Coherent excitation

We saw in Sect. 2.10.1 that in a coherently excited system of atoms, well-defined phase relations exist between the time-dependent wavefunctions of the atomic 

When an additional radio frequency field B = cos cot added with B L 

Excitation by visible or UV light may also create a coherent superposition of Zeeman sublevels. As an example, we consider the transition of 

However, if the exciting light is polarized perpendicularly to the magnetic field (E B), it may be regarded as superposition of and a light traveling into the z-direction, which is chosen as the quantization axis. 

In this case, the levels with m = zb 1 are populated. As long as the Zeeman splitting is smaller than the homogeneous width of the Zeeman levels (e.g., the natural linewidth Aco = 1/r), both components are excited coherently (even with monochromatic light ). The wave function of the excited state is represented by a linear combination = a ffa - of the two wavefunctions of the Zeeman sublevels m = zb 1. The fluorescence is nonisotropic, but shows an angular distribution that depends on the coefficients a,b (Vol. 2, Sect. 7.1). 

When now an additional radio frequency field = B2ocoso t is added with B Bq the dipoles are forced to process synchroneously with the RF field Bi in the xy-plane, if w = u l. This results in a macroscopic magnetic moment M = N/x, which rotates with in the x-y plane and has a phase angle tt/2 against B (Fig.2.29c). The precession of the atoms becomes coherent through their coupling to the RF field. In the quantum-mechanical description the RF field induces transitions between the Zeeman sublevels (Fig.2.29d). If the RF field B is sufficiently intense, the atoms are in a coherent superposition of both Zeeman wave functions. 

The time-dependent fluorescence from these coherently excited states shows, besides the exponential decay exp(-t/r) a beat period = ft/(Ejj-Eb) due to the different frequencies w and Wj, of the two fluorescence components (quantum beats. Sect. 12.2). 

Precession of a magnetic dipole in a homogeneous magnetic field Bq (a) Incoherent precession of the different dipoles (b) Synchronization of dipoles by a radio frequency (RF) field (c) Coherent superposition of two Zeeman sublevels (d) as the quantum-mechanical equivalent to the classical picture (c) 

Excitation by visible or UV light may also create a coherent superposition of Zeeman sublevels. As an example, we consider the transition 6 6 Pi of the Hg atom at Z = 253.7nm (Fig.2.34). In a magnetic field B= 0, 0, Bz, the upper level 6 Pi splits into three Zeeman sub-levels with magnetic quantum numbers = 0, 1. Excitation with linear polarized light (E B) only populates the level mj = 0. The fluorescence emitted from this Zeeman level is also linearly polarized. 

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A3.13.4.5 IVR DURING AND AFTER COHERENT EXCITATION GENERAL ASPECTS... 

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

McMorrow D and Lotshaw WT 1991 Dephasing and relaxation in coherently excited ensembles of intermolecular oscillators Cham. Phys. Lett. 178 69-74... 

Biegert, J., Diels, J.-C., and Milonni, P. W., 2000, Bi-chromatic 2-photon coherent excitation of sodium to provide a dual wavelength guide star. Optics... 

A light pulse of a center frequency Q impinges on an interface. Raman-active modes of nuclear motion are coherently excited via impulsive stimulated Raman scattering, when the time width of the pulse is shorter than the period of the vibration. The ultrashort light pulse has a finite frequency width related to the Fourier transformation of the time width, according to the energy-time uncertainty relation. 

A monochromatic beam of X-rays with about 1 eV bandwidth is produced by the standard beamline equipment, the undulator and the high-heat-load premonochromator being the most important parts among them. Further monochromatiza-tion down to approximately the millielectronvolt bandwidth is achieved with the high-resolution monochromator. The width of a band of a millielectronvolt, however, is much more than the inherent linewidth of the Fe y-radiation, F 10 eV, or the full range of hyperfine-split Mossbauer lines, A m 10 eV. Yet, NFS is detectable because the coherent excitation of the nuclei is caused in the... 

Kim CH, Joo T (2010) Coherent excited state intramolecular proton transfer probed by time-resolved fluorescence. Phys Chem Chem Phys. doi 10.1039/b915768a... 

Recently, Scherer et al. have used the 10-fs laser pulse with A,excitation = 860 nm to study the dynamical behavior of Rb. Sphaeroides R26 at room temperatures. In this case, due to the use of the 10-fs pulse both P band and B band are coherently excited. Thus the quantum beat behaviors are much more complicated. We have used the data given in Table I and Fig. 19 to simulate the quantum beat behaviors (see also Fig. 22). Without including the electronic coherence, the agreement between experiment and theory can not be accomplished. 

Fig. 14 Schematic representation of the STARTMAS experiment. The CT coherence excited by the initial pulse is suppressed by phase-cycling...

CARS signal originates from a coherent excitation of vibrational level nsing a pair of optical pulses, tUj ( pump ) and (o ( Stokes ), separated by a freqnency of this vibrational level, Q i.e.. 

The third pulse at frequency (o ( probe ) is scattered off the coherently excited vibration to generate the signal at the CARS freqnency, (Fignre 6.13) ... 

Coherent excitation of quantum systems by external fields is a versatile and powerful tool for application in quantum control. In particular, adiabatic evolution has been widely used to produce population transfer between discrete quantum states. Eor two states the control is by means of a varying detuning (a chirp), while for three states the change is induced, for example, by a pair of pulses, offset in time, that implement stimulated Raman adiabatic passage (STIRAP) [1-3]. STIRAP produces complete population transfer between the two end states 11) and 3) of a chain linked by two fields. In the adiabatic limit, the process places no temporary population in the middle state 2), even though the two driving fields - pump and Stokes-may be on exact resonance with their respective transitions, 1) 2)and... 

One of the most interesting applications of Femtochemistry is the stroboscopic measuring of observables related to molecular motion, for instance the vibrational periods or the breaking of a bond [1], Because femtosecond laser fields are broadband, a wave packet is created by the coherent excitation of many vibrational states, which subsequently evolves in the electronic potential following mostly a classical trajectory. This behavior is to be contrasted to narrow band selective excitation, where perhaps only two (the initial and the final) states participate in the superposition, following typically a very non-classical evolution. In this case one usually is not interested in the evolution of other observables than the populations. 

The double proton transfer of [2,2 -Bipyridyl]-3,3 -diol is investigated by UV-visible pump-probe spectroscopy with 30 fs time resolution. We find characteristic wavepacket motions for both the concerted double proton transfer and the sequential proton transfer that occur in parallel. The coherent excitation of an optically inactive, antisymmetric bending vibration is observed demonstrating that the reactive process itself and not only the optical excitation drives the vibrational motions. We show by the absence of a deuterium isotope effect that the ESIPT dynamics is entirely determined by the skeletal modes and that it should not be described by tunneling of the proton. 

Two consequences arise from this model First, the coherent excitation of normal modes can result from the reactive process and must not be caused by the optical excitation. Optically inactive modes can be excited if they contribute to the reaction path. Second, the proton is passively shifted by the skeletal movements and stays all the time in its local potential well. A substitution of the proton by a deuteron should therefore not influence the dynamics. In contrast strong variations are expected, if tunneling of the proton is the central step. 

The 196 cm"1 mode is antisymmetric and thereby optically inactive and does not appear in the Raman spectrum. Since a direct optical excitation of the mode is excluded by symmetry selection rules we conclude that it is solely excited by the single proton transfer which breaks the symmetry. This demonstrates for the first time that the coherent excitation of a vibrational mode results exclusively from an ultrafast reactive process. 

The protons of the hydroxy groups were deuterated by dissolving BP(OH)2 in cyclohexane and shaking the solution with deuterated water for several hours. After precipitation pump-probe measurements of BP(OD)2 in cyclohexane were recorded and are compared to BP(OH)2 in Fig. 4. Both samples were excited at 350 nm and probed at 505 nm. The delay of the emission rise of about 50 fs is equal in both cases and the coherent excitation of the vibrations is identical with respect to frequencies, phases and amplitudes. The ESIPT dynamics is obviously not altered by the deuteration and the mass of the proton has no influence on the transfer speed. This excludes that tunneling of the proton determines the speed of the transfer and the measurements provide the first proof for the passive behavior of the proton in the ESIPT. 

We observe the coherent excitation of an optically inactive mode proving that the reactive process itself and not only the optical excitation drives the observed vibrational motions. Further we demonstrate that during the ESIPT the proton is adiabatically shifted from one site to the other and tunneling of the proton is not rate determining. The dynamics is entirely controlled by the skeletal modes. Interestingly, this is quite similar to ground state proton transfer of HC1, where the fluctuations of the water environment enable the adiabatic process [8]. 

Fig. 2. Transmission change of CN-DHA induced at 350 nm and probed at 545 nm exponential dynamics and oscillatory behavior of the coherently excited vibronic wavepacket. Ring opening (1.2 ps) and internal conversion (13 ps) to CN-VHF-cis take place on different time scales.

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