Quantum Optics 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 ‘Circuit QED’
Blais et al. Phys. Rev. A 69, 062320 (2004)
Wallraff et al. [cond-mat/0407325] Nature (in press)
2 Atoms Coupled to Photons
2s 2p Irreversible spontaneous decay into the photon continuum:
2 ps→+1 γ T1 ∼ 1 ns 1s
Vacuum Fluctuations: (Virtual photon emission and reabsorption) Lamb shift lifts 1s 2p 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 Quantum optics with an electrical circuit
Future Directions
4 Cavity Quantum Electrodynamics (cQED)
2g = vacuum Rabi freq. κ = cavity decay rate γ = “transverse” decay rate t = transit time
Strong Coupling = g > κ , γ , 1/t
Jaynes-Cummings Hamiltonian
E E Hˆ =+ ω (aa††+ 1 ) el σσˆˆ− J − g(aσ−++σa) r 2 2 xz2 Electric dipole Quantized Field 2-level system Interaction 5 Cavity QED: Resonant Case ω = ω r 01 with interaction eigenstates are: 1 +=,0 (↑,1 +↓,0 ) 2 1 −=,0 ()↑,1 −↓,0 2
vacuum Rabi oscillations
“dressed state ladders” 6 Microwave cQED with Rydberg Atoms
vacuum Rabi oscillations beam of atoms; prepare in |e>
3-d super- conducting observe dependence of atom final cavity (50 GHz) state on time spent in cavity measure atomic state, or …
Review: S. Haroche et al., Rev. Mod. Phys. 73 565 (2001) 7 cQED at Optical Frequencies
State of photons is detected, not atoms.
… measure changes in transmission of optical cavity 8 (Caltech group H. J. Kimble, H. Mabuchi) A Circuit Analog for Cavity QED 2g = vacuum Rabi freq. κ = cavity decay rate γ = “transverse” decay rate out
cm 2.5 transmission λ ~ line “cavity” L =
Cross-section of mode: DC + B 5 µm E 6 GHz in - ++ - Lumped element equivalent circuit 9 Blais, Huang, Wallraff, SMG & RS, PRA 2004 10 µm Advantages of 1d Cavity and Artificial Atom gd= i E/ Vacuum fields: Transition dipole: zero-point energy confined de~40,000 a in < 10-6 cubic wavelengths 0 10 x larger than E ~ 0.25 V/m vs. ~ 1 mV/m for 3-d Rydberg atom cm 2.5 λ ~ L =
10 µm Cooper-pair box “atom” 10 Resonator as Harmonic Oscillator
1122 L r C H =+()LI CV r 22L
Φ ≡ LI = momentum
ˆ † 1 V = coordinate Hacavity =+ ωr ()a2
† VV=+RMS ()aa
112 ⎛⎞1 CV00= ⎜⎟ ω 22⎝⎠2 ω V = r ∼ 12− µV RMS 2C 11 Implementation of Cavities for cQED Superconducting coplanar waveguide transmission line Q > 600,000 @ 0.025 K
Optical lithography 1 cm at Yale Niobium films gap = mirror
6 GHz: