1. Calorimetry and finite bath thermodynamics Jukka Pekola, Low Temperature Laboratory Aalto University, Helsinki, Finland

2. Calorimetry for measuring the photons Requirements for calorimetry on single microwave quantum level. Photons from relaxation of a superconducting qubit. Typical parameters: Operating temperature T = 0.1 K E/k B = 1 K, C = 300...1000k B  T ~ 1 - 3 mK,  ~ 0.01 - 1 ms NET = 10  K/(Hz) 1/2 is sufficient for single photon detection  E = NET (C G th ) 1/2 JP, P. Solinas, A. Shnirman, and D. V. Averin., NJP 15, 115006 (2013).  T = E / C  = C / G th E photon source “artificial atom” absorber temperature readout electronics T(t) V(t)

3. 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

4. Josephson thermometer (at 5 GHz) O.-P. Saira, M. Zgirski, D. Golubev, K. Viisanen and JP, arXiv:1604.05089 (2016).arXiv:1604.05089 P(E) theory: Only one fit parameter: R S = 57.4 .

5. Josephson thermometer (at 5 GHz) Expected 1 K photon resolution

6. Towards calorimetry of a superconducting qubit J. Senior, O.-P- Saira et al., 2016

7. Measurement of thermal coupling G th and heat capacity C of a normal wire  E = NET (C G th ) 1/2 Copper and silver thin film wires measured K. L. Viisanen and JP, in preparation (2016).

8. G th - electron-phonon coupling T (K)  Cu = 2 GW/m 3 K 5 in literature  Ag = 0.5 GW/m 3 K 5 inferred from data of A. Steinbach et al., PRL 1996

9. Heat capacity C |s 21 | 2 (arb) T bath C,T G th C of copper films is anomalously high (x10) Silver follows free-electron Fermi-gas model C = (  2 /3) N(0)k B 2 V T

10. 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 TIME T0T0 E T(t) V(t)

11. Fluctuating energy of a finite bath TT TIME T C,  E,  T ? !

12. (a) (b) (c) QUBIT TLS- CALORIMETER HO- CALORIMETER TLS- CALORIMETER TLS-BATH DRIVE Simple models of a finite calorimeter J. P. Pekola, S. Suomela, and Y. M. Galperin, arXiv:1602.00474, J. Low Temp. Phys. (2016). arXiv:1602.00474J. Low Temp. Phys See also: S. Suomela, A. Kutvonen, T. Ala- Nissila, arXiv:1601.05317arXiv:1601.05317

13. TLS calorimeter and bath: equal level spacing and coupling

14. Quantum jump trajectories 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). Stochastic wave function of the qubit Qubit rates Calorimeter rates Evolution of the qubit state when no jumps occur

15. Initially: Population of the calorimeter at the end of the drive is enhanced. This has naturally no effect on the fluctuation relations. Overheating of the calorimeter

16. Distributions of work, Crooks relation Qubit + calorimeter only Initially thermalized Qubit + calorimeter + big bath Initially thermalized Blue – all heat included Black – heat to big bath ignored Line: P(W)/P(-W)=e  W G. Crooks, 1999

17. More realistic model: resistor bath (free Fermi-gas) E T(t) V(t) For an Ag wire with V = 10 -22 m 3 at T = 100 mK, C/k B < 100 T/T F = 10 -6 Energy fluctuations become strongly non- gaussian in this regime JP, P. Muratore-Ginanneschi, A. Kupiainen, and Yu. M. Galperin, arXiv:1605.05877 arXiv:1605.05877 Analysis of equilibrium energy fluctuations for a free-electron gas with finite heat capacity T C, E

18. Calculation of the energy distribution

19. Equilibrium energy distribution Gaussian E 0 corresponds to filled Fermi-sea  

20. 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

21. 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)