Experimental observation of a photon bouncing ball Marco
Experimental observation of a photon bouncing ball Marco Finazzi GRANIT workshop, February 19 th 2010
2 /19 Quantum-optical analogy y Electric field distribution in a weakly-guiding structure …obeys paraxial wave equation: By changing… Marco Finazzi - GRANIT workshop, February 19 th 2010
3 /19 Quantum-optical analogy – some examples… Light in an infinite waveguide array: the analogue of a particle in a lattice (e. g. discrete diffraction, discrete solitons, etc. ) Tilted index profile or curved array: the analogue of an applied field or (e. g. Bloch oscillations, Zener tunneling, dynamic localization, etc. ) Waveguide side-coupled to an infinite array: the analogue of discrete-continuum coupling (e. g. non-classical decay dynamics, etc. ) Marco Finazzi - GRANIT workshop, February 19 th 2010
4 /19 Fabrication of guides Titanium mask Ag+ Na+ (K+ ) N 03 Molten Salts (330 °C) Ag+ Na+ Titanium mask phosphate glass Marco Finazzi - GRANIT workshop, February 19 th 2010 5 µm opening
5 /19 Retrieving information about the wavefunction Light intensity at the end of guide (no information on “time” evolution of wavefunction) CCD Sensor e Commercial phosphate glass heavily doped with Er and Yb. X The cumulative up-conversion process 80 9 Green fluorescence Marco Finazzi - GRANIT workshop, February 19 th 2010 ag st nm LD Ys tag e
STOM – scanning tunneling optical microscopy 6 /19 (www. witec. de) m n 0 0 -2 60 Signal proportional to the light intensity in the guide (the guide must sustain a single vertical mode) Marco Finazzi - GRANIT workshop, February 19 th 2010
Infinite waveguide array 7 /19 t=0 z=z 1 z=z 2 z=z 3 z=z 4 Marco Finazzi - GRANIT workshop, February 19 th 2010 t=t 1 t=t 2 t=t 3 t=t 4
Discrete diffraction 8 /19 Optical map Topography G. Della Valle, S. Longhi, P. Laporta, P. Biagioni, L. Duò, and M. Finazzi, Appl. Phys. Lett. 90, 261118 (2007) Marco Finazzi - GRANIT workshop, February 19 th 2010
Quantum bouncing ball Particle in a “triangular” potential well m m g ü Aperiodic motion of the center of mass ü Airy wavefunctions ü Wavefunction collapses and revivals ü Fractional revivals Marco Finazzi - GRANIT workshop, February 19 th 2010 9 /19
Quantum bouncing ball optical analogue 10 /19 “Whispering gallery” waveguide Effective one-dimension potential well Marco Finazzi - GRANIT workshop, February 19 th 2010 Eigenvalues and wave packet spectra
Wavefunction collapses and revivals 11 /19 Center of mass position Experiment Theory Classical trajectory Marco Finazzi - GRANIT workshop, February 19 th 2010 G. Della Valle, M. Savoini, M. Ornigotti, P. Laporta, V. Foglietti, M. Finazzi, L. Duò, and S. Longhi, Phys Rev. Lett. 102, 180402 (2007)
Quantum bouncing ball: wavefunctions 12 /19 First two bounces First collapse 2 First fractional revival First integer revival Marco Finazzi - GRANIT workshop, February 19 th 2010
13 /19 The quantum Zeno effect Zeno of Elea (5 th century BC) reductio ad absurdum paradoxes of motion The arrow paradox: “If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless” [Aristotle, Physics VI: 9, 239 b 5] Observation collapse of the wavefunction Re-initialization of the process dynamics (“observed pot” paradox) Marco Finazzi - GRANIT workshop, February 19 th 2010
Non-exponential decay Nature 387, 575 (1997) Ultra-cold Na atoms in an optical potential mimicking an electron moving in a periodic lattice with a DC electric field Marco Finazzi - GRANIT workshop, February 19 th 2010 14 /19
15 /19 Quantum Zeno and Anti-Zeno effect Zeno Marco Finazzi - GRANIT workshop, February 19 th 2010 Anti-Zeno
The optical Zeno effect: theory Optical analogue of discrete-continuum coupling 16 /19 Sample for the optical Zeno effect S. Longhi, Phys. Rev. Lett. 97, 110402 (2006) Marco Finazzi - GRANIT workshop, February 19 th 2010
The optical Zeno effect: experiment 17 /19 P. Biagioni, G. Della Valle, M. Ornigotti, M. Finazzi, L. Duò, P. Laporta, and S. Longhi, Opt. Exp. 16, 3762 (2008) Marco Finazzi - GRANIT workshop, February 19 th 2010
Conclusions 18 /19 • Quantum-optical analogies represent a rather unique approach to directly visualize wave-function dynamics • Scanning tunneling optical microscopy with hollow-pyramid tips is the ideal tool for quantitative analysis of quantum-optical analogies • Observation of collapses and revivals in an optical analogue of a quantum bouncer • First experimental demonstration of tunneling decay inhibition in a waveguide array by the optical Zeno effect Marco Finazzi - GRANIT workshop, February 19 th 2010
19 /19 Acknowledgments Politecnico di Milano Matteo Savoini Paolo Biagioni Lamberto Duò Politecnico di Milano Marco Ornigotti Giuseppe della Valle Stefano Longhi Paolo Laporta Istituto di Fotonica e Nanotecnologie Vittorio Foglietti Marco Finazzi - GRANIT workshop, February 19 th 2010
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