Photon emission statistics and photon tracking in single-molecule spectroscopy of molecular aggregates: Dimers and trimers

We investigate the distribution of the number of photons emitted by a single molecule undergoing a spectral diffusion process and interacting with a continuous wave laser field. The spectral diffusion is modeled based on a stochastic approach, in the spirit of the Anderson-Kubo line shape theory. Using a generating function formalism we solve the generalized optical Bloch equations and obtain an exact analytical formula for the line shape and Mandel's Q parameter. The line shape exhibits well-known behaviors, including motional narrowing when the stochastic modulation is fast and power broadening. The Mandel parameter, describing the line shape fluctuations, exhibits a transition from a quantum sub-Poissonian behavior in the fast modulation limit to a classical super-Poissonian behavior found in the slow modulation limit. Our result is applicable for weak and strong laser fields, namely, for arbitrary Rabi frequency. We show how to choose the Rabi frequency in such a way so that the quantum sub-Poissonian nature of the emission process becomes strongest. A lower bound on Q is found and simple limiting behaviors are investigated. A nontrivial behavior is obtained in the intermediate modulation limit, when the time scales for spectral diffusion and the lifetime of the excited state become similar. A comparison is made between our results and previous ones derived, based on the semiclassical generalized Wiener-Khintchine formula.

For the first time, we report the effect of interference between different optical channels on the two-photon absorption (TPA) process in three dimensions. We have employed response theory as well as a sum-over-states (SOS) approach involving few intermediate states to calculate the TPA parameters like transition probabilities (δ(TP)) and TPA tensor elements. In order to use the limited SOS approach, we have derived a new formula for a generalized few-state-model (GFSM) in three dimensions. Due to the presence of additional terms related to the angle between different transition moment vectors, the channel interference associated with the TPA process in 3D is significantly different and much more complicated than that in 1D and 2D cases. The entire study has been carried out on the two simplest Reichardt's dyes, namely 2- and 4-(pyridinium-1-yl)-phenolate (ortho- and para-betain) in gas phase, THF, CH(3)CN and water solvents. We have meticulously inspected the effect of the additional angle related terms on the overall TPA transition probabilities of the two 3D isomeric molecules studied and found that the interfering terms involved in the δ(TP) expression contribute both constructively and destructively as well to the overall δ(TP) value. Moreover, the interfering term has a more conspicuous role in determining the net δ(TP) associated with charge transfer transition in comparison to that of π-π* transition of the studied systems. Interestingly, our model calculations suggest that, for o- and p-betain, the quenching of destructive interference associated with a particular two-photon process can be done with high polarity solvents while the enhancement of constructive interference will be achieved in solvents having relatively small polarity. All the one- and two-photon parameters are evaluated using a range separated CAMB3LYP functional.

By measuring, as a function of temperature, the nonlinear light transmittance from neodymium and ruby lasers, the ZnTe two-photon absorption (TPA) has been studied both near the direct band gap and close to the critical point ${E}_{1}$. The TPA absolute coefficients have been determined by means of the two-channel normalization technique. It has been found that for $2\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\ge}{E}_{g}$, the TPA spectrum line shape has a dependence that is peculiar to absorption involving exciton levels, while for $2\ensuremath{\hbar}\ensuremath{\omega}$ close to ${E}_{1}$, the line shape has a ${(2\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{-}{E}_{g})}^{\frac{3}{2}}$ dependence, which is typical of the "allowed-forbidden" mechanisms corresponding to the two-band model. By comparing the TPA experimental and theoretical values, it has been found that the TPA is strongly influenced both by the exciton effect and by the valence-band degeneracy.

Our work is devoted to theoretical study of the two-photon coherent spectroscopy of 7Li atoms continuously cooled in a magneto-optical trap (MOT) on the 2S–2P transition. The ultracold atoms are transferred to highly excited Rydberg states in a two-step coherent excitation process by red and UV lasers. The red laser is detuned by -600 MHz from 2S–2P transition frequency and UV laser frequency detuning is scanned in the vicinity of +600 MHz from 2P-nS(D) transition where n∼40-100 is principal quantum number. The fluorescence signal on the 2P–2S cooling transition makes it possible to obtain a two-photon absorption spectrum. Atom-field interaction is considered in the simple three-level approximation involving a density matrix formalism. It is shown that the effect of the MOT beams on the shape of the two-photon absorption line can be taken into account by an appropriate change in the 2S–nS(D) coherence decay rate.

We compare the photocarrier lifetime measured in Br-irradiated InGaAs and cold Fe-implanted InGaAsP. We also demonstrate the possibility of a two-photon absorption (TPA) process in ErAs:GaAs. The lifetime and the TPA were measured with a fiber-based 1550 nm time-resolved differential transmission (ΔT) set-up. The InGaAs-based materials show a positive ΔT with sub-picosecond lifetime, whereas ErAs:GaAs shows a negative ΔT consistent with a two-photon absorption process.

Distance measurement using two-photon absorption (TPA) process in a Si-avalanche photodiode (Si-APD) can provide a wide measurement range and high precision. The principle is based on a characteristic of TPA photocurrent that is proportional to the mean square of the optical intensity. Thanks to this square characteristic, the intensity correlation between the probe and reference lights sinusoidally modulated at the same frequency is obtained without using a complicated electrical circuit, and then the distance to the target is measured. The TPA-based distance measurement can also be applied to a multi-point fiber Bragg grating (FBG) sensor and a multicore FBG curvature sensor, where multiple FBGs with the same reflection spectrum is discriminated from the distance to each FBG. In these applications, FBGs with low reflectance should be used to suppress the interference noise due to multiple reflection between the FBGs. However, it also weakens the reflected light from the FBG and deteriorates the signal-to-noise ratio (SNR) of the detected signal. This problem cannot be solved by simply increasing the probe and pump power, because it can damage the optical components. In this study, we propose using pulsed reference light with a high peak power and synchronously sampling the signal with the pulsed light. The principle is confirmed by a distance measurement of a 5-km-long optical fiber.

A laser distance measurement using two-photon absorption (TPA) process in a Si-APD is reported. A newly developed configuration introducing serrodyne modulation suppresses the coherent interference noise, enhances TPA detection sensitivity, and reduces the system components.

We investigated a simple method to observe the growth of stimulated Brillouin scattering along an optical fiber using two-photon absorption (TPA) process in a silicon avalanche photodiode. The principle is based on the fact that the TPA photocurrent is proportional to the intensity correlation between reference light and Stokes light.

We study by an exact method the infrared multiphoton dissociation of a rotationless diatomic molecule and calculate the fragment relative momentum distribution as a function of the laser intensity and frequency, using either a square or smoothly varying pulse shape. The distribution has peaks due to multiphoton transitions. The nature of the peak structure depends on the laser intensity and whether the laser frequency is comparable to (i.e., within 20%) the ν=0 to ν=1 transition frequency (ω10) of the diatomic: If it is the distribution has bands spaced by the photon energy which contain peaks due to transitions from many bound states; if the laser frequency is not comparable to ω10, the distribution consists of isolated peaks spaced by the photon energy, which result from multiphoton transitions from the ground vibrational state. Changing the pulse shape from smoothly varying to square adds additional structure to the distributions. At sufficiently high intensities (1015 W/cm2) the high momentum peaks increase in intensity and the low momentum peaks are suppressed as the laser intensity is increased (this effect is often referred to as peak switching). At high laser intensities and frequencies comparable to ω10, classical mechanical calculations of the fragment momentum distribution give a smoothed out approximation to the quantum results and display a shifting similar to peak switching. Classical mechanics is unable to reproduce the quantum results at low intensities or at frequencies not comparable to ω10.

A theoretical study is made of the steady-state intensity and squeezing properties of the fluorescent light from a three-level-atom system in a ladder configuration, which is subject to spontaneous-emission decay to the electromagnetic-field vacuum. Two cases are examined: in the equispaced (ES) level case, the two atomic transition frequencies are nearly equal and two photon absorption processes occur from a single coherent laser field that couples both transitions and has a small detuning from each; in the non- equispaced (NES) level case, the atomic transition frequencies are rather different and two photon absorption processes occur from two coherent laser fields, each coupled to a single transition and in near resonance with it. In both cases, a situation of small two-photon detuning occurs. Optical Bloch equations for the atomic density matrix in rotating frames are given and matrix expressions for determining the steady-state populations and coherences are obtained. Analytic expressions are also given for special cases. The fluorescent intensity is obtained from the populations of the intermediate and upper states, with the normally ordered variance (NOV) for quadrature components of the fluorescent field involving, in addition, the atomic coherences. The fluorescent intensities are shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases. In both cases, the fluorescent intensities show the well known resonances from the upper state at zero two-photon detuning and from the intermediate state at zero one-photon detuning for the lower transition. However, further resonances are also found. The intermediate-state intensity displays a resonance at zero two-photon detuning. Also, the upper-state intensity shows a resonance at zero one-photon detuning for the upper transition, but only for the NES case; evidently, the transfer rate from upper to lower transition coherences destroys this resonance for the ES case. The time-averaged NOV is also shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases. For the ES case, the quadrature frequency is chosen as the single laser frequency and for the NES case, it is chosen as either the average of the two laser frequencies or the lower transition laser frequency. Squeezing occurs near zero two-photon detuning for both ES and NES cases, though only for the quadrature frequency equal to the average laser frequency in the latter case. It also occurs near zero detuning for the lower transition for both cases, though only for the quadrature frequency equal to the lower transition laser frequency in the NES case. The squeezing minima show a splitting effect for large Rabi frequencies corresponding to two-photon or one-photon Rabi splitting of the dressed atom levels for the situation near two-photon or one-photon resonance, respectively. The large squeezing near two-photon resonance for moderate Rabi frequencies and large one-photon detuning corresponds to essentially pure three-level squeezing, while that near one-photon resonance for weak Rabi frequencies involves two-level squeezing.

We report the results of an experimental study of the effects of velocity-changing collisions on two-photon and stepwise-absorption line shapes. Excitation spectra for the $3{S}_{\frac{1}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}\ensuremath{\rightarrow}4{D}_{\frac{1}{2}}$ transitions of sodium atoms undergoing collisions with foreign gas perturbers are obtained. These spectra are obtained with two cw dye lasers. One laser, the pump laser, is tuned 1.6 GHz below the $3{S}_{\frac{1}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}$ transition frequency and excites a nonthermal longitudinal velocity distribution of excited $3{P}_{\frac{1}{2}}$ atoms in the vapor. Absorption of the second (probe) laser is used to monitor the steady-state excited-state distribution which is a result of collisions with rare gas atoms. The spectra are obtained for various pressures of He, Ne, and Kr gases and are fit to a theoretical model which utilizes either the phenomenological Keilson-St\"orer or the classical hardsphere collision kernel. The theoretical model includes the effects of collisionally aided excitation of the $3{P}_{\frac{1}{2}}$ state as well as effects due to fine-structure state-changing collisions. Although both kernels are found to predict line shapes which are in reasonable agreement with the experimental results, the hard-sphere kernel is found superior as it gives a better description of the effects of large-angle scattering for heavy perturbers. Neither kernel provides a fully adequate description over the entire line profile. The experimental data is used to extract effective hard-sphere collision cross sections for collisions between sodium $3{P}_{\frac{1}{2}}$ atoms and helium, neon, and krypton perturbers.

Optical components based on two-photon absorption process in functionalized polymers

We successfully realized three-dimensional bending measurement using multi-core fiber Bragg gratings (FBGs) and two-photon absorption (TPA) process in a silicon avalanche photodiode. By the TPA-based distance measurement along with laser wavelength scanning, we identified the FBGs in four cores having almost the same Bragg wavelength and measured their reflection spectra.

A high-speed optical millimeter wave scanner has been developed and introduced into the distance displacement measurement based on two-photon absorption (TPA) process in a Si-APD. The TPA-based distance displacement measurement can measure the displacement of an object at 10 mm to 10 km away in principle. The measurement for the long distance of 10 m to 10 km was already realized by using intensity modulated light with a modulation frequency range of 10 GHz in the last study. The high-speed optical millimeter wave scanner developed in this study scanned over 100 GHz in 10 ms at its highest speed. We have successfully measured the short distance of 10 mm with a data acquisition time of 1 s and an accuracy of 6.34×10 -3 .

We have developed a fiber optic curvature sensor based on a multicore fiber Bragg grating (MCFBG) and an optical signal intensity correlation processing that uses two-photon absorption (TPA) process in a silicon avalanche photodiode (Si-APD). The developed sensor can use a relatively low cost MCFBG in which all the inscribed gratings have basically the same Bragg wavelength. The overlapped reflection spectra of the gratings are simultaneously obtained and discriminated by using intensity correlation measurement based on TPA photocurrent from a single Si-APD without using optical switches or multiple photodetectors. Our MCFBG curvature sensor can be applied to medical use such as bending, force, or shape sensors for a medical catheter and body plethysmography.