2015 AMO Summer School. Quantum Optics with Propagating Microwaves in Superconducting Circuits I. Io-Chun, Hoi
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1 2015 AMO Summer School Quantum Optics with Propagating Microwaves in Superconducting Circuits I Io-Chun, Hoi
2 Outline 1. Introduction to quantum electrical circuits 2. Introduction to superconducting artificial atom 3. Quantum optics with superconducting circuits 4. Single atom scattering
3 Introduction to quantum electrical circuits
4 Quantum electrical circuits Coherent superposition states: Charge Flux Q Φ Macrosopic system Properties: The superposition states collapse when measure. Probabilistic character. Charge on a capacitor: Current or magnetic flux in an inductor: ( ) ( )
5 Basic elements: Conventional electrical circuits First transistor 1947 Dual-core Intel processor Fig. from Intel Introduced 2007 Clock speed >3GHz Number of transistors 820million Manufacturing technology 45nm Fig. from Intel
6 Introduction to superconducting artificial atom
7 Superconducting circuits are like LEGOS
8 Basic Elements of Superconducting Circuits Josephson Junction: Non-disspative nonlinear inductance Al Tunnel barrier between two superconductors C L L J Capacitance Inductance Al
9 Fabrication of Josephson Junction
10 Constructing linear quantum electrical circuits U Quantization +Q Q Classical physics: H = Q2 2C + Φ2 2L H = p2 2m kx2 C Φ L Analogy with a moving particle in a harmonic potential ω = 1 LC GHz H = ˆQ 2 2C + ˆΦ 2 2L Quantum mechanics: H = ω(a a ) ω Φ ˆΦ, ˆQ = i M. H. Devoret, A. Wallraff, and J. M. Martinis. Superconducting qubits: A short review
11 Constructing nonlinear Quantum circuit: Artificial atom Replace linear inductance by Josephson junction (Nonlinear inductance) U = E J cosφ U Energy(EJ) L J = C 4eI c cos π Φ ext Φ 0 L J Transition become addressable! Anharmonicity: α = ω 01 ω 12 Emission spectrum Phi (rad) ω 12 ω 01 0 φ Frequency
12 How to operate electrical circuits quantum mechanically? Avoid dissipation Avoid broaden energy levels Work at low temperatures Provide reset of the circuit(ground state) k B T << ω << Δ s Superconducting gap energy ω /2π 4 8GHz
13 Family of superconducting artificial atom Fig. from Michel Devoret. Linneaus summer school in quantum engineering Focus on Cooper Pair Box and Transmon! J. Clarke and F. K. Wilhelm. Nature, 453: , G. Wendin and V. S. Shumeiko Low Temp. Phys., 33(9): , 2007.
14 Artificial atom I: The Single-Cooper Pair Box E J / E c < 1 H = 1 2 E chσ z 1 2 E Jσ x Map to a spin 1/2 particle in magnetic field. 4 1> EJ/Ec=0.5 0> Depends on external flux 3 Energy(Ec) 2 1 1/ 2( 0>- 1>) > 0.2 1/ 2( 0>+ 1>) ng 0.8 1> 1.0 E ch = E Q (1 2n g ) C Σ = C g + C J E Q = 4E C = (2e)2 2C Σ σ z,σ x :Pauli matrix n g = C g V g /(2e) Coherent oscillations between ground state and excited state in time domain, demonstrated by Y. Nakamura et al. Nature, 398: , But the coherence time is short (few ns)due to charge noise!
15 Decoherence of artificial atom (Effect from the environment) Relaxation rate Γ 01 Pure dephasing rate Γ ϕ Enviroment Enviroment ω 01 Random switching 1 0 ω 01 ω 01 + δω 01 (t) Phase randomization e iω 01t
16 Artificial atom II: The transmon 20 < E J / E c < EJ/Ec=30 C S Energy(Ec) ng Insensitive to the charge noise Long coherence time. Jens Koch et al. Physical Review A, 76(4):042319, 2007.
17 Energy(Ec) ng EJ/Ec= Energy(Ec) ng EJ/Ec= Energy(Ec) ng EJ/Ec= Energy(Ec) ng EJ/Ec=30
18 Energy(EJ) Natural atom Optical photons Phi (rad) Superconducting artificial atom Microwave photons Compare with optical photon, the frequency of microwave photon is 10 6 less.
19
20 Comparison of the toolboxes Quantum optics Superconducting circuits Detect I, Q Optical photons Microwave photons
21 Advantages of quantum circuit E 0 d Atom-light interaction on single photon level 1. Photons and atom interaction can be engineered 2. The photons can be guided by waveguides; beam alignment is not needed. 3. Large vacuum field E 0,rms 0.2V / m due to small mode volume 4. Standard on-chip fabrication technique 5. Tunable transition energy of the atom 6. Mechanical stable
22 Quantum optics with superconducting circuits
23
24 Resonant scattering Fig: O. Astafiev, et al. 327, 840 Science (2010)
25 Resonant scattering in 3D space Incoming light Atom/dipole emits light
26 Resonant scattering in 3D space Incoming light Atom/dipole emits light Sum The extinction signal is due to interference G. Wrigge et al. Nature Phys. 4, 60 (2008). M. Tey et al. Nature Phys. 4, 924 (2008). Fig. from U. Håkanson
27 Resonant scattering in 1D waveguide D.E. Chang et al. Nature Physics 3, 807(2007) Fully coherent: no transmission, perfect reflection.
28 Resonant scattering in 1D waveguide D.E. Chang et al. Nature Physics 3, 807(2007) Fully coherent: no transmission, perfect reflection. Al λ >> d Point like atom/dipole! λ cm Wavelength of EM field d μm Size of atom Relaxation dominated by transmission line. O. Astafiev, et al. 327, 840 Science (2010) IoChun, Hoi et al. PRL 107, (2011) Al
29 Resonant scattering in 1D waveguide D.E. Chang et al. Nature Physics 3, 807(2007) Fully coherent: no transmission, perfect reflection. Fig. from E. Olsson & S. M. Nik JJ Al 2nm λ >> d Point like atom/dipole! λ cm Wavelength of EM field d μm Size of atom Relaxation dominated by transmission line. O. Astafiev, et al. 327, 840 Science (2010) IoChun, Hoi et al. PRL 107, (2011) Al
30 Quantum circuit model φ 2 L L 0 L 0 L 0 L 0 φ 1L φ 0 φ 1R φ 2 R C C C JS φ J C 0 C 0 C 0 C 0 Relaxation rate into 1D transmission line, indicates the strength of coupling! Γ 10 ω 2 01C 2 c Z C Σ = C c + C Z = JS 4C Σ L 0 C 0
31
32
33 Transmission and reflection Strong interaction limit: Fully coherent.
34
35 Saturation of transmission Nonlinear nature of the atom!
36 Transmission comparing to theory
37 Coherent vs Incoherent scattering Ω p / 2π [MHz] Output Power (nw) Total scattered 2 V R BW=10MHz BW=100MHz V R 2 Elastic scattered Input field ω 10 Ω p Ω p /2π 30 MHz 83 MHz 250 MHz [dbm] P p BW δω p /2π I.-C. Hoi et al.
38 Low power Tunable artificial atom Only 0-1 transition occurs! High power Only two-photon transition occurs! f 12 f 01 Extract: E J,Max = 13GHz E c = 590MHz E J / E c = 23 ( f 12 + f 01 )/2 Φ ext / Φ 0 Φ ext / Φ 0 Two-Photon Transition
39 Fully coherent: perfect reflected by the atom. measure the phase coherent signal.
40
41 Two-Tone Spectroscopy
42 Two-Tone Spectroscopy
43 Higher level effect 1.0 T ω p = ω GHz Pump off -135dBm -131dBm -127dBm -123dBm -119dBm -115dBm (Low Power) GHz ω p /2π 7.4 Anharmonicity: α = ω 01 ω MHz ω 12 /2π = 6.38GHz ω 10 /2π = 7.1GHz
44 Mollow triplet T p,1 P 01 [dbm] ω p /2π [GHz] ω 10 Ω p B.R. Mollow, Phys.Rev. 188, 1969 (1969) O. Astafiev, et al. 327, 840 Science (2010)
45 T P c [dbm] ω p /2π [GHz] A. A. Abdumalikov, Jr et al. PRL 104, (2010)
46 To be continued
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