Photon Echo Experiments Research Articles

Elliptical billiard-ball echo model

The billiard-ball echo model is expanded to include the effects of using sub-Doppler-linewidth lasers in photon-echo experiments. The simple heuristic model which emerges explains such echo phenomena in gases as the echo time width and the degradation of echo intensity with angling of the excitation pulses. We derive simple results in the small-pulsearea limit and give formal expressions for excitation pulses of arbitrary area.

The theory of photon echoes for strongly coupled electron–phonon systems

We calculate the photon echo decay for a strongly coupled electron–phonon system, without making unrealistic assumptions about excitation pulse durations. We find that asymptotically, the photon echo decay is exponential, and we provide a formal expression for the decay rate 1/T2 which is independent of pulse duration. In contrast to the usual results, our expression for 1/T2 is nonperturbative in the electron–phonon interaction. We calculate the dependences of the echo amplitude on pulse power and duration, finding that the strong electron–phonon coupling modifies the simple two level system result. We also focus on the relationship between the zero phonon line shape in the homogeneous optical absorption spectrum, and the photon echo decay rate. We find that the zero phonon line shape is Lorentzian, with width 1/πT2. We show that the usual optical Bloch equation approach to analyzing time-domain experiments, which normally is only applicable if the electron–phonon coupling is weak, can be extended to the case of strong coupling. These strong coupling Bloch equations are adequate for analyzing the time dependence, but not the pulse power and duration dependences, of time-domain experiments. Our results indicate that within the Condon approximation, electron–phonon coupling cannot explain the very low temperature anomaly of recent photon echo experiments on impurities in molecular crystals.

Nonphotochemical hole burning and antihole production in the mixed molecular crystal pentacene in benzoic acid

Results of narrowband hole burning experiments and picosecond photon echo experiments on pentacene in benzoic acid are presented. On burning, several new discrete pentacene absorptions (antiholes) are created. These spontaneously revert to the unburned form at low temperatures, but may also be induced to revert by optical excitation. Deuteration of the host acidic protons markedly changes the pentacene fluorescence lifetime and hole burning and recovery behavior, indicating the strong interaction of pentacene and the benzoic acid dimer hydrogen bonds. Hole burning and antihole formation are attributed to hydrogen bond tautomerism of benzoic acid dimers near excited pentacenes. Two mechanisms for this tautomerization are suggested. The homogeneous linewidth of the pentacene S0→S1 transition is measured by both photon echo and hole burning experiments. A preliminary study of the homogeneous linewidth measured by hole burning indicates the transition broadens with an 11 cm−1 thermal activation energy, which differs from measurements made by other methods.

Optical Dephasing Due to Virtual Transfer of Excitation Energy as Observed in Photon Echo Experiments of Pentacene Molecules in Crystals

Optical dephasing due to intermolecular interaction is studied for pentacence molecules introduced in naphthalene and p -terphenyl crystals by measuring the ordinary photon echo and the accumulated three-pulse echo. It is found that the reciprocal of pure dephasing time increases linearly with the guest molecule concentration at low temperature where pure dephasing is known to be temperature-independent. A new model based on virtual transfer of excitation energy, i.e. energy transfer without phonon asistance, between guest molecules is presented to interpret this dephasing process. It is shown that observed linear dependence of the line width representing pure dephasing is well interpreted by this model, and that the calculated relationship between the line width and concentration agrees with the experimental one within a factor of about two.

Temperature-dependent dephasing of delocalized dimer states of pentacene in p-terphenyl: picosecond photon echo experiments

Optical dephasing of pentacene dimers in p-terphenyl is studied. Dimer statesR 3 and R 4 exhibit an exponential temperature activation of T′ 2 which is inconsistent with a mechanism involving scattering between delocalized dimer states. Other dephasing mechanisms are discussed. An upper limit is placed on the relaxation rate from the upper dimer state, R 1, to R 3

Collision kernels and laser spectroscopy

Collisional processes occurring within an atomic vapor can be conveniently described in terms of collision kernels. The population kernel ${W}_{\mathrm{ii}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}})$ gives the probability density per unit time that an "active" atom in state $i$ undergoes a collision with a perturber that changes the active atom's velocity from ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}$ to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$. For active atoms in a linear superposition of states $i$ and $j$, there is an analogous coherence kernel ${W}_{\mathrm{ij}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}) (i\ensuremath{\ne}j)$ reflecting the effects of collisions on the off-diagonal density-matrix element ${\ensuremath{\rho}}_{\mathrm{ij}}$. In this work, we discuss the general properties of the collision kernels which characterize a two-level active atom which, owing to the action of a radiation field, is in a linear superposition of its two levels. Using arguments based on the uncertainty principle, we show that collisions can be divided roughly into the following two categories: (1) collisions having impact parameters less than some characteristic radius which may be described classically and (2) collisions having impact parameters larger than this characteristic radius which give rise to diffractive scattering and must be treated using a quantum-mechanical theory. For the population kernels, collisions of type (1) can lead to a large-angle scattering component, while those of type (2) lead to a small-angle (diffractive) scattering component. For the coherence kernel, however, assuming that the collisional interaction for states $i$ and $j$ differ appreciably, only collisions of type (2) contribute, and the coherence kernel contains a small-angle scattering component only. The absence of a large-angle scattering component in the coherence kernel is linked to a collision-induced spatial separation of the trajectories associated with states $i$ and $j$. Interestingly enough, the width of the diffractive kernel, as measured in the laboratory frame, is found to be insensitive to the perturber to active-atom mass ratio. To illustrate these features, a specific calculation of the kernels is carried out using a hard-sphere model for the scattering. The relationship of the present description of collisions to that of traditional pressure-broadening theory in which trajectory separation effects are ignored is discussed. It is explained why traditional pressure-broadening theory correctly describes collision effects in linear spectroscopy, but fails to provide an adequate description of some saturation spectroscopy and photonecho experiments in which velocity-changing collisions associated with the coherence kernel play a significant role. An expression for the collisionally modified photon-echo amplitude is derived which clearly displays the role played by velocity-changing collisions associated with the coherence kernel.

Angular dependence of the spin-packet width in dilute ruby samples

The spin-packet width Delta h of the inhomogeneous resonance lines of dilute ruby samples (Cr2O3:Al2O3) has been measured as a function of the orientation of the external field H0 with respect to the crystal c axis. The results show that the broadening of the packet lines arising from the fluctuations of the superhyperfine interaction occurs within a few degrees around the parallel orientation. Moreover, this broadening mechanism is shown to be peculiar to the low-field lines of very dilute samples, since no angular dependence of Delta h was detected either in high magnetic fields or in concentrated samples. The relationship between the reported results and the results of spin-echo, photon-echo and stirring effect experiments is examined and the lack of a rigorous theory is pointed out. The authors also discuss some advantages of the method used here for measuring Delta h with respect to the traditional ones.

Optical density effects in photon echo experiments

The effects of optical density (OD) on photon echo experiments is examined both theoretically and experimentally. The theoretical treatment involves coupled Maxwell-Optical Bloch equations, and the experiments are picosecond photon echo studies of the mixed molecular crystal, pentacene in naphthalene. Under high power excitation (π/2, π) in high OD samples, the echo decays are predicted and observed to be faster than decays arising solely from the intrinsic molecular T2. The increase in the echo decay rate vanishes in the limit of low power or low OD, permitting the intrinsic molecular T2 to be measured. Previously reported concentration effects are shown to actually be optical density effects. The experimentally determined intrinsic molecular T2 of pentacene in naphthalene is shown to be independent of concentration and temperature (below ∼2 K) and T2≠2T1. It is suggested that the difference between T2 and 2T1 is due to the static multiplet level structure arising from the electronic state-phonon coupling.

Optical dephasing in a glass-like system: a photon echo study of pentacene in benzoic acid

Optical absorption and picosecond photon echo experiments are used to study the dephasing of pentacene in benzoic acid. It is shown that, while the absorption spectrum of pentacene is effected by proton transfer in the benzoic acid dimer, the dephasing is caused by elastic and inelastic phonon scattering processes.

Influence of the source bandwidth on the observation of microwave photon echoes

The fluctuations of the source frequency are shown to be responsible of an extra damping of the optical precession and of the photon echoes observed in the experiments involving many shots and an averaging of the detected signals. Assuming a phase diffusing model and various profiles for the frequency power spectrum, the r.m.s. accumulated phase error is calculated and two asymptotic behaviours are pointed out according to the relative values of the sequence duration and of the frequency correlation time. The calculation is well supported by a photon echo experiment at a 3-mm wavelength.

Delocalized electronic excitations of pentacene dimers in a p-terphenyl host: picosecond photon echo experiments

Photon echo experiments are performed on delocalized electronic excitations of optical dimer states. The delocalized dimer states are found to have very long coherence times, close to the coherent limit The dimer dephasing is qualitatively similar to dephasing of pentacene monomers.

Optical dephasing and energy migration in disordered molecular mixed crystals

Photon-echo and stimulated photon-echo experiments are used to study concentration-dependent dephasing in the mixed crystal of naphthalene in durene. The observed broadening of the homogeneous lineshape is interpreted as the effect of dipolar broadening among sets of resonant guest molecules.

Picosecond dephasing and relaxation in vibronic states of molecules in the condensed phase

We demonstrate that picosecond photon-echo and absorption-recovery experiments can be used to determine the elastic and inelastic scattering contribution to the relaxation of vibronic transitions in molecules in solids. For pentacene in naphthalene we find that, up to 14 K, dephasing is only determined by vibrational relaxation. The observed exponential activation of this process is interpreted as a decay of the initial level, via a resonant phonon, into other molecular vibrations.

High-J assignments in the 105-μm SF_6 spectrum: identification of the levels pumped by CO_2P(12) and P(22)

Quantum numbers (J values and octahedral symmetry types) of the SF6 transitions from the vibrational ground state to υ3 = 1 that fall near the CO2P(12) and P(22) laser lines have been assigned. The significance of these assignments for the results of self-induced transparency and photon-echo experiments is discussed briefly.

Polarization rotation of photon echoes in cesium vapor in a magnetic field

We report observations of the rotation of the plane of polarization of photon echoes by a weak axial magnetic field. The echoes are generated on the $6{S}_{\frac{1}{2}}$ to $7{P}_{\frac{1}{2}}$ transition in cesium (4593 \AA{}) by a sequence of two collinear laser pulses polarized in the same direction. When a magnetic field is applied along the propagation axis the polarization vector of the echo is rotated from that of the exciting pulses. We measure the intensity of the photon echo signal polarized orthogonal to the excitation pulse polarization as a function of magnetic field and pulse separation. The theoretical analysis decribes cesium atoms as a nondegenerate multilevel system, consisting of ground and excited Zeeman-split hyperfine-structure levels. The theory presented predicts the observed dependence on magnetic field strength, pulse separation, and excited- and ground-state $g$ factors. A novel method of observing photon echoes is described which uses the polarization rotation effect to replace electro-optical shutters often employed in photon echo experiments.

Quantum-beat phenomena described by quantum electrodynamics and neoclassical theory

We propose and analyze the use of quantum-beat phenomena to test neoclassical radiation theory (NCT) and quantum electrodynamics (QED). For a beam-foil type of experiment with atoms having one upper level and two closely spaced lower levels, all coherently excited, NCT predicts the presence of quantum beats in the emitted radiation; beats are not expected in QED. QED predicts beats when many atoms are present, in agreement with recent photon-echo experiments. An experiment to test NCT and QED is suggested.

Superradiant damping and absorption

We obtain a relationship between the absorption coefficient and the superradiant lifetime which shows that superradiant damping can be large only in an optically thick sample. Accordingly, we reexamine the recent photon-echo experiment of Compaan and Abella.

Line shifts in cooperative spontaneous emission

Cooperative spontaneous emission, such as observed in photon echo experiments, is proved to be frequency shifted by a measurable amount with respect to the atomic transition frequency. The theory presented here is based on a renormalization procedure which rules out unobservable contributions.

Superradiant Effects on Pulse Propagation in Resonant Media

A theoretical model for the propagation of coherent light pulses in resonant media where a large number of atoms cooperate in spontaneous emission (superradiance) is discussed. The medium is supposedly free of inhomogeneous broadening, and no lossy relaxation mechanisms are taken into account. The conditions for the emission of all spontaneous radiation in the direction of pulse propagation are described. A semi-classical model is used and, at each point in the medium, the propagation field and the spontaneous damping field are considered separately. The equation governing the evolution of a superradiant system in the presence of an applied pulse is derived. A mechanism of energy transfer from the traveling pulse to the medium is described which includes superradiant spontaneous emission effects. As a result of the neglect of all lossy relaxation processes, all energy stored in the medium is eventually returned to the pulse by coherent spontaneous emission. Therefore, in this theory, all pulses travel through the medium without energy loss. Numerical results for square input pulses are discussed which show two possible types of propagation behavior: (a) Low input intensities produce a negative tail to the input (positive) pulse and sharpening of the tail with the advance in the medium; (b) higher input intensities produce, after sufficient penetration, a steady-state pulse envelope somewhat similar to the $2\ensuremath{\pi}$ pulses of self-induced transparency. The steady-state solutions of the equations of motion are found numerically and the pulse shapes are computed for different degrees of superradiance. In the limit of strong superradiance, very asymmetric pulse envelopes of large area are found. For negligible superradiance, approximately $2\ensuremath{\pi}$ hyperbolic-secant pulses are obtained. The effects of inhomogeneous broadening are briefly considered, and the consequences of important superradiant damping in photon-echo experiments are qualitatively discussed.