Strong tunable coupling between a charge and a phase qubit

Transcription

1 Strong tunable coupling between a charge and a phase qubit Wiebke Guichard Olivier Buisson Frank Hekking Laurent Lévy Bernard Pannetier Aurélien Fay Ioan Pop Florent Lecocq Rapaël Léone Nicolas Didier Julien Claudon Franck Balestro CNRS Université Joseph Fourier Institut Néel- LP2MC GRENOBLE Zhihui Peng Emile Hoskinson Alex Zazunov Scientific collaborations: PTB Braunschweig ( Germany)- EuroSQIP project LTL Helsinki (Finland) KTH Stockholm (Sweden) Rutgers (USA) Projects: EuroSQIP.

2 Introduction In the last decade: new experiences in quantum mechanics using superconducting quantum circuits - realisation of a two level system (Saclay) - anharmonic quantum oscillator (multi-level system) (Grenoble) - two level system coupled to high Q cavity (Yale,Zurich,Boulder) - two coupled qubits (Control-NOT, i-swap, ) (NEC,Delft,Santa Barbara) Tunable coupling qubit 1 qubit 2 Motivations: - quantum dynamics in macroscopic system - new quantum phenomena * very strong coupling with external field * strong coupling with environment - model system for the quantum nano-electronics

3 Outline Introduction to superconducting quantum circuits Description of the circuit dc-squid: phase qubit Asymmetric transistor: charge qubit Tunable coupling between the charge and phase qubit Summary

4 Introduction of the superconducting state In many metals, T smaller than a critical temperature : the conduction electrons condenses to electron pairs : Cooper pairs Δ e 2e All the pairs forms a Macroscopic Quantum State: Ψ G > Ψ G > is analog to the coherent state of a laser beam the phase is very well defined Ψ G > is a very stable ground state because no excitations below the gap Persistent current without any decay! To perform complex quantum experiments, we need excited levels Josephson junction

5 The Josephson energy (I) Coupling between two superconductors : a tunnel barrier n s Supra 1 Supra 2 n 1 e i! 1 Tunnel barrier n 2 e i! 2 x Josephson equations : I = I c sin(! 1 "! 2 ) V =! 0 2" d(# 1 $# 2 ) dt where I c =!" and! 0 = 2e h = "15 T.m 2 2eR n The Josephson energy : E J =! 0 I c 4" Energy = " EJ cos(! ) 1 "! 2

6 The Josephson energy (II) Josephson inductance: Linear limit: sin(!) "! Josephson equations : Josephson junction Because of «sin» current-phase relation: SQUID: Non-linear inductance : L V I = I c = 0 I) = " 2 # I # 0 2" Inductance: sin(!) d! dt L J = 1 / I " 0 2! I J ( 2 C (1! ( I C ) C / 3) I b Josephson energy: flux dependent ϕ Φ b I c I c! 0 Ic E J (! b) = cos( "! b /! 0) 2" I c (µa) (loop inductance neglected)

7 The charging energy Capacitance effect: 2e Q= -2e Q=+2e The charging energy: (2e) Ec = 2C 2 Energy = E C 2 ˆn

8 The Josephson junction dynamics I b H = E C # I cos(! ˆ) $! ˆ 2" 2 0 b ˆ n Q Conjugate variables: $ E J [ n ˆ,!ˆ ] = i C I c level quantization ϕ ω p E >> c E J E c blocks the charge Δϕ>>1 ΔQ<<1 Coulomb blocade E J blocks the phase E << c E J Δϕ<<1 ΔQ>>1 Supra

9 Outline Introduction Description of the circuit dc-squid: phase qubit Asymmetric transistor: charge qubit Tunable coupling between the charge and phase qubit Summary

10 Hybrid superconducting two-qubits system Asymmetric Cooper pair transistor (ACPT) Superconducting island ~ 0.12 µm nm dc-squid: superconducting loop interrupted by 2 Josephson junctions Nanofab I bias V g Phase qubit Charge qubit 10 µm 3-angle shadow evaporation

11 Outline Description of the circuit dc-squid: phase qubit Asymmetric transistor: charge qubit Tunable coupling between the charge and phase qubit Summary

12 dc-squid: phase qubit I b J. Claudon et al., PRL 2004 H = E C # I cos(! ˆ) $! ˆ 2" 2 0 b ˆ n $ E A quantum anharmonic oscillator H s = J I control (t) Excitation Microwave flux: Φ(t) level quantization Φ = 0.02 Φ 0 ΔU (I b,φ S ) Δν=13MHz ω p (I b,φ S )

13 Quantum measurements J. Claudon, A. Fay, E. Hoskinson, and O. B, PRB2007 I b ΔU (I b,φ b ) ϕ Φ b (t) I measure (t) A nano-second flux pulse reduces the barrier Hysteretic junction: escape leads to voltage ω p (I b,φ b ) Γ 2 Γ 1 Γ 0 I b (µa) I c V (µv) Probability of escape Nanosecond flux pulse amplitude (Φ 0 )

14 Phase qubit spectroscopy Φ S = 0.02 Φ 0 I bias = 1890 na Microwave flux Nanosecond flux pulse I b (µa) I c Φ = 0.02 Φ 0 ν S (GHz) P esc

15 Coherent oscillations in a dc SQUID J. Claudon, A. Fay, E. Hoskinson, and O. B, PRL2004, PRB2008 Anharmonic oscillator: E/h (GHz) ν Flux-pulse sequence: ν MW =ν 01 7 levels Anharmonicity:ν 01 ν 12 = 160 MHz 5 T MW : tunable measurement P esc P esc P esc Rabi like oscillations! Ω RLO = 66 MHz Ω RLO = 122 MHz Ω RLO = 208 MHz T mw (ns) P = -6 dbm Ω 1 /2π = 65 MHz P = 0 dbm Ω 1 /2π = 130 MHz P = +6 dbm Ω 1 /2π = 260 MHz

16 Outline Description of the circuit dc-squid: phase qubit Asymmetric transistor: charge qubit Tunable coupling between the charge and phase qubit Summary

17 Charge qubit spectroscopy Asymmetric Cooper pair transistor 500nm n g = C g V g /2e δ(φ T, Φ S, I b ) H ˆ T = (2e)2 ( n ) " n g ) 2 " #e 2C j cos($ /2)cos(% ) d ) 0.5 µm # " &e j sin($ /2)sin(% ) d ) A charge qubit: P esc ν (GHz)

18 Charge qubit frequency versus n g C 2 n g C 1 ν T (GHz) P esc n g = 0.5 ν (GHz) n g - 0.5

19 Charge qubit frequency versus δ E j2 δ(φ T, Φ S, I b ) n g = 0.5 E j1 ν T (GHz) Josephson asymmetry optimal point (δ = 0, n g = 0.5) Quantronium Saclay optimal point (δ = π, n g = 0.5) 0 π/2 π

20 Rabi oscillations (charge qubit) V g µwave duration Α µw T 2 Rabi ~ 110 ns P esc µw duration (ns)

21 Relaxation (charge qubit) P esc T 1 ~ 0.8 µs

22 Outline Description of the studied circuit dc-squid : phase qubit Asymmetric transistor: charge qubit Tunable coupling between the charge and phase qubit Summary

23 Coupling between the two qubits Coupling?

24 Coupled qubits spectroscopy Spectroscopy at I bias = 1890 na n g =1/2 I 50% (µa) Frequency (GHz) Phase qubit Frequency (GHz) Charge qubit

25 Spectroscopy versus ng ACPT ν T Resonant coupling at n g = 0.5 dc-squid ν S ν S does not depend on n g ν r = GHz g ~ 110 MHz

26 Spectroscopy versus flux Spectroscopy at I bias = na na I 50% (µa) Frequency (GHz) Frequency (GHz) ν r ~ 16.6 GHz g ~ 250 MHz ν r ~ 10.4 GHz g ~ 900 MHz ν r ~ 18.1 GHz g ~ 160 MHz Two qubits can be in resonance from 9 GHz to 20 GHz. Strong variation of the coupling strength.

27 Resonant coupling Coupling varies from 60 MHz to 1100 MHz g (GHz) factor of 18 ν r (GHz)

28 Electrical schematic of the circuit

29 Hamiltonian of the coupled qubits Capacitive coupling Josephson coupling Capacitance asymmetry Josephson energy asymmetry

30 Resonant coupling A. Fay et al., PRL 100, (2008) We consider λ = µ = 41.6% g (GHz) ν r (GHz)

31 Resonant coupling A. Fay et al., PRL 100, (2008 We consider λ = 37.7% and µ = 41.6% g (GHz) ν r (GHz) If transistor was symmetric (λ=µ=0) coupling would be zero

32 Outline Description of the studied circuit dc-squid: phase qubit Asymmetric transistor: charge qubit Tunable coupling between the charge and phase qubit Summary

33 Summary Two different qubits Strong tunable coupling between a charge and phase qubit (x18) Zero coupling and non-zero coupling