detection of finite frequency current moments with a dissipative resonant circuit
DESCRIPTION
Detection of finite frequency current moments with a dissipative resonant circuit. Sendai 07. Thierry Martin Centre de Physique Théorique & Université de la Méditerranée. With: A. Zazunov (CPT, LPMMC) M. Creux (CPT, thesis) E. Paladino (Universita di Catania) Crépieux (CPT) - PowerPoint PPT PresentationTRANSCRIPT
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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
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Outline:
•Noise
•Situations where finite frequencies are needed
•Capacitive coupling schemes…
•Inductive coupling scheme with dissipation
•Noise correlations
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The noise is the signal (R. Landauer)
Ambiguity: symmerize or not-symmetrize noise?
Not important at « low » frequencies
Important at « high » frequencies
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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
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- 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:
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Noise + noise cross-correlations Crépieux PRB03
in a nanotube:
HERE, POSITIVE CORRELATIONS FOR AN INTERACTING FERMIONIC SYSTEM !!!
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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
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Noise measurement: Inductive coupling
FIRSTWithout dampingLesovik + Loosen JETP97,Gavish…PRB2000
Repetitive
Mesurement of the charge:
histogram
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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
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Non-symmetrized noise,
once again
Capacitive coupling schemes
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Experimental implementation: Deblock et al.
Also:
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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)
….
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Theoretical suggestion. Measure charge noise due to a nearby mesoscopic circuit?
Use continuity equation to convert charge noise to current noise ?
PRL05
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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
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Noise measurement: Inductive coupling
NOWWith damping
Propose to measure
excess width and
excess
displacement
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Free oscillator (LC circuit, coordinate q)
Keldysh
Resistance: coupling to a bath of oscillators
Caldeira-Legett
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LC Greens function is dressed by bath
Add coupling to the mesoscopic circuit + η
Integrate out LC circuit
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Derivatives with respect to η to get charge
and fluctuations
(contains all higher moments of current
time derivatives) NOW EXPAND in α !
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Result for fluctuations:
Generalized susceptibility
Bath spectral function
N(ω) Bose Einstein distribution
Square of a Lorentzian flucuations diverge with zero damping !
Noise correlators
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Underdamped regime, low T
Finite temperature
and overdamped
regime
(Sharp cusps are for no-damping)
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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
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Low temperature,
under damped
Fix T, vary γ/2<T
or (inset)
Fix γ, vary T
(similar behavior,
« LC is a bath »)
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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…
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Hamiltonian for the circuit with two inductances
Minimal coupling:
For series circuit
For parallel circuit
Charge fluctuations with 2 possible wirings:
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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)
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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.
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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
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CNRS POST DOC POSITION AVAILABLE:
24 months
Equipe de Nanophysique du CPT, Marseille
Theoretical mesoscopic
physics/nanophysics
Molecular electronics, QI,…
Deadline April 30th
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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.
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Model
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Photo-assisted current
1 quasiparticle, 2quasiparticle, and Andreev current
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Andreev current blowup