Permanent: Wiebke Guichard Olivier Buisson Frank Hekking Laurent Lévy Cécile Naud Bernard Pannetier Quantum dynamics in nano Josephson junctions CNRS Université Joseph Fourier Institut Néel- LP2MC GRENOBLE Scientific collaborations: PTB Braunschweig ( Germany) LTL Helsinki (Finland) Rutgers (USA) Projects: ANR QUNATJO PhD: Thomas Weissl Etienne Dumur Ioan Pop Florent Lecocq Aurélien Fay Rapaël Léone Nicolas Didier Julien Claudon Franck Balestro Post-doc: Alexey Feofanov Iulian Matei Zhihui Peng Emile Hoskinson H. Jirari Alex Zazunov
Coherent oscillations in a dc SQUID Anharmonic oscillator: Flux-pulse sequence: MW = 01 measurement 0.8 0.6 0.4 0.2 0.8 0.6 0.4 0.2 RLO = 66 MHz RLO = 122 MHz RLO = 208 MHz T mw (ns) P = -6 dbm = 65 MHz P = 0 dbm = 130 MHz P = +6 dbm = 260 MHz Pesc Pesc E/h (GHz) 01 60 40 20 0 0 1 7 levels Pesc Anharmonicity: 01 12 = 160 MHz 2 5 T MW : tunable 0.8 0.6 0.4 0.2 0 20 40 60 80
Outline Introduction to superconducting qubits Multi-levels artificial atom - current-biased Josephson junction and dc SQUID - quantum measurements - quantum dynamics in a multilevel quantum system - quantum or classical description - optimal control - decoherence processes Two-degrees of freedom artificial atom - inductive dc SQUID - spectroscopy measurements - strong non-linear coupling - coherent oscillations Multi-degrees of freedom system - Josephson junction chains - quantum phase slip - charging effects
Optimal control for a current-biased SQUID (H. Jirari, FH and O. Buisson, EPL 2009) Total Hamiltonian: system control
Statement of the problem Desired time evolution of quantum system: 0> We seek a control field : (t) To have a reasonable control field, we add constraints: - on the amplitude - on its time dependence 0(t)>= d> (example: 1> and 4>)
0 1 Test for a two-level system: -pulse (H. Jirari, FH and O. Buisson, EPL 2009)? guess
0 1 Use -pulse as a guess for optimal control (H. Jirari, FH and O. Buisson, EPL 2009)?
0 1 Effect of -pulse in the presence of other levels (H. Jirari, F. Hekking and O. Buisson, EPL 2009)? guess
0 1 Optimal control in the presence of other levels (H. Jirari, F. Hekking and O. Buisson, EPL 2009)?
Optimal control for more complicated transitions (H. Jirari, F. Hekking and O. Buisson, EPL 2009)? 0 4
Outline Introduction to superconducting qubits Multi-levels artificial atom - current-biased Josephson junction and dc SQUID - quantum measurements - quantum dynamics in a multilevel quantum system - quantum or classical description - optimal control - decoherence processes Two-degrees of freedom artificial atom - inductive dc SQUID - spectroscopy measurements - strong non-linear coupling - coherent oscillations Multi-degrees of freedom system - Josephson junction chains - quantum phase slip - charging effects
Relevant noise sources Heavy filtering and shielding significant fluctuation sources located close to the SQUID L oc R p () R mcs L f LF flux noise C p C msc chip ~ 25mK HF fluctuations from electric circuit quantum fluctuation dissipation theorem LF flux noise MQT analysis Parasitic Two level fluctuators electric circuit (long correlation time ~30ns)
Decoherence processes J. Claudon, A. Fay, L.P. Lévy, and O. Buisson (PRB2006) SQUID coupling terms environment eigenbasis { 0, 1 } linear f ( ) ˆ 01 ˆ 2 C x I 0 p b I z I current fluctuations 2 f ( ) 01 ˆ L C x ˆ b z S 0 p 2 flux fluctuations 1> 0> T 1 T 2 transverse longitudinal relaxation pure dephasing T 1 T 2 Not working at an optimum point!
8 6 4 2 0 J. Claudon, A. Fay, L.P. Lévy, and O. Buisson (PRB2006) Relaxation measurements I b = 2.222 A, b = -0.117 0 1/T 1 for different bias points 01 D m 12 11 10 9 8 7 120 0 0.1 0.2 0.3 0.4 0.5 0.6 D m (s) solid line 1 = 90 ns Q r = 6000 100 80 60 40 0.5 1 1.5 2 2.5 I b (A) Pesc (%) T1 (ns) 01 (GHz) 1 0 r -0.368 0-0.117 0 exp(d m / T 1 ) I c I c
Relaxation measurements J. Claudon, A. Fay, L.P. Lévy, and O. Buisson (PRB2006) Environment at high frequencies (> 5GHz) 12 11 10 9 8 7 120 1/T 1 for different bias points -0.117 0 100 Effective resistance ~ 10 5! 0.5 1 1.5 2 2.5 Long T I b (A) 1 for a connected circuit 80 60 T1 (ns) 01 (GHz) L oc R p () gold capacitor -0.368 0 consistent with skin effect estimations 40 I c I c
J. Claudon, A. Fay, L.P. Lévy, and O. Buisson (PRB2006) Low power spectroscopy 3 12 11 10 9 8 01 (GHz) 2 1 0 I b (A) I c -0.5 0 0.5 b / 0 7 60 30-0.368 0-0.117 0 1> 0> 10 5 I c I c (ns) T 2-1 8 8.1 8.2 8.3 8.4 8.5 (GHz) 0.5 1 1.5 2 2.5 I b (A) Pesc (%)
Low power spectroscopy J. Claudon, A. Fay, L.P. Lévy, and O. Buisson (PRB2006) Main effect: inhomogenous broadening due to current noise 12 11 10 9 8 01 (GHz) 7-0.368 0-0.117 0 60 30 10 (ns) Pesc (%) 8 8.1 8.2 8.3 8.4 8.5 (GHz) 01 I 2 I with 2 I 6 na kt L OC 5 I c I c No free parameter!! 0.5 1 1.5 2 2.5 I b (A)
At zero current: Hoskinson, Lecocq et al, PRL (2009) Manipulation at zero current bias ˆ 2 ( ˆ 2 H P X X ˆ 4 ) p (I b, b ) Manipulation Microwave current: I b (t)
Hoskinson, Lecocq et al, PRL (2009) Manipulation at zero current bias called: the Camelback phase qubit
At zero current: Hoskinson, Lecocq et al, PRL (2009) Camelback phase qubit ˆ 2 ( ˆ 2 H P X X ˆ 4 ) p (I b, b ) Manipulation Microwave current: I b (t)
(1) Spectroscopy at zero current bias Hoskinson, Lecocq et al, PRL (2009) (2) (3) V? Nanosecond flux pulse and switching current measurement (1) (2) (3) 01 = 10.17 GHz The probability of escape increases when the system is excited FWHM = 18 MHz
Demonstration of optimal current bias Frequency is maximum at zero current biased 01 0 I Width 01 (FWHM) due to low frequency fluctuations of 01 Close to the optimal line Flux noise limited : 40μ (RMS) Away from the optimal line Current noise limited : 9nA (RMS)
Side band resonances Side bands disappears @ sweet point
Coherent oscillations along the optimal line Rabi oscillation 140 120 100 80 60 40 20 Rabi Frequency (MHz) 0.6 0.5 0.4 0.3 0.2 f p = 10.6 GHz f Rabi = 38 MHz T 2,Rabi = 57 ns Escape probability Ramsey oscillations 0.4 0.1 0 20 40 60 80 100 120 Pulse duration [ns] 0 0 0.5 1 1.5 MW amplitude [10 dbm/20 ] Energy relaxation 0.35 0.3 T 1 100 ns 0.25 0.2 Escape probability 0.15 0 10 20 30 Ramsey delay [ns]
Coherent oscillations along the optimal line Rabi oscillation Anharmonicity Ramsey oscillations 0,6 Energy relaxation 0,5 0,4 0,3 0,2 T 1 =200ns Escape probability 0,1 0 200 400 600 800 Delay time (ns)
Spectroscopy versus flux bias, TLS limitation I bias = -73nA ~ 20 parasitical two level system (TLS) per GHz with a coupling to the Qubit varying from 5MHz to 150MHz
Conclusion Improvement of the coherence time along the optimal line. New potential along this line, preliminary results on double escape processes. Limitations : - Residual dephasing can be explained by a 40 0 RMS flux noise. - Too many parasitical two levels systems. - Unknown sources of noise (low frequency current noise) Current works: - improvement on the Josephson junction quality