QUBITS AS DEVICES TO DETECT THE THIRD MOMENT OF SHOT NOISE FLUCTUATIONS

1. QUBITS AS DEVICES TO DETECTTHE THIRD MOMENT OF SHOT NOISE FLUCTUATIONS V. Brosco1, R. Fazio2 , F. W. J. Hekking3, J. P. Pekola4 1. Dipartimento di Fisica, Università di Pisa , Italia 2. Scuola Normale Superiore, Pisa, Italia 3. Laboratoire de physique et Modèlisation des Milieux Condensés, CNRS & Université Joseph Fourier , Grenoble, France 4. Low Temperature Laboratory, Helsinki University of Technology, Helsinki, Finland

2. Non-equilibrium current noiseassociated with the randomness in the trasmission of charge through conductors Two-level quantum system with tunable hamiltonian I(t) = < I > + dI(t) Motivation: Qubits as devices to detect the third moment of shot noise fluctuations

3. OUTLINE • SQUID dynamics • Quantum systems as noise detectors • MODEL, MASTER EQUATION, TWO-LEVEL CASE, RABI OSCILLATIONS • Experimental setup

4. Classical dynamics of a DC-SQUID L=0 One dimensional approximation One dimensional classical dynamics: Static solution : dj/dt = 0 U(x) Dissipative solution x

5. Quantum dynamics of a DC-SQUID Three energy scales: Localized states : Rabi oscillations in presence of microwave Macroscopic quantum tunneling (MQT)

6. SQUID dynamics in presence of noise Flux and current fluctuations : Time-dependent potential : Effective time-dependent hamiltonian: System plus bath model: Bath hamiltonian Squid hamiltonian Interaction potential

7. MODEL Bath operator System operator Hamiltonian S+B Observed quantum system System bath interaction Basic hypothesis • Stationarity of the bath • Weak coupling • Markov approximation Pertubative approach Local equations

8. Master Equation • Interaction picture equation : • Basic evolution equation for the system density matrix : • Master Equation : Time independent! Relaxation matrix:

9. Relaxation matrix Second order contribution :

10. Two limiting cases • Secular approximation : • Transverse coupling :

11. Third moment spectrometer Protocol • Initial state preparation : Third order effect ! • Measurement of the ground state population : Assumptions • Two level system with transverse coupling : • Negligible frequency dependence of the third order coefficients:

12. Results Third order oscillations in the ground state populations Third order peak !

13. Effects of a microwave field Two-level case Transverse coupling hypothesis: Microwave contribution System-bath hamiltonian

14. Rabi Oscillations Transversal field Longitudinal field Rabi peak Rabi peak w0 peak Third order peak Microwave contribution

15. t Shot noise measurements Experimental setup Interaction with the bath Effect of the pulse Measurement procedure : System response Excited states Probing pulse Vout Biasing current IP IN t Ground state

16. Summary • Dynamics of Josephson devices in presence of noise. • Third order master equation for a quantum system coupled with a bath. • Qubits as detectors of third moment. • Experimental setup. Open problems • Study of other types of noise. • Effect of noise on other types of superconducting circuits