Thierry Martin

Centre de Physique Théorique &

Université de la Méditerranée

Detection of finite frequency current moments with a

dissipative resonant circuit

Sendai 07

With:A. Zazunov (CPT, LPMMC)M. Creux (CPT, thesis)E. Paladino (Universita di Catania)A. Crépieux (CPT)cond-mat/0702247, PRB 74, 115323 2006

Outline:

•Noise

•Situations where finite frequencies are needed

•Capacitive coupling schemes…

•Inductive coupling scheme with dissipation

•Noise correlations

The noise is the signal (R. Landauer)

Ambiguity: symmerize or not-symmetrize noise?

Not important at « low » frequencies

Important at « high » frequencies

Test entanglement: Bell inequalities in NSTorres EPJB 99Lesovik EPJB 2001Chtchelkatchev PRB 2002Diagnosis via a DC measurement.

Energy filters +E -E on each armOnly split Cooper pairs in the two arms2 spin filters with opposite directions on each arm

- Assume local density matrix (LDM)

- Convert particle number into noise correlators

-Derive corresponding inequality for zero -Frequency noise

THEN

- Compute noise correlations for an NS fork using QM

- Choose angles

RESULT: maximal violation of Bell inequality.

On the one hand, τ should be large (ω=0 noise)On the other hand, it should be « small » (irreducible correlations)

Number correlators in terms of noise:

Noise + noise cross-correlations Crépieux PRB03

in a nanotube:

HERE, POSITIVE CORRELATIONS FOR AN INTERACTING FERMIONIC SYSTEM !!!

Nanotube with leads: finite frequency cross correlations are needed to measure charges

(Lebedev PRB05)

Several round trips

No round trips

Alternative: LL with leads with an impurity in the middle

(Trauzettel et al. PRL04)

High frequencies also needed

Noise measurement: Inductive coupling

FIRSTWithout dampingLesovik + Loosen JETP97,Gavish…PRB2000

Repetitive

Mesurement of the charge:

histogram

Two unsymmetrized noise correlators:

emission to the measuring circuit

absorption from the measuring circuit

Measured noise (from charge fluctuations on the capacitor)

is a combination of emission and absorption term.

X charge on capacitor, η adiabtic parameter

Lesovik 97, Gavish 00

1) Symmetrized correlator does not happen here

2) Measured noise diverges with η=0

Non-symmetrized noise,

once again

Capacitive coupling schemes

Experimental implementation: Deblock et al.

Also:

ALSO: Combination of inductive and capacitive coupling

Yale (Schoelkopf group 97)

Paris (Glattli group 2004)

HBT experiment in GHz range for photons emitted by the conductor (noise of noise)

….

Theoretical suggestion. Measure charge noise due to a nearby mesoscopic circuit?

Use continuity equation to convert charge noise to current noise ?

PRL05

THIS WORK: quantum LC circuit with dissipation

Need to address this problem from a microscopic

point of view:

•What is the origin of η ?

Look at « old » literature:

Radiation Line width for Josephson effect

(Larkin+ Ovchinikov, JETP 60’s)

Line width occurs because of fluctuations in the neighboring circuit.

•For noise measurement, add dissipation modeled by

a bath of oscillators.

•Use Keldysh approach assuming bath+ LC decoupled

at t=-infinity

Noise measurement: Inductive coupling

NOWWith damping

Propose to measure

excess width and

excess

displacement

Free oscillator (LC circuit, coordinate q)

Keldysh

Resistance: coupling to a bath of oscillators

Caldeira-Legett

LC Greens function is dressed by bath

Add coupling to the mesoscopic circuit + η

Integrate out LC circuit

Derivatives with respect to η to get charge

and fluctuations

(contains all higher moments of current

time derivatives) NOW EXPAND in α !

Result for fluctuations:

Generalized susceptibility

Bath spectral function

N(ω) Bose Einstein distribution

Square of a Lorentzian flucuations diverge with zero damping !

Noise correlators

Underdamped regime, low T

Finite temperature

and overdamped

regime

(Sharp cusps are for no-damping)

Average charge on the LC circuitfirst order term in inductive coupling α vanishes

for stationary case

Third moment vanishes for incoherent tranport

No singular behavior for zero damping

Low temperature,

under damped

Fix T, vary γ/2<T

or (inset)

Fix γ, vary T

(similar behavior,

« LC is a bath »)

What about noise correlations?

How to measure them with a LC circuit ?

Two inductances are needed: in parallel

or in series

Then invert the wiring…

Hamiltonian for the circuit with two inductances

Minimal coupling:

For series circuit

For parallel circuit

Charge fluctuations with 2 possible wirings:

Subtract signals with two different wirings

Define 2 noise cross correlators:

Charge fluctuations on the capacitor:

The result is of course real (properties of correlators)

Simple illustration: noise correlations at finite frequency

Noise correlations

display singularities at

Chemical potential differences, as expected.

Negative noise correlations if measuring circuit has

« low enough » temperature.

CONCLUSION:

-Inductive coupling scheme to measure the noise, Using a dissipative LC circuit. -Dissipation included in Caldeira Legett model-Essential to get a finite result for the noise.-Yet dissipation blurs the noise measurement.-Measured third moment identified. -Temperature changes the sign of both noise and third moment

cond-mat/0702247, PRB 74, 115323 2006

CNRS POST DOC POSITION AVAILABLE:

24 months

Equipe de Nanophysique du CPT, Marseille

martin@cpt.univ-mrs.fr

Theoretical mesoscopic

physics/nanophysics

Molecular electronics, QI,…

Deadline April 30th

Photoassisted Andreev reflection as a probe to finite frequency noise (with Nguyen T. K. Thanh)

DC current in detector circuit

pairs of electrons

can be emitted from/

absorbed in the

Superconductor.

Model

Photo-assisted current

1 quasiparticle, 2quasiparticle, and Andreev current

Andreev current blowup