departments of physics and applied physics, yale...

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

3



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

Remarkable Progress in Coherence

Progress = 10 x every 3 years!

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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

R R

Can read out qubit state by measuring cavity resonance frequency

cavi

ty re

spon

se

cavity circulator quantum limited amplifier

xreflection phase

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

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

27



cQED ‘phase diagram’

28

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

30



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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( ) ( )

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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35



Photon number parity

36

†

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

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

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