Femtosecond Infrared Emission Resulting from …

1 VOLUME76, NUMBER23 PHYSICAL REVIEW LETTERS3 JUNE1996 Femtosecond Infrared Emission Resulting from coherent Charge Oscillationsin Quantum WellsA. Bonvalet,1,2J. Nagle,3V. Berger,3A. Migus, Martin,1and M. Joffre11 Laboratoire d Optique Appliqu e, Ecole Nationale Sup rieure de Technique Avanc es, Ecole Polytechnique,Centre National de la Recherche Scientifique URA 1406-INSERM U451, F-91125 Palaiseau Cedex, France2 SBEyDBCM Commissariat l Energie Atomique-Saclay, F-91191 Gif-sur-Yvette, France3 Laboratoire Central de Recherches, Thomson-CSF, F-91404 Orsay Cedex, France(Received 27 February 1996)We excite quantum beats in a quantum well using 12 fs optical pulses.

2 The Resulting coherentcharge oscillation, in the tens-of-tetrahertz range, radiates a corresponding Infrared electromagneticwave which is monitored through heterodyne detection using as a reference a nearly single-cycle Infrared pulse. The direct observation of this wave-packet oscillation yields information onthe relaxation of intersubband coherence in quantum , the experiment yieldssimultaneously the Femtosecond dynamics of both diagonal and off-diagonal matrix elements of thedensity operator.

3 [S0031-9007(96)00349-3]PACS numbers: , , +pThe detection of the electromagnetic wave radiated bythe oscillation of a wave packet in a quantum-well struc-ture [1,2] has been an important step forward in semicon-ductor physics in that it demonstrated unambiguously theexistence of coherent charge oscillations in such , up to now, the coherent charge oscillation in theconduction band has been observed only between differentquantum wells, , in a structure made of two adjacentwells of different widths, placed in an electric field so thattunneling could take place [1].

4 Another related examplehas been the observation of Bloch oscillations in a super-lattice in the Wannier-Stark regime [2]. In both cases, acoherent superposition of states was prepared through ex-citation by a 100 fs pulse. The subsequent far-IR emissionwas detected using standard electro-optic gating techniques[3], limiting the bandpass to a few THz at most, , to tran-sition energies of about 10 meV. In this Letter, we reporton the light Emission associated with wave-packet oscil-lations of electrons within asingle well,associated withmuch higher oscillating frequencies.

5 Because of the largertransition energy, in the 100 meV range, the wave packetoscillation can now be observed even at room energies, above the LO-phonon energy, also corre-spond to a totally different physical regime. The observa-tion of wave-packet oscillations at such high frequencieswas made possible through the use of shorter pulses of du-ration 12 fs, and also by using light detection in the mid- Infrared in a coherent heterodyne detection scheme basedon time-domain interferometry with an ultrashort mid-IRreference pulse.

6 Furthermore, we show in this Letter thatwe measure not only the coherence, but also the popula-tion decay, thus fully determining the time evolution of thedensity operator after an ultrashort impulsive creation of a wave packet involves the simultane-ous excitation of more than one energy level, all withinthe coherent bandwidth of a short laser pulse. In ourcase, shown in the inset of Fig. 1, two energy levels ofan asymmetric multiple quantum well (MQW) structureare excited through optical transitions from the valenceband.

7 The wave function just after pump absorption isthen a coherent linear superposition of both excited statesE1andE2. The difference in Bohr frequencies resultsin a quantum beat oscillating at the transition frequencyv21between the two states. One consequence of thisbeat is a coherent charge oscillation [1], giving rise to anemitted mid-IR electromagnetic wave. This mid-IR emis-sion can also be viewed as difference-frequency mixingin a resonant medium. Therefore, since it originates froma second-order nonlinear process, the Emission can oc-cur only in noncentrosymmetric systems, hence our initialchoice of a compositionally asymmetric quantum well [4],FIG.

8 1. Experimental setup. BS, beam splitter; TS, translationstage; PM, gold-coated parabolic mirror; S, sample; D, HgCdTedetector. The inset shows the sample excitation condition, herein the case of an asymmetric quantum well. The short pumppulse excites a coherent superposition ofE1andE2from thevalence state HH1, Resulting in a midinfrared (23)y4392(4)$ 1996 The American Physical SocietyVOLUME76, NUMBER23 PHYSICAL REVIEW LETTERS3 JUNE1996whose structure was optimized [5] to enhance the productof matrix elements involved in the Infrared Emission .

9 Thedensity matrix of the system in the presence of the excit-ing pulse is assumed to obey the Bloch equation, whichtakes into account population and coherence a three-level model and developing the density ma-trix up to second order in the electric fieldEstd, we findrs2dijstd 2mi0m0jGijstd EstdhfG0jstd1Gi0stdg Estdj,(1)wheremnmis the dipolar matrix element andGnmstd iy hQstdexps2ivnmt2 Gnmtdis the Green function as-sociated with the optical transition from the Heaviside the decay rate cor-responding, respectively, to dephasing whennfimandto population relaxation whenn m.

10 Equation (1) canbe numerically computed in a straightforward manner us-ing a few Fourier transforms and simple multiplicationsin frequency and time domains, successively [6]. In casethe pump pulse is much shorter than all relaxation timesand if its spectrum encompasses both statesE1andE2,the induced coherencers2d21stdis directly proportional tothe Green functionG21std~Qstdexps2iv21t2tyT2d,wher eT2 1yG21is the dephasing time. As a result ofthis evolution of the density operator, a time-dependentpolarization is induced in the systemPs2dstd m12r21std,whose oscillation in time is responsible for the mid-IR ra-diation.