Optics Communications 264 (2006) 471–474 www.elsevier.com/locate/optcom
Coherent control of laser pulse temporal duration: An experimental proposal R. Buffa b
a,*
, S. Cavalieri b, L. Fini b, E. Sali b, M.V. Tognetti
a,1
a Dipartimento di Fisica, Universita` di Siena, Via Roma 56, I-53100 Siena, Italy Dipartimento di Fisica, and European Laboratory for Nonlinear Spectroscopy, Universita` di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
Received 31 October 2005; accepted 16 February 2006
Abstract We present a study of temporal compression resulting from the coherent control peculiarities of electromagnetically induced transparency propagation dynamics. We discuss the crucial conditions required to accomplish temporal compression in an experiment with a sample of hot atoms. 2006 Elsevier B.V. All rights reserved. PACS: 42.50.Gy; 32.80.Qk; 42.50.Hz
1. Introduction In the last decade there has been a great deal of interest in the optical properties of coherently prepared atomic media, a field in which Bruce Shore has been a prominent actor [1]. Particular attention has been paid to electromagnetically induced transparency (EIT), and its use in the control of propagation of light [2–6]. More specifically, as far as this work is concerned, experimental evidence of the possibility to control the temporal shape of laser fields in the visible spectral region and in the microsecond temporal regime has been reported in cold atoms by Liu et al. [7]. A theoretical study which discusses and explains how to exploit the peculiarities of EIT propagation dynamics to achieve coherent control of the temporal shaping and compression of laser pulses has also been recently published [8]. So far this appears to be a unique technique in the far vacuum ultraviolet (VUV) *
Corresponding author. E-mail address: buff
[email protected] (R. Buffa). 1 Present address: CLOQ/Departamento de Fı´sica, Faculdade de Cieˆncias, Universidade do Porto, R. do Campo Alegre 687, 4169-007 Porto, Portugal. 0030-4018/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2006.02.063
or even extreme ultraviolet (XUV) spectral regions and may provide an important tool for nonlinear optics applications at very short wavelengths. Fig. 1 shows a schematic diagram of the physical system at the basis of EIT: a three-level atom in interaction with two laser pulses, of electric-field envelopes Ep (probe) and Ec (coupling), and frequencies xp and xc, resonant with the atomic transitions 1–2 and 2–3, respectively. The lambda scheme shown on the left (a) is the one that allows the use of a metastable final state, which in turns may lead to a coherence q13 with a small dephasing rate c13: a crucial parameter when the goal is to attain ultra slow light propagation. However, if the goal is the control of VUV probe pulses by using coupling field still in the visible spectral region, then it may not be possible to find a suitable high-energy metastable state. Since, in this case, there is no substantial difference between the lambda and the ladder scheme shown on the right (b), the last one provides a further possible choice in the planning of an experiment. In this paper, we present a study in which the main specific conditions required for an experimental realization of pulse compression are highlighted. A plan of a first proofof-principle experiment in hot atoms and in the visible spectral region is also discussed.
R. Buffa et al. / Optics Communications 264 (2006) 471–474
(a)
2
|E / E | p p0
|3>
ωp
(a)
< Tc >
Z=0
5
4
4
3
3
2
|1>
|1>
6
5
ωc ωp
6
2
ωc
|3>
c0
|2>
c
|2>
|E / E |
472
2
< Tp > 1
(b)
Fig. 1. Schematic diagram of the three-level atomic systems at the basis of EIT.
1
0
0
-4
-2
0
2
4
6
8
10
12
t - Z/c (ns)
Here N is the density of the atomic sample, d12 and d23 are the electric-dipole moments of the transitions 1–2 and 2–3, respectively, and the coherences qnm(v) are averaged over the velocity distribution fD(v): Z þ1 hqnm iv ¼ qnm ðvÞfD ðvÞ dv ð2Þ 1
For a weak probe laser pulse (q11 = 1), the coherences qnm(v) that appear in Eqs. (1) and (2) satisfy the following Liouville equation: q_ 12 ¼ iXp iXc q13 ðiDp þ c12 Þq12 q_ 13 ¼ iXc q12 ½iðDp þ Dc Þ þ c13 q13 q_ 23 ¼ 0
ð3Þ
where Xp = d12Ep/2 h and Xc = d23Ec/2 h are the Rabi couplings, Dp and Dc are detunings from resonance, cnm represent all kind of dephasing rates and the explicit dependence
6
0
