Presentazione di PowerPoint

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Scheme for Entangling Micromeccanical
Resonators by Entanglement Swapping
Paolo Tombesi
Stefano Mancini David Vitali
Stefano Pirandola
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Microworld is quantum, macroworld is classical.
Is there a boundary, or classical physics
naturally emerges from quantum physics ?
How far can we go in the search and demonstration
of macroscopic quantum phenomena ?

• Recent spectacular achievements
• Superposition of two magnetic flux states in a
  rf-SQUID (Stony Brook, 2000)
• Entanglement of internal spin states of two
  atomic ensembles (Aarhus, 2001)
• Interference of macromolecules with hundred atoms
  (Vienna 2003)
• 40 photons-microwave cavity field in a
  superposition of macroscopically
• distinct phases (Paris 2003)
• several optical photons in a superposition with
  distinct phases (Roma 2004)

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Displacement x is generally given by the
superposition of many acoustic modes. A single
mode description is valid when the detection
is limited to a frequency bandwidth including a
single mechanical resonance.
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Lucent Techn. Lab.
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Very light mirrors
A matter wave grating such as that created by
cold atoms in an optical lattice acts as a
dielectric mirror
R. Scheunemann, F. S. Cataliotti, T. W. Hänsch,
and M. Weitz Physical Review A (Rapid
Communication) 62, 051801(R) (2000)
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Huang et al. Nature 2003
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Focused light beams are able to excite Gaussian
acustic modes in which only a small portion of
the mirror vibrates
x(r,t)???a e-iWt aeiWt)exp-r2/w2 fundamental
Gaussian mode where w is its waist.
Frequency W and mass M
H ?d2r P(r,t) x(r,t)
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Represented by the Gaussian characteristic
function
F(m,n,z,0) e- n 2Nth

• F(m,n,z,t) is the evolution of F(m,n,z,?)
  which is still Gaussian
• F(m,n,z,t) e- ? V ? T
  xT (m1,m2,n1,n2,z1,z2 )
  

Where A,B,C,D,E, F depend on r, Nth, ?, t , I is
the identity 2x2 matrix and Z diag 1,-1
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Vac , Vbc
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The basic idea of entanglement swapping is to
transfer the bi-partite entanglement within the
near pairs Alice-Charlie and Charlie-Bob to the
distant pair Alice-Bob, by means of a suitable
local operation and classical communica- tion
performed by Charlie.
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The final output state ?ab is still Gaussian
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Optimal value t 1µs ENout 1.1
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Living time of entanglement depends on ?-1 with
? the vibrations damping constant
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Experimental detection
Requires the measurement of the relative distance
Xrel xa-xb and the total momentum Ptot papb
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Pinard et al. in Europhys. Lett. 05
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Conclusion
A scheme for entangling two micromechanical
oscillators by entanglement swapping, exploiting
the radiation pressure force and changing the
nature of entanglement, from optomechanical to
pure mechanical
The mechanical entanglement could last for quite
long time
It could be a sensitive test to discriminate
different theories of quantum gravity
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