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QUBITS AS DEVICES TO DETECT THE THIRD MOMENT OF SHOT NOISE
FLUCTUATIONS
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
V. Brosco1, R. Fazio2 , F. W. J. Hekking3, J. P. Pekola4
Motivation:Qubits as devices to detect the third moment of shot noise
fluctuations
Two-level quantum system with tunable hamiltonian
Non-equilibrium current noise associated with the randomness in the trasmission of charge through conductors
I(t) = < I > + I(t)
p(I)
I< I >
OUTLINE
•SQUID dynamics
•Quantum systems as noise detectors
MODEL, MASTER EQUATION, TWO-LEVEL CASE, RABI OSCILLATIONS
•Experimental setup
Classical dynamics of a DC-SQUID
Dissipative solution
U(
)
Static solution : d/dt = 0
x
U(x)
One dimensional classical dynamics:
L=0 One dimensional approximation
Quantum dynamics of a DC-SQUID
Three energy scales:
Localized states :
Macroscopic quantum tunneling (MQT)
Rabi oscillations in presence of microwave
SQUID dynamics in presence of noise
Flux and current fluctuations :
Time-dependent potential :
Effective time-dependent hamiltonian:
System plus bath model:
Squid hamiltonian
Interaction potential
Bath hamiltonian
MODEL
Hamiltonian S+BBath
operator
System operator
System bath interaction
Observed quantum system
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:
Relaxation matrix
Second order contribution :
Two limiting cases
• Secular approximation :
• Transverse coupling :
Third moment spectrometerAssumptions
• 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 !
Results
Third order peak !
Third order oscillations in the ground state populations
Effects of a microwave field
Microwave contribution
System-bath hamiltonian
Two-level case
Transverse coupling hypothesis:
Rabi OscillationsMicrowave
contribution
Transversal fieldRabi peak
Third order peak
Longitudinal fieldRabi peak
0 peak
Experimental setup Shot noise measurements
Measurement procedure :
t
IN
IP
t
VoutExcited states
Ground state
Interaction with the bath
Effect of the pulse
Biasing currentProbing pulse
System response
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