Nanoscale quantum calorimetry with electronic temperature fluctuations

F. Brange, P. Samuelsson, B. Karimi, and J. P. Pekola

Phys. Rev. B 98, 205414 – Published 20 November 2018

Abstract

Motivated by the recent development of fast and ultrasensitive thermometry in nanoscale systems, we investigate quantum calorimetric detection of individual heat pulses in the sub-meV energy range. We propose a hybrid superconducting injector-calorimeter setup, with the energy of injected pulses carried by tunneling electrons. It is shown that the superconductor constitutes a versatile injector, with tunable tunnel rates and energies. Treating all heat transfer events microscopically, we analyze the statistics of the calorimeter temperature fluctuations and derive conditions for an accurate measurement of the heat pulse energies. Our results pave the way for fundamental quantum thermodynamics experiments, including calorimetric detection of single microwave photons.

Received 7 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.205414

Physics Subject Headings (PhySH)

Quantum thermodynamics Quantum transport

Calorimetry

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

F. Brange and P. Samuelsson

Department of Physics and NanoLund, Lund University, Box 188, SE-221 00 Lund, Sweden

B. Karimi and J. P. Pekola

QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-000 76 Aalto, Finland

Noninvasive Thermometer Based on the Zero-Bias Anomaly of a Superconducting Junction for Ultrasensitive Calorimetry

Bayan Karimi and Jukka P. Pekola

Phys. Rev. Applied 10, 054048 (2018)

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Vol. 98, Iss. 20 — 15 November 2018

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Images

Figure 1
(a) Two representative Monte Carlo simulated (see appendix) time traces of the absorber electron temperature $T_{e} (t)$ , with a jump $Δ T_{e}$ caused by a single particle absorption event followed by a decay, rate $τ$ . The superimposed fluctuations are due to stochastic heat exchange with a phonon bath at low (red) and intermediate (black) temperatures $T_{b}$ (see text). Noise free case, Eq. (1), is shown with a dashed line. Inset: Effective circuit model of a calorimeter with heat capacity $C$ and heat conductance $κ$ to the bath. (b) Schematic of the nanoscale injector-calorimeter setup: A normal metallic island (green) contains a thermalized electron gas, with fluctuating temperature $T_{e} (t)$ , constituting the absorber. The island is well coupled to an electrically grounded superconductor (upper, blue) acting as a heat mirror. It is further tunnel coupled to another superconductor (lower, blue), kept at a temperature $T_{s}$ and biased at a voltage $V$ , serving as a particle source with tunable injection rate $Γ_{i} (T_{s}, V)$ . A thermometer, coupled to the island, is also shown (yellow). The island phonons, at temperature $T_{b}$ , constitute a thermal bath weakly coupled to the island electron gas.
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Figure 2
(a) Probability distribution of energies transferred to the absorber $P (ɛ)$ from injector-absorber quasiparticle tunneling, for four different sets of ${k_{B} T_{s} / Δ, k_{B} T_{e} / Δ, e V / Δ} = {0.02, 0.02, 0}$ (dashed), ${0.05, 0.01, 0}$ (orange, solid), ${0.01, 0.05, 0}$ (green, solid), and ${0.01, 0.05, 0.5}$ (blue, solid). Corresponding injector regimes (I), (II), and (III) shown, see text. (b) Probability distribution for bath-absorber energy transfers due to phonon creation and annihilation, for different temperature ratios $T_{e} / T_{b}$ .
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Figure 3
(a) Temperature probability distribution $P (θ)$ for $T_{s} = 10 T_{b}$ (red, solid) and $T_{s} = 0.1 T_{b}$ (yellow, solid), corresponding to injector cases (I) and (II), respectively. Dashed lines show the respective best Gaussian fits. In both plots $V = 0$ , $T_{b} = 0.01 Δ / k_{B}$ , $C = 20 Δ / T_{b}$ , and $τ Γ_{i} = 0.1$ . (b)–(g) The first three cumulants as a function of $T_{s} / T_{b}$ , at $V = 0$ [(b)–(d)] and $e V / Δ$ , at $T_{s} = T_{b}$ [(e)–(g)]. In all panels $T_{b} = 0.01 Δ / k_{B}$ , $C = 20 Δ / T_{b}$ , and $τ Γ_{i} = 0.1$ at $T_{s} = 5 T_{b}$ and $e V = 0.4 Δ$ , respectively. The total cumulants are shown with thick, solid lines. In (b) and (e), $τ Γ_{i}$ is also shown (purple, thin solid). In (c), (d), (f), (g) the injector-absorber (thin, solid) and bath-absorber (thin, dashed) contributions to the respective cumulants are shown. In (d) and (g) the back-action component (dash dotted) is shown.
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Figure 4
Examples of Monte Carlo generated time traces of the temperature fluctuations for (a) $T_{b} = 5 mK$ , (b) $T_{b} = 30 mK$ , and (c) $T_{b} = 100 mK$ . Every time trace contains an injector event at $t = 0$ . In all cases, $C = 1000 k_{B}$ , $ɛ = 200 μ eV$ , and $τ$ denotes the relaxation time.
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