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Physical review. B, Condensed matter

Bichromatic excitation of coherent Raman beats in rare-earth solids

Tilo Blasberg, Dieter Suter

Published Mar 1, 1995• 14 citations
Publisher

Abstract

In coherent Raman beat experiments a laser field coherently scatters off a material excitation that evolves under the internal Hamiltonian of the system. The Raman signal, which is observed as a beat signal between the test laser and the scattered Raman field, provides information on energy-level splittings and dephasing rates. We propose a modification of this technique, which allows, in contrast to the conventional method, the excitation of coherent Raman beats also in systems with large sublevel splittings and small oscillator strengths. For this purpose, we use a bichromatic laser field to excite the coherent superposition in the medium. We calculate the evolution of the coherence during the laser excitation analytically and discuss its dependence on various experimental parameters. We compare the theoretical results with experimental data from ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$.

DOI
10.1103/physrevb.51.6309

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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). 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Optics Letters•Oct 1, 1993•1 citation
In coherent Raman beat experiments a laser field coherently scatters off a material excitation that evolves under the internal Hamiltonian of the system. The Raman signal, which is observed as a beat signal between the test laser and the scattered Raman field, provides information on energy-level splittings and dephasing rates. We propose a modification of this technique, which allows, in contrast to the conventional method, the excitation of coherent Raman beats also in systems with large sublevel splittings and small oscillator strengths. For this purpose, we use a bichromatic laser field to excite the coherent superposition in the medium. We calculate the evolution of the coherence during the laser excitation analytically and discuss its dependence on various experimental parameters. We compare the theoretical results with experimental data from Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​.
We have observed coherent Raman beat signals from a Lambda-type three-level system in a sodium atomic vapor. The sample is first prepared in a coherent superposition state of the ground-state hyperfine levels, or a dark state, by resonant bichromatic radiation. A following sudden frequency shift of one of the excitation beams causes the beat signals. Detailed analytical calculations based on the three-level Liouville equations are presented and are compared with experimental results. This simple technique is particularly suited for the obtaining of information on the generated sublevel coherence, including magnitude, phase, and decay time.
The phenomenon of coherent Raman beats observed recently by Shoemaker and Brewer is analyzed through solutions of the coupled Maxwell-Schr\"odinger equations. The effect arises in coherently prepared molecular samples where the level degeneracy is suddenly removed by Stark-pulse switching. The problem divides into two parts: (a) a steady-state preparative regime whereby the initially degenerate quantum levels are placed in superposition by a resonant laser field, and (b) a transient regime in which coherent forward Raman scattering decays in the presence of the same laser field during a nonresonant condition. The laser and Raman light thus propagate together and produce at a detector a coherent beat with a frequency that corresponds to the level splitting between initial and final states. The beat signal possesses the remarkable property of being entirely independent of longitudinal molecular velocity in the case of a plane-wave laser beam and of being almost so for milliradian divergence. It follows that relaxation involving velocity-changing collisions and that Doppler dephasing effects are absent in coherent Raman beats, in agreement with experimental measurements of the decay rate. The effect of off-resonance excitation on the dephasing time and on the period of the beat signal is also discussed, and the possibility of a small rotation of the plane of polarization of the scattered light is included. The subject presents a new aspect of Raman scattering which can now yield precise radio-frequency splittings directly and offers a selective way of examining relaxation phenomena.
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 authors study the phenomenon of coherent Raman beats in 15N^{15}\mathrm{N}15NH3{\mathrm{H}}_{3}H3​ using a CO2{\mathrm{O}}_{2}O2​ laser and Stark switching. In particular, a three-level system in which the two upper levels always remain split by a few MHz is prepared by switching the transitions into resonance with a short Stark pulse whose bandwidth is large enough to coherently excite both transitions. When one of the coherently excited levels remains in resonance with the laser after the Stark pulse, this system exhibits a qualitatively new effect which has not been seen heretofore. For Stark shifts on the order of the upper-state splitting or smaller, the Raman beat is amplitude modulated at a frequency related to the optical nutation frequency. This is interpreted as being due to an interaction between the two-photon coherent Raman beat process and a single-photon optical nutation process which occurs simultaneously. Numerical calculations as well as a simple analytic model are presented to support this interpretation. By reducing the laser power, one can make the modulation of the Raman beat disappear. From the Raman signal in this regime the permanent electric dipole moment of 15N^{15}\mathrm{N}15NH3{\mathrm{H}}_{3}H3​ in an excited vibrational state is determined and the Raman beat decay rate measured. By comparing the latter result with a delayed optical nutation measurement we show that phase-changing collisions are negligible for the transition studied.
We show that utmost possible Raman coherence between equally populated levels can be excited by two-photon resonant bichromatic field far from one photon resonance by means of relaxation processes. On this basis we suggest a mechanism for generation of extremely short pulses with high pulse duty factor and large energy in the pulse. It can be realized in solid materials, such as the rare-earth doped dielectrics with long-lived spin coherence or nitrogen-vacancy $(N\ensuremath{-}V)$ centers in diamond and provide a simple, reliable, and convenient technique for many practical applications.
Light propagating through an optically anisotropic resonant medium excites coherent Raman fields that propagate together with the original wave; the interference between the two fields generates the well-known Raman beats. We solve the coupled-wave equations for finite optical path lengths and show how the coherent exchange of energy between the two fields leads to interference effects that distort the observed signal for different detection schemes. Theoretical analysis is compared with experimental results from the Na D1 transition.