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The Journal of Chemical Physics

Pump-probe spectroscopy of H-bonds as the level-crossing problem

Anatoly I. Burshtein, B. M. Chernobrod, Andrey Sivachenko

Published Jun 15, 1998• 7 citations
Publisher

Abstract

Saturation of the H-bond absorption spectra by a strong laser field is described as a level-crossing problem with diffusional motion along the reaction coordinate. The stationary populations of the ground and excited vibronic states were found, assuming that the light induced transitions between them occur only at the point of exact resonance and the nonradiative decay of the upper state is uniform. The stationary distributions in both states are also obtained and shown to be Gaussian at slow vibrational relaxation, but essentially distorted when relaxation is faster than diffusion. The absorption spectra of the weak probe light in the frame of two-level and three-level models are calculated, which show either loss or gain in different spectral regions. The existence of bleaching and superabsorption branches in corresponding transmission spectra are confirmed.

DOI
10.1063/1.476454

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Theory of resonance fluorescence from vibronic systems: intensity and intensity correlation

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A nonperturbative treatment of the dynamical behavior of a vibronic system in a resonant, coherent, driving light field is developed. The potential energy surfaces for the vibrational motion in the electronic ground and excited state are assumed to be displaced and distorted relative to one another. A system of three integrodifferential equations is derived from the infinite set of density-matrix equations. Both approximate analytical and numerical solutions are presented for the intensity and the intensity-correlation function of the scattered light. The results are valid for arbitrary ratios of the Rabi frequency to the relaxation rates. A system with fast vibrational relaxation behaves as a two-level system. For systems with slow vibrational relaxation, the applicability of perturbation theory requires pump fields that are weaker than those of a two-level system. The Rabi oscillations occurring in a strong pump field are damped less than those of a two-level system, and the intensity substantially decreases. The long-time behavior (determined by the vibrational relaxation time) is characterized by the increase of the intensity toward its stationary value.

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Pump-probe spectra modeled with inclusion of a dipole-coupled but not dipole-probedF'state, for the case of85Rb 5S1/2(F)↔5P3/2(F') transitions

A. Żaba, E. Paul-Kwiek, K. Kowalski +5 more

We have simulated spectra of weak probe absorption from one of two hyperfine structure (hfs) components of an atomic ground state, to a hfs manifold of an upper state. A stronger coupling transition was assumed to bind the other hfs component of the ground state with the same upper hfs manifold. The purpose of this simulation was to study the impact on the spectral features in probe absorption from the presence of a state to which the electric-dipole transition is allowed for coupling, but forbidden for probing. In relation to our other (experimental) work, we considered the D2-line transitions for 85Rb. With coupling from the 5S1/2(F=2) state, as in our experiment, the 5P3/2(F'=1) state is coupled but not-probed from the 5S1/2(F=3) state. In calculations we searched for steady-state solutions of optical Bloch equations assuming a 5-level model and RWA. The collisionless (cold) atoms were considered, and we assumed that decoherence was entirely due to natural decay and exciting lasers' linewidths. We investigated probe absorption spectra as a function of both coupling-field-induced Rabi frequency Ωc, and coupling field detuning from the atomic resonances. The 5-level model spectra were compared with the corresponding spectra result of 4-level model calculations performed by omission of the 5P3/2(F'=1) level. Even for small Ωc values close to the natural linewidth, for some detunings a considerable influence of the 5P3/2(F'=1) state on the spectra was observed which cannot be ignored in interpretations.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 15, 2013•1 citation

Experimental investigations of the absorption and dispersion profiles of a strongly driven transition: Two-level system with a weak probe

Changjiang Wei, Neil B. Manson

The paper reports on experimental investigations of absorption and dispersion profiles of a strongly driven hyperfine transition at various pump field intensities and detunings when probed by a weak field. The transition lies at 5.4 MHz and corresponds to the ${\mathit{I}}_{\mathit{z}}$=0\ensuremath{\leftrightarrows}-1 nuclear magnetic transition within the electron spin singlet of the $^{3}$A ground state of the nitrogen-vacancy (NV) center in diamond. The inhomogeneous linewidth of the transition is 8 kHz whereas the homogeneous linewidth is 2.7 kHz, which is a factor of 3 larger than that limited by the population relaxations. The absorption and dispersion are obtained using Raman heterodyne detection, a coherent optically detected magnetic-resonance technique. Measurements are performed in a situation where there is an anticrossing of the ground-state electron-spin levels, as this leads to an enhancement of the hyperfine transition strengths and the optical sensitivity. Weak probe fields with Rabi frequency 0.6 kHz could then be used. The absorption and dispersion profiles were recorded for on-resonance pump fields of various strengths with Rabi frequencies of 0, 2.1, 3.7, 6.6, 11.8, and 21 kHz. In addition, the responses were recorded for an off-resonance field with a Rabi frequency of 55 kHz and detunings between -40 and +40 kHz. The corresponding response of an idealized driven two-level system has been calculated using an established density-matrix equation of motion formalism.When normalized to the profiles with no driving field, the calculated and experimental profiles are in excellent agreement. The nitrogen-vacancy system provides a very clear experimental illustration of a driven two-level system and some aspects are highlighted. For on-resonance pumping, the dispersion profile consists of a positive and a negative absorptionlike peak separated by twice the pump Rabi frequency. The peaks correspond to a significant signal strength (index of refraction) whereas at the frequency of the peaks in dispersion, the absorption is zero. The corresponding absorption profile consists of two dispersionlike features separated by twice the pump Rabi frequency, and between the two features there is negative absorption or gain. For off-resonance pumping, there are again two features. For example, in absorption response, there is an absorption peak and an amplification peak symmetrically displaced from the pump frequency by the generalized Rabi frequency. In this off-resonance pumping situation, it is pointed out that gain occurs where there is inversion in the dressed state whereas gain for the on-resonance pumping situation is achieved without population inversion in either the bare or dressed state.

Physical Review A•Jun 1, 1994•39 citations

Pump-probe spectroscopy in degenerate two-level atoms with arbitrarily strong fields

T. Zigdon, A. D. Wilson‐Gordon, Chana Goren +2 more

We review our previous work on pump-probe spectroscopy in realistic degenerate two-level systems and model systems. In particular, we discuss the role of transfer of coherence (TOC) between the ground and excited hyperfine states in producing electromagnetically-induced transparency (EIA) peaks in the probe spectrum, when an Fg goes to Fe = Fg +1 transition in an alkali-metal atom interacts with a strong pump and weak probe that have perpendicular polarizations. When the pump is rho+ polarized and the probe pi polarized, this system can be modelled by an N system. We also discuss the role of transfer of population (TOP) between the Zeeman levels of the ground hyperfine state in producing EIA peaks when the pump and probe have the same polarization. This system can be modelled using a double two-level system. The role of Doppler broadening and phase-changing collisions in modifying the EIA-TOC and EIA-TOP absorption and refraction spectra is also discussed. All these spectra were calculated using MATLAB programs that both construct and solve the relevant Bloch equations. In our recent work, we consider the effect of a strong probe on the pump absorption and refraction spectra when the pump and probe polarizations are linear and perpendicular. It is difficult to solve this problem numerically due to the large number frequencies involved. In order to simplify the problem, we considered two cases: (i) rho+ polarized pump and pi polarized probe, and (ii) rho+ polarized pump and rho- polarized probe, and investigated a series of transitions in both Rb and Cs, using modified versions of the MATLAB programs devised for the weakprobe case. A number of interesting differences from the weak-probe case were found. For example, when the probe is sufficiently strong, we found the pump and probe spectra to show complementary behavior. In addition, as the number of Zeeman levels increase, the EIA peaks become progressively sharper, and are accompanied by steeper dispersion.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 2, 2007•2 citations
Saturation of the H-bond absorption spectra by a strong laser field is described as a level-crossing problem with diffusional motion along the reaction coordinate. The stationary populations of the ground and excited vibronic states were found, assuming that the light induced transitions between them occur only at the point of exact resonance and the nonradiative decay of the upper state is uniform. The stationary distributions in both states are also obtained and shown to be Gaussian at slow vibrational relaxation, but essentially distorted when relaxation is faster than diffusion. The absorption spectra of the weak probe light in the frame of two-level and three-level models are calculated, which show either loss or gain in different spectral regions. The existence of bleaching and superabsorption branches in corresponding transmission spectra are confirmed.
The effects of a strong standing wave field on the absorption behaviour of a weak probe field are studied. An absorptive medium is assumed to consist of stationary two-level atoms with arbitrary decay and pumping scheme. The spectrum with a resonant saturator does not exhibit emissive behaviour as in the travelling wave cases. With a detuned saturator the spectrum closely resembles the corresponding three-level spectrum. These features are explained from the standing wave induced spatial selectivity and inhomogeneity. The connections to Doppler-broadened spectra are discussed.
A nonperturbative treatment of the dynamical behavior of a vibronic system in a resonant, coherent, driving light field is developed. The potential energy surfaces for the vibrational motion in the electronic ground and excited state are assumed to be displaced and distorted relative to one another. A system of three integrodifferential equations is derived from the infinite set of density-matrix equations. Both approximate analytical and numerical solutions are presented for the intensity and the intensity-correlation function of the scattered light. The results are valid for arbitrary ratios of the Rabi frequency to the relaxation rates. A system with fast vibrational relaxation behaves as a two-level system. For systems with slow vibrational relaxation, the applicability of perturbation theory requires pump fields that are weaker than those of a two-level system. The Rabi oscillations occurring in a strong pump field are damped less than those of a two-level system, and the intensity substantially decreases. The long-time behavior (determined by the vibrational relaxation time) is characterized by the increase of the intensity toward its stationary value.
The stationary second-order spectrum of the resonance-fluorescence light from a vibronic system is studied in a nonperturbative manner. In the model used the potential energy surfaces for the vibrational motion in the electronic ground state and in the excited state are assumed to be displaced and distorted relative to each other. The calculations are performed for the case when the frequency of the driving laser field is tuned to the vibrationless electronic transition. In particular, in the high-driving-field limit the vibrationless transition exhibits a triplet structure, the sidebands being narrower and higher in comparison with the well-known two-level case. The Raman lines are shifted and split into doublets, the linewidths being determined by the electronic as well as the vibrational relaxation rates.
We have simulated spectra of weak probe absorption from one of two hyperfine structure (hfs) components of an atomic ground state, to a hfs manifold of an upper state. A stronger coupling transition was assumed to bind the other hfs component of the ground state with the same upper hfs manifold. The purpose of this simulation was to study the impact on the spectral features in probe absorption from the presence of a state to which the electric-dipole transition is allowed for coupling, but forbidden for probing. In relation to our other (experimental) work, we considered the D2-line transitions for 85Rb. With coupling from the 5S1/2(F=2) state, as in our experiment, the 5P3/2(F'=1) state is coupled but not-probed from the 5S1/2(F=3) state. In calculations we searched for steady-state solutions of optical Bloch equations assuming a 5-level model and RWA. The collisionless (cold) atoms were considered, and we assumed that decoherence was entirely due to natural decay and exciting lasers' linewidths. We investigated probe absorption spectra as a function of both coupling-field-induced Rabi frequency Ωc, and coupling field detuning from the atomic resonances. The 5-level model spectra were compared with the corresponding spectra result of 4-level model calculations performed by omission of the 5P3/2(F'=1) level. Even for small Ωc values close to the natural linewidth, for some detunings a considerable influence of the 5P3/2(F'=1) state on the spectra was observed which cannot be ignored in interpretations.
The paper reports on experimental investigations of absorption and dispersion profiles of a strongly driven hyperfine transition at various pump field intensities and detunings when probed by a weak field. The transition lies at 5.4 MHz and corresponds to the Iz{\mathit{I}}_{\mathit{z}}Iz​=0\ensuremath{\leftrightarrows}-1 nuclear magnetic transition within the electron spin singlet of the 3^{3}3A ground state of the nitrogen-vacancy (NV) center in diamond. The inhomogeneous linewidth of the transition is 8 kHz whereas the homogeneous linewidth is 2.7 kHz, which is a factor of 3 larger than that limited by the population relaxations. The absorption and dispersion are obtained using Raman heterodyne detection, a coherent optically detected magnetic-resonance technique. Measurements are performed in a situation where there is an anticrossing of the ground-state electron-spin levels, as this leads to an enhancement of the hyperfine transition strengths and the optical sensitivity. Weak probe fields with Rabi frequency 0.6 kHz could then be used. The absorption and dispersion profiles were recorded for on-resonance pump fields of various strengths with Rabi frequencies of 0, 2.1, 3.7, 6.6, 11.8, and 21 kHz. In addition, the responses were recorded for an off-resonance field with a Rabi frequency of 55 kHz and detunings between -40 and +40 kHz. The corresponding response of an idealized driven two-level system has been calculated using an established density-matrix equation of motion formalism.When normalized to the profiles with no driving field, the calculated and experimental profiles are in excellent agreement. The nitrogen-vacancy system provides a very clear experimental illustration of a driven two-level system and some aspects are highlighted. For on-resonance pumping, the dispersion profile consists of a positive and a negative absorptionlike peak separated by twice the pump Rabi frequency. The peaks correspond to a significant signal strength (index of refraction) whereas at the frequency of the peaks in dispersion, the absorption is zero. The corresponding absorption profile consists of two dispersionlike features separated by twice the pump Rabi frequency, and between the two features there is negative absorption or gain. For off-resonance pumping, there are again two features. For example, in absorption response, there is an absorption peak and an amplification peak symmetrically displaced from the pump frequency by the generalized Rabi frequency. In this off-resonance pumping situation, it is pointed out that gain occurs where there is inversion in the dressed state whereas gain for the on-resonance pumping situation is achieved without population inversion in either the bare or dressed state.
We review our previous work on pump-probe spectroscopy in realistic degenerate two-level systems and model systems. In particular, we discuss the role of transfer of coherence (TOC) between the ground and excited hyperfine states in producing electromagnetically-induced transparency (EIA) peaks in the probe spectrum, when an Fg goes to Fe = Fg +1 transition in an alkali-metal atom interacts with a strong pump and weak probe that have perpendicular polarizations. When the pump is rho+ polarized and the probe pi polarized, this system can be modelled by an N system. We also discuss the role of transfer of population (TOP) between the Zeeman levels of the ground hyperfine state in producing EIA peaks when the pump and probe have the same polarization. This system can be modelled using a double two-level system. The role of Doppler broadening and phase-changing collisions in modifying the EIA-TOC and EIA-TOP absorption and refraction spectra is also discussed. All these spectra were calculated using MATLAB programs that both construct and solve the relevant Bloch equations. In our recent work, we consider the effect of a strong probe on the pump absorption and refraction spectra when the pump and probe polarizations are linear and perpendicular. It is difficult to solve this problem numerically due to the large number frequencies involved. In order to simplify the problem, we considered two cases: (i) rho+ polarized pump and pi polarized probe, and (ii) rho+ polarized pump and rho- polarized probe, and investigated a series of transitions in both Rb and Cs, using modified versions of the MATLAB programs devised for the weakprobe case. A number of interesting differences from the weak-probe case were found. For example, when the probe is sufficiently strong, we found the pump and probe spectra to show complementary behavior. In addition, as the number of Zeeman levels increase, the EIA peaks become progressively sharper, and are accompanied by steeper dispersion.