Doing Atomic Physics with Electrical Circuits: Strong Coupling Cavity QED
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1 Doing Atomic Physics with Electrical Circuits: Strong Coupling Cavity QED Ren-Shou Huang, Alexandre Blais, Andreas Wallraff, David Schuster, Sameer Kumar, Luigi Frunzio, Hannes Majer, Steven Girvin, Robert Schoelkopf Yale University
2 Atoms Coupled to Photons s 1s p Irreversible spontaneous decay into the photon continuum: p 1 s+ γ T 1 ns 1 Vacuum Fluctuations: (Virtual photon emission and reabsorption) Lamb shift lifts 1s p degeneracy Cavity QED: What happens if we trap the photons as discrete modes inside a cavity?
3 Outline Cavity QED in the AMO Community Optical Microwave Circuit QED: atoms with wires attached What is the cavity? What is the atom? Practical advantages Recent Experimental Results Coupling a single photon to a SC qubit Future Directions 3
4 Jaynes Cummings Hamiltonian (no losses) ω σ ω σ σ ( + ) 01 z H = + Ra a+ g a + a g = de rms d e x atom cavity vacuum Rabi rate = g 4
5 cqed at Optical Frequencies State of photons is detected, not atoms. Caltech group H. J. Kimble, H. Mabuchi 5
6 cqed with Rydberg Atoms at Microwave Frequencies State of atoms is detected, not photons. 6
7 Dressed Atom Picture ω σ ω σ σ ( + ) 01 z H = + Ra a+ g a + a Zero detuning: 3 ω = ω 01 R Splitting: 1 ng 1 0 Excitations are partly photon and partly atom 0, n, n 7
8 Vacuum Rabi Oscillations vacuum Rabi frequency g π 47 khz 8
9 A Circuit Analog for Cavity QED g = vacuum Rabi freq. κ = cavity decay rate γ = transverse decay rate transmission line cavity L = λ ~.5 cm out 10 µm 10 GHz in Cooper-pair box atom Blais, Huang, Wallraff, SMG & RS, cond-mat/04016; to appear in PRA 9
10 Advantages of 1d Cavity and Artificial Atom Vacuum fields: zero-point energy confined in < 10-6 cubic wavelengths g = d ie/ E ~ 0. V/m vs. ~ 1 mv/m for 3-d L = λ ~.5 cm Transition dipole: d ~40,000 ea x 10 larger than Rydberg atom 0 10 µm 10
11 Transmission Line Resonator: Microwave Fabry-Perot Each pole looks like a single LC L r C r Transmission κ ω r 1 kt = ~π 6GHz > LC r r ω/ω 0 11
12 Resonator as Harmonic Oscillator 1 1 H = ( LI) + CV L L r C r Hˆ = ω ( a a+ ) cavity V = V a+ a r 1 RMS( ) C 0 V 0 = ω ωr VRMS = 1µ V C Φ LI = V = momentum coordinate 1
13 Implementation of Cavities for cqed Superconducting coplanar waveguide transmission line Q > 0.05 K Optical lithography at Yale 1 cm Niobium films gap = mirror 6 GHz: ω = 300mK n Internal losses negligible Q dominated by coupling γ 13
14 Superconducting Circuit Realization of cqed The atom 14
15 Superconducting Tunnel Junction as a Covalently Bonded Diatomic Molecule (simplified view) 8 N 10 N +1 pairs N pairs aluminum island tunnel barrier aluminum island N pairs N +1 pairs 1µ m Cooper Pair Josephson Tunneling Splits the Bonding and Anti-bonding Molecular Orbitals anti-bonding bonding 15
16 Bonding Anti-bonding Splitting 1 ψ = ± ± ( ) E E = E 7 GHz 0.3 K anti-bonding bonding J Josephson coupling = = bonding anti-bonding H = E J σ z 16
17 Coupling to Electric Fields U = E d Transition dipole matrix element 1/ C d = el 1/ C 1+ 1/ C + 1/ C 3 V g C 1 L C C 3 0 Electrical engineering version of the Stark effect U = d V L σ g x 17
18 Spectrum of Qubit H E = J σ z d L V g σ x Energy V g E J Spec Frequency (GHz) Cavity Phase 1 n = C V / e g g g n g = C V g g 18 e
19 H E J z = σ g Coupling of Effective Spin to Resonator Photons d x Vσ L = e V RMS V = V + V a + a 1/ C 1/ C + 1/ C + 1/ C 1 3 ( ) dc RMS V 0 Polarizability of atom pulls the cavity frequency 19
20 Dispersive Quantum Non-Demolition Measurement QND = Qubit remains in measured eigenstate = ω 01 ωr g H g 1 g ωr + σz a a+ ω01 + σz cavity freq. shift or ac Stark shift Lamb shift g / reverse of Nogues et al., 1999 (Ecole Normale) QND of photon using atoms! Transmission Frequency 0
21 Measurement of Cavity Transmission (no atom) Nb resonator 0 mk Linewidth κ=π x 0.6MHz κ -1 = 50 ns ν r = GHz Q = π ν r /κ ~ 10,000 1
22 Measurement of Qubit: Dispersive case ν 01 = π ( ν ) 01 ν r ν r EJ / h ν r = GHz min ~ 300 MHz Phase Shift 0 δθ ~5 δθ = g / minκ ~5 g / π = 5MHz vacuum Rabi frequency
23 Gate Sweep with Qubit Crossing Resonator ν r = 0 EJ / h tune qubit thru resonance w/ cavity Phase Shift (a.u.) 0 phase shift changes sign at resonance 3
24 Tuning Josephson Energy with Flux V gate N g max EJ = EJ Cos( π Φ ) Φ 0 tune E el w/ gate voltage Φ I coil tune E J w/ small global field E E J max J Φ/Φ 0 map out response of cavity as qubit transition is tuned 4
25 Φ / Φ ν 01 (GHz) Using Cavity to Map Qubit Parameter Space Transition frequency of qubit Cavity phase shift > 0 < C gvg ng = e Slice at =0 = ω E max ~ 6.7 GHz J ω 01 r Φ / Φ E C 0 Φ 0 > 0 = 0 < 0 e ~ 5.5 GHz n g = C 5 g V e g
26 Dressed Artificial Atom: Resonant Case ω = ω 01 R? T T g γ + κ vacuum Rabi splitting 1 ω ω / 6 R
27 First Observation of Vacuum Rabi Splitting for a Single Atom Cs atom in an optical cavity (on average) 7 Thompson, Rempe, & Kimble 199
28 SUMMARY Cavity Quantum Electrodynamics cqed circuit QED Coupling a Superconducting Qubit to a Single Photon 8
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 9
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