{(k)}$ is the JJ capacitance, and $X \to Φ_{x} / Φ_{0}$ is the linked flux.
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Figure 2
Scattering parameters in dB as a function of detuning from the optimal signal frequency, $δ ω = ω_{k} - ω_{opt}$ . Vertical dashed lines indicate the positions of excited states of the ring, which get transiently excited in the scattering process (see S.4 of the Supplemental Material [35]). The bandwidth at the $- 10 dB$ point is $> 500 MHz$ , as indicated by the grey shaded areas.
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Figure 3
$S$ -matrix elements (in dB) as a function of input power at the optimal signal frequency and central bias, demonstrating the strong nonlinearity of the ring.
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Figure 4
$S$ -matrix elements as a function of the variation in the central bias parameter, $δ X = X - X_{opt}$ (in dB). For the JJ ring, $X = Φ_{X} / Φ_{0}$ ; for the QPS ring, $X = Q_{X} / (2 e)$ . The notional output is to port 3; outputs to other ports arise from bias variations. The bars in the left of the figure indicate typical variation in the central bias for a JJ-based implementation due to flux noise [42], and a QPS-based implementation due to charge noise [43].
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Figure 5
Effect of deviations in the node bias on the forward transmittance $1 - S_{31}$ (in dB), with $δ N_{S}^{(k)} = N_{S}^{(k)} - N_{S, opt}$ . The disks at the left of the diagram indicate the scale of typical slow bias fluctuations in JJ devices due to charge noise [43] and in QPS devices due to flux noise [42].
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Figure 6
Effect of imperfections in the tunneling energies $E_{T}^{(a, b)}$ on forward transmittance $1 - S_{31}$ (in dB). For each point in parameter space, central bias $X$ and segment biases $N_{S}^{(k)}$ are optimized independently to find maximum forward transmission. The disks at the left indicate the scale of fabrication disorder in JJ [44, 45] and QPS devices [30, 46].
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