nano Josephson junctions Quantum dynamics in

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1 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

2 Coherent oscillations in a dc SQUID Anharmonic oscillator: Flux-pulse sequence: MW = 01 measurement 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) levels Pesc Anharmonicity: = 160 MHz 2 5 T MW : tunable

3 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

4 Optimal control for a current-biased SQUID (H. Jirari, FH and O. Buisson, EPL 2009) Total Hamiltonian: system control

5 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>)

6 0 1 Test for a two-level system: -pulse (H. Jirari, FH and O. Buisson, EPL 2009)? guess

7 0 1 Use -pulse as a guess for optimal control (H. Jirari, FH and O. Buisson, EPL 2009)?

8 0 1 Effect of -pulse in the presence of other levels (H. Jirari, F. Hekking and O. Buisson, EPL 2009)? guess

9 0 1 Optimal control in the presence of other levels (H. Jirari, F. Hekking and O. Buisson, EPL 2009)?

10 Optimal control for more complicated transitions (H. Jirari, F. Hekking and O. Buisson, EPL 2009)? 0 4

11 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

12 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)

13 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!

14 J. Claudon, A. Fay, L.P. Lévy, and O. Buisson (PRB2006) Relaxation measurements I b = A, b = /T 1 for different bias points 01 D m D m (s) solid line 1 = 90 ns Q r = I b (A) Pesc (%) T1 (ns) 01 (GHz) 1 0 r exp(d m / T 1 ) I c I c

15 Relaxation measurements J. Claudon, A. Fay, L.P. Lévy, and O. Buisson (PRB2006) Environment at high frequencies (> 5GHz) /T 1 for different bias points Effective resistance ~ 10 5! Long T I b (A) 1 for a connected circuit T1 (ns) 01 (GHz) L oc R p () gold capacitor consistent with skin effect estimations 40 I c I c

16 J. Claudon, A. Fay, L.P. Lévy, and O. Buisson (PRB2006) Low power spectroscopy (GHz) I b (A) I c b / > 0> 10 5 I c I c (ns) T (GHz) I b (A) Pesc (%)

17 Low power spectroscopy J. Claudon, A. Fay, L.P. Lévy, and O. Buisson (PRB2006) Main effect: inhomogenous broadening due to current noise (GHz) (ns) Pesc (%) (GHz) 01 I 2 I with 2 I 6 na kt L OC 5 I c I c No free parameter!! I b (A)

18 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)

19 Hoskinson, Lecocq et al, PRL (2009) Manipulation at zero current bias called: the Camelback phase qubit

20 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)

21 (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 = GHz The probability of escape increases when the system is excited FWHM = 18 MHz

22 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)

23 Side band resonances Side bands sweet point

24 Coherent oscillations along the optimal line Rabi oscillation Rabi Frequency (MHz) f p = 10.6 GHz f Rabi = 38 MHz T 2,Rabi = 57 ns Escape probability Ramsey oscillations Pulse duration [ns] MW amplitude [10 dbm/20 ] Energy relaxation T ns Escape probability Ramsey delay [ns]

25 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, Delay time (ns)

26 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

27 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