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Coherent control and third-harmonic generation: theory and experiment
Roberto Buffa 1, Stefano Cavalieri 2, Lorenzo Fini 2
Abstract.
(1) Istituto Nazionale per la Fisica della Materia, Unità di Siena,
Dipartimento di Fisica, Università di Siena, E-mail:[email protected]
In the framework of the coherent control of photoreactions 1-10 we present an
experimental study on the temporal coherent control on a process of twophoton-resonant third-harmonic (TH) generation in vapors of atomic sodium,
where evidence of quantum interference in the TH generation is reported for
the first time.
(2)
Istituto Nazionale per la Fisica della Materia, Unità di Firenze,
Dipartimento di Fisica and European Laboratory for Non-Linear
Spectroscopy (LENS), Università di Firenze, E-mail:[email protected],
[email protected]
The experimental results agree with the predictions of a theoretical model.8,9
Theory
Experiment
A sample of sodium vapors, generated in a cross-shaped oven cell operating
at 350°C and filled with some mbar of argon as buffer gas, is exposed to
pairs of laser pulses produced by a Nd:Yag-pumped dye laser. Each pulse
has 5 ns duration, 31 GHz spectral bandwidth, linear polarization and
wavelength tunable around the two-photon resonance of the 4 2D doublet of
sodium. Pairs of collinear and identical laser pulses are obtained by passing
the laser beam into a Michelson-type interferometer, which also allows to
control the relative pulse delay t. The generated TH field is separated from
the excitation field by a quartz prism followed by some dichroic filters and
then detected by an UV photomultiplier. The evidence of quantum
interference in the TH generation is shown by changing the relative pulse
delay t.
In the single atom approximation (arbitrary thin sample),
the frequency integrated TH intensity Ig(t) around wg = 3wp
is given by:
w
w
Ig ( t ) | x1 ( t )x*2 ( t )|2 I p ( t )
g
The Schrödinger equation provides the equations of motion
a n x n exp( iwn t)
for the probability amplitudes
of the bound states.
In the approximation of arbitrary weak field, the expression
for the TH energy yield is:
p

t


STH   dt{|  dt'[ E2p ( t' ) exp( it' )dt' ] |2 | Ep ( t ) |2 }
Interaction scheme, showing
the involved states of sodium
where the expression of Ep(t) is given by
Ep(t)=E0[fp(t)+fp(t-t)exp(-iwpt)]
Experiment vs. Theory
Measurement:
Theory:
TH energy yield
vs. pulse delay t
TH energy yield
vs. pulse delay t
The experimental results have been compared with the predictions of a theoretical
model8,9 which makes use of a pair of identical Fourier-trasform-limited pulses.
The spectral characteristics of the actual multimode laser pulses have been
measured by a linear autocorrelation technique.
The best fit for the power spectrum has been found when the electric field
envelope of the laser pulses has been assumed to have a Lorentzian shape with a
temporal width of 7.1 ps (FWHM).
In the theoretical analysis we have then used such pulses.
STH (arb. units)
Contrast versus two-photon detuning
(a)
1.5
t = 0
1
STH (arb. units)
2
2
(a)
1.5
1
0.5
0.5
0
0
0
0
1
2
3
4
5
6
7
8
9
1
2
3
4
Delay ( t - t) (fs)
STH (arb. units)
0.35
STH Contrast
0.9
0.8
STH (arb. units)
0.4
1
(b)
0.6
0.3
0.2
0.5
0.15
0.4
0.1
0.3
t = 68 ps
0
0.1
1
2
3
4
5
6
7
8
9
10
Delay ( t - t) (fs)
0
50
100
150
8
9
10
0. 3
(c)
0. 2
0. 15
0. 1
0
0
0
7
0. 05
0.05
0.2
6
0. 25
0.25
0.7
5
Delay ( t -  t) (fs)
10
0
1
2
3
4
5
6
7
8
9
10
Delay ( t -  t) (fs)
200
Two-photon detuning (GHz)
Dots represent the experimental results while lines reproduce
theoretical calculations. The dashed line is obtained taking into
account only the contribution of the second TH pulse, while in the
case of the continuous line the computation has been performed on
the whole TH field.
Attività nel campo e prospettive future
Conclusion
The temporal coherent control of two-photon resonant
TH generation into the continuum of ionization of
sodium atoms has been experimentally investigated by
using two delayed broadband laser pulses of identical
electric-field shape.
The experimental results have been compared with the
theoretical predictions obtained using Fourier-transformlimited pulses of much shorter temporal duration but
same spectral bandwidth.
The good agreement confirms that coherent control of
TH generation can be achieved through quantum
interference even with broadband laser pulses, and that,
for such purpose, broadband pulses are equivalent to
Fourier-transform-limited pulses.
References
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9. S. Cavalieri, L. Fini, R. Buffa, in stampa
Journal of the Optical Society of America B, vol. 21 (2004)
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Nel quadro più generale dell’interazione coerente radiazione-materia ci
stiamo occupando anche di:
Possibilità di variare caratteristiche temporali di un impulso tramite
controllo della polarizzazione atomica ovvera tramite controllo della
velocità di gruppo dell’impulso stesso. E’ stato condotto uno studio
teorico che mostra questa possibilità (Roberto Buffa, Stefano
Cavalieri, and Marco V. Tognetti: Coherent Control of Temporal
Pulse Shaping by Electromagnetically Induced Transparency,
Physical Review A, in stampa)
E’ nostro obiettivo lo studio sperimentale della tematica:
Applicazione di tecniche interferometriche per ottenere alta
risoluzione spettrale con sorgenti a impulsi corti (<= 100fs) per
superare il limite intriseco di purezza spettrale (vedi poster n. )