V. Brosco1, R. Fazio2 , F. W. J. Hekking3, J. P. Pekola4

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Presentation transcript:

V. Brosco1, R. Fazio2 , F. W. J. Hekking3, J. P. Pekola4 QUBITS AS DEVICES TO DETECT THE 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

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

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

L=0 One dimensional approximation Static solution : dj/dt = 0 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

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

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

System bath interaction 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

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

Second order contribution : Relaxation matrix Second order contribution :

Two limiting cases Secular approximation : Transverse coupling :

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

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

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

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

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

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