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Theory of Pump-Probe and 4-WAVE Mixing Spectroscopy

G. Khitrova

Published Jan 1, 1986• 1 citation
OpenAlex

Abstract

This thesis presents theoretical calculations relating to pump-probe and four-wave mixing spectroscopy. In pump-probe spectroscopy, one measures the absorption profile for the situation when an arbitrarily strong pump field drives a given atomic transition and a weak probe field drives the same transition. We have carried out calculations of probe absorption in vapors for arbitrary ratios of natural width and detuning to the Doppler width associated with a given transition. New line shape features which were absent in previous theories are observed.

Related papers

Theory of pump-probe and four-wave mixing spectroscopy

P. R. Berman, G. Khitrova

In this paper we present theoretical calculations relating to pump-probe and four-wave mixing spectroscopy. In pump-probe spectroscopy, one measures the absorption profile for the situation when an arbitrary strong pump field drives a given transition and a probe (weak) field drives the same transition. We have studied the influence of level degeneracy and field polarization on pump-probe and four-wave mixing signals. Our results indicate that for some closed systems (no population loss to the reservoir) it is possible to observe resonances that are characterized by the ground state width. Previous calculations indicate that for a nondegenerate system this resonance can appear only for an open system, the so-called "pressure induced resonances.”1 Our result, which contradicts this conclusion, can be understood by noting the fact that there are in general three irreducible tensor2 (in general) contributions to the line shape (K = 0 population, K = 1 orientation, and K = 2 alignment). Thus, even if the system is closed for the population it may still remain open for orientation or alignment; this effect is responsible for the narrow resonance. Specific calculations are presented for J = 1/2 → 1/2 and J = 1→2 transitions.

Conference on Lasers and Electro-Optics•Jan 1, 1986•0 citations

New line shape profiles in two-wave mixing

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A theory of saturation spectroscopy in three-level gas-vapor systems, including collisional effects, is presented. Using a model of collisions in which they are phase interrupting in their effect on level coherences and velocity changing in their effect on level population densities, the authors calculate the absorption profile of a weak probe field on a given transition when an arbitrarily strong pump field acts on a coupled transition. Line shapes are derived for an arbitrary collision kernel describing the velocity-changing collisions, and these line shapes are evaluated for the collision kernel proposed by Keilson and Storer. Various limiting forms for the line shapes are derived and representative line shapes are displayed. Several new features of the line shapes, including collisionally induced increased probe absorption are discussed. The line shapes are seen to reflect the various collisional processes that may occur in atomic or molecular systems.

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Recoil-induced resonances in nonlinear, ground-state, pump-probe spectroscopy

Christopher P. Search, P. R. Berman

A theory of pump-probe spectroscopy is developed in which optical fields drive two-photon Raman transitions between ground states of an ensemble of three-level atoms. Effects related to the recoil the atoms undergo as a result of their interactions with the fields are fully accounted for in this theory. The linear absorption coefficient of a weak probe field in the presence of two pump fields of arbitrary strength is calculated. For subrecoil cooled atoms, the spectrum consists of eight absorption lines and eight emission lines. In the limit that ${\ensuremath{\chi}}_{1}\ensuremath{\ll}{\ensuremath{\chi}}_{2},$ where ${\ensuremath{\chi}}_{1}$ and ${\ensuremath{\chi}}_{2}$ are the Rabi frequencies of the two pump fields, one recovers the absorption spectrum for a probe field interacting with an effective two-level atom in the presence of a single pump field. However, when ${\ensuremath{\chi}}_{1}\ensuremath{\gtrsim}{\ensuremath{\chi}}_{2},$ new interference effects arise that allow one to selectively turn on and off some of these recoil-induced resonances.

arXiv:physics/0012002•Physical Review A•May 16, 2001•1 citation

Theory of saturation spectroscopy including effects of level degeneracy

Christopher Feuillade, P. R. Berman

A theory of saturation spectroscopy is developed which accounts for effects of level degeneracy. The theory can be applied to those situations in which a pump laser field of arbitrary strength and polarization acts between two manifolds of degenerate or nearly degenerate atomic levels, while a probe laser field of arbitrary strength and polarization acts between a coupled manifold of levels. As such, this theory of "three-level" systems could, in principle, include effects arising from level degeneracy, optical pumping, atomic motion, transient laser fields, different polarizations and strengths for pump and probe fields, and atomic transit across the laser fields. The present calculation, however, is limited to a study of optical pumping and field polarization effects for pump fields of arbitrary strength and weak probe fields interacting with a single velocity subclass of atoms. Probe absorption line shapes clearly display the effects of pump-field strength (Rabi splittings), pump-field polarization (positions and number of Rabi-split resonance peaks), pump-field detuning (positions of resonance peaks), and optical pumping (relative strengths of the resonance peaks). The calculation is carried out with the use of an irreducible tensor basis for the atomic density matrix although a standard ($m$-basis) calculation is included in an appendix.

Physical Review A•Mar 1, 1984•34 citations
This thesis presents theoretical calculations relating to pump-probe and four-wave mixing spectroscopy. In pump-probe spectroscopy, one measures the absorption profile for the situation when an arbitrarily strong pump field drives a given atomic transition and a weak probe field drives the same transition. We have carried out calculations of probe absorption in vapors for arbitrary ratios of natural width and detuning to the Doppler width associated with a given transition. New line shape features which were absent in previous theories are observed.
In this paper we present theoretical calculations relating to pump-probe and four-wave mixing spectroscopy. In pump-probe spectroscopy, one measures the absorption profile for the situation when an arbitrary strong pump field drives a given transition and a probe (weak) field drives the same transition. We have studied the influence of level degeneracy and field polarization on pump-probe and four-wave mixing signals. Our results indicate that for some closed systems (no population loss to the reservoir) it is possible to observe resonances that are characterized by the ground state width. Previous calculations indicate that for a nondegenerate system this resonance can appear only for an open system, the so-called "pressure induced resonances.”1 Our result, which contradicts this conclusion, can be understood by noting the fact that there are in general three irreducible tensor2 (in general) contributions to the line shape (K = 0 population, K = 1 orientation, and K = 2 alignment). Thus, even if the system is closed for the population it may still remain open for orientation or alignment; this effect is responsible for the narrow resonance. Specific calculations are presented for J = 1/2 → 1/2 and J = 1→2 transitions.
We calculate the two-level pump-probe absorption coefficient including both upper-to-lower-level decay and level decays to a still lower lying reservoir level. We carried out calculations of probe absorption profile for arbitrary ratios of natural width and detuning to the Doppler width associated with a given transition. This theory accounts for contributions from all velocity subclasses of atoms, not only those which are Doppler shifted into resonance with the laser field (Doppler limit).1 We observe and explain new line shape features based on dissimilar decays.
A theory of saturation spectroscopy in three-level gas-vapor systems, including collisional effects, is presented. Using a model of collisions in which they are phase interrupting in their effect on level coherences and velocity changing in their effect on level population densities, the authors calculate the absorption profile of a weak probe field on a given transition when an arbitrarily strong pump field acts on a coupled transition. Line shapes are derived for an arbitrary collision kernel describing the velocity-changing collisions, and these line shapes are evaluated for the collision kernel proposed by Keilson and Storer. Various limiting forms for the line shapes are derived and representative line shapes are displayed. Several new features of the line shapes, including collisionally induced increased probe absorption are discussed. The line shapes are seen to reflect the various collisional processes that may occur in atomic or molecular systems.
A theory of pump-probe spectroscopy is developed in which optical fields drive two-photon Raman transitions between ground states of an ensemble of three-level atoms. Effects related to the recoil the atoms undergo as a result of their interactions with the fields are fully accounted for in this theory. The linear absorption coefficient of a weak probe field in the presence of two pump fields of arbitrary strength is calculated. For subrecoil cooled atoms, the spectrum consists of eight absorption lines and eight emission lines. In the limit that ${\ensuremath{\chi}}_{1}\ensuremath{\ll}{\ensuremath{\chi}}_{2},$ where ${\ensuremath{\chi}}_{1}$ and ${\ensuremath{\chi}}_{2}$ are the Rabi frequencies of the two pump fields, one recovers the absorption spectrum for a probe field interacting with an effective two-level atom in the presence of a single pump field. However, when ${\ensuremath{\chi}}_{1}\ensuremath{\gtrsim}{\ensuremath{\chi}}_{2},$ new interference effects arise that allow one to selectively turn on and off some of these recoil-induced resonances.
A theory of saturation spectroscopy is developed which accounts for effects of level degeneracy. The theory can be applied to those situations in which a pump laser field of arbitrary strength and polarization acts between two manifolds of degenerate or nearly degenerate atomic levels, while a probe laser field of arbitrary strength and polarization acts between a coupled manifold of levels. As such, this theory of "three-level" systems could, in principle, include effects arising from level degeneracy, optical pumping, atomic motion, transient laser fields, different polarizations and strengths for pump and probe fields, and atomic transit across the laser fields. The present calculation, however, is limited to a study of optical pumping and field polarization effects for pump fields of arbitrary strength and weak probe fields interacting with a single velocity subclass of atoms. Probe absorption line shapes clearly display the effects of pump-field strength (Rabi splittings), pump-field polarization (positions and number of Rabi-split resonance peaks), pump-field detuning (positions of resonance peaks), and optical pumping (relative strengths of the resonance peaks). The calculation is carried out with the use of an irreducible tensor basis for the atomic density matrix although a standard (mmm-basis) calculation is included in an appendix.