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