a superconducting qubit and a single-electron transistor Jukka - PowerPoint PPT Presentation

Experiments on quantum heat transport through a superconducting qubit and a single-electron transistor Jukka Pekola, Aalto University, Helsinki, Finland 1. Heat in circuits: measurement and control 2. Thermometry 3. Single-electron transistor: heat transport and thermopower 4. Circuit quantum thermodynamics (cQTD): quantum of heat conductance, quantum heat valve, local and global picture, rectification of heat current 5. Fast thermometry, calorimetry

Measuring heat currents Measurement of temperature by a (fast) thermometer . Q TEMPERATURE < D T>= . <Q>/G th C, T+ D T TIME TIME G th Single quantum detection (calorimetry T Energy resolution: ideally

NIS-thermometry Probes electron temperature of N electrode (and not of S!) Phys. Rev. Appl. 4, 034001 (2015).

Single-electron transistor cot 𝑜 Γ LR + 𝑜 + 𝑜 𝜖𝑄 𝑜 Γ L Γ 𝑆 • = 𝜖𝑢 −𝑄 𝑜 Γ + 𝑜 + Γ − 𝑜 𝑜 + 𝑄 𝑜 − 1 Γ + 𝑜 − 1 − 𝑜 − 𝑜 cot 𝑜 cot 𝑜 Γ L Γ 𝑆 Γ RR Γ LL cot 𝑜 +𝑄 𝑜 + 1 Γ − 𝑜 + 1 . Γ RL Master equation: – Probabilities: 𝑄 𝑜 + 𝑜 − Γ 𝑀 − (𝑜) I = e 𝑄 𝑜 Γ 𝑀 – Sequential Tunneling: Γ + 𝑜 , Γ − 𝑜 cot 𝑜 − Γ cot (𝑜) . + e 𝑄 𝑜 Γ 𝑀𝑆 𝑆𝑀 – Co-tunneling: Γ cot 𝑜 3/15/2019 Thermoelectricity in Single Electron Systems 4

Heat through a single-electron transistor – deviation from Wiedemann-Franz law V SET V g B. Dutta, J. Peltonen et al., PRL 119 , 077701 (2017)

Thermopower in a single- No free parameters in model : red sawtooth – 2-state sequential, black – includes electron transistor cotunneling T H = 190 mK T L = 134 mK T H = 342 mK T L = 63 mK P. Erdman et al, arXiv:1812.06514

Qubit as an open quantum system Superconducting qubits H = H Q + V + H E

Refrigerator and heat engine R H R H Refrigerator Heat engine Q 1 Q 1 W W qubit qubit Q 2 Q 2 R C R C

Quantum Otto refrigerator Otto cycle Niskanen, Nakamura, Pekola, PRB 76, 174523 (2007); B. Karimi and JP, Phys. Rev. B 94 , 184503 (2016).

Heat transported between two resistors Johnson, Nyquist 1928 S v 1 S v 2 Photons R 1 R 2 Schmidt et al., PRL 93, 045901 (2004) T 1 T 2 R 1 R 2 Meschke et al., Nature 444, 187 (2006) Timofeev et al., PRL 102, 200801 (2009) Partanen et al., Nature Physics 12, 460 (2016) Phonons K. Schwab et al., Nature 404, 974 (2000) For small temperature difference D T = T 1 – T 2 : Electrons Jezouin et al., Science 342, 601 (2013) Banerjee et al., Nature 545, 75 (2017)

Experimental realization of photonic heat transport 170 x e n G n T 0 = 167mK 165 Thermal x 160 model 157mK R R 155 F T (mK) 2 1 x 118mK 125 120 e1 Tunable x 115 105mK coupling using 110 SQUIDs 105 L 100 J 75mK 95 C 60mK 90 J 10 µm F (a.u.) Meschke, Guichard and JP (2006)

Classical or quantum heat transport? w w w C w C ”Classical” ”Quantum” high T , macroscopic circuit low T , small circuit 300 K, centimetres 50 mK, micrometres

Measurements of quantum of heat conductance by photons ...via a 1 m long transmission line Partanen et al., Nature Phys. 12, 460 Timofeev et al., PRL 102, 200801 (2016) (2009)

Quantum heat valve A. Ronzani, B. Karimi, J. Senior, Y.-C. Chang, J. Peltonen, C. D. Chen, and JP, Nature Physics 14, 991 (2018). R H P C F qubit P C R C B. Karimi, J. Pekola, M. Campisi, and R. Fazio, Quantum Science and Technology 2 , 044007 (2017).

Temperature of a qubit? BATH Couple the qubit to a true thermal bath T Alternative approach to initialize a qubit to a given ” temperature ”: Y. Masuyama et al., Nature Comm. 9, 1291 (2018)

Idea of the experiment T 1 T 2 Power to each bath (in steady-state):

Experimental realization of the heat valve George et al. (2017) QUBIT WITHOUT ABSORBERS 10 m m 3 m m 1 mm TRANSMON QUBIT RESERVOIR AND THERMOMETERS

l / 4 resonators terminated by heat bath R Q = p Z 0 / 4 R R ≈ 2 W Yu-Cheng Chang et al., in preparation See also: M. Partanen et al., Nat. Phys. 12 , 160 (2016); arXiv:1712.10256 Superconducting shunt, Q = 17 000 Normal (copper) shunt, Q = 18

Low-Q regime Q = 3 Cooling at distance of 4 mm by mw photons gQ << 1, ” non- R H R C Hamiltonian ” g ’  Q -1 g g g ’  Q -1 model works Resonator SQUID Resonator

Intermediate-Q regime Q = 20 R H R C g g g ’  Q -1 g ’  Q -1 gQ ~ 1, ” quasi- Resonator SQUID Resonator Hamiltonian ” model works

Current experiment: asymmetric device T_bath=140 mK 2,0 1,6 Estimated D T (mK) 1,2 0,8 100 aW T S  200 mK 0,4 T S  100 mK 0,0 -0,4 -0,8 -400 -200 0 200 400 I coil ( m A) 3 GHz 7 GHz

Forward and reverse powers

Rectification ratio from measurement - 1 Theory: Rectification of heat in spin-boson model, D. Segal and A. Nitzan, PRL 2005

Rectification of photonic heat current by a qubit For small asymmetry:

n-level system Equidistant levels 0.4, 0.8, 1.6 Rectification vanishes in a linear system (harmonic oscillator) even when couplings are unequal.

What next? Quantum Otto refrigerator Time-domain measurements of temperature: temperature fluctuations, single microwave photon detection temperature photon source readout electronics “artificial atom” E absorber

Quantum Otto refrigerator Expect about 1 fW cooling power at 1 GHz driving frequency

Fast NIS thermometry on electrons Read-out at 600 MHz of a NIS S. Gasparinetti et al., junction, 10 MHz bandwidth Phys. Rev. Applied 3, 014007 (2015). -30 Proof of concept: D. Schmidt et al., Appl. Phys. Lett. 83, 1002 (2003). -32 -34 S 21 (dB) 400 -36 350 -38 300 147 m V -40 T (mK) 250 150 m V 153 m V 200 -42 156 m V 159 m V 150 162 m V -44 165 m V 100 168 m V -400 -200 0 200 400 50 V th ( m V) 0 -36 -35 -34 -33 -32 -31 S 21 (dB)

ZBA based thermometry B. Karimi and JP, Phys. Rev. Applied 10, 054048 (2018) non-invasive, operates at low temperature 500 N S 400 T (mK) 300 S I 200 100 Proximity NIS junction -120 dB 0 -50 -48 -46 -44 -42 -40 -38 S 21 (dB) 100 80 T (mK) 60 40 20 -120 dB 0 -50 -48 -46 S 21 (dB) See also, O.-P. Saira et al., Phys. Rev. Appl. 6, 024005 (2016); J. Govenius et al., PRL 117, 030802 (2016)

Time-resolved measurements by fast thermometer C,T G th T bath K. Viisanen and JP, PRB 97, 115422 (2018)

Noise of heat current and equilibrium temperature fluctuations Noise of electrical current , i.e. Johnson-Nyquist noise Fluctuation-dissipation theorem for heat current Low frequency noise: Finite frequencies (classical):

Preliminary results on temperature fluctuations B. Karimi et al., in preparation Equilibrium noise: phonons photons, tunneling Equilibrium noise

Non-equilirium temperature noise Thermometer V inj B. Karimi et al., in preparation Theory: F. Brange, P. Samuelsson, B. Karimi, J. P., PRB 98, 205414 (2018).

Requirements for single microwave photon detection Detector noise bounded from below by effective Standard copper absorber temperature fluctuations of the absorber coupled to the bath. Noise-equivalent temperature, NET Required NET = E /( G th C ) 1/2 Lines: Green dashed one: current amplifier limited noise Black : fundamental temperature fluctuations Blue : threshold for detecting a single E = 1 K microwave photon Red : threshold for detecting a single E = 2.5 K quantum

Summary Discussed: measurement of heat in circuits, thermometry Heat transport and thermo-electricity of a single-electron transistor open quantum systems based on superconducting qubits photonic heat transport, quantum of heat conductance quantum heat valve, local and global picture, rectification of heat current calorimetry, temperature fluctuations

Main collaborators Bayan Karimi, Alberto Ronzani, Jorden Senior, Azat Gubaydullin, Yu-Cheng Chang, Joonas Peltonen Bivas Dutta, Clemens Winkelmannn, Herve Courtois (CNRS Grenoble) Paolo Erdman, Fabio Taddei (Pisa), Rosario Fazio (ICTP Trieste) Hans He, Samuel Lara Avila, Sergey Kubatkin (Chalmers, graphene calorimeter)