1. 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

2. 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

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

4. L=0 One dimensional approximation Static solution : dj/dt = 0
Classical dynamics of a DC-SQUID
L= 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. 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

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

9. Second order contribution :
Relaxation matrix
Second order contribution :

10. Two limiting cases
Secular approximation :
Transverse coupling :

11. 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 !

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

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

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

15. 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

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