Quantum Imaging with Trapped Ions

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Quantum Imaging with Trapped Ions
Joachim von Zanthier1 Christoph Thiel1 Thierry
Bastin2 Enrique Solano3 Girish S. Agarwal4
1Institut für Optik, Information und Photonik,
Universität Erlangen-Nürnberg, Germany 2Institut
de Physique Nucléaire, Atomique et de
Spectroscopie, Université de Liège au Sart
Tilman, Belgium 3Departamento de Química Física,
Universidad del País Vasco - Euskal Herriko
Unibertsitatea, Bilbao, Spain 4Department of
Physics, Oklahoma State University, Stillwater,
USA
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Quantum Imaging with Trapped Ions
Content
I. First and Second Order Correlations in
the Fluorescence Light of trapped
Ions II. Using higher Order Correlation
Functions for Quantum Imaging III.
Quantum Imaging of a photon source and an aperture
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First-order correlation function
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I. First-order correlations in the fluorescence
light of trapped ions
two trapped ions
U. Eichmann et al., Phys. Rev. Lett. 70, 2359
(1993)
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first-order correlation function
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Mollow Triplett
-4 -2 0 2
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(w w0)/G
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I. Second-order correlations in the fluorescence
light of trapped ions
no which-way-information available regarding two
possible quantum paths
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Introducing (Glaubers) correlation functions
R. J. Glauber, Phys. Rev. 130, 2529 131, 2766
(1963)
Spatial (intensity) correlation functions
Roy J. Glauber
for his contribution to the quantum theory of
optical coherence
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II. Using higher order correlation functions for
Quantum Imaging
e
N trapped2-level ions
g
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Example Second order correlation function in the
fluorescence light of two
trapped ions
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Example Second order correlation function in the
fluorescence light of two
trapped ions
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Example Second order correlation function in the
fluorescence light of two
trapped ions
-1
-0
G. S. Agarwal et al., PRA 70, 063816 (2004)
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Higher order correlations in the fluorescence
light of trapped ions
Far-field
Laser pulse

Intensity-intensity correlation G(2)
N-times Intensity correlation G(N)
R2
d
R1
Trap
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Example 4th order correlation function for 4
ions and 4 detectors (N 4)
for any detector positions d1, d2, d3, d4
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Higher order correlations in the fluorescence
light of trapped ions
G(2)
r2 r1
Detector position
r2 const.
r2 -r1
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One can show
for any n N, one can always find suitable
detector positions so that one obtains a single
sinusoidal modulation with wave number
C. Thiel, T. Bastin, J. Martin, E. Solano, J. von
Zanthier, G. S. Agarwal, PRL 99, 133603 (2007)
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Higher order correlations in the fluorescence
light of trapped ions
G(2)
r2 r1
Detector position
r2 const.
r2 -r1
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Resolution in classical optics
Abbes theory of the microscope to construct an
image from an object the first diffraction order
in the Fourier plane must be at least visible
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III. Application quantum imaging of 8 trapped
ions
example 8 ions with separation 2l detected
with versus
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III. Application quantum imaging of 8 trapped
ions
example 8 ions detected with
versus
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III. Application quantum imaging of an object
Light from two atoms passing through an aperture
Ch. Thiel et al., quant-ph/0805.1831
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III. Application quantum imaging of an object
classical and quantum imaging of a rectangular
aperture

• in analogy to classical diffraction theory
• Fresnel-Kirchhoff diffraction
• Fraunhofer approximation
• paraxial approximation

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III. Application quantum imaging of an object
Generalization of the quantum imaging scheme
Quantum imaging of an aperture with G(2)
G(2)
for r2 - r1
1
r1
0
r2
detector position
r2 r1
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Conclusion
- Higher order correlation functions show
interference pattern even if measured
with (in 1. order) incoherent light
- Interference pattern of second order
correlation function displays visibility of
100 and resolution enhanced by a factor of 2
- Same scheme can be used for quantum imaging of
an object, either in the Fourier
plane of the object or in the image plane of
a lens
- Same scheme can be used for generating
entangled states in long-living internal levels
of the photon emitting atoms (see
poster session today and Thursday)
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Thank you