Rob Schoelkopf, Applied Physics, Yale University

PI’s:RSMichel DevoretLuigi Frunzio Steven Girvin Leonid Glazman

Quantum Optics in Circuit QED: From Single Photons to Schrodinger Cats….

Postdocs & grad students

wanted!

Thanks to cQED Team Thru the Years!

Theory

Experiment (past)

Steve Girvin, Michel Devoret, Luigi Frunzio, Leonid Glazman

Alexandre BlaisLev BishopJay GambettaJens KochEran GinossarA. NunnenkampG. CatelaniLars TornbergTerri YuSimon NiggDong ZhouMazyar MirrahimiZaki Leghtas

Andreas WallraffDave SchusterAndrew HouckLeo DiCarloJohannes MajerBlake JohnsonJerry ChowJoe Schreier

Experiment (present)Hanhee PaikLuyan SunGerhard KirchmairMatt ReedAdam SearsBrian VlastakisEric HollandMatt ReagorAndy FragnerAndrei PetrenkoJacob BlumhoffTeresa Brecht

Outline

• Cavity QED vs. Circuit QED

• How coherent is a Josephson junction?

• Scaling the 3D architecture

• A bit of nonlinear quantum optics

• Deterministic Schrödinger cat creation

Cavity Quantum Electrodynamics (cQED)

2g = vacuum Rabi freq.k = cavity decay rateg = “transverse” decay rate

† †12

ˆ ( )( ) ˆ2a

zr a a a agH H Hk g

Quantized Field Electric dipole Interaction

2-level system

Jaynes-Cummings Hamiltonian

Strong Coupling = g > k , g

Dissipation

2012: Year of Quantum Measurement"for ground-breaking experimental methods that enable

measuring and manipulation of individual quantum systems"

Serge Haroche (ENS/Paris)Cavity QED

w/ Rydberg atoms

Dave Wineland (NIST-Boulder)Quantum jumpsw/ trapped ions

Josephson-junctionqubits7 GHz in

outtransmissionline “cavity”

Thy: Blais et al., Phys. Rev. A (2004)

Qubits Coupled with a Quantum Bus

“Circuit QED”

use microwave photons guided on wires!

Superconducting Qubits

nonlinearity from Josephson junction

(dissipationless)electromagnetic oscillator 01 ~ 5 10 GHz

See reviews: Devoret and Martinis, 2004; Wilhelm and Clarke, 2008

Ener

gy

0

101

1201 12 Superconductor

Superconductor (Al)

Insulating barrier1 nm

• Engineerable spectrum• Lithographically produced features• Each qubit is an “individual”• Decoherence mechanisms?

CCj

Lj

Transmon

5 mm

Vacuum fields: mode volumezero-point energy density enhanced by

Transition dipole:0 /g d E

0~ 40,000d ea

L = l ~ 2.5 cm

coaxial cable

R l

6 310 l

610

Supports a TEM modelike a coax:

Advantages of 1d Cavity and Artificial Atom

x 10 larger than Rydberg atom

Vacuum fields: mode volumezero-point energy density enhanced by

Transition dipole:0 /g d E

0~ 40,000d ea6 310 l

610

Advantages of 1d Cavity and Artificial Atom

x 10 larger than Rydberg atom

1 100 MHz~ ~ 0.025 GHz

g

6~ 10g

Circuit QED

compare Rydberg atomor optical cQED:

much easier to reach strong interaction regimes!

The Chip for Circuit QED

Qubittrapping

easy:it’s

“soldered”down!

Nb

Nb

Si Al

Expt: Wallraff et al., Nature (2004)

Cavity QED: Resonant Case

r a

vacuumRabi

oscillations

“dressed state ladders”

g e

# ofphotons

qubit state

+ ,0 ,1e g

- ,0 ,1e g

(see e.g. “Exploring the Quantum…,” S. Haroche & J.-M. Raimond)

“phobit”

“quton”

Strong Resonant Coupling: Vacuum Rabi Splitting

Review: RS and S.M. Girvin, Nature 451, 664 (2008).Nonlinear behavior: Bishop et al., Nature Physics (2009).

2g ~ 350 MHz

Can achieve “Fine-Structure Limit”

6.75 6.85 6.95 7.05

25 9~ ~ 10 10g

kgCooperativity:

g >> [k, g]

200 MHz~ ~ ~ 0.045 GHz r

g

ra

But does it “compute”?

Algorithms: DiCarlo et al., Nature 460, 240 (2009).

1 ns resolution

cavity: “entanglement bus,” driver, & detector

transmon qubits

DC - 2 GHz

A Two-Qubit Processor

T = 10 mK

General Features of a Quantum Algorithm

Qubitregister

Workingqubits

M

createsuperposition

encode functionin a unitary

processinitialize measure

will involve entanglementbetween qubits

Maintain quantum coherence

1) Start in superposition: all values at once!2) Build complex transformation out of one-qubit and two-qubit “gates”3) Somehow* make the answer we want result in a definite state at end!

*use interference: the magic of the properly designed algorithm

Total pulse sequence:104 nanoseconds

Coherence time ~ 1 ms

The correct answer is found

>80% of the time!

ideal 10 Grover Algorithm Step-by-Step

Previously implemented in NMR: Chuang et al., 1998Ion traps: Brickman et al., 2003Linear optics: Kwiat et al., 2000

Will it ever scale?

or,

“Come on, how coherent could this squalid-state thing ever really get?”

(H. Paik et al., PRL, 2011)

Progress in Superconducting Charge Qubits

Similar plots can probably be made for phase, flux qubits

Schoelkopf’s Law:Coherence increases 10x every 3 years!

Materials: Dirt Happens!Qubit: two 200 x 300 nm junctions

Rn~ 3.5 kOhmsIc ~ 40 nA

Current Density ~ 30- 40 A/cm2

Dolan Bridge TechniquePMMA/MAA bilayerAl/AlOx/Al

Why Surfaces Matter…

Increase spacings decreases energy on surfaces

increases Q Gao et al. 2008 (Caltech)O’Connell et al. 2008 (UCSB)Wang et al. 2009 (UCSB)

as shown in:

+ + --E d

-Al2O3

Nb

“participation ratio” = fraction of energy stored in material

even a thin (few nanometer) surface layer will store ~ 1/1000 of the energy

5 mm

If surface loss tangent is poor ( tand ~ 10-2) would limit Q ~ 105

One Way to Be Insensitive to Surfaces…3-D waveguide cavity

machined from aluminum(6061-T6, Tc ~ 1.2 K)

TE101 fundamental mode

50 mm

Observed Q’s to 5 MIncreased mode volume

decreases surface effects!

cav 100T sm

Transmon Qubit in 3D Cavity

50 mm

~ mm

g 100 MHz

Still has same net coupling! Smaller fields compensated by larger dipole

Vacuum capacitor

-50

0

50

Sig

nal (

a.u.

)

20151050Delay Time (ms)

-50

0

50

Sig

nal (

a.u.

)

20151050Delay Time (ms)

100

50

0

T1 S

igna

l (a.

u.)

4003002001000Delay Time (ms)

T1 = 60 ms

T2 = 14 msmeas.

p/2 p/2Dtp/2

Coherence Dramatically ImprovedDt

p

Dtp/2/2p/2 p/2p Dtp/2/2Techo = 25 ms

61 2 10Q T

Ramsey Experiment/Hahn Echo

T2echo = 145 ms

Remarkable Frequency Stability

f01 = 6 808 737 605 (608) Hz

No change in Hamiltonian parameters > 80 ppb in 12 hours!?

608 Hzf

Overall precision after 12 hours: ~ 19 Hz or 3 ppb

Charge Qubit Coherence, Revised

QEC limit?

Schoelkopf’s law 10x every 3 years!

Ringdown of TE011

Fit (Black):τ = 3.7msQL=ωτ=265M

Milliseconds and Beyond?

M. Reagor et. al. to be published

Now this is aQuantum Memory for qubits!!

0.6 Billion

E

best qubits

Building Blocks for ScalingOne AtomOne Cavity

Two AtomsOne Cavity

One AtomTwo Cavities

Many AtomsMany Cavities

Two-Cavity Design

45mm

1.2mm

900μm Al2O3

500nm

Strong dispersive limit:QND measurement of single photons

Algorithms: DiCarlo et al., Nature 460, 240 (2009).

Dispersive Limit of cQED

cavity

qubit

2 242

rE n

g n

D

Diagonalizing J-C Hamilt.:

r a D

Dispersive (D>>g): 24 3

, ,0

2 ( / )rg n g

gE E n O g

D D

2g

D,0 ,1e g

“phobit”

,0 ,1e g “quton”

reff† †

2 a z za a a aH

Strong Dispersive Hamiltonian:

n=0

n=1

n=0

n=1

n=2

n=2

Photon Numbersplitting

2~ 0n

~ 0.5n

~ 1n

0n1n2n

Qubit Frequency (GHz)

2

~ ,g g kD

qubi

t abs

orpt

ion

“doubly-QND” interaction

QND Measurement of Photon Number

nXp

“Got any ‘s?1n

Quantum “go-fish”

gg e

cavity

qubit2) then measure qubit state using second cavity

1) perform n-dependent flip of qubitRepeated QND of n=0 or n=1:B. Johnson, Nature Phys., 2010

“Click!”

Coherent Displacementscreate

Coherent Displacements

Using a cavity as a memory:Schrodinger cats on demandexperiment theoryG. Kirchmair M. MirrahimiB. Vlastakis Z. Leghtas

“No, no mini-Me, we don’t freeze our kitty!”

Driving a Quantum Harmonic OscillatorGiving a classical ‘drive’ to a quantum system:

Where:

with

Our state is described by two continuous variables, an amplitude and phase.A ‘coherent’ state.

Phase-space portrait of oscillator state:

x̂

p̂

ˆ cos( )

ˆ sin( )

x

p

What’s a Coherent State?

E

x

x

2 / 2x mD Glauber (coherent) state

2E

0t

maxx x D

What’s a Coherent State?

E

x

x

2Glauber (coherent) state

2E

2t p

What’s a Coherent State?

E

x

x

2Glauber (coherent) state

2E

t p

Measured Q functions of a Coherent State

21( , )Q e p

D D

nXp gg e

Deterministic Cat Creation

cavity

qubit

• • •

Deterministic Cat Creation

cavity

qubit

• • • •

Deterministic Cat Creation

cavity

qubit

• • •

cavity transmission

5nspulse

•

Deterministic Cat Creation

cavity

qubit

• • • •

Deterministic Cat Creation

cavity

qubit

• • • •

Deterministic Cat Creation

cavity

qubit

• • • •

Deterministic Cat Creation

cavity

qubit

• • • •

Deterministic Cat Creation

cavity

qubit

• • • •

So, What’s a Cat State?

E

x

x

2Schrödinger cat state

2E

0t

/ 2x mD

12

2D x DSuperposition with distinguishability, D

So, What’s a Cat State?

E

x

x

2Schrödinger cat state

2E

/ 2x mD

12

2t p

What happens now, when packets collide?

Seeing the Interference: Wigner Function

Parity

Thy:

Negative fringes =“whiskers”

Expt’l. Wigner tomography: Leibfried et al., 1996 ion traps (NIST)Haroche/Raimond , 2008 Rydberg (ENS)Hofheinz et al., 2009 in circuits (UCSB)

Seeing the Interference: Wigner FunctionDcavity 1

cavity 2

qubit q wait Xp/2

mapXp/2

measurement

Wigner Function: Interpretation

x

2 / 2x mD

Wigner Function: Interpretation

x

2 / 2x mD

2t p

Fringes for different cat sizes

Creating Curious Cats

State used for a

protected memory

multicomponent interference fringesZ. Leghtas ,M. Mirrahimi et.al. arXiv. 1207.0679

(2012)

“Bulldog State?” Y

Curiouser and Curiouser…

So Now What?

“Age of Coherence”

“Age of Entanglement”

“Age of Measurement.”

“Age of Qu. Feedback.”

“Age of Qu. Error Correction.”

So Now What?• Coherence won’t be the reason it doesn’t work…

• In next few years, we will be building non-trivial (i.e. non-calculable) quantum systems from the “bottom-up”

• Beginning era of “active” quantum devices – incorporating: – quantum feedback – quantum error-correction – engineered dissipation

• Advent of analog quantum simulations and artificial many-body physics?

• What (if any?) are the medium-term applications of quantum information technology?

Error Correction with Minimal HardwareLeghtas, Mirrahimi, et al., arXiv 1207:0679

also known as a Zurek “compass state”

Then photon loss can be monitored/corrected by repeated photon parity measurement using qubit

0 ( )L C N

1 ( )L i i i C N10e eg Lg Lc cc c

• Correction for a single bit / phase flip: at least 5 qubits• A single cavity mode: infinite dimensional Hilbert Space• Minimal QEC hardware: a single cavity mode coupled to a qubit

Idea: encode a qubit in a 4 component parity state

Numerical simulations

2p

40 MHz, T1,qubit T2,qubit 100ms, Tcav 2 ms, 2 4.

Circuit QED Team Members 2012

KevinChouHanhee

Paik

BrianVlastakis

JacobBlumhoff

LuyanSun

LuigiFrunzio

MattReed

SteveGirvin

AndreiPetrenko

Funding:

AdamSears

Eric Holland

TeresaBrecht

NissimOfek

AndreasFragner

MichelDevoret

MattReagor

GerhardKirchmair

LeonidGlazman

Z. Leghtas M. Mirrahimi

Summary

• We won’t be able to use coherence as an excuse anymore!Qubits: T2 ~ 2*T1 ~ 0.0001 secCavities: T1 ~ 0.01 sec

• 3D approach has led to 2+ orders of magnitude improvements!

Paik et al., PRL 107, 240501 (2011).

• New physics: single-photon Kerr and dispersive revivals

• New approaches: cats in cavities as logical qubits!

Kirchmair, Vlastakis et al., in preparation.

Leghtas, Mirrahimi et al., ArXiv:1205.2401 and ArXiv:1207.0679