Thierry Martin

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Detection of finite frequency current moments
with a dissipative resonant circuit

• Thierry Martin
• Centre de Physique Théorique
• Université de la Méditerranée

Sendai 07

• With
• A. Zazunov (CPT, LPMMC)
• M. Creux (CPT, thesis)
• E. Paladino (Universita di Catania)
• 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 NS
Torres EPJB 99 Lesovik EPJB 2001 Chtchelkatchev
PRB 2002 Diagnosis via a DC measurement.
Energy filters E -E on each arm Only split
Cooper pairs in the two arms 2 spin filters with
opposite directions on each arm
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Number correlators in terms of noise

• - 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, t should be large (?0 noise) On
the other hand, it should be  small 
(irreducible correlations)
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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
FIRST Without damping Lesovik Loosen
JETP97, GavishPRB2000
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, ? adiabtic
parameter Lesovik 97, Gavish 00 1) Symmetrized
correlator does not happen here 2) Measured noise
diverges with ?0
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Capacitive coupling schemes
Non-symmetrized noise, once again
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Experimental implementation Deblock et al.
Also
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.
ALSO Combination of inductive and capacitive
coupling
Paris (Glattli group 2004)
Yale (Schoelkopf group 97)
HBT experiment in GHz range for photons emitted
by the conductor (noise of noise)
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PRL05
Theoretical suggestion. Measure charge noise due
to a nearby mesoscopic circuit? Use continuity
equation to convert charge noise to current noise
?
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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 ? ?
• Look at  old  literature
• Radiation Line width for Josephson effect
• (Larkin Ovchinikov, JETP 60s)
• 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
NOW With 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 ?
Integrate out LC circuit
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Derivatives with respect to ? to get charge and
fluctuations
(contains all higher moments of current time
derivatives) NOW EXPAND in a !
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Result for fluctuations
Noise correlators
Generalized susceptibility
Bath spectral function
N(?) Bose Einstein distribution Square of a
Lorentzian flucuations diverge with zero
damping !
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Underdamped regime, low T
(Sharp cusps are for no-damping)
Finite temperature and overdamped regime
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Average charge on the LC circuit first order term
in inductive coupling a 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 ?/2ltT or (inset) Fix ?, 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 martin_at_cpt.univ-mrs.fr 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