Dispersive Thermometry with a Josephson Junction Coupled to a Resonator

O.-P. Saira, M. Zgirski, K. L. Viisanen, D. S. Golubev, and J. P. Pekola

Phys. Rev. Applied 6, 024005 – Published 10 August 2016

Abstract

We embed a small Josephson junction in a microwave resonator that allows simultaneous dc biasing and dispersive readout. Thermal fluctuations drive the junction into phase diffusion and induce a temperature-dependent shift in the resonance frequency. By sensing the thermal noise of a remote resistor in this manner, we demonstrate primary thermometry in the range of 300 mK to below 100 mK, and high-bandwidth (7.5 MHz) operation with a noise-equivalent temperature of better than $10 μ K / \sqrt{Hz}$ . At a finite bias voltage close to a Fiske resonance, amplification of the microwave probe signal is observed. We develop an accurate theoretical model of our device based on the theory of dynamical Coulomb blockade.

Received 18 April 2016

DOI:https://doi.org/10.1103/PhysRevApplied.6.024005

Physics Subject Headings (PhySH)

Coulomb blockade

Josephson junctions Microwave techniques Superconducting devices

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

O.-P. Saira¹, M. Zgirski², K. L. Viisanen¹, D. S. Golubev¹, and J. P. Pekola¹

¹Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, P.O. Box 13500, 00076 AALTO, Finland
²Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, PL-02668 Warsaw, Poland

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Vol. 6, Iss. 2 — August 2016

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Images

Figure 1
The studied system. (a) Electrical schematic of the device and essential external components. The left and right halves of the device are functionally equivalent. Coplanar waveguides are used to define microwave resonance modes (at 4.688 and 5.668 GHz for blue and red elements in the illustration, respectively). The combination of low and high characteristic impedance (30 and $125 Ω$ , respectively) sections of approximately $λ / 4$ length allow dc biasing while increasing only slightly the losses of the microwave resonance. The resonators couple capacitively to a common feed line for frequency-multiplexed readout. The resonators terminate at small tunnel junctions between an Al electrode and a proximitized Al/Cu/Al (SNS) wire. The two SNS wires are part of the same superconducting loop [14] that couples electrical fluctuations from one wire to the other. Lastly, a microwave line is capacitively connected to a section of the loop and can be used to heat the SNS wires. Detailed wiring is shown in the Supplemental Material [15]. (b) Physical layout of device chip. The CPWs are fabricated from etched Nb on Si substrate. Bandpass filter for the heating line is implemented as an in-line half-wave resonator. (c) Scanning electron micrograph of one of the tunnel junctions fabricated with three-angle shadow evaporation. The disconnected copies of the mask pattern are a by-product of the fabrication method and do not affect the device characteristics. (d) Reduced circuit model used in theory. The dc shunt impedance $Z_{s} (ω = 0)$ is denoted by $R_{s}$ .
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Figure 2
Primary thermometry in phase diffusion regime of the Josephson junction. (a) Measured change in the resonance frequency as a function of bias voltage at different bath temperatures relative to a baseline (approximately 5.668 GHz) established from Lorentzian fits (lines). Above 12 mK, data are vertically offset by one order of magnitude per temperature point for clarity. (b) The width of the zero-bias feature as a function of the bath temperature and a linear fit with zero intercept. (c) Resonance lines at $V = 0$ at different bath temperatures. Marker symbols (data) and line color (fits) indicate the temperature as in panel (a).
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Figure 3
Bias dependence of microwave response together with detailed theory. (a), (b) Resonance frequency and quality factor, respectively, versus bias voltage at different temperatures. Data at temperatures other than 12 mK are offset for clarity. Thin lines are experimental data, thick faded lines are fits with full small-signal theory. We use $R_{s} = 57.4 Ω$ and choose the critical currents $I_{c} = 3.25$ , 3.21, 3.14, 3, 2.7, 2.42, 2.06 nA and for the bath temperatures $T = 12$ , 20, 70, 120, 170, 220, and 270 mK, respectively. The noise temperature sensed by the junction is set in accordance with the width of the Lorentzian zero-bias feature; cf. Fig. 2. The inset (c) highlights a region of negative $Q_{i}$ observed at base temperature as predicted by theory.
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Figure 4
Effect of large probe power on resonance line at zero bias. The experimental data (left) are obtained at the base temperature of the cryostat (13 mK). The theory data are calculated using a nonlinear model that describes the effect of large phase oscillations on effective junction dynamics. In the simulation, we use an artificially elevated constant temperature (75 mK) for the electromagnetic environment to suppress hysteresis in the model.
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Figure 5
Sensitivity and noise of temperature readout with quadrature detection. (a) Voltage responsivity at the output of the readout chain using heterodyne detection with $f_{IF} = 1 MHz$ . Magnitude of the complex quantity is shown. (b) Mean spectral density of voltage noise in the frequency band from 10 kHz to 0.3 MHz. (c) Noise-equivalent temperature inferred from (a) and (b) including a $\sqrt{2}$ gain from ideal homodyne detection (experiment, symbols) with superimposed theoretical models: Constant probing power in the small-signal regime (dashed line). Same with responsivity enhancement from explicit temperature dependence of $I_{c}$ (thin solid line). Minimum achievable NET with optimized probing power at each temperature from a nonlinear model (thick line).
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