Doing Atomic Physics with Electrical Circuits:Strong Coupling Cavity QED

Yale University

Ren-Shou Huang, Alexandre Blais, Andreas Wallraff, David Schuster, Sameer Kumar, Luigi Frunzio, Hannes Majer,

Steven Girvin, Robert Schoelkopf

2

Atoms Coupled to Photons

1s

2p2sIrreversible spontaneous decay into the photon continuum:

12 1 1 nsp s Tγ→ + ∼

Vacuum Fluctuations:(Virtual photon emission and reabsorption)Lamb shift lifts 1s 2p degeneracy

Cavity QED: What happens if we trap the photonsas discrete modes inside a cavity?

3

OutlineCavity QED in the AMO Community

Optical Microwave

Circuit QED: atoms with wires attachedWhat is the cavity?What is the ‘atom’?Practical advantages

Recent Experimental ResultsCoupling a single photon to a SC qubit

Future Directions

4

( )† †01R2

zH a a g a aω σ ω σ σ− += − + + +

atom cavity vacuum Rabi rate = 2g

rmsdEg

d e x

=

≡ − ↑ ↓

Jaynes Cummings Hamiltonian (no losses)

5

cQED at Optical Frequencies

Caltech group H. J. Kimble, H. Mabuchi

State of photons is detected, not atoms.

6State of atoms is detected, not photons.

cQED with Rydberg Atoms at Microwave Frequencies

7

0

1

2

3

0

1

2

,n↑ ,n↓

Excitations are partly photonand partly atom

Zero detuning: 01 Rω ω=

2 ng

Splitting:

Dressed Atom Picture

( )† †01R2

zH a a g a aω σ ω σ σ− += + + +

8

Vacuum Rabi Oscillations

vacuum Rabi frequency 47 kHzgπ

≈

9

A Circuit Analog for Cavity QED2g = vacuum Rabi freq.κ = cavity decay rateγ = “transverse” decay rate

L = λ ~ 2.5 cm

Cooper-pair box “atom”10 µm10 GHz in

out

transmissionline “cavity”

Blais, Huang, Wallraff, SMG & RS, cond-mat/0402216; to appear in PRA

10

Advantages of 1d Cavity and Artificial Atom

10 µm

Vacuum fields:zero-point energy confined in < 10-6 cubic wavelengths

Transition dipole:/g d E= i

0~ 40,000d ea

E ~ 0.2 V/m vs. ~ 1 mV/m for 3-dx 10 larger than Rydberg atom

L = λ ~ 2.5 cm

11

Transmission Line Resonator: Microwave Fabry-Perot

1 ~ 2 6rr r

kTGHzL C

ω π= × >

Lr Cr

Each pole looks

like a single LC

Tran

smis

sion

ω/ω0

κ

12

Resonator as Harmonic Oscillator

Lr Cr2 21 1( )

2 2H LI CV

L= +

mome m ntuLIΦ ≡ =

coordi te naV =

†RMS

2

RMS

( )1 1 10 02 2 2

21r

V V a a

C V

V VC

ω

ω µ

= +

=

= ∼

† 12

ˆ ( )cavity rH a aω= +

13

1 cm

Implementation of Cavities for cQEDSuperconducting coplanar waveguide transmission line

Niobium filmsOptical

lithographyat Yale

gap = mirror

Q > 600,000 @ 0.025 K

• Internal losses negligible – Q dominated by coupling

300mKω = 1 @20n mKγ

6 GHz:

14

Superconducting Circuit Realization of cQED

The ‘atom’

15

Superconducting Tunnel Junction as aCovalently Bonded Diatomic ‘Molecule’

Cooper Pair Josephson Tunneling Splits the Bonding and Anti-bonding ‘Molecular Orbitals’

bondinganti-bonding

(simplified view)

1 pairsN +

pairsN1 pairsN +

pairsN810N ∼ 1 mµ∼tunnel barrier

aluminum island

aluminum island

16

Bonding Anti-bonding Splitting

anti-bonding bonding J 7 GHz 0.3 KE E E− = ∼ ∼Josephson coupling

( )12

ψ ± = ±810 1+

810 1+

810

810

J

2zEH σ= −

bonding

anti-bonding

↑ =

↓ =

17

Coupling to Electric Fields

U E d= − ⋅

Electrical engineering version of the Stark effectL

2

1 2 3

1/1/ 1/ 1/

Cd eLC C C

=+ +

Vg

0

1C

2C

3Cx

gdU VL

σ= −

Transition dipole matrix element

18

Spectrum of Qubit

J

2z x

gE dH V

Lσ σ= − −

Vg

/g g gn C V e=1

EJ

Ene

rgy

gg

gCn

eV

=

Spe

c Fr

eque

ncy

(GH

z)

Cavity Phase

19

Coupling of Effective Spin to Resonator Photons

J

2z xE dH VL

σ σ= − −

V

0

†dc RMS( )V V V a a= + +

Polarizability of ‘atom’ pulls the cavity frequency

2RMS

1 2 3

1/1/ 1/ 1/

Ceg VC C C

=+ +

20

Dispersive Quantum Non-Demolition MeasurementQND = Qubit remains in measured eigenstate

reverse of Nogues et al., 1999 (Ecole Normale)

QND of photon using atoms!

01 r gω ω∆ = −2 2

†01

12r z z

g gH a aω σ ω σ

≈ + + + ∆ ∆

cavity freq. shiftor

ac Stark shift

Lamb shift

Tran

smis

sion

Frequency

↑ ↓

22 /g ∆

21

Measurement of Cavity Transmission(no atom)

Nb resonator20 mK

νr = 6.04133 GHzQ = 2π νr/κ ~ 10,000

Linewidthκ=2π x 0.6MHzκ-1 = 250 ns

22

Measurement of Qubit: Dispersive case

~ 5δθ °

∆

6.04133 GHzrν =rν /JE h

0Pha

se S

hift

2min2 / ~ 5gδθ κ= ∆ °

M/ 5 Hzg π =vacuum Rabi

frequency

min ~ 300 MHz∆

012 ( )rνπ ν∆ = −ν01

23

Gate Sweep with Qubit Crossing Resonator

0

Pha

se S

hift

(a.u

.)

tune qubit thruresonance w/

cavity

0∆ =

rν /JE h

phase shiftchanges signat resonance

24

tune EJ w/small global field

ΦIcoil

Ng

Vgate

tune Eel w/gate

voltage

map out response of cavity as qubit transition is tuned

max0

( )J JE E Cos π Φ= Φ

Φ/Φ0

maxJ

J

EE

Tuning Josephson Energy with Flux

25

0/Φ Φ

gg

gCn

eV

=

0∆ <

0∆ >

ν 01(G

Hz)

0

1

2

Using Cavity to Map Qubit Parameter Space

Transition frequency of qubit01 rω ω∆ = −

max ~ 6.7 GHz ~ 5.25 GHzJ CE E

Cavity phase shift

gg

gCn

eV

=

0/Φ Φ0∆ >

0∆ =

0∆ <

2e

Slice at ∆=00 1 2 3 4

Φ0

26

Dressed Artificial Atom: Resonant Case

? T01 Rω ω=

2g

/ Rω ω

T

2γ κ+

1“vacuum Rabi splitting”

27

First Observation of Vacuum Rabi Splitting for a Single Atom

Thompson, Rempe, & Kimble 1992

Cs atom in an optical cavity(on average)

28

SUMMARY

Coupling a Superconducting Qubit to a Single Photon

Cavity Quantum Electrodynamics

cQED

“circuit QED”

29

FUTURE DIRECTIONS

- strongly non-linear devices for microwave quantum optics- single atom optical bistability- photon `blockade’

- single photon microwave detectors- single photon microwave sources- quantum computation

- QND dispersive readout of qubit state via cavity- resonator as ‘bus’ coupling many qubits- cavity enhanced qubit lifetime