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Calorimetry and finite bath thermodynamics Jukka Pekola, Low Temperature Laboratory Aalto University, Helsinki, Finland Calorimetry for measuring the photons Requirements for calorimetry on single microwave quantum level. Photons from relaxation of a superconducting qubit. photon source “artificial atom” temperature readout electronics absorber E V(t) T(t) DT = E / C t = C / Gth Typical parameters: Operating temperature T = 0.1 K E/kB = 1 K, C = 300...1000kB DT ~ 1 - 3 mK, t ~ 0.01 - 1 ms NET = 10 mK/(Hz)1/2 is sufficient for single photon detection dE = NET (C Gth)1/2 JP, P. Solinas, A. Shnirman, and D. V. Averin., NJP 15, 115006 (2013). Fast NIS thermometry on electrons Read-out at 600 MHz of a NIS junction, 10 MHz bandwidth S. Gasparinetti et al., Phys. Rev. Applied 3, 014007 (2015); K. L. Viisanen et al., New J. Phys. 17, 055014 (2015). Proof of the concept: Schmidt et al., 2003 Josephson thermometer (at 5 GHz) P(E) theory: Only one fit parameter: RS = 57.4 W. O.-P. Saira, M. Zgirski, D. Golubev, K. Viisanen and JP, arXiv:1604.05089 (2016). Josephson thermometer (at 5 GHz) Expected 1 K photon resolution Towards calorimetry of a superconducting qubit J. Senior, O.-P- Saira et al., 2016 5µm Measurement of thermal coupling Gth and heat capacity C of a normal wire K. L. Viisanen and JP, in preparation (2016). dE = NET (C Gth)1/2 Copper and silver thin film wires measured Gth - electron-phonon coupling T (K) SCu = 2 GW/m3K5 in literature SAg = 0.5 GW/m3K5 inferred from data of A. Steinbach et al., PRL 1996 Heat capacity C C,T Gth |s21|2 (arb) Tbath C of copper films is anomalously high (x10) Silver follows free-electron Fermi-gas model C = (p2/3) N(0)kB2V T Calorimetry on quantum two-level systems: ”errors” 1. Hidden environments/noise sources K. L. Viisanen et al., New J. Phys. 17, 055014 (2015). 2. Finite heat capacity of the absorber (non-Markovian) TEMPERATURE 1,15 1,10 E V(t) B 1,05 T(t) T0 1,00 0,95 0,90 0 2 4 6 A TIME 8 10 Fluctuating energy of a finite bath C, dE, dT ? ! T 1,15 1,10 B dT 1,05 1,00 0,95 0,90 0 2 4 6 A TIME 8 10 Simple models of a finite calorimeter (a) QUBIT TLSCALORIMETER DRIVE J. P. Pekola, S. Suomela, and Y. M. Galperin, arXiv:1602.00474, J. Low Temp. Phys. (2016). TLS-BATH (c) QUBIT (b) DRIVE QUBIT DRIVE TLSCALORIMETER HOCALORIMETER See also: S. Suomela, A. Kutvonen, T. AlaNissila, arXiv:1601.05317 TLS calorimeter and bath: equal level spacing and coupling Quantum jump trajectories Stochastic wave function of the qubit Qubit rates Calorimeter rates Evolution of the qubit state when no jumps occur F. Hekking and JP, PRL 111, 093602 (2013); J. Horowitz and J. Parrondo, NJP 15, 085028 (2013); JP, Y. Masuyama, Y. Nakamura, J. Bergli, and Y. M. Galperin, PRE 91, 062109 (2015). Overheating of the calorimeter Initially: Population of the calorimeter at the end of the drive is enhanced. This has naturally no effect on the fluctuation relations. Distributions of work, Crooks relation Line: P(W)/P(-W)=ebW G. Crooks, 1999 Qubit + calorimeter only Initially thermalized Qubit + calorimeter + big bath Initially thermalized Blue – all heat included Black – heat to big bath ignored More realistic model: resistor bath (free Fermi-gas) E V(t) T(t) Analysis of equilibrium energy fluctuations for a free-electron gas with finite heat capacity C, E T For an Ag wire with V = 10-22 m3 at T = 100 mK, C/kB < 100 T/TF = 10-6 Energy fluctuations become strongly nongaussian in this regime JP, P. Muratore-Ginanneschi, A. Kupiainen, and Yu. M. Galperin, arXiv:1605.05877 Calculation of the energy distribution Equilibrium energy distribution Gaussian E0 corresponds to filled Fermi-sea e m Summary Metallic calorimeters are just about sensitive enough to monitor single microwave photons Fast thermometry and qubit in a cavity tested Anomalous heat capacity of copper vs silver observed Physics of finite heat capacity absorber discussed – work in progress Collaboration Olli-Pentti Saira (AALTO) Klaara Viisanen (AALTO) Simone Gasparinetti (AALTO, now ETH) Jorden Senior (AALTO) Joonas Peltonen (AALTO) Matthias Meschke (AALTO) Maciej Zgirski (Warsaw) Dmitry Golubev (AALTO) Yuri Galperin (Oslo) Frank Hekking (Grenoble) Joachim Ankerhold (Ulm) Paolo Muratore-Ginanneschi (Univ. Helsinki) Antti Kupiainen (Univ. Helsinki) Samu Suomela (AALTO) Tapio Ala-Nissila (AALTO) Kay Schwieger (Univ. Helsinki)