Non-linear driving and Entanglement of a quantum bit with a quantum readout

Transcription

1 Non-linear driving and Entanglement of a quantum bit with a quantum readout Irinel Chiorescu Delft University of Technology

2 Quantum Transport group Prof. J.E. Mooij Kees Harmans Flux-qubit team visitors Yasunobu Nakamura (NEC Japan, ) Kouichi Semba (NTT Japan, ) PhD students Alexander ter Haar Adrian Lupascu Jelle Plantenberg postdocs Patrice Bertet Irinel Chiorescu students technical staff collaborations NTT, NEC, MIT, TU Delft (theory), U Munich acknowledgements FOM (NL), IST (EU), ARO (US)

3 Outline basics about the flux-qubit qubit initialization, operation & readout Rabi oscillations, Ramsey fringes present status - extreme stability during qubit operation - strong microwave driving multi-photon induced coherent oscillations experimental demonstration of entanglement quantum bit quantum readout (squid) conclusions

4 3 Josephson-junctions Quantum Bit J.E. Mooij et al, Science, 285, 1036 (1999) superconducting loop, with 3 Josephson junctions 2 are identical and the 3rd is smaller (α= ) Josephson Potential: U=ΣE J I u = U/E J u = 2 + α - cosγ 1 - cosγ 2 - αcos(γ 2 - γ 1 + 2πf) φ 1 = (γ 1 - γ 2 )/2, φ 2 = (γ 1 + γ 2 )/2 u = 2(1 - cosφ 1 cosφ 2 ) + 2αsin 2 (φ 1 - πf)

5 Josephson potential - phase space 2 wells separated by a barrier for f=0.5, symmetric barrier α=0.8, f=0.5 T in T out T out

6 Flux Qubit two level system C. van der Wal et al, Science, 290, 773 (2000) Exact diagonalisation: two levels at the bottom of the spectra Two wells separated by a barrier Persistent currents of opposite direction and SQUID critical current qubit persistent current Microwave induced excitation level structure see also, J. Friedman et al, Nature, 6, 43 (2000)

7 Coherent oscillations Magnetic resonance with a single, macroscopic quasi-spin Bloch sphere Ψ>=α >+β > Rabi oscillations microwave excitation with frequency ω and amplitude A coherent rotations with Ω Rabi A A MW pulse ω = E Ω Rabi A e> g>

8 Qubit operated at the magic point Hamiltonian and eigenstates H = -ε/2 σz /2 σx tan2θ = / ε 0 = cosθ + sinθ 1 = -sinθ + cosθ Initialization, ε = 0 Q = 0 = ( + )/ 2 Operation, ε = 0 Q = α 0 + β 1 Q 0 MW pulse ON (rotating frame) <σx> = α 2 - β 2 1 Q MW pulse OFF (lab frame) 1 0 shift Readout, ε > 0 Q = α 0 + β 1

9 Switching event measurements Device qubit merged with the SQUID strong coupling L I pulse ~ns rise/fall time t Readout bias current to switch the SQUID ramping generates the shift (preserving the qubit information) switching current depends on qubit state (spin up or down) pulse height: I sw0 < I b < I sw1 shift

10 Single shot resolution (in an ideal sample) switching probability (%) ground state excited state pulse AW generator (V)

11 Sample E J /E C = E C = 7.36 GHz α = 0.8 = 3.4 GHz I p = 3 na large junctions I c = 2 µa strong coupling L=10 ph shunt capacitance C = 10 pf bias line R b = 150 Ω voltage line R v = 1 kω

12 Cavity, wiring

13 Qubit spectroscopy Energy (GHz) total flux (Φ 0 ) (I sw - I bg ) / I ctr (%) F (GHz) GHz 16 GHz π = 3.4 GHz Φ ext / Φ 0

14 Rabi: pulse scheme RF line: one microwave pulse with varying length bias line: Ib pulse trigger MW pulse operation Ib pulse read-out time voltage line: detection of the switching pulse

15 Rabi coherent oscillations decay time 150 ns switching probability (%) A = 0 dbm A = -6 dbm Rabi frequency (GHz) F Larmor = 6.6 GHz pulse length (ns) A = -12 dbm MW amplitude 10^(A/20) (a.u.) I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, J.E. Mooij, Science, 299, 1869 (2003)

16 Fast oscillations Switching probability (%) Psw (%) Psw (%) RF pulse length (ns) RF pulse length (ns) RF pulse length (ns)

17 Ramsey interference Ramsey: two π/2 pulses with varying time in between trigger π/2 free run π/2 Ib pulse time operation read-out

18 Ramsey fringes 0 MHz F L = 5.61 GHz detuning P SW (%) time between two π/2 pulses (ns) 310 MHz

19 Ramsey interference Ramsey: decoherence time τ φ 20 ns 80 P SW (%) π/2 π/ distance between two p/2 pulses (ns) F L = 5.7 GHz, df= 220 MHz, TRamsey: 4.5 ns

20 Relaxation measurements one π pulse and read-out pulse delayed trigger π delay time Ib pulse time operation read-out 100 switching probability (%) delay time (µs) 8.3 ns, A=-12dBm 6 ns, A=-9dBm 4.5 ns, A=-6dBm 3.2 ns, A=-3dBm ns, A=0 dbm exp fit of A=-12dBm τ φ = 870 ns

21 quasi-particle traps strong coupling with the MW line heat sinks on the current and voltage lines current injection: high frequency noise ground via the shunt capacitance Sample (2003) qp traps V heat sink I b

22 Spectroscopy Larmor frequency (GHz) Resonant frequencies (GHz) = GHz I q = 272 na spectroscopy peaks fit: E J /E C =.834 E C =7.281 GHz α= F/F 0 12 Q + ω DF/F 0 Q Q - ω (Q + ω)/2 Q/2 ω switching probability (%) level repulsion GHz persistent current 272 na spectroscopy peaks: Q qubit ω plasma frequency 2.91GHz Q+/-ω sidebands 2-, 3-photon peaks Q/3 3 (Q+3) /2 Q/2 Q frequency (GHz) Q Q+3

23 Rabi oscillations at the magic point low coherence time, but extreme stability of the qubit energy levels switching probability (%) distance between pulses Rabi oscillations: F mw = Rabi oscillations: F mw = + F Rabi 20 Hadamard gate Ramsey with π pulses (Hadamard) pulse length (ns)

24 Ramsey fringes at the magic point coherence time ~15-20 ns (mostly limited by the relaxation time) 6.1 P sw (%) Frequency (GHz) = GHz distance between two p/2 pulses (ns)

25 Coherence time at the magic point coherence time ~20 ns (mostly limited by the relaxation time) τ φ and τ r (ns) Larmor frequency (GHz) Φ-Φ 0 /2 (mφ 0 ) when optimizing the readout τ φ ~120 ns switching probability (%) Ib=2.841µA Ib=2.976µA Ib=2.565µA delay between two p/2 pulses (microseconds)

26 Multi-photon processes ONE-PHOTON F mw =7.16GHz TWO-PHOTON F mw =3.62 GHz Switching probability (%) A = -14 dbm A = -18 dbm A = -15 dbm A = -17 dbm A = -22 dbm pulse length (ns) A = -19 dbm

27 Multi-photon processes One-photon Rabi frequency (GHz) one-photon Rabi frequency J 1 (b10 A/20 ) with b=0.92, =5.344 GHz A/20 (a.u.) power calibration (check the b fit parameter) Two-photon Rabi frequency (GHz) Rabi frequency: n = J n (ε mw /F L ) can be renormalized ~ by noise ( < ) two-photon Rabi frequency J 2 (b10 A/20 ) with =5.344 GHz, b= A/20 (a.u.)

28 Coherent rotations in the non-linear regime several peaks in the Fourier transform of the oscillations Rabi frequencies higher than the Larmor frequency 7 6 Rabi frequency (FFT) (GHz) =5.03 GHz b=1.41 J 1 (b10 A/20 ) ^(A/20)

29 Peaks in FFT of the Rabi oscillations (GHz) Numerical simulations H/h=ω 0 σ z /2+ω x σ x /2+(ω 1 σ x cosωt)/2 ~12.25 GHz 6 ω w 1 (GHz) ω x =0.1 GHz 2ω 0

30 Qubit entangled with a quantum readout QUBIT, two-level system hf L SQUID, harmonic oscillator 0>, 1> 0>, 1>,..., N> MI q I circ... hω p microwave field 11> 10> 12>... F L 00> ω p 01> 02>

31 Coherent oscillations of the coupled system qubit Larmor frequency 7.16 GHz plasma frequency : 2.91 GHz coupled system at GHz 10> blue-side band 00> 11> 01> switching probability (%) Rabi oscillations F=10.15 GHz, A=-5dBm 26 qubit: F 24 L =7.16 GHz squid: ω pl =2.91 GHz pulse length (ns) switching probability (%) Rabi oscillations F=10.15 GHz, A=3dBm qubit: F L =7.16 GHz squid: ω pl =2.91 GHz pulse length (ns)

32 Blue-side band qubit Larmor frequency 6.43 GHz, plasma frequency : 2.91 GHz coupled system at 9.38 GHz Rabi oscillations at F L =6.43 GHz switching probability (%) coherent oscillations 01> 11> coherent oscillations 00> 10> pulse length (ns) 10> 11> 00> 01> π pulse

33 switching probability (%) qubit Larmor frequency 6.43 GHz plasma frequency : 2.91 GHz coupled system at 9.38 GHz p pulse Rabi oscillations at F L =6.43 GHz Red-side band switching probability (%) red-side band: coherent oscillations 01> <10 switching probability (%) pulse length (ns) red-side band 3.52 GHz F L = 6.43 GHz blue-side band 9.38 GHz +10 db MW frequency (GHz) after π after 2π pulse length (ns) 11> 10> π 2π 00> 01>

34 Conclusion entanglement of the qubit with its quantum readout multi-photon induced coherent oscillations very strong (non-linear) qubit driving, F Rabi >F L qubit operated at the magic point extreme stability of the qubit operation τ rel 1 µs, τ Rabi 150 ns Ramsey interference: decoherence time 20 ns