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

This research paper explores the use of qubits as devices to detect the third moment of shot noise fluctuations. It discusses the dynamics of a Josephson device in the presence of noise and presents a third-order master equation for a quantum system coupled with a bath. The experimental setup and open problems are also presented.

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

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  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

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