Marco Bellini, Silvia Viciani, Alessandro Zavatta

1
Quantum optical effects with pulsed lasers
Marco Bellini, Silvia Viciani, Alessandro
Zavatta Istituto Nazionale di Ottica Applicata
(Firenze) Francesco Marin, F. Tito
Arecchi Università di Firenze - Dipartimento di
Fisica
Università degli Studi di Firenze Dipartimento di
Fisica
Istituto Nazionale di Ottica Applicata
Generation of two-photon entangled states
Quantum Computation

• Parametric down-conversion (SPDC) in non-linear
  crystals

Classical-Bit
0 or 1
Well defined by a single measurement.
State of a quantum system (atomic energy levels,
nuclear spin, polarization of photons, etc)
or
Quantum-Bit qubit
wpwiws kpkiks
and more generally
Superposition state ?2 and ?2 are the
probabilities to find the qubit in the 0 and 1
state respectively after a single measurement.
The properties of a single photon are not defined
individually but are completely correlated to
those of the other
Energy and momentum conservation
2-qubit state
SPDC Entangled state
Entangled state
entangled pair of qubits.
Non-local pulse shaping with entangled photon
pairs

• Measurement of the coherence time (1/Dn)

... also the UV pump can be filtered by an
etalon!
Visibilities of fourth-order interference fringes
vs. width of the spectral filter
The monochromator filter can be replacend by
etalons
1
No filter
Pump coherence time
2
Di
Detection of photon 1 after the monochromator
collapses the SPDC wavefunction on a spectrally
filtered state (with a longer coherence time
Filter on
The correlation time tc is limited by the pump
coherence.

• Measurement of the signal spectrum conditioned
  on photodetection in Di

Ghost interference
The Michelson interferometer is kept unbalanced,
a click is observed by Di if
S. Viciani et al., in press (2004)
SPDC emission probability
The coincidence count rate is given by
convolution of the SPDC emission probability with
the transmission function of the filters and the
spectral response of the Michelson interferometer.
Idler-filter transmission function Monochromator
or etalon.
Detection of an idler photon after the Michelson
collapses the SPDC wavefunction onto a coherent
superposition of pulses displaced by T.
ghost spectral interference fringes appear!
M. Bellini et al., Physical Review Letters 90,
043602 (2003)
Quantum Homodyne Tomography
vacuum
Preliminary results...
T is the relative phase between signal and local
oscillator
unknown state ygt
Single-photon state
Control of LO phase
82 MHz pulse train
q
Marginal distribution
The Wigner function is reconstructed from
marginal distributions via quantum tomography
The measured field is an attenuated version of
the laser output (coherent state)
Overall Efficiency ? 16
P?(x?)
Marginal distributions for different values of
the detection efficiency
x?

• Reconstruction of weak coherent states

x
Single-photon Wigner function
Strong coherent field
Time
Photocurrent difference
Quantum sampling method
Negative values !
Density matrix elements
Complete set of marginal distributions
ltngt 1
Vacuum field
Wigner function sections
G.M. DAriano in Quantum Optics and the
Spectroscopy of Solids 175-202 (T. Hakioglu et
al. eds., Kluwer, 1997).

Inverse Radon transform
Radon transform of the Wigner function
Evaluation of density-matrix elements(Poissonian
photon-number distributions)
Wigner function
More than 50 of detection efficiency needed to
observe negative valued Wigner functions
A. Zavatta et al., Journal of the Optical Society
of America B 19, 1189 (2002)