Experiments: T. Niemczyk et al., Nature Physics 6, 772(2010) Title: Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime 01mm10x) qubit position 5 mm 20 um VNA+ e300K amplifier 4 K cryogenic amplifier o2c 0.6K circulator 1 um 1 um 15 mK lbit resonator YYY C L e FIG 1: Quantum circuit and experimental setup
Experiments: T. Niemczyk et al., Nature Physics 6, 772 (2010) Title: Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime FIG. 1: Quantum circuit and experimental setup
P. Forn-Diaz and J E Mooij et al., PRL 105, 237001(2010) arXiv:1005.1559 Spectrum of the flux qubit coupled to the lc resonator. 9 001 g85 Ble 22r sideband Qubit >10 更重-0.5x10 001 8 Photon 002 excited 6 Two-photoh qubit blue 403 sidebands 二 0246810 ①/Φ-0.5 x10
P. Forn-Diaz and J. E. Mooij et al., PRL 105, 237001 (2010). arXiv: 1005.1559. Spectrum of the flux qubit coupled to the LC resonator
RAPID COMMUNICATIONS PHYSICAL REVIEW A 78. 051801(R)(2008) Numerically exact solution to the finite- size dicke mod Qing-Hu Chen, Yu-Yu Zhang, Tao Liu, and Ke-Lin Wang 4 Center for Statistical and Theoretical Condensed Matter Physics, Zhejiang Normal University, Jinhua 321004, China Department of Physics, Zhejiang University, Hangzhou 310027, China Department of Physics, Southwest University of Science and Technology, Mianyang 621010, China Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China (Received 26 December 2007: published 3 November 2008) RAPID COMMUNICATIONS PHYSICAL REVIEW B 81. 121105(R)(2010) Quantum phase transition in the sub-Ohmic spin-boson model: An extended coherent-state approach Yu-Yu Zhang, Qing-Hu Chen, 2.1, and Ke-Lin Wang.4 Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China -Center for Statistical and Theoretical Condensed Matter Physics, Zhejiang Normal University, Jinhua 321004 People's Republic of china Department of Physics, Southwest University of Science and Technology, Mianyang 621010, People's Republic of China Department of Modern Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China (Received 27 January 2010; revised manuscript received 14 February 2010: published 26 March 2010
Theory of Qubit-Oscillator Systems(Biased QRM) QHC, Tao Liu, and Kelin Wang, ar Xiv: 1007. 1747 Chin. Phys. Lett. 29, 014208(2012) The flux qubit behaves effectively as a two-level system )/ 6+△a)/2 △ is the tunnel coupling The model hamiltonian can be expressed as H=-(cos 0o. +sin (o )+oaa+gla +a)o Wa is the atomic Larmor frequency w is the cavity frequency +(2n∞,) sinb=△/hon=∠ 2+(2·8.) g is the qubit-resonator coupling strength, enhanced by Josephson junction inductance Cavity QED Circuit QED g/c 103 0.01 0.1 Nature 431, 162(2004). Nature Physics 4, 686(2008) Nature Physics 6, 772 (2010)
Theory of Qubit-Oscillator Systems (Biased QRM) QHC, Tao Liu, and Kelin Wang, arXiv: 1007.1747, Chin. Phys. Lett. 29, 014208 (2012) ( )/ 2 H q z x = − + ωq is the atomic Larmor frequency, ω is the cavity frequency. The flux qubit behaves effectively as a two-level system The model Hamiltonian can be expressed as 2 2 2 2 (2 ) sin (2 ) q p x q p x = + = = + I I (cos sin ) ( ) 2 q H a a g a a z x z + + = − + + + + Δ is the tunnel coupling g is the qubit-resonator coupling strength, enhanced by Josephson junction inductance g/ω ~ 10-6 Cavity QED: 10-3 0.01 0.1 Circuit QED Nature 431, 162 (2004). Nature Physics 4, 686 (2008) Nature Physics 6, 772 (2010)
Numerically exact solution to QRM for E#0 (8+0 QHC et al. arXiv: 1007. 1747 Transformation(w=1) A=a+a, a=8 B=a-a AT A H g △/2BB-g2+ Ansatz for the wavefunction A a+a A ∑。"(-1)an|n) -e m-g ∑ mg+1-2.DB, aguerre polynomia o For strong coupling or highly excited states, much better than exact diagonalization in a-space
A a , B a = + = − Transformation (ω=1) = g 2 2 2 2 A A g H B B g + + − + − = − − + ( ) 0 0 1 tr tr N n n A N n n n B c n d n = = = − 2 2 2 2 m mn n m n m mn n m n m g c D d Ec m g d D c Ed − − − = − + − = Ansatz for the wavefunction Numerically exact solution to QRM for ε≠0 (δΦ≠0) QHC et al, arXiv: 1007.1747 ( ) ( ) 1 2 2 0 0 ! ! 0 0 n n A A A g ga A a A a n n n e + + + − − + = = = ( ) ( ) ( ) 2 2 1 2 ! 2 exp 2 (4 ) ! m mn B A n m n m B m A D m n m m n g g L g n − − = − = Laguerre polynomial ◇ For strong coupling or highly excited states, much better than exact diagonalization in a-space