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Departments of Physics and Applied Physics, Yale University
Introduction to Circuit QED
TheorySMGLiang JiangLeonid GlazmanM. Mirrahimi
Marios MichaelVictor AlbertRichard BrierleyClaudia De GrandiZaki LeghtasJuha SalmilehtoMatti SilveriUri VoolHuaixui ZhengYaxing Zhang+…..
ExperimentMichel DevoretLuigi FrunzioRob Schoelkopf
Andrei Petrenko Nissim OfekReinier HeeresPhilip ReinholdYehan LiuZaki LeghtasBrian Vlastakis+…..
http://quantuminstitute.yale.edu/
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Lecture 1: Introduction to Circuit QED
• ‘Blackbox’ Quantization (BBQ)• Dispersive Coupling and Readout• Strong Dispersive Limit• Photon ‘Number Splitting ‘• Photon Number Parity Measurement
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Lecture 1: Introduction to Circuit QED
• ‘Blackbox’ Quantization (BBQ)• Dispersive Coupling and Readout• Strong Dispersive Limit• Photon ‘Number Splitting ‘• Photon Number Parity Measurement
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spin
50 mm
~ mm
Transmon Qubit in 3D Cavity
Josephsonjunction
rmsd Egh
g 100 MHz
72 1 mm 10 Debye!!d e
Huge dipole moment: strong coupling
†dipole ( )xV g a a
Spin flip
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Remarkable Progress in Coherence
Progress = 10 x every 3 years!
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Lecture 1: Introduction to Circuit QED
• ‘Blackbox’ Quantization (BBQ)• Dispersive Coupling and Readout• Strong Dispersive Limit• Photon ‘Number Splitting ‘• Photon Number Parity Measurement
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R R
Qubit-Cavity cross-Kerr for two lowest levels of dressed transmon.
ˆ2QZ Z
RH n
‘Dispersive’ coupling
† †
†
†
ˆ
1 0,12
Z
Bn
B
A A BA A
B
Can read out qubit state by measuring cavity resonance frequency
cavi
ty re
spon
se
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R R
Can read out qubit state by measuring cavity resonance frequency
cavi
ty re
spon
se
cavity circulator quantum limited amplifier
xreflection phase
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X
Y
in
outi i
a b
a e b e
State of qubit is entangled with the ‘meter’ (microwave phase)Then ‘meter’ is read with amplifier.
cavity circulator quantum limited amplifier
xreflection phase
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Quantum Jumps of a 3D Transmon Qubit
0
5
-5
0 50 100 150Time (s)
Results from Devoret group, Yale: Hatridge et al., Science 2013*
dispersive circuit QED readout + JJ paramp
Readout fidelity > 99.5% in ~ 300 nsec
Many groups now working with JJ paramps & feedback, including: Berkeley, Delft, JILA, ENS/Paris, IBM, Wisc., Saclay, UCSB, …
*First jumps: R. Vijay et al., 2011 (Berkeley)
g
e
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Lecture 1: Introduction to Circuit QED
• ‘Blackbox’ Quantization (BBQ)• Dispersive Coupling and Readout• Strong Dispersive Limit• Photon ‘Number Splitting ‘• Photon Number Parity Measurement
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cQED ‘phase diagram’
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Cavity-qubit detuning
Cav
ity-q
ubit
coup
ling
( , ), linewidth of cavity or qubit
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Strong Dispersive Hamiltonian
q† †r damping2
z zH a a a a H
resonator qubit dispersivecoupling
rcavity frequency z
eg
r r
‘strong-dispersive’ limit
32 ~ 2 10
,
2
~ g
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Lecture 1: Introduction to Circuit QED
• ‘Blackbox’ Quantization (BBQ)• Dispersive Coupling and Readout• Strong Dispersive Limit• Photon ‘Number Splitting ‘• Photon Number Parity Measurement
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Using strong-dispersive coupling to measure the photon number distribution in a cavity
Strong Dispersive Hamiltonian
q† †r damping2
z zH a a a a H
resonator qubit dispersivecoupling
,
Quantized Light Shift of Qubit Transition Frequency
† †r q damping2
1 2zH a a a a H
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Coherent state is closest thing to a classicalsinusoidal RF signal
0( ) ( )
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Microwaves are particles!
3 124…
- quantized light shift of qubit frequency(coherent microwave state)
†q 2
2za a
N.B. power broadened100X
New low-noise way to do axion dark matter detection?Zhang et al. arXiv:1607.02529
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Lecture 1: Introduction to Circuit QED
• ‘Blackbox’ Quantization (BBQ)• Dispersive Coupling and Readout• Strong Dispersive Limit• Photon ‘Number Splitting ‘• Photon Number Parity Measurement
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Photon number parity
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†
0
ˆ ( 1) ( 1)a a n
n
nP n
Remarkably easy to measure usingour quantum engineering toolbox
and
Measurement is 99.8% QND
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- use quantized light shift of qubit frequency
†q 2
2za a
Measuring Photon Number Parity
ˆ ˆ22 2ez z
i nt i ne
ˆ 0,2,4,...n ˆ 1,3,5,...n x
z
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Parity
Time s4000 300200100
38Nature 511, 444 (2014) 400 consecutive parity measurements (99.8% QND)
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The ability to measure photon number parity without measuring photon number is an incredibly powerful tool.
Lecture 2: Using parity measurements for:
• Wigner Function Measurements• Creation and verification of photon cat
states
Lecture 3: Using parity measurements for:
• Continuous variable quantum error correction