The optical response of a two-site system driven by a pair of optical pulses in an interferometric set up has been studied theoretically by applying the density operator formalism. The one-exciton approach is taken for modeling two coupled two-level systems (TLS), the external field is presented semiclassically and bath-induced dissipative processes are included. In the δ-pulse limit the population of the excited state has been formulated to the lowest order perturbation expansion in the external field. In the limit of slow luminescence the interferogram of time-integrated total fluorescence has been calculated for pulses with constant relative phase. For phase-randomized pulses the variance of the correlated fluorescence signal as a function of the pulse delay allows direct interrogation of coherent transients and dephasing processes. Our analysis follows the principle of coherence observation by interference noise, COIN [O. Kinrot, I. Sh. Averbukh, and Y. Prior, Phys. Rev. Lett. 75, 3822 (1995)], but is a generalization of this concept to expand on electronically interacting TLS. The theoretical results demonstrate that analysis of fluorescence interference fluctuations may provide a powerful diagnostic tool for probing the initial quantum coherence of energy transfer, i.e., excitation oscillations by employing fs-fluorescence correlation measurements in stable interferometric configurations.
The optical response of a two-site system driven by a pair of optical pulses in an interferometric set up has been studied theoretically by applying the density operator formalism. The one-exciton approach is taken for modeling two coupled two-level systems (TLS), the external field is presented semiclassically and bath-induced dissipative processes are included. In the δ-pulse limit the population of the excited state has been formulated to the lowest order perturbation expansion in the external field. In the limit of slow luminescence the interferogram of time-integrated total fluorescence has been calculated for pulses with constant relative phase. For phase-randomized pulses the variance of the correlated fluorescence signal as a function of the pulse delay allows direct interrogation of coherent transients and dephasing processes. Our analysis follows the principle of coherence observation by interference noise, COIN [O. Kinrot, I. Sh. Averbukh, and Y. Prior, Phys. Rev. Lett. 75, 3822 (1995)], but is a generalization of this concept to expand on electronically interacting TLS. The theoretical results demonstrate that analysis of fluorescence interference fluctuations may provide a powerful diagnostic tool for probing the initial quantum coherence of energy transfer, i.e., excitation oscillations by employing fs-fluorescence correlation measurements in stable interferometric configurations.
The technique of COIN (coherence observation by interference noise) relies on the measurement of correlated fluorescence fluctuations subsequent to two-pulse excitation with randomized relative phase [Kinrot et al., Phys. Rev. Lett. 75, 3822 (1995)]. In this paper, a comprehensive theoretical study on the use of random-phase fluorescence interferometry in the measurement of solid-state, molecular coherence is given. Optical response functions in terms of populations expanded to second order in a perturbational approach are presented for a guest/host system that are based on a generalized Bloch–Liouville formalism including inhomogeneous site broadening and harmonic vibrational modes. The theoretical treatment is intended to explain the coherence and coherence loss mechanisms measured, very recently, in the pentacene/p-terphenyl mixed crystal at low phonon temperatures. The expressions derived within the limits of the usual approximations are quite general and valid for both δ- and finite-width pulses. The perturbative solutions reproduce the temperature variation of the experimental COIN interferograms and reveal the effects of inhomogeneous dephasing and impurity–bath coupling, quite satisfactorily.
We have measured the variance in fluorescence intensity and the spectrum of those fluctuations for two-level atoms in a phase-diffusing laser field. We compare our results with recent theoretical predictions that have been extended to include the effects of Doppler broadening and spatial variation of the laser intensity. Our study includes the effects of laser power, bandwidth, and shape (Lorentzian and non-Lorentzian) of the laser spectrum. At lower laser intensities, our measured variances versus detuning are in quantitative agreement with the theoretical predictions. At intensities above saturation, the variance is sensitive to inhomogeneities in the distribution of laser intensity in the interaction region, and only qualitative agreement is achieved. Asymmetries in the variance versus detuning resulting from correlated amplitude and phase noise have been observed. Spectra of the phase-noise-induced fluorescence-intensity fluctuations are shown to contain contributions from transients excited by the phase noise and are more sensitive to artifacts in the noise modulation process than the intensity spectrum of the laser field itself.
Spontaneous fluorescence has been used to measure the coherent femtosecond response of the organic, binary crystal pentacene/p-terphenyl. By using two-pulse excitation with phase-randomized pulses in an interferometric setup and analyzing the variance of the fluctuating intensity of correlated fluorescence photons, femtosecond beatings have been observed. The pattern of these terahertz oscillations is strongly dependent on the detuning frequency range of the exciting pulses, but is rather invariant with regard to the spectral position of the fluorescence probe window. In the interferometric regime of freely propagating pulses novel, ultrafast fluorescence carrier-wave oscillations superimposed to the beat structure have been obtained. The oscillatory signals evolve from a coherent superposition of optical free induction decays, caused by the different electronic transition energies of the pentacene absorber sites O1, O2, O3, and O4, respectively, are monitored as intrinsic, heterodyne beats by the fluorescence square detector. The major part of oscillations is thus considered to result from typical polarization interferences, but vibrational quantum beats are also extractable from the interferogram in the ultimate frequency regime of the pentacene S0→S1ν=1, S0→S1ν=2 resonances. The early picosecond-decay of the fluorescence beats reveals the mechanism of the loss of coherence to be mainly controlled by inhomogeneous dephasing at low phonon temperatures. A model of uncoupled two-level systems that includes Gaussian inhomogeneous broadening of the individual absorber sites and a Gaussian frequency distribution for the excitation pulses can account for the experimental data, quite adequately.
The ability to modify the character of fluorescent emission by a laser-controlled, optically nonlinear process has recently been shown theoretically feasible, and several possible applications have already been identified. In operation, a pulse of off-resonant probe laser beam, of sufficient intensity, is applied to a system exhibiting fluorescence, during the interval of excited-state decay following the initial excitation. The result is a rate of decay that can be controllably modified, the associated changes in fluorescence behavior affording new, chemically specific information. In this paper, a two-level emission model is employed in the further analysis of this all-optical process; the results should prove especially relevant to the analysis and imaging of physical systems employing fluorescent markers, these ranging from quantum dots to green fluorescence protein. Expressions are presented for the laser-controlled fluorescence anisotropy exhibited by samples in which the fluorophores are randomly oriented. It is also shown that, in systems with suitably configured electronic levels and symmetry properties, fluorescence emission can be produced from energy levels that would normally decay nonradiatively.
A theoretical analysis of the optical coherent transients that arise when a sample of two-level atoms is irradiated by a sequence of three broad-bandwidth pulses is presented. The first two pulses have a relative delay time of order of the correlation time of the pulse fluctuations and are sent into an atomic vapor from different directions. These pulses, whose temporal width is much greater than the delay time, can be correlated with one another and can be strong enough to saturate the two-level atomic transition. The third pulse is weak, noncorrelated with the first two, and is delayed in time so that it does not overlap them. We present a detailed examination of the transient signal that is produced when the third pulse is scattered by the spatial gratings in the population difference of atoms created by the first two pulses. Taking into account the effects of inhomogeneous and homogeneous broadening, we calculate the intensity of the transient signal, emitted in different directions, as a function of delay time. The signal is found to depend dramatically on the intensities of the excitation pulses. It is shown that, for strong excitation pulses, there is a direct dependence of the signal on the cross-correlation time of pulses ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$ that does not exist when the pulses are weak. In particular, the strongest signals exhibit a peak of width of order ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$. This peak can have a very narrow dip near its maximum whose width is much smaller than ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$, if the pulses are fully correlated. We develop a representation of the time evolution of the Bloch vector of a two-level atom, driven by time-delayed pulses, that enables us to explain our results. In this representation, the two time-delayed pulses are replaced by two fully overlapping pulses having some effective amplitudes and atomic field detunings.
The problem of the interaction between a two-level atom and a quantum electromagnetic field is treated without the use of perturbation theory, without introduction of classical fields or factorization conditions for the states, and without assumptions about loss of memory. The calculation is carried out in the Heisenberg picture, without mode decomposition, and the conclusions all refer to physically measurable quantities, such as the fluorescence detected in the far field of the atom. It is shown that in a coherent field of constant amplitude the system always settles down to a quasistationary state, and that the stationarity is a manifestation of the quantum fluctuations. A solution for the growth of the fluorescent light intensity is presented that holds for any coherent exciting field. The two-time correlation function and the spectral density of the fluorescence are calculated, and are found to agree in the long-time limit with earlier results of Mollow. The two-time intensity correlation function of the field is derived, which corresponds to measurable photoelectric pair correlations, and it is found that this reflects several quantum features of the field. It is shown that quantum fluctuations are manifest more explicitly in two-time correlations in the steady state than in transient effects, like spontaneous emission in the vacuum. The measurement of such correlations therefore presents an opportunity for further experimental tests of quantum electrodynamics.