After the sequence of introductory chapters that collected the necessary tools, we are now ready to discuss complete experiments. The first type of experiment we consider is the creation and detection of order in multilevel atoms through coherent Raman processes. The atoms that we use to study these processes are rare earth ions in a crystal matrix. Enclosing them in a crystal allows long interaction times, but also makes it necessary to consider their interaction with neighbouring atoms. Overview Raman processes Introduction In the preceding chapters, we mentioned several types of Raman processes. Their common feature is a resonant change of the energy of the photons that interact with the material system. The energy of the scattered photons may be lower (Stokes process) or higher (anti-Stokes) than that of the incident photons. The energy difference is transferred to the material system, where it must match an energy level separation. The photon energy itself, however, does not have to match exactly a transition frequency of the medium. This is commonly expressed by the statement that the Raman scattering proceeds through a virtual state, represented by the dashed line in Figure 7.1. The presence of a real state of the atom, indicated by the full line, nevertheless increases the coupling efficiency, as discussed in Chapter 3. The earlier sections on three-level effects and optical anisotropy dealt with the mathematical formalism of Raman processes, using generic level systems to describe them.
After the sequence of introductory chapters that collected the necessary tools, we are now ready to discuss complete experiments. The first type of experiment we consider is the creation and detection of order in multilevel atoms through coherent Raman processes. The atoms that we use to study these processes are rare earth ions in a crystal matrix. Enclosing them in a crystal allows long interaction times, but also makes it necessary to consider their interaction with neighbouring atoms. Overview Raman processes Introduction In the preceding chapters, we mentioned several types of Raman processes. Their common feature is a resonant change of the energy of the photons that interact with the material system. The energy of the scattered photons may be lower (Stokes process) or higher (anti-Stokes) than that of the incident photons. The energy difference is transferred to the material system, where it must match an energy level separation. The photon energy itself, however, does not have to match exactly a transition frequency of the medium. This is commonly expressed by the statement that the Raman scattering proceeds through a virtual state, represented by the dashed line in Figure 7.1. The presence of a real state of the atom, indicated by the full line, nevertheless increases the coupling efficiency, as discussed in Chapter 3. The earlier sections on three-level effects and optical anisotropy dealt with the mathematical formalism of Raman processes, using generic level systems to describe them.
The traditional Raman process alluded to in Chap. 13 is a three-state sequence of transitions in which radiative excitation (induced by a pump field) is followed by spontaneous emission that produces a final state differing from the initial state [Her50b] [Sho90, § 17.5]. When the final state of the sequence is more energetic than the initial state the resulting emission line (to the red of the pump wavelength) is known as a Stokes spectral line. The difference between the pump frequency and the Stokes frequency, the Raman frequency , defines the excitation energy of the final state relative to the initial state. When, instead, the final state has lower energy than the initial state, as can occur when the initial quantum state is already excited, then the emission is an anti-Stokes line, at a bluer wavelength than the pump field. The overall Raman scattering is a two-photon process. Typically Raman spectroscopy deals with molecules; the two-photon transitions are then between vibrational-rotational states, through electronically excited intermediate states, that are characterized in part by vibrational quantum number v and rotational angular momentum quantum numbers J, M . From any given excited electronic state there are many fluorescing transitions, corresponding to various vibrational and rotational quantum numbers of the final state. The wavelengths of the various Stokes and anti-Stokes lines (i.e. the Raman frequencies) characterize the particular molecular species, and so they have provided a valuable diagnostic tool for spectroscopists.
Raman scattering is a two-photon process [1]. As illustrated in Fig. la, an incident photon is annihilated and a new photon of a different frequency is created. This implies that the scattering is inelastic, and the medium is left in a different energy state. When the scattered photon is lower in energy, or frequency, it is said to be Stokes shifted. The shift in frequency of the Stokes photon is related to a characteristic frequency of the medium. This is illustrated in Fig. 2a. Calling this characteristic material excitation frequency ω)v, the Stokes frequency is then ωs = ΩL — ωv, where ωL is the incident laser frequency. Thus, Raman (Stokes) scattering results in an excitation from the ground state of the medium to an excited state mediated by a two-photon inelastic scattering. The internal material excitation can involve the creation of an excited electronic state, an excited vibrational-rotational state, a lattice vibration, a spin flip in semiconductors, or electron waves in plasmas [2]. The phenomenon occurs in gases, liquids, solids, and plasmas.
T. Blasberg: Coherent Raman scattering for optical detecti¬ on of NMR in Pr3+:YA103. Nuclear magnetic resonance (NMR) is a powerful and versatile spec¬ troscopic technique. However, conventional NMR requires samples, which has to consist of at least 1017 nuclear spins. One of the most promising approaches to increase the sensitivity of this method relies on the resonant interaction of laser fields with atoms. The main goal of this thesis was the investigation and the improvement of coherent Raman scattering techniques for an optical heterodyne detection of NMR. All ex¬ periments were performed at cryogenic temperatures on Pr3+-ions, which were added to the host lattice YAIO3 (YAP). The coherent Raman scattering experiments consist of two distinct stages: firstly, the transient or continuous excitation of a coherent superposition between two nuclear spin states and secondly, its optical detection through coherent Raman scattering of a resonant, frequency-tunable test laser field from this sublevel coherence. For the theoretical description of the experiments, coherent Raman scattering in multilevel atoms is discussed in detail and a common solution for the Raman heterodyne beat signal in pump-and-probe experiments is derived. The dynamics of a three-level atom that interacts with two resonant electromagnetic fields is treated making use of the density-matrix formalism. The method of Raman heterodyne detection of NMR uses a resonant radio frequency field to drive the magnetic-dipole transition between two nuclear spin states. This technique was used to determine the orientation of the nuclear quadrupole tensors of Pr3+ at its two non-equivalent lattice sites in YAP by measuring the dependence of the transition frequencies on the orientation of an external magnetic field. In the electronic ground state 3H4, the quantization axes of the nuclear spin eigenfunctions are ro¬ tated by po=±56.4° relative to the crystal b-axis. The corresponding rota¬ tion angle in the electronically excited state !D2 is Po=±105.2°. With this new value for the relative orientation of the quantization axes in both electronic states, the relative strengths of all 3H4 1D2 transitions could be calculated. The different orientation of the quantization axes in the two electronic states gives rise to a strong state mixing of the nuclear spin eigenfunctions and is the reason, why most of the optical transitions be¬ tween nuclear spin substates of different electronic states have similar oscillator strengths. Pr:YAP is therefore an ideal model system for the investigation of coherent Raman scattering. A new rf-optical triple-resonance experiment was developed that is a combination of Raman heterodyne detection of NMR and spectral holeburning. This technique allows the unambiguous determination of the ab¬ solute sign of nuclear quadrupole coupling constants. In the electronic ground state of PnYAP, the quadrupole coupling constant was found to be negative (D=-3.5289 MHz) being the result of dominant pseudoquadrupole contributions. The pump-and-probe technique, which uses a frequency-tunable test laser beam, was used to investigate the influence of an inhomogeneous broadening of the optical resonance line on Raman heterodyne detection of NMR. A hitherto unknown interference effect could be predicted and verified by the experiments. A prerequisite for this interference effect is that coherent Raman scattering in different opti¬ cal transitions can contribute to the total Raman heterodyne beat signal. These optical transitions represent different 'scattering pathways', whose contributions to the total beat signal can interfere destructively with each other, since the heterodyne beat signal depends linearly on the relevant transition matrix elements. The rf-optical triple resonance technique al¬ lows to circumvent this interference effect, since the frequency-tunable test laser field can be used to select only one of the various scattering pathways. A new and efficient excitation scheme was developed, which allows the observation of coherent Raman beats in systems with arbitrary wide sublevel spectra and small oscillator strengths. The method utilizes a bichromatic laser field for the purely optical excitation of a coherent superposition between two nuclear spin substates. For the preparation of the sublevel coherence, the two frequency components couple two different nuclear spin substates of the same electronic state to a different electronic state. With the help of the density-matrix formalism, the dyna¬ mics of a three-level atom during the bichromatic excitation were calcu¬ lated. Those experimental parameters could be identified that determine the excitation efficiency. While in the purely optical method of coherent Raman beats almost 10_1 of the incident test laser photons were coherent¬ ly Raman scattered, the corresponding figure of merit of Raman hetero¬ dyne detection of NMR was less man 10-3. From the decay of hole-burning spectra in the presence of a saturating rf-field the temperature-dependence of the nuclear spin relaxation rates of Pr:YAP was determined in the temperature range 3-9 K. At low tem¬ peratures, the relaxation is dominated by mutual spin flips whereas at higher temperatures Orbach and Raman relaxation become of importan¬ ce. A simple rate-equation model allowed to calculate the entire hole-bur¬ ning spectrum of the crystal.
The optical mixing of sufficiently coherent radiations of frequency (omega) 1 and (omega) 2 inside a suitable molecular medium can result coherent radiation at new frequency (omega) 3 equals [(omega) 1 + ((omega) 1 - (omega) 2)]. If (omega) 1 is kept fixed and (omega) 2 is varied so that a condition (omega) 1 - (omega) 2 equals (omega) is reached where (omega) is a molecular frequency of the medium, then (omega) 3 equals (omega) 1 + (omega) equals 2(omega) 1 - (omega) 2. In this case (omega) 3 coincides with the anti- Stokes Raman frequency associated with the molecular frequency (omega) . This process of coherent anti-Stokes Raman Scattering (CARS) is an important nonlinear optical process which provides intense collimated signal beams and is also an excellent spectroscopic tool. CARS being a four-wave mixing process, it is of interest to study the process in multi-level system to obtain a better insight into the problem. In the current paper we investigate the different quantum statistical properties of CARS in a inhomogeneously broadened three-level system based on density-matrix formalism where both the atomic system and the radiation fields are quantised. The photon-statistics, coherence characteristics and the occurrence of anti-bunching of the CARS field, in the steady state, are investigated.
Light gets scattered when it encounters an obstacle or inhomogeneity even on a microscopic scale. A well-known example is the blue color of the sky, resulting from Rayleigh scattering of light by molecules in the air. Such redirection of energy can be used to amplify signals by taking power from a “pump” wave co-propagating with the signal in an appropriate optical medium. An example of this is provided by Raman scattering. Having said that, it is important to realize that scattering does not always occur when light interacts with a material [1]. In some cases, photons get absorbed in the medium, and their energy is eventually dissipated as heat. In other cases, the absorbed light may be re-emitted after a relatively short time delay in the form of a less energetic photon [2], a process known as fluorescence. If fluorescence takes place after a considerable delay, the same process is called phosphorescence [3]. For a photon to get absorbed by a material, its energy must correspond to the energy required by the atoms or molecules of that material to make a transition from one energy level to a higher energy level. In contrast, the scattering of photons from a material can take place without such a requirement. However, if the energy of the incident photon is close to an allowed energy transition, significant enhancement of scattering can occur.
The theory of resonant Raman scattering in the presence of intense incident and scattered light waves has been developed, using the quantum-mechanical master-equation approach. When the optical matrix elements between the resonant intermediate state and the initial and final states of the atomic system are larger than the relevant relaxation frequencies, it is shown that instead of the usual power broadening and shift of the Stokes or anti-Stokes line, each line can split into as many as five or seven lines, depending upon whether both the fields are exactly at resonance or otherwise.