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