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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:

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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
  • f heat conductance, quantum heat valve, local and

global picture, rectification of heat current

  • 5. Fast thermometry, calorimetry
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SLIDE 2

Measuring heat currents

T C, T+DT Gth Q

.

Measurement of temperature by a (fast) thermometer

TIME

TEMPERATURE TIME

<Q>/Gth <DT>= .

Energy resolution: ideally Single quantum detection (calorimetry

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SLIDE 3

NIS-thermometry

  • Phys. Rev. Appl. 4, 034001 (2015).

Probes electron temperature of N electrode (and not of S!)

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SLIDE 4

Master equation: – Probabilities: 𝑄 π‘œ – Sequential Tunneling: Ξ“+ π‘œ , Ξ“βˆ’ π‘œ – Co-tunneling: Ξ“cot π‘œ

  • πœ–π‘„ π‘œ

πœ–π‘’

=

βˆ’π‘„ π‘œ Ξ“ + π‘œ + Ξ“βˆ’ π‘œ + 𝑄 π‘œ βˆ’ 1 Ξ“ + π‘œ βˆ’ 1 +𝑄 π‘œ + 1 Ξ“ βˆ’ π‘œ + 1 . I = e 𝑄 π‘œ Γ𝑀

+ π‘œ βˆ’ Γ𝑀 βˆ’(π‘œ) + e 𝑄 π‘œ Ξ“

𝑀𝑆 cot π‘œ βˆ’ Ξ“ 𝑆𝑀 cot(π‘œ) .

Single-electron transistor

3/15/2019 Thermoelectricity in Single Electron Systems 4

Γ𝑆

+ π‘œ

Ξ“L

+ π‘œ

π‘œ

Γ𝑆

βˆ’ π‘œ

Ξ“L

βˆ’ π‘œ

Ξ“LR

cot π‘œ

Ξ“

RL cot π‘œ

Ξ“LL

cot π‘œ

Ξ“RR

cot π‘œ

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SLIDE 5

Heat through a single-electron transistor – deviation from Wiedemann-Franz law

  • B. Dutta, J. Peltonen et al., PRL 119, 077701 (2017)

Vg VSET

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SLIDE 6

Thermopower in a single- electron transistor

  • P. Erdman et al, arXiv:1812.06514

TH = 190 mK TL = 134 mK TH = 342 mK TL = 63 mK No free parameters in model: red sawtooth – 2-state sequential, black – includes cotunneling

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SLIDE 7

Qubit as an open quantum system

Superconducting qubits

H = HQ + V + HE

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SLIDE 8

W

RH RC

Q1 Q2

qubit Refrigerator

Refrigerator and heat engine

Heat engine

W

RH RC

Q1 Q2

qubit

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SLIDE 9

Quantum Otto refrigerator

Niskanen, Nakamura, Pekola, PRB 76, 174523 (2007);

  • B. Karimi and JP, Phys. Rev. B 94, 184503 (2016).

Otto cycle

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SLIDE 10

Heat transported between two resistors

For small temperature difference DT = T1 – T2: R1 T1 R2 T2 R1 R2 Sv1 Sv2 Johnson, Nyquist 1928

Photons Schmidt et al., PRL 93, 045901 (2004) 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) Electrons Jezouin et al., Science 342, 601 (2013) Banerjee et al., Nature 545, 75 (2017)

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SLIDE 11

Experimental realization of photonic heat transport

10 Β΅m

R

2

R

1

x x x x

L

J

C

J

Tunable coupling using SQUIDs

F

en Gn

90 95 100 105 110 115 120 125 155 160 165 170

105mK 118mK T0 = 167mK 60mK 75mK 157mK

T (mK)

F (a.u.)

e1

Thermal model Meschke, Guichard and JP (2006)

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Classical or quantum heat transport?

w wC w wC

”Classical” high T, macroscopic circuit 300 K, centimetres ”Quantum” low T, small circuit 50 mK, micrometres

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Measurements of quantum of heat conductance by photons

Partanen et al., Nature Phys. 12, 460 (2016) Timofeev et al., PRL 102, 200801 (2009) ...via a 1 m long transmission line

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SLIDE 14

Quantum heat valve

F

RH RC

PC PC

qubit

  • A. Ronzani, B. Karimi, J. Senior, Y.-C. Chang, J. Peltonen,
  • C. D. Chen, and JP, Nature Physics 14, 991 (2018).
  • B. Karimi, J. Pekola, M.

Campisi, and R. Fazio, Quantum Science and Technology 2, 044007 (2017).

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SLIDE 15

Temperature of a qubit?

Alternative approach to initialize a qubit to a given ”temperature”:

  • Y. Masuyama et al.,

Nature Comm. 9, 1291 (2018)

BATH T

Couple the qubit to a true thermal bath

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SLIDE 16

Idea of the experiment

Power to each bath (in steady-state): T1 T2

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Experimental realization of the heat valve

TRANSMON QUBIT RESERVOIR AND THERMOMETERS QUBIT WITHOUT ABSORBERS

10 mm 3 mm 1 mm George et al. (2017)

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SLIDE 18

l / 4 resonators terminated by heat bath R

Superconducting shunt, Q = 17 000 Normal (copper) shunt, Q = 18

Q = pZ0 / 4R R β‰ˆ 2 W

Yu-Cheng Chang et al., in preparation See also:

  • M. Partanen et al., Nat.
  • Phys. 12, 160 (2016);

arXiv:1712.10256

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SLIDE 19

Low-Q regime

gQ << 1, ”non- Hamiltonian” model works

RH

g’  Q-1 g g g’  Q-1

RC

Resonator SQUID Resonator Cooling at distance

  • f 4 mm by mw

photons

Q = 3

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SLIDE 20

Intermediate-Q regime

gQ ~ 1, ”quasi- Hamiltonian” model works

RH

g’  Q-1 g’  Q-1

RC

Resonator SQUID Resonator

Q = 20

g g

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Current experiment: asymmetric device

  • 400
  • 200

200 400

  • 0,8
  • 0,4

0,0 0,4 0,8 1,2 1,6 2,0

TS ο‚» 200 mK TS ο‚» 100 mK

Estimated DT (mK) Icoil (mA)

T_bath=140 mK 100 aW

3 GHz 7 GHz

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SLIDE 22

Forward and reverse powers

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SLIDE 23

Rectification ratio from measurement

  • 1

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

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SLIDE 24

Rectification of photonic heat current by a qubit

For small asymmetry:

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n-level system

0.4, 0.8, 1.6

Equidistant levels

Rectification vanishes in a linear system (harmonic oscillator) even when couplings are unequal.

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SLIDE 26

What next?

Quantum Otto refrigerator Time-domain measurements of temperature: temperature fluctuations, single microwave photon detection

E

photon source β€œartificial atom” absorber temperature readout electronics

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SLIDE 27

Quantum Otto refrigerator

Expect about 1 fW cooling power at 1 GHz driving frequency

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SLIDE 28

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).

Proof of concept: D. Schmidt et al.,

  • Appl. Phys. Lett. 83, 1002 (2003).
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50 100 150 200 250 300 350 400

147 mV 150 mV 153 mV 156 mV 159 mV 162 mV 165 mV 168 mV

T (mK) S21 (dB)

  • 400
  • 200

200 400

  • 44
  • 42
  • 40
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  • 34
  • 32
  • 30

S21 (dB) Vth (mV)

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SLIDE 29

ZBA based thermometry

non-invasive, operates at low temperature

  • B. Karimi and JP, Phys. Rev. Applied 10,

054048 (2018)

S I N S

Proximity NIS junction

See also, O.-P. Saira et al., Phys. Rev. Appl. 6, 024005 (2016); J. Govenius et al., PRL 117, 030802 (2016)

  • 50
  • 48
  • 46

20 40 60 80 100

  • 120 dB

T (mK) S21 (dB)

  • 50
  • 48
  • 46
  • 44
  • 42
  • 40
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100 200 300 400 500

  • 120 dB

T (mK) S21 (dB)

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Time-resolved measurements by fast thermometer

Tbath C,T Gth

  • K. Viisanen and JP, PRB 97,

115422 (2018)

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Noise of electrical current

, i.e. Johnson-Nyquist noise Fluctuation-dissipation theorem for heat current

Noise of heat current and equilibrium temperature fluctuations

Low frequency noise: Finite frequencies (classical):

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SLIDE 32

Preliminary results on temperature fluctuations

  • B. Karimi et al., in preparation

Equilibrium noise:

phonons photons, tunneling

Equilibrium noise

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Non-equilirium temperature noise

Vinj

Theory: F. Brange, P. Samuelsson, B. Karimi, J. P., PRB 98, 205414 (2018). Thermometer

  • B. Karimi et al., in preparation
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Requirements for single microwave photon detection

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

Detector noise bounded from below by effective temperature fluctuations of the absorber coupled to the bath. Noise-equivalent temperature, NET Required NET = E/(GthC)1/2

Standard copper absorber

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SLIDE 35

Summary

Discussed: measurement of heat in circuits, thermometry Heat transport and thermo-electricity of a single-electron transistor

  • pen 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

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SLIDE 36

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)