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Coherent Control of the Optical Emission in a Single Organic Quantum Wire Jeremy Holcman, Antoine Al Choueiry, Alexandre Enderlin, Sophie Hameau, Thierry Barisien,* and Laurent Legrand Institut des NanoSciences de Paris (INSP), UMR 7588 CNRS/UPMC (Universite Pierre et Marie Curie), 4 place Jussieu, 75252 Paris Cedex 05, France ABSTRACT: We report on the first coherent control experiments on a purely electronic exciton state in an extended quasiperfect organic quantum wire, a polydiacetylene chain isolated in the crystalline matrix of its own monomer. The timeintegrated luminescence of a single wire is measured as the relative phase between two exciting sub-picosecond laser pulses is varied. From visibility functions the exciton dephasing time is extracted and its temperature dependence studied. Our work points the predominant role of thermalization upon the phase relaxation dynamics. By means of microscopic imaging spectroscopy we also show that despite local excitation coherent control is achieved on states delocalized over the chain at the micrometric scale. KEYWORDS: Quantum wire, single molecule, coherent control, exciton coherence, energy transfer uantum coherence is at play in many different fields. It is a crucial aspect, e.g., for coherent manipulation of quantum states in quantum computing using multifaceted systems13 as well as for natural phenomena like photosynthetic light harvesting. The latter relies indeed on efficient and unidirectional coherent excitonic energy transfer during the ultrafast initial stages of photosynthesis as recently evidenced and discussed by several groups46 The implementation of optical coherent control (CC) techniques grew up rapidly together with the emergence of the concept of selective control of chemical reactions: CC of the transfer and dynamics of nuclear wavepackets in the excited states of molecules is primarily at the center of the studies as illustrated by the work of Scherer et al. precursor in the field.7 More recently nonlinear optical techniques such as two-dimensionnal (2D) electronic spectroscopy enabled significant advances in the identification and characterization of coherent energy transport and electronic temporal coherence in complex systems such as photosynthetic proteins,5,8 molecular aggregates,9 and artificial polymers.10 Most elaborate techniques in CC now combine phase control and shaping schemes of optical pulses and usual wave mixing processes of 2D spectroscopy.1113 Specific interaction mechanisms or nonlinear signal contributions can thus be isolated, and a better robustness to noise is expected. CC of electronic states and most especially of the neutral exciton in a single object is not common despite the sustained activity in the field (see for instance refs 1315). In a single quantum dot (QD) coherence has been investigated by a few groups,16,17 using a pair of picosecond phase-locked excitation pulses since the pioneering work of Bonadeo et al.18 This type of excitation combined with detection at the single object scale is a
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powerful approach to explore the quantum coherent physics of individual molecules as well: very recently the coherent superposition of ground and excited states of a single molecule was established and monitored at room temperature; the feasibility of a manipulation of the molecular two level Bloch vector at the femtosecond scale was also demonstrated.19 CC of single objects is thus a sophisticated tool to reveal decoherence mechanisms like scattering with phonons for a QD, structural relaxation for a single molecule. The present work concerns a single true 1D extended system. To our knowledge, this is the only study of CC of an excitonic state in a single extended system, a highly ordered conjugated polymer, except for our preliminary results where a vibronic state was prepared and studied.20 Let us note that the coherence of resonant Rayleigh scattering has already been probed in conjugated poly(phenylene vinylene) chains21 but in contrast to the present work this early study delt with averaged signals from a large ensemble of poorly characterized material as far as order is concerned. The topochemical character of the diacetylene polymerization reaction allows us to obtain extended quasi-1D systems: polydiacetylene (PDA) chains diluted in their monomer crystalline matrix. Detailed operations for the host crystal growth can be found in ref 22. Once obtained, the crystals are kept in the dark at low temperature (∼250 K) to preserve them from polymerization. In this manner the chain average concentration is brought down to 108 in weight.23 In these highly dilluted mixed systems, the π-conjugated chains are several micrometers Received: September 13, 2011 Published: September 19, 2011 4496
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Nano Letters long (see Figure 2 below) and isolated from one another within the crystal matrix; they provide an excellent experimental model for the study of electronic properties of conjugated polymers. These are 1D crystals as close as possible to the ideal representation used by theoreticians for modeling a conjugated chain and exploring the relation between chain conformation and its electronic structure.2427 Note that for embedded PDA chains in single crystals, selective excitation of ground state vibrational modes by a stimulated Raman process (using a feedback-controlled selflearning loop) was demonstrated by Zeidler and co-workers.28 The PDA chains studied here behave like semiconducting quantum wires with a radiative lifetime temperature variation following the characteristic behavior for a thermalized exciton band,25,2932 also observed in a single inorganic nanostructure33 and ensembles of single-walled carbon nanotubes.34,35 We have previously demonstrated the spatial macroscopic coherence of the excitonic radiative steady state of a single polymer chain36 thanks to an interferometric method also used by Wertz et al. to evidence the spatial macroscopic coherence in very extended polariton condensates.37 It seems important to emphasize that in the systems under focus, the long-range spatial coherence develops in chains carrying in average a single excitation; coherence thus cannot result from purely photonic effects in the crystal such as lasing enabled by efficient light confinement, as observed in various nanowires made of organic38,39 or inorganic materials.4042 In this paper we study single PDA chains with a typical length close to 10 μm emitting a strong excitonic resonance fluorescence (zero-phonon line) and several weaker vibronic replicas.43 The possible very high dilution of such chains and their emission properties allow addressing the response of a single isolated object in a microphotoluminescence experiment with a high spectral resolution and a spatial resolution at the laser wavelength scale.23,44 In these conditions, complete elimination of ensemble averaging is reached. To achieve the coherent control of the excitonic emission, a pair of phase-locked pulses is produced in a stabilized Michelson interferometer having a λ/50 resolution. The principle of the active stabilization can be found in ref 45. At λ0 = 543 nm the pulses, delivered by an optical parametric oscillator, have temporal widths slightly less than 1 ps. The pulses are focused on the sample using a 0.6 numerical aperture objective through which the luminescence is also collected. The transverse size of the spot in the waist region is in the micrometer range (∼1 μm) so that a single polymer chain can be addressed individually.23 The far field luminescence is detected by a cooled CCD camera combined to a Jobin-Yvon imaging spectrometer with an overall energy resolution of 50 μeV. In the matrix the chains are all parallel and their axis define the orientation of the transition dipoles43 which are excited using linearly polarized fields. The experiments are performed at low temperature between 4 and 25 K; to that purpose the samples are fixed on the coldfinger of a microphotoluminescence cryostat with enhanced mechanic stability. In this work we study isolated red chains of the 3BCMU polydiacetylene (see formula and crystal structure in ref 46). The zero phonon emission of such chains is resonant in energy with the excitonic transition so that it cannot be separated from the laser Rayleigh scattering contribution. In the control process the laser is thus tuned onto the excitonic transition (λ0 ∼ 543 nm) but the measured signal is a secondary emission displaced in energy (D luminescence at λD ∼ 592 nm). A photon is created in the D line as the exciton recombines and an optical phonon associated to the CdC stretching mode of the polymer backbone with energy ED = 184 meV is emitted in the ground state
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Figure 1. Schematic representation of the processes at play in the relaxation of excitons in a single chain of poly-3BCMU. Due to energy conservation and momentum selection rules only photons with k < kph max can transfer momentum to the chain; the photon dispersion curves appear as blue lines on the figure. X is the exciton band considered as parabolic in the relevant energy range; Δrad contains the excitonic states coupled to light in absorption and emission which contribute to the homogeneous zero-phonon line (emission process (1)). The D emission originates from a band of states ΔD rad (processes (2) and (3)) and corresponds to recombinations of exciton states to the ground state of the chain plus one optical D phonon which dispersion can be neglected in the relevant energy range. States within ΔD rad are populated through excitonphonon scattering.32
(see energy diagram of Figure 1). The vibronic D emission is thus a leakage channel useful for probing the exciton state coherence and population properties and their optical manipulation. The excited state dynamics is driven, at resonance, by a train of two pulses: in a two levels system with bare eigenstates |aæ, |bæ, a coherent superposition of |aæ and |bæ is created through the first pulse interaction; in absence of both energy and phase relaxation the superposition at t is determined by the “pulse area” parameter Z t μE 0 ðt 0 Þ=p dt 0 θt ¼ ∞
E 0 being the pulse envelope and μ the dipolar moment of the transition. The linear combination left by the first pulse is then probed by the second pulse.17 For identical nonoverlapping pulses (with a square envelope) delayed by a time τ, in absence of relaxation and under the assumption of resonant excitation, an analytic solution is possible and the wave function prepared by the pulse sequence reads: ψðT þ τÞ i Ω T Ω T 0 0 ¼ cos2 sin2 eij ai 2 2
+ Ω0 T Ω0 T ij iω0 T þ i cos sin ð1 þ e Þ e b 2 2 ð1Þ 4497
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Figure 2. Spectrally resolved D emission of a single chain at 4 K (blue curve) and 22 K (red curve). Inset: spatial emission pattern of the chain at 4 K and associated longitudinal cross section (line plus square symbols in the inset). A length of ∼10 μm is deduced from the emission profile.
Figure 3. (a) Variation of the D line emission intensity with the relative phase between the exciting pulses at 4 K: τ = 3.0 ps (filled circles) and τ = 7.0 ps (open circles); the red continuous lines are the fits obtained using the model of Figure 5. (b) Visibility decays measured on the same single chain at 4 K (filled squares) and 8 K (filled diamonds) and their numerical adjustments (dashed lines). The rapidly decreasing curve (open squares) is the experimental autocorrelation function of the laser pulse; the superimposed continuous line is the fit from simulations using Fourier transform limited pulses of width Δt = 0.7 ps.
)
)
the chain direction, with a matrix index n ∼ 1.56 and an objective focal length f = 8 103 m calculations show weak alteration in the incident Gaussian spectrum which defines the Gaussian plane waves wavepacket the chain is coupled to. In this representation a wavepacket of low energy states is thus photocreated with a cutoff in its spectrum at k = kph max and kph max = (2π/λ0) sin θmax where θmax is determined by the objective numerical aperture (NA = sin θmax). Knowing the exciton effective mass26,31 and considering the quantization of k in the wire, we estimate that ∼25 states are coupled to light through resonant excitation in a chain of length 10 μm.36 Let us note that those states are enclosed in a band of width Δrad ∼ 10 μeV (Figure 1) so the components of the photogenerated wavepacket are quasidegenerate states in energy. Figure 2 displays the single chain spectrum of the D emission measured at 4 K under resonant excitation of the excitonic transition. Since the phonon band dispersion is much smaller than the exciton, it can be neglected: any k state with energy E can participate to the emission process as inferred by momentum and energy conservation. k is conserved in the transition (vertical transition) and the exciton energy shared between the phonon and the emitted photon: E = ED + hc/λD. The D emission thus corresponds to transitions originating both from the states initially )
)
where Ω0T = θ∞ and T stands for the pulse duration. j is the pulse dephasing corresponding to a delay shorter than the optical cycle of the laser, 2π/ω0. If j = 0, eq 1 shows, as expected, that the sequence of pulse is equivalent to a unique pulse with a doubled area. If j = π, the system is left in its ground state |aæ and the luminescence from |bæ is completely suppressed. By adjusting the dephasing, j, chosen combinations can be attained. In the peculiar situation of perfectly isolated systems not subjected to spontaneous emission, |ψ(T + τ)æ is obviously independent of τ. In real systems inelastic scattering processes such as exciton exciton or excitonphonon interaction or spontaneous emission will affect the phase of the excitonic wave function within the pulses interval so the combination prepared by the first pulse (to be probed by the second pulse) will be modified. The analysis of the final states structure through emission measurements then provides a relatively straightforward access to the dephasing dynamics of the exciton. For instance, phase relaxation will blur the formation of the pure |aæ state obtained for π-dephased pulses in the ideal frame of eq 1 hence leading to only partial extinction of luminescence. The level of extinction is the main experimental criterion addressed in the present work. At low temperature, the exciton lifetime is several tens of picoseconds31 and remains much shorter than the interval given by the repetition rate of the laser (τr ∼ 12.2 ns) so that the system has entirely relaxed far before the arrival of a new sequence of pulses. For a given phase and delay the measured time integrated signal thus corresponds to the same control experiment averaged ∼82 106 times per second. Temporal pulse characterization is achieved through interferometric autocorrelation using elastic scattering as a probe. An autocorrelation trace is presented in Figure 3b showing that the nominal resolution is attained. In the experiments the pump fluence is also kept sufficiently low so that θ∞ is effectively much smaller than unity. Due to momentum conservation only states in the 1D exciton band having their wavevector k = k equal to kph, the photon momentum, will be populated through light interaction (in Figure 1 the blue lines stand for the light dispersion curves). The spatial Fourier spectrum of the electric field component parallel to the chain was estimated in the focal region taking into account the experimental configuration of strongly focused fields near planar surfaces;47 for an incident field linearly polarized in
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coupled to light, at k ∼ 0, and those at higher energy in the band; they are all enclosed in an energy band of width ΔDrad. Population of the latter results in a complex dynamics involving the absorption of an acoustic phonon and subsequent relaxation in the band assisted by the emission of 3D acoustic phonons of the matrix (see Figure 1 caption).32 An accurate description of the control process should thus take intraband relaxation into account (see model further below). One also notes that the D line keeps a Lorentzian shape indicating a weak influence of the 1D density of states on the occupation function in the explored temperature range (T < 25 K). As shown in the inset of Figure 2 the extension of the D emission reaches several micrometers despite the localized nature of the excitation and will be associated to extended single exciton states on which quantum control is carried out. Let us point that in polydiacetylene chains, homogeneous line broadening of a given vibronic transition in emission is dominated by the relaxation properties (population and phase) of the emitted phonon not by the initial k state involved in the transition.32,48,49 This means that ΓD ∼ 1 meV at 4 K does not provide the extension in energy of the emitting band contributing to the D line (ΔD rad). To sum up the interaction between the wire (polymer chain) and light can be depicted as follows: Excitations are generated in a narrow band of the exciton band (gray region of width Δrad in Figure 1). Photoexcitation outside this band (green region) is prohibited by momentum conservation as the momentum of photons (the blue lines represent the light dispersion curves) is smaller than the momentum of excitons anywhere outside the Δrad band. The photogenerated excitations, however, can scatter from phonons and travel from the gray region into the green region.32 Emission to the ground state is possible from either gray or green bands to the ground state (green arrow) or to the vibrationaly excited ground state (orange arrows into the D band). In this work, the conjugated chain is excited by a pair of pulses with variable delays and controllable relative phases; only states of the gray region are coupled to light. We study how the relative phase and delay of the two excitations affect the quantity of photoemission into the D band. Phase sensitivity of spontaneous emission and dynamics of exciton dephasing are evaluated through a visibility function Cj1 , j2 ðτÞ ¼
IFmax ðj1 Þ IFmin ðj2 Þ IFmax ðj1 Þ þ IFmin ðj2 Þ
where IF corresponds to the time integrated D luminescence measured at a given delay τ and the phase argument is the interpulse phase difference. In a two level framework (j1,j2) = (0,π) if excitation is purely resonant. The presence of a detuning shifts both the absolute j1 and j2 values but the difference j = j2 j1 remains equal to π. In our experiments the excitation energy is always within the homogeneous width of the absorption, so detuning is always less or comparable to half the line width. To reach the visibility function j is thus scanned between 0 and 2π and corresponding IF(j) measured (see Figure 3a as illustration). Within the experimental accuracy Cj1,j2 was always found to coincide with Cj1,j2=j1+π. Figure 3b shows typical visibility decays measured on the same chain at different temperatures. Apart from very early (subpicosecond) delays, the curves are well fitted by decreasing monoexponential functions of τ. It will be checked later on that in the weak coupling regime the constant decay identifies with the exciton dephasing time, T2. A dephasing dynamics of the
Figure 4. Upper panel: spatially resolved emission of a single chain with varying phase between excitation pulses (T = 6 K); there is nearly no temporal overlap between the pulses at the considered delay, τ = 2.5 ps. Spatial resolution is ∼1 μm well below the chain length estimated here around 18 μm. Correction for the background (due to dark counts) was applied to the data. Lower panel: visibility associated with the emission pattern.
photogenerated exciton is thus characterized and optical control of the excitonic population is demonstrated in the addressed wire. It is worth noting that a significant visibility is measured outside the time interval corresponding to the pulses overlap so that the extracted dynamics can be distinguished from coherent effects related to the superposition of the excitation fields. As temperature is raised, the number of scattering events is increased and faster dephasing dynamics are measured. The loss of temporal coherence is almost 3 times faster at 8 K than at 4 K. Further insights into the nature of the controlled states is gained through luminescence imaging. Figure 4 compares the D emission of a single chain, of length ∼18 μm, for three different values of the relative phase of the pulse sequence for a delay τ = 2.5 ps and a temperature of 6 K. Despite the localized nature of the excitation, the control operates at any point along the chain; the emission profiles remain the same as j is varied and the visibility estimated at each position along the chain remains constant. Numerical integration of the spatial intensity distribution provides a mean visibility value of ∼0.55 which fits with the measured value when spatially integrating the emission signal at this temperature. The present results can hardly be understood if extended states are not considered: the control of the whole emission from a local excitation is fully consistent with the quasimacroscopic coherence (at the chain scale) of the single exciton states demonstrated in a previous contribution.36 As previously 4499
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Nano Letters mentioned the initially photocreated wavepacket, peaked at the spot position, is made of extended k states. Rapid intercomponent temporal dephasing leads to the wavepacket spreading and thus determines the delocalization dynamics. This picture is compatible with the idea of large spatial area explored by the exciton center of mass and the ultrashort dynamics associated to it, as demonstrated through time-resolved spectroscopy in imaging configuration.20 Assuming that the control is effective on each component of such wavepacket, one explains that a spatially extended control is achieved even if both excitations are focused at the same single point. It will be considered in the following that due to the close packing in energy of the involved states (Δrad , ΔEp where ΔEp ∼ 1.7 meV is the energy pulse width) effects which could result from varying detunings can be neglected; the control is thus achieved in a similar manner onto all wavepacket components. To adjust the visibility decays at each temperature and gain insights into the origin of the fast recorded dynamics, one has to look closer at the influence of the exciton band structure. As mentioned earlier the D line from which visibility is extracted is indeed composed of transitions (assisted by phonon emission) from any k state in the exciton band to the ground state whereas the control operates on the restricted ensemble of states coupled to light in absorption, those in the band of width Δrad. One may thus question the influence of emitting hot states, populated through thermalization but not subjected to control since not probed by the second pulse. Taking into account the temporal evolution of the exciton distribution function is a very complex task well beyond the objectives of the present work. This has been addressed in 2D geometry in semiconducting structures, for instance in refs 50 and 51, but to our knowledge was never attempted in quantum wires. As a first approach the dynamics of thermalization was thus considered using an elementary four discrete levels model whose dynamics is ruled by Bloch equations (see Figure 5). |0æ is the vacuum state. The excitonic wavepacket is described using a single level (state |1æ) whereas level |2æ stands for higher energy states in the band not directly coupled to the excitation fields (states in the interval ΔD rad but outside Δrad). Equilibrium dynamics is driven by two transfer rates kup and kdown and the ratio r = kup/kdown is adjusted at each temperature T, so that the populations of levels 1 and 2 at times beyond the initial transitory regime, reflect the distribution of states in the band at thermal equilibrium. r(T) is estimated in the limit of a continuous energy distribution of states in the band52,53 taking into account the 1/(E E0)1/2 dependence of the density of states.32,52 The D emission intensity is proportional to the population of states 1 and 2; hyperbolic secant functions model the pulses envelopes E 0. Note that E 0 is kept low enough so that the emission intensity remains proportionnal to the excitation intensity (E 20) in a one pulse experiment (weak coupling regime). In the present model the effective lifetime T1 is implicitly taken independent of k and its temperature dependence extracted from the data of ref 31. Population of |2æ physically results from thermal excitation which is expected to be an incoherent process; the latter cannot produce any coherent superposition mixing |2æ and the other states. On the contrary a dephasing time T2 is included in the model to describe the damping of coherence between the ground state and the exciton, |1æ. The following additionnal approximation is done: T2 = 2T1Tup/(T1 + Tup),Tup = 1/kup. This means that the coherence time of the exciton state is determined by its overall effective lifetime; so processes which affect the phase of |1æ without causing energy relaxation (such processes contribute to a
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Figure 5. A four level model used to simulate the temperature dependence of the visibility decays; the excitonic wavepacket is replaced by a single state, |1æ, whereas |2æ stands for higher energy states populated through thermalization. kup/kdown is adjusted with temperature so that the equilibrium ratio of populations F22/F11 reflects the actual one in a 1D band for a bosonic distribution of excitons. The green arrow marks the excitation transition; visibility is calculated using the total emission |1æ f |0Dæ plus |2æ f |0Dæ (orange arrows) where |0Dæ stands for the state of the chain dressed with one optical phonon (associated to the stretching mode of the CdC bond).
pure dephasing time54,55) have much slower dynamics compared to the one defined by T10 = T1Tup/(T1 + Tup). Global consistency of this assumption will be checked below. Detected emission originates from both |1æ f |0Dæ and |2æ f |0Dæ transitions where |0Dæ stands for the ground state of the chain dressed with one D phonon. Luminescence of the D line is thus proportional to the total excited state population F11 + F22. It is reasonable to consider that the residual vibrational energy in the ground state is dissipated before a sequence of pulses excites the system again. Note also that τ is 1 order of magnitude smaller than T1 which determines the population dynamics of |0Dæ so that, in good approximation, there is no channel feeding the vacuum state in the interpulse duration. Within the two previous assumptions it is no longer necessary to explicitly describe the |0Dæ f |0æ dynamics. At that point kup is the only adjustable parameter remaining in the simulations. The exponential nature of the visibility decays is preserved up to 24 K, and a quasi-perfect adjustment is possible whatever the temperature (two fits are shown in Figure 3b). In the weak coupling regime the decay time in C(τ) is found to identify with T2 and the amount of detuning has no influence on the simulation. As we also have Tup , T1 in the simulations, T2 ∼ 2Tup and the measured dephasing time thus more directly reflects the short effective lifetime of the prepared excitonic states in the k ∼ 0 region. It is however not representative of purely dephasing processes which would affect long lifetime species not subjected to energy relaxation. For low excitonic density, scattering of excitons by acoustic phonons is assumed to be the mechanism ensuring thermalization;50 C(τ) is directly related to the fraction of these states having not experienced any scattering events after a time τ. In Figure 6, T2, deduced from 25 experiments on several chains, is plotted versus temperature together with the quantity τ0 = 1/(2πΔν0), Δν0 being the homogeneous line width of the zero phonon line. Within experimental accuracy T2 ∼ 2τ0. This relation corroborates the assumption of large pure dephasing times, T2* (.τ0), through eq 2 in which T10 equals τ0. 1 1 1 ¼ 0 þ T2 T2 2T1 4500
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Figure 6. Temperature dependence of the exciton dephasing time, T2, deduced from the model (red open squares). T2 is compared to τ0, the caracteristic time extracted from the homogeneous width of the zero phonon line (filled diamonds) and twice its value (open diamonds). The extraction of dephasing times from the visibility decays leads to uncertainty typically less than 5%; consequently error bars were not added to enhance clarity. The moderate dispersion of data can be assigned to slight differences in the chainmatrix coupling. Inset: Comparison, at 4 K, between the zero phonon emission line (red solid circles) and the vibronic D line (black open circles). The blue lines correspond to the Lorentzian fits; the D spectrum is displaced in energy by an amount ED = 184 meV for clarity reasons. The D line width, ΓD∼1 meV, is almost 5 times the zero phonon line width (Γ0∼220 μeV). The additional broadening in the D line is due to contribution from the final state in the transition32 (optical phonon). The homogeneous width of the vibronic line does not reflect the coherence properties of the bare excitonic states, explaining why τ0 has to be extracted from the homogeneous width of the zero phonon line.
To sum up, the coherence of primary excitations in the wire is limited by the short lifetime of an optically prepared state before scattering to another band state. Prepared k ∼ 0 states are initially cold states redistributed in the 1D band at the picosecond scale. The homogeneous width of the zero phonon line is a direct measurement of the scattering dynamics of photogenerated exciton to upper states. The semiquantitative relation found between T2 and τ0 in a simplified discrete levels model clearly points to difference in time scales whether pure dephasing or scattering processes are considered. Thermalization occurs within a few picoseconds and pure dephasing time seems to be at least 1 order of magnitude larger. To our knowledge this is one of the first estimations, at the single molecule scale, of pure dephasing time of spatially extended excitonic states. It is important to point that the T2 values measured in this work compare well with the values deduced from line width measurements in another conjugated polymer presenting reduced conformational disorder (β-phase of poly(dioctylfluorene)).56 The authors stress the idea of the “control” by the chain conformation of the excitonic line width transition: strong intersite coupling restrains exciton scattering hence leads to enhanced temporal coherence and reduced line widths. As pointed up in the present work, in the limit of long-range quasi-ideal intramolecular order, coupling to the environment also becomes decisive in determining the dephasing properties. In this direction intraband relaxation resulting from the interaction between a 1D conjugated crystal and the phonon modes (delocalized or not) of its surrounding matrix still asks for rigorous theoretical developments. Finally let us note that very narrow line widths were detected in the fluorecence spectra of single MEH-PPV chains
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embedded in poly(methyl methacrylate);57 the homogeneous width is not determined by the excited state lifetime and has to be associated to at least 1 order of magnitude larger coherence times. Unlike the present situation where long-range spatial coherence develops, the observation refers to a coiled conformation of the polymer best described in terms of conjugation length distribution. The narrow emission is attributed to the excitation of a chromophoric units composed of a few repeat units of the polymer; it is the signature of a relatively localized excitation less efficiently coupled to the surrounding medium and which description instead is more relevant to single molecule spectroscopy. Coherent control clearly helps elucidate the mechanisms by which phase relaxation occurs in single conjugated chains having excitons as primary excitations. The control is performed here through sequential excitation of the wire at the same single point. The spatial extension of the excitonic states as well as the wavepacket nature of the photocreated excitations open intriguing future prospects. All optical control of energy transfer along the wire at the molecule scale indeed seems possible in wavepacket interferometry experiments where the two pulses are focused at different positions along the wire and generate phase locked wavepackets. Such experiments will be at the center of forthcoming work.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We warmly thank Dr. Michel Schott for fruitful discussions. We are indebted to Charlotte Bourgeois for providing the monomer molecules. We thank Michel Menant and Mathieu Bernard for technical support in cryogenics. Financial support from the C’Nano IdF Foundation (CEFQUO project) is also gratefully acknowledged. ’ REFERENCES (1) Benett, C. H.; DiVicenzo, D. P. Nature 2000, 404, 247–255. (2) Imamoglu, A.; Awschalom, D. D.; Burkard, G.; DiVicenzo, D. P.; Loss, D.; Sherwin, M.; Small, A. Phys. Rev. Lett. 1999, 83, 4204–4207. (3) Cirac, J. I.; Zoller, P. Nature 2000, 404, 579–581. (4) Collini, E.; Wong, C. Y.; Wilk, K. E.; Curmi, P. M. G.; Brumer, P.; Scholes, G. D. Nature 2010, 463, 644–648. (5) Lee, H.; Cheng, Y.-C.; Fleming, G. R. Science 2007, 316, 1462–1465. (6) Engel, G. S.; Calhoun, T. R.; Read, E. L.; Ahn, T. K.; Mancal, T.; Cheng, Y.-C.; Blankenship, R. E.; Fleming, G. R. Nature 2007, 446, 782–786. (7) Scherer, F.; Carlson, R. J.; Matro, A.; Du, M.; Ruggiero, A. J.; Romero-Rochin, V.; Cina, J. A.; Fleming, G. R.; Rice, S. A. J. Chem. Phys. 1991, 95, 1487–1511. (8) Harel, E.; Fidler, A. F.; Engel, G. S. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 16444–16447. (9) Ginsberg, N. S.; Cheng, Y. C.; Fleming, G. R. Acc. Chem. Res. 2009, 42, 1352–1363. (10) Collini, E.; Scholes, G. D. Science 2009, 323, 369–373. (11) Tian, P.; Keusters, D.; Suzaki, Y.; Warren, W. S. Science 2003, 300, 1553–1555. (12) Tekavec, P. F.; Lott, G. A.; Marcus, A. H. J. Chem. Phys. 2007, 127, 214307. (13) Stone, K. W.; Gundogdu, K.; Turner, D. B.; Li, X.; Cundiff, S. T.; Nelson, K. A. Science 2009, 324, 1169–1173. 4501
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