M arco Bellini , Silvia Viciani, Alessandro Zavatta Istituto Nazionale di Ottica Applicata...
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p i s C oin cid e n ce counter M on oc h rom a t or -400 -200 0 200 400 Counts/s D t (fs) M M arco arco Bellini Bellini , Silvia Viciani, Alessandro , Silvia Viciani, Alessandro Zavatta Zavatta Istituto Nazionale di Ottica Applicata (Firenze) Francesco Marin, Francesco Marin, F. Tito Arecchi F. Tito Arecchi Università di Firenze - Dipartimento di Fisica 920 940 960 980 1000 1020 1040 1060 1080 1100 0 50000 100000 150000 C o un ts/s P Z T scan 200 210 220 230 240 250 260 270 280 290 300 310 320 0 200 400 600 800 1000 1200 D t= 333 fs C o incide n ces/s P Z T scan No filter No filter Filter on Filter on Detection of photon 1 after the Detection of photon 1 after the monochromator monochromator collapses the SPDC collapses the SPDC wavefunction wavefunction on a spectrally filtered on a spectrally filtered state (with a longer coherence time state (with a longer coherence time The correlation The correlation time time τ c is limited is limited by the pump by the pump coherence. coherence. Pump coherence time Visibilities of fourth- order interference fringes vs. width of the spectral filter Detection of an idler photon after the Michelson collapses the SPDC wavefunction onto a coherent superposition of pulses displaced by T. The Michelson The Michelson interferometer interferometer is kept is kept unbalanced, a unbalanced, a “click” is “click” is observed by D observed by D i i if: if: • Measurement of the signal spectrum Measurement of the signal spectrum conditioned on photodetection in D conditioned on photodetection in D i M. Bellini et al., Physical Review Letters 90, 043602 (2003) Non-local pulse shaping with entangled photon pairs Non-local pulse shaping with entangled photon pairs Quantum Homodyne Tomography Quantum Homodyne Tomography Photocurrent Photocurrent difference difference P θ (x θ ) x θ x Time Θ Θ is the is the relative phase relative phase between signal between signal and local and local oscillator oscillator Strong coherent field unknown state |> x Marginal Marginal distribution distribution M od e -lo ck e d lase r 82 MHz pulse train The measured field is an attenuated version of the laser output (coherent state) Control of LO phase Vacuum field <n> ~ 1 • R R econstruction econstruction of of weak coherent weak coherent states states Evaluation of density-matrix Evaluation of density-matrix elements elements (Poissonian photon-number distributions) A. Zavatta et al., Journal of the Optical Society of America B 19, 1189 (2002) -5.0x10 -10 -4.0x10 -10 -3.0x10 -10 -2.0x10 -10 -1.0x10 -10 1000 2000 3000 4000 x Single-photon Single-photon state state Preliminary Preliminary results... results... vacuum vacuum Overall Overall Efficiency Efficiency 16% 16% -2 0 2 x -2 0 2 y -1 -0.5 0 w -2 0 2 x -2 0 2 y Single- Single- photon photon Wigner Wigner function function -2 0 2 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 W (x,0) x 0.0 0.25 0.5 0.75 1.0 -2 0 2 0.0 0.1 0.2 0.3 0.4 0.5 p(x) x 1.0 0.75 0.5 0.25 0.0 Marginal Marginal distributions for distributions for different values of different values of the detection the detection efficiency efficiency Wigner function Wigner function sections sections Negative Negative values ! values ! More than 50% of More than 50% of detection efficiency detection efficiency needed to observe needed to observe negative valued Wigner negative valued Wigner functions functions Complete set of marginal distributi ons ≡ Radon transform of the Wigner function Wigner function Density matrix elements nm Inverse Radon transform Quantum sampling method G.M. D’Ariano in Quantum Optics and the Spectroscopy of Solids 175-202 (T. Hakioglu et al. eds., Kluwer, 1997). Quantum optical effects with pulsed lasers Quantum optical effects with pulsed lasers p = i + s k p =k i +k s • Parametric Parametric down-conversion down-conversion (SPDC) in non- (SPDC) in non- linear crystals linear crystals Energy and momentum conservation i s i s SPDC Entangled state: SPDC Entangled state: or The properties of a single photon are not The properties of a single photon are not defined individually but are completely defined individually but are completely correlated to those of the other correlated to those of the other s s k p p k i i i s s s i s p i s p i s d d , k , k ) k k k ( ) ( 0 Generation of two-photon entangled states Generation of two-photon entangled states )) cos( 1 )( ( ) ( ) ( ) , ( d d ) , ( 2 T M F F T R s m i i i s s i s i s m c The monochromator The monochromator filter can be replacend filter can be replacend by by etalons etalons : : SPDC emission SPDC emission probability probability ... also the UV pump ... also the UV pump can be filtered by can be filtered by an etalon! an etalon! convolution of the SPDC convolution of the SPDC emission probability with emission probability with the transmission function the transmission function of the filters and the of the filters and the spectral response of the spectral response of the Michelson interferometer. Michelson interferometer. Idler-filter transmission Idler-filter transmission function: Monochromator or function: Monochromator or etalon. etalon. S. Viciani et al., in press (2004) “ “ Ghost” Ghost” interference interference …“ …“ ghost” spectral interference fringes ghost” spectral interference fringes appear! appear! • Measurement of the coherence time Measurement of the coherence time (1/ (1/ D D) 1 2 2 Università degli Studi di Firenze Università degli Studi di Firenze Dipartimento di Fisica Dipartimento di Fisica Quantum Computation Quantum Computation The coincidence count rate is The coincidence count rate is given by given by 1 or 0 Classical-Bit Quantum-Bit qubit qubit 0 or 1 Well defined by a single measurement. State of a quantum system (atomic energy levels, nuclear spin, polarization of photons, etc…) and more generally 1 0 Superposition state: || 2 and || 2 are the probabilities to find the qubit in the 0 and 1 state respectively after a single measurement. 0 1 11 10 01 00 11 10 01 00 11 00 2 1 2-qubit state: 2-qubit state: Entangled state: Entangled state: D i The Wigner The Wigner function is function is reconstructed reconstructed from marginal from marginal distributions distributions via quantum via quantum tomography tomography T i:S a Laser BBO LBO 2 Pum p PZ T LO PBS l/2 l/2 SPCM SF ET T D S 7104 D igitalScope M TS Signal Trigger t 0 t +T 0 + = T i i k Istituto Nazionale di Istituto Nazionale di Ottica Applicata Ottica Applicata entangled pair of qubits.
description
Quantum optical effects with pulsed lasers. M arco Bellini , Silvia Viciani, Alessandro Zavatta Istituto Nazionale di Ottica Applicata (Firenze) Francesco Marin, F. Tito Arecchi Universit à di Firenze - Dipartimento di Fisica. Istituto Nazionale di Ottica Applicata. - PowerPoint PPT Presentation
Transcript of M arco Bellini , Silvia Viciani, Alessandro Zavatta Istituto Nazionale di Ottica Applicata...
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Coincidencecount er
M onochr omat or
-400 -200 0 200 400
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Dt (fs)
MMarcoarco Bellini Bellini, Silvia Viciani, Alessandro Zavatta, Silvia Viciani, Alessandro ZavattaIstituto Nazionale di Ottica Applicata (Firenze)
Francesco Marin,Francesco Marin, F. Tito ArecchiF. Tito ArecchiUniversità di Firenze - Dipartimento di Fisica
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No filterNo filter
Filter onFilter onDetection of photon 1 after the Detection of photon 1 after the monochromator monochromator collapses the SPDC collapses the SPDC wavefunctionwavefunction on a spectrally filtered state on a spectrally filtered state (with a longer coherence time(with a longer coherence time
The correlation time The correlation time ττcc is limited by the pump is limited by the pump coherence.coherence.
Pump coherence time
Visibilities of fourth-order interference fringes vs. width of
the spectral filter
Detection of an idler photon after the Michelson collapses the SPDC wavefunction onto a coherent superposition of pulses displaced by T.
The Michelson The Michelson interferometer is interferometer is kept unbalanced, kept unbalanced, a “click” is a “click” is observed by Dobserved by Di i if:if:
• Measurement of the signal spectrum conditioned Measurement of the signal spectrum conditioned on photodetection in Don photodetection in Dii
M. Bellini et al., Physical Review Letters 90, 043602 (2003)
Non-local pulse shaping with entangled photon pairsNon-local pulse shaping with entangled photon pairs
Quantum Homodyne TomographyQuantum Homodyne Tomography
Photocurrent differencePhotocurrent difference
P θ(x
θ)
xθ
x
Time
ΘΘ is the relative is the relative phase between phase between signal and local signal and local oscillatoroscillator
Strong coherent field
unknown state |>
x
Marginal Marginal distributiondistribution
M ode- locked laser
82 MHz pulse train
The measured field is an attenuated version of the laser output (coherent state)
Control of LO phase
Vacuum field <n> ~ 1
• RReconstruction of econstruction of weak coherent weak coherent statesstates
Evaluation of density-matrix Evaluation of density-matrix elementselements
(Poissonian photon-number distributions)
A. Zavatta et al., Journal of the Optical Society of America B 19, 1189 (2002)
-5.0x10-10 -4.0x10-10 -3.0x10-10 -2.0x10-10 -1.0x10-10
1000
2000
3000
4000
x
Single-photon Single-photon statestate
Preliminary Preliminary results...results...
vacuumvacuum
Overall Efficiency Overall Efficiency 16% 16%
-2
0
2x
-2
0
2y
-1
-0.5
0
w
-2
0
2x
-2
0
2y
Single-photonSingle-photon Wigner Wigner functionfunction
-2 0 2-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
W (x
,0)
x
0.0
0.25
0.5
0.75
1.0
-2 0 20.0
0.1
0.2
0.3
0.4
0.5
p(x)
x
1.0
0.75
0.5
0.25
0.0
Marginal distributions Marginal distributions for different values of for different values of
the detection efficiencythe detection efficiency
Wigner function Wigner function sectionssections
Negative Negative values !values !
More than 50% of detection More than 50% of detection efficiency needed to efficiency needed to observe negative valued observe negative valued Wigner functions Wigner functions
Complete set of
marginal distributions
≡
Radon transform of the Wigner function
Wigner function
Density matrix
elements nm
Inverse Radon
transform
Quantum sampling method
G.M. D’Ariano in Quantum Optics and the Spectroscopy of Solids 175-202 (T. Hakioglu et al. eds., Kluwer, 1997).
Quantum optical effects with pulsed lasersQuantum optical effects with pulsed lasers
p=i+s
kp=ki+ks
• Parametric down-Parametric down-conversion (SPDC) conversion (SPDC) in non-linear in non-linear crystalscrystals
Energy and momentum conservation
isis
SPDC Entangled state:SPDC Entangled state:
or
The properties of a single photon are not defined The properties of a single photon are not defined individually but are completely correlated to individually but are completely correlated to those of the otherthose of the other
ss k
pp k
iiisssispispisdd ,k,k)kkk()(0
Generation of two-photon entangled states Generation of two-photon entangled states
))cos(1)(()()(),(dd),( 2 TMFFTR smiiissisismc
The monochromator filter The monochromator filter can be replacend by can be replacend by etalonsetalons: :
SPDC emission probabilitySPDC emission probability
... also the UV pump ... also the UV pump can be filtered by an can be filtered by an etalon! etalon!
convolution of the SPDC convolution of the SPDC emission probability with the emission probability with the transmission function of the transmission function of the filters and the spectral response filters and the spectral response of the Michelson interferometer.of the Michelson interferometer.
Idler-filter transmission function: Idler-filter transmission function: Monochromator or etalon.Monochromator or etalon.
S. Viciani et al., in press (2004)
““Ghost” interferenceGhost” interference
…“…“ghost” spectral interference fringesghost” spectral interference fringes appear!appear!
• Measurement of the coherence time Measurement of the coherence time (1/(1/DD))
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22
Università degli Studi di FirenzeUniversità degli Studi di FirenzeDipartimento di FisicaDipartimento di Fisica
Quantum Computation Quantum Computation
The coincidence count rate is given The coincidence count rate is given byby
1or 0
Classical-Bit
Quantum-Bit qubitqubit
0 or 1 Well defined by a single measurement.
State of a quantum system (atomic energy levels, nuclear spin, polarization of photons, etc…)
and more generally 10
Superposition state: ||2 and ||2 are the probabilities to find the qubit in the 0 and 1 state respectively after a single measurement.
0
1
11100100 11100100
11002
1
2-qubit state:2-qubit state:
Entangled state:Entangled state:
Di
The Wigner The Wigner function is function is
reconstructed reconstructed from marginal from marginal
distributions via distributions via quantum quantum
tomographytomography
Ti:Sa Laser
BBO
LBO
2Pump PZT
LO
PBSl/ 2 l/ 2
SPCM
SF ETTDS7104
Digital Scope
MTS
Signal
Trigger
t 0
t +T0
+ =T
ii k
Istituto Nazionale di Ottica Istituto Nazionale di Ottica ApplicataApplicata
entangled pair of qubits.
