20 40 60 ν0=1 0 20 40 60 ν0=2 0 20 40 60 ν0=3 0 20 40 60 ν0=4 0 20 40 60 0 2 4 6 8 10 12 ν ν0=5 ν0=6 ν0=7 ν0=8 ν0=9 0 2 4 6 8 10 12 ν ν0=10 Population (%)
Figure 10.15: Distributions de populations finales pour des impulsions LCT, pour diff´erent cibles ν0
10.4 Conclusion
La th`ese pr´esente des ´etudes th´eoriques dans le domaine du contrˆole par impulsions laser de syst`emes quantiques, o`u l’interaction avec un environnement joue un rˆole cl´e dans la dynamique et le sc´enario de contrˆole. En particulier, deux sujets ont ´et´e consid´er´es: la cr´eation d’excitons et biexcitons dans des boites quantiques sous l’influence des phonons, et l’excitation vibrationnelle du mode d’´elongation de CO dans le carboxy-h´emoglobine.
Dans le premier volet, le r´esultat principal est que la cr´eation d’excitons ou biexcitons est possible grˆace `a des impulsions courtes, fortes et avec une faible d´erive de fr´equence. Le m´ecanisme est alors un passage adiabatique, o`u la perforation des ´etats habill´ees par l’impulsion forte est suffisamment grande pour permettre un d´ecouplage effectif des phonons. Ce r´esultat, confirm´e par des exp´eriences dans le cas de l’exciton, reste `a confirmer exp´erimentalement pour la g´en´eration des biexcitons. La caract´eristique int´eressante est que ce m´ecanisme m`ene `a des probabilit´es quantiques proches de un, mˆeme `a des temp´eratures au dessus de 77 K, donc accessibles par des m´ethodes de refroidissement bas´ees sur l’azote liquide, et non sur l’h´elium. Savoir si le m´ecanisme reste valable pour des temp´eratures encore plus ´elev´ees, voire `a la temp´erature ambiante, reste `
a explorer dans des travaux futurs.
Dans le deuxi`eme volet, le r´esultat principal est qu’avec des impulsions mises en forme dans le domaine spectral de l’infrarouge, des ´etats tr`es excit´es peuvent ˆetre atteints avec une tr`es bonne s´electivit´e, malgr´e la pr´esence d’un environnement complexe. Parce que l’´energie d´epos´ee ainsi peut ˆetre plus grande que celles des liaisons ou barri`eres configurationnelles, ces r´esultats peuvent mener `a des changements structuraux tout en restant sur l’´etat ´electronique fondamental. Ceci pr´esente une nouvelle discipline ´emergeante, appel´e ”controlled ground state chemistry”. Un deuxi`eme aspect tr`es int´eressant est que la possibilit´e de peupler des ´etats tr`es ´elev´es d’une fa¸con
10 R´esum´e
Figure 10.16: Spectre d’absorption obtenu par une impulsion sonde de faible intensit´e, qui suit l’impulsion de contrˆole. Le signal montre le succ`es de l’excitation vers l’´etat cible.
tr`es s´elective, et leur d´etection exp´erimentale, offre la possibilit´e de mesures directes des dur´ees de vie de tels ´etats hors ´equilibre. Des exp´eriences de ce type sont en cours de r´ealisation dans le groupe de M. Joffre, et les r´esultats obtenus dans le cadre de cette th`ese aident a guider leur mise en place, et seront tr`es utiles pour l’interpr´etation des spectres exp´erimentaux `a venir.
List of Figures
2.1 Variation of density of states (bottom) with confinement in increasing dimensions (top) are shown schematically, adapted from Ref.[49]. Note that the DOS become peaked with increasing confinement. . . 8 2.2 Schematic depiction of typical energy levels of an shaped single quantum dot.
States |X⟩, |Y⟩ denote the energy split (by an amount δf, that is exaggerated in
the figure) exciton states, whose degeneracy is lifted as a result of shape or interface asymmetry. Also shown, is the biexciton detuning: ∆b. . . 9
2.3 We show the typical dispersion curves from GaAs (left panel) and InAs (right panel), adapted from Ref.[56] . . . 12 4.1 A schematic diagram for the adiabatic transfer under frequency swept laser driving.
For positive chirp parameter (α > 0) the dynamics proceeds via the lower adiabatic surface, whereas for a negative chirp parameter (α < 0) it proceeds via the upper one as determined by the initial conditions in dressed state basis. . . 29 4.2 Exciton population for a single InAs/GaAs quantum dot as a function of pulse
area, for a τ0 = 5 ps pulse at 4 K. Upper panel: pulse with a small residual
chirp (ϕ′′ =−7 ps2) in resonance with the transition; Lower panel: ϕ′′=−40 ps2; diamonds: experimental results from [10], circles: numerical simulations (Eq.[4.5]). The solid line in the lower panel is the analytical expression (Eq.[4.34]), valid in the adiabatic regime Note that all the parameters if the fits are identical in the two panels, except the value of ϕ′′. . . 36 4.3 Numerical simulation of the exciton population, (Eq.[4.5]) compared to the analyt-
ical expression (Eq.[4.34]), full black line) for different temperatures, as indicated. The laser parameters are: τ0 = 5 ps, ϕ′′=−40ps2 (red, circles), ϕ′′= 40ps2 (blue,
diamonds). Note the difference with respect to the sign of ϕ′′, disappearing with increasing temperature. . . 37 4.4 Exciton population as a function of laser pulse area for a temperature of T = 80 K.
The pulse parameters are τ0 = 500 fs, ϕ′′ = πτ02 = 0.78 ps2. Blue diamonds:
numerical result, Eq.[4.5]; full black line: analytical expression, Eq.[4.34]. On the top axis the corresponding value of Ωp is given, indicating the rise in Pf when
List of Figures
4.5 Exciton population as a function of laser pulse energy and τ0, for a temperature
of T = 80K and ϕ′′= πτ02. . . 39 5.1 A schematic representation of the field dressed adiabatic eigen-energies of the
quantum dot. The curly arrows indicate that the adiabatic dynamics occurs on one of the adiabatic surface determined by the chirp sign through the initial conditions (see Appendix[5.7.1,& 5.7.2]). . . 49 5.2 Population of the biexciton state measured after the pulse is over, plotted as
a function of peak interaction strength Ωp (proportional to the pulse area), for
laser pulse width τ0 = 1 ps, ϕ” = 20 ps2 [upper panel] and ϕ” = −20 ps2 [lower
panel]. The non-Markovian numerical simulation is indicated by with (circles) and without (diamond) phonons while dashed line represents adiabatic Markovian master equation of Eq.[5.19] . . . 53 5.3 Biexciton population as a function of peak interaction strength Ωp for different
temperatures, as indicated, for a pulse with τ0 = 1 ps and ϕ′′ = ±20 ps2. A
drastic loss of transfer efficiency is found for higher temperatures, predicted by the analytical model, valid in the adiabatic regime. . . 54 5.4 Biexciton population for a short (τ0 = 350f s) and only weakly chirped pulse
(blue: ϕ′′ = 0.5 ps2, red: ϕ′′ = −0.5 ps2), calculated by numerical solution of Eq.[5.6]. Pf ≈ 1 is achieved when both Ωp > Ω±ad and Ωp > Ω±dc is fulfilled. . . 55
5.5 Biexciton population as a function of intensity and chirp parameter, based on a FT limited pulse with τ0 = 350 fs pulse and a maximum intensity corresponding to a
pulse with θ = 7π, at a temperature of 80 K. The lines correspond to the threshold values (Eq.[5.35]), which, together with |ϕ′′| > πτ2
0, define regions in parameter
space where Pf ≈ 1 could be realized (red areas correspond to Pf > 0.99). . . . 57
6.1 Hemoglobin model. Left Panel: Original structure of the FeP(Im)-CO complex embedded in the HbCO alpha chain protein. Right Panel: Corresponding active site model and point charges [41]. . . 63 6.2 A schematic diagram explaining order of interactions: a strong pump excitation
followed by a weak probe pulse. Note that the interval between the pulses are slightly exaggerated in the figure. . . 66 6.3 Loop diagram, describing the strong pulse pump interaction followed by a weak
probe pulse. For details see text. . . 67 7.1 Pulse envelope, total vibrational energy and vibrational population Pν(t) in the
CO-stretch in HbCO for a typical set of parameters: τ0= 100 fs, ω0 = 1980.0 cm−1,
List of Figures
7.2 Energy transfer achieved by linearly chirped laser pulses as a function of detuning form the center of the absorption band ∆ω0 and the chirp parameter ϕ′′ with
a pulse duration of τ0 = 100 fs (A,B,C,D) and τ0 = 300 fs (E,F,G,H) and a
peak power of W0 = 2.6× 1011W cm−2 (A,B,E,F) and W0 = 5.2× 1011W cm−2
(C,D,G,H). . . 73 7.3 Optimal detuning δopt of the excitation laser with respect to the center of the
absorption band, required to obtain maximum vibrational energy transfer as a function of the peak power. The chirp parameter is set to ϕ′′ = −0.1 ps2 (full lines), and compared to an unchirped (Fourier-transform limited) (dashed lines). 74 7.4 Effect of chirp parameter ϕ′′and fluctuations onto vibrational excitation of HbCO.
Optimal detunings for ϕ′′ = −0.1 ps2 were used and a peak power of W0 =
5.2× 1011 W.cm−2.. . . 75 7.5 Distribution of vibrational populations after strong IR pulse excitation, using dif-
ferent pulse lengths including or suppressing protein fluctuations. The other pulse parameters are ϕ′′ = −0.1 ps2, W0 = 5.2× 1011 W cm−2 and the corresponding
optimal detunings. . . 76 7.6 Red: Distribution of vibrational populations after strong IR pulse interaction, for
different pulse lengths and chirp parameters. Optimal detunings for ϕ′′=−0.1 ps2 were used and a peak power ofW0 = 5.2× 1011 W.cm−2. Blue: as above, but the
vibrational populations are calculated by weighting the individual wavepackets by the projection onto the laser polarization axis. . . 77 7.7 Differential transient absorption spectra ∆σ(ω;I0) (see Eq.[6.13]) for different
pulse lengths and chirp parameters, as indicated. Optimal detunings for ϕ′′ =
−0.1 ps2 were used and a peak power of W
0 = 5.2× 1011 W cm−2. . . 78
7.8 Top panel: simulated differential transient absorption signal ∆S(ω; I0), using dif-
ferentpulse intensities, based on an orientational averaging and averaging over the spatial beam profile (Eq.[6.14]. A pulse duration of τ = 100 fs, a detuning of ∆ω =−61.7 cm−1 and a chirp parameter ϕ′′ =−3.2 × 10−2 ps2 were used. Bot- tom panel: experimental spectra, taken from [112] and based on the same set of parameters. . . 79
8.1 Results for a LCT optimization for ν = 7 is presented. In the upper panel, the populations corresponding to the different states are shown. Corresponding control pulse with several sub structures is shown in the lower panel. After the pulse gets over the resulting population distribution is displayed in the inset. . . 86
List of Figures
8.2 LCT runs for different target states are shown w.r.t the intensity of the pulse (plotted along x axis), with fluctuations (left panel) and without fluctuations (right panel). Note that after a certain pulse intensity the control yields in both the cases saturate. Also note that, though the fluctuations have detrimental effects on the control scenario (as clear from diminishing final population), selective excitations of high lying states are possible.. . . 88 8.3 Here we show the results of the LCT runs for different target states νta with the
optimal pulses obtained from Fig.[8.2]. For each run populations corresponding to all the states ν are plotted. It can be seen from the the dominant populations along the diagonal that state selective excitation are possible. The leftover populations present in the figure is due to the orientational averaging as discussed in the text. 89 8.4 Transient absorption spectrum measured by a weak probe pulse, following the
different strong control pulses Eν. The transient absorption signal clearly reflects
the success of the preceding control. . . 90 10.1 Population de l’exciton pour un puits quantique, en fonction de l’aire de l’impulsion.
Partie sup´erieure: impulsion avec un faible chirp r´esiduelle, en r´esonance avec la transition. Partie inf´erieur: impulsion avec forte d´erive de fr´equence avec
ϕ′′ = −40ps2. Points noirs: r´esultats exp´erimentaux (Ref. [10]), rouge: r´esul- tats num´eriques, trait noir continu: expression analytique. . . 97 10.2 Sch´ema du transfert adiabatique. Pour α > 0, le passage adiabatique s’effectue
via la surface inf´erieure, pour α < 0 sur la surface sup´erieure. . . 98 10.3 Mod´elisations num´eriques de la population de l’exciton, avec les r´esultats des ex-
pressions analytiques (en trait noir), pour diff´erents temp´eratures. Les param`etres du laser sont: τ0 = 5 ps, ϕ′′=−40ps2 (rouge), ϕ′′= 40ps2 (bleu). . . 99
10.4 Population de l’exciton en fonction de l’intensit´e pour une temp´erature de 80K. Les param`etres du laser sont: τ0 = 500f s, ϕ′′ = πτ02 = 0.78ps2. Bleu: r´esultats
num´eriques; trait noir: expression analytiques. Sur l’axe sup´erieure la valeur Ωp
est donn´e, indiquant l’augmentation de Pf pour Ωp > wc. . . 100
10.5 Population de l’exciton en fonction de l’intensit´e et τ0, pour une temp´erature de
T = 80K et ϕ′′= πτ02. . . 101 10.6 Sch´ema des ´etats adiabatiques. Pour α > 0, le passage adiabatique s’effectue sur
la surface sup´erieure, pour α < 0 sur la surface inf´erieure. . . 103 10.7 Population du biexciton, en fonction de l’intensit´e Ωp, τ0= 1ps, ϕ′′= 20ps2 (par-
tie sup´erieure) et ϕ′′ = −20ps2 (partie inferieure). Cercles: solution num´erique, losanges: sans phonons, traits: expressions analytiques. La temp´erature est de
T = 4K. . . . 104 10.8 Population du biexciton en fonction de Ωp pour diff´erents temp´eratures. Les
List of Figures
10.9 Population du bieciton pour une impulsion courte (τ0 = 350f s) avec faible d´erive
de fr´equence (bleu: ϕ′′= 0.5ps2, rouge: ϕ′′ =−0.5ps2), calcul´ee num´eriquement. On trouve Pf ≈ 1 pour Ωp > Ω±ad et Ωp> Ω±dc. . . 106
10.10Population du biexciton en fonction de l’intensit´e et param`etre de chirp. Les param`etres de l’impulsion sont τ0 = 350f s etPm correspondant `a une impulsion
avec θ = 7π. La temp´erature est 80K. . . . 107 10.11Distributions de populations finales pour des impulsions `a d´erive de fr´equence,
avec deux dur´ees diff´erents. Partie gauche: simulations en prenant compte des fluctuations, partie droite: simulations en supprimant les fluctuations . . . 108 10.12Structure du syst`eme consid´er´e pour les mod´elisations . . . 109 10.13Spectre d’absorption obtenu par une impulsion sonde de faible intensit´e, qui suit
l’impulsion `a d´erive de fr´equence. Le signal montre l’excitation vers des ´etats tr`es ´elev´es, ainsi que l’inversion de population. . . 110 10.14Populations finales apr`es interaction avec des impulsions de contrˆole en fonction
de l’´energie du pulse, (a) en tenant compte de l’environnement, (b) avec les fluc- tuations supprim´ees . . . 112 10.15Distributions de populations finales pour des impulsions LCT, pour diff´erent cibles
ν0 . . . 113
10.16Spectre d’absorption obtenu par une impulsion sonde de faible intensit´e, qui suit l’impulsion de contrˆole. Le signal montre le succ`es de l’excitation vers l’´etat cible. 114
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Acknowledgements
Doing the work presented in thesis over the last four years have been a wonderful experience on many counts, especially considering my predetermined transgression from a disciple of Chemistry to AMO physics community. Here the stress is always over fundamentals which are always vali- dated with utmost rigor, unlike chemistry where there is some room for speculative plausibility to guide the intuition. However, the top-down perspective on fundamental phenomena which is the main arsenal of a chemist has helped me amply in several situations. The fact that I survived emboldens my belief in myself and the journey that had started with a conscious decision will continue for the rest of my career.
My advisor, Christoph Meier, has been a wonderful source of ideas, insights and inspiration that helped me start the transition to become a ’scientist’ from somebody who once was just a curious student. Chris was available for scientific discussions at any point of time and even bothered to talk at length about the stupidest of my queries. His concern for the students well-being in and outside the lab is something I have greatly appreciated over these years.
I extend my sincere regard for the rappourteurs : Prof. Stephane Gu´erin, Prof. Christiana Koch and the members of the referring committee: Prof. Volker Engel, Prof. M. Desouter-Lecomte, Prof. Nathalie Guih´ery, Dr. Thiery Amand for taking the trouble to evaluate the dissertation work and coming down to Toulouse, despite the busy schedule that they were keeping. I ap- preciate their constructive inputs to the research work presented in the thesis. Professionally, I have had the pleasure of working and discussing with not only with Chris himself but also with Dr. B. Chatel (LCAR) & Dr. T. Amand (LPCNO). For me, it was a steady source of learning leading to newer insights from an experimentalists perspective. Beatrice, in her administrative capacity, has taken the Lab management to a new level and I convey my appreciation to her. When I arrived to LCAR in 2009, J. Vigue was the Director of the lab and I also thank him for the warm welcome provided to me. My heartfelt gratitude also extend to all the members in the LCAR for making my stay comfortable and so easy going