Transcript M. Greiner et al., Nature 415, 39 (2002)

Interazioni e transizione superfluido-Mott
Interacting bosons in a lattice
Bose-Hubbard model for interacting bosons in a lattice:
SUPERFLUID
MOTT INSULATOR
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Long-range phase coherence
Poissonian number fluctuations
Gapless excitation spectrum
Compressible
No phase coherence
No number fluctuations (Fock states)
Gap in the excitation spectrum
Not compressible
Superfluid to Mott Insulator transition
momentum distribution of the 87Rb atomic sample after expansion (LENS, 2006)
measuring coherence
via matter-wave interference
first experimental demonstration in M. Greiner et al., Nature 415, 39 (2002)
Time-of-flight imaging
P. Pedri et al., Phys. Rev. Lett. 87, 220401 (2001)
Time-of-flight imaging
M. Greiner et al., Nature 415, 39 (2002)
Superfluid-Mott transition
M. Greiner et al., Nature 415, 39 (2002)
measuring coherence after time-of-flight: superfluid-Mott transition
Superfluid-Mott transition
M. Greiner et al., Nature 415, 39 (2002)
reversible quantum phase transition
Restoring phase coherence from
a Mott insulator
Collapse & Revival
M. Greiner et al., Nature 419, 51 (2002)
Excitation spectrum
Example: weakly-interacting BEC
Bogoliubov spectrum
Small momentum k  collective excitations, phonons
Large momentum k  single particle spectrum
BEC Excitation spectrum
Excitation spectrum of a weakly interacting BEC in harmonic trap
J. Steinhauer et al., PRL 88, 120407 (2002)
Excitation spectrum
measurement of excitation spectrum via lattice modulation
(T. Stöferle et al., PRL 92, 130403 (2004))
Mott Insulator spectrum
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U
2U
Excitation spectrum
application of a magnetic
field gradient
M. Greiner et al., Nature 415, 39 (2002)
In-situ density measurement
N. Gemelke et al., Nature 460, 995 (2009).
in-situ imaging
of the density distribution
incompressible central
region with 1 atom/site
Quantum information
Qubits
Quantum bit (qubit)
 0  1
coherent superposition
Entanglement
Entangled states
   01  10 
Quantum gates via ultracold collisions
Quantum Logic via the Exchange Blockade in Ultracold Collisions
D. Hayes, P. Julienne, I. Deutsch, PRL 98, 070501 (2007)
Example of implementation of a quantum gate for identical fermionic particles:
Symmetrization of the wavefunction:
 collisional phase-shift
 no collisional phase-shift
Implementation of the
gate with fidelity ~ 1
Quantum gates via ultracold collisions
Controlled exchange interactions between pairs of neutral atoms in OL
M. Anderlini et al., Nature 448, 452 (2007)
Experimental realization of the exchange
phase-shift in a lattice of double wells:
Detecting correlations
Hanbury-Brown & Twiss effect
correlations between joint probability at detector positions
2
interference between quantum-mechanical paths of identical particles
U. Fano, Am. J. Phys. 29, 539 (1961)
HBT interferometry in quantum gases
absorption image of a Mott Insulator state
d
approx. 50000 detectors in a single image!
Noise correlations
Noise interferometry: bunching for bosons (Mott)
S. Foelling et al., Nature 434, 481 (2005)
Noise interferometry: antibunching for fermions
T. Rom et al., Nature 444, 733 (2006)
Detecting correlations
M. Schellekens et al., Science 310, 648 (2005)
Time-resolved time-of-flight detection of metastable He atoms
Bunching for bosons (thermal)
M. Schellekens et al., Science 310, 648 (2005)
Antibunching for fermions
T. Jeltes et al., Nature 445, 402 (2007)
He-4
He-3