Transcript T - Department of Applied Physics

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)