Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review

One- and Two-Photon Transitions of Atoms in Solids

Albert Gold, John P. Hernandez

Published Sep 13, 1965• 32 citations
Publisher

Abstract

The theory of one- and two-photon transitions between a given pair of impurity levels of the same parity is developed. As is well known, lattice vibrations assist the otherwise forbidden one-photon transition, increasing its intensity with temperature. The two-photon transition rate is shown to have a complementary decrease with increasing temperature. A measurement of both temperature dependences determines the effective frequency and coupling constant for the interaction. The formalism is applied to predicting the two-photon transition rate for the $4{d}^{10}\ensuremath{-}4{d}^{9}5s$ transition of the silver ion in NaCl:Ag. For an experiment using a ruby laser and an ultraviolet beam the maximum absorption coefficient predicted for the ultraviolet beam is $3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}48}\mathrm{FN}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ at low temperatures, where $F$ is the flux (photons/${\mathrm{cm}}^{2}$ sec) of the laser and $N$ is the ${\mathrm{Ag}}^{+}$ concentration. This should be within reach of present experimental techniques.

DOI
10.1103/physrev.139.a2002

Related papers

Theory of resonance two-photon absorption

Z.A. Demidenko

A theory of resonance two-photon absorption, which describes this effect as a combination of two-stage and two-photon processes, is developed in a unified mathematical formalism. Expressions for the transition probabilities and kinetic equations are derived, the absorption coefficient is determined for different and identical frequencies, and the shift of the maximum of the resonance two-photon absorption line is obtained. Investigations are made of the intensity dependences of these expressions and of the kinetics of resonance two-photon transitions. The results are compared with available experimental data.

Soviet Journal of Quantum Electronics•Jul 31, 1979•1 citation

Two-Photon Doppler Cooling of Calcium Atoms

Wictor C. Magno, Reinaldo L. Cavasso Filho, Flávio C. Cruz

A new possibility of laser cooling of Calcium atoms using a two-photon transition is analyzed We investigate the possibility of Doppler cooling of Calcium using its two-photon (4s 2 ) 1 S0 - (4s5s) 1 S0 transition, with excitation in near resonance with the (4s4p) 1 P1 level. The two-photon absorption of l aser beams at 423 and 1 034 nm greatly increases the two-photon rate, allowing an effective transfer of momentum. The ex perimental i mplementation o f t his technique is discussed a nd we show that two-photon cooling can be used to achieve a temperature limit of about 1/7 of the onephoton Doppler limit reached in a conventional MOT.

•Jan 1, 2003•0 citations

Two-Photon Laser Spectroscopy of Transition Ions in Crystals: Inter- Configurational Transitions

Mohammed Daoud A, M. Kibler

Symmetry adaptation techniques are applied to the determination of the intensity of two-photon absorption transitions, between Stark levels of configurations with opposite parities, for transition ions in finite symmetry environments. The equivalence between third-order mechanisms and second- plus first-order mechanisms is clearly established. A compact formula is derived for the intensity of a two-photon transition between two levels with well-defined symmetries. A set of (selection) rules which controls the number of intensity parameters for inter-configurational transitions is given. The formalism is illustrated with the case of an ion with 4f configuration in tetragonal symmetry.

arXiv:physics/9811033•Nov 18, 1998•0 citations

Temperature limits in laser cooling of free atoms with three-level transitions

Flávio C. Cruz, Michael Lee Sundheimer, Wictor C. Magno

Summary form only given. We consider laser cooling of free atoms with simultaneous two-color excitation of three-level cascade transitions [1], [2], [3], [4], [5], [6] finding theoretically that temperatures below the Doppler limits associated with each one of the individual transitions are obtained. We use standard laser cooling analysis [7], [8] and the dressed state picture in order to identify different cooling regions, and determining optimum parameters for guiding further experiments. These new “sub-Doppler” limits are reached at the two-photon resonance where a significant increase of the damping coefficient and decrease of the diffusion take place. In the dressed state picture, this point corresponds to a crossing of the narrow and a (partially) dark state.Figure 1 shows a plot of temperature (normalized to the Doppler limit for cooling only on the lower transition) as function of single-photon detunings, for the 1S0-1P1-1D2 transition of Magnesium, in which the lower 1S0-1P1 transition is the usual cooling one (λ1 = 2πc/ω1 = 285 nm, λ2 = 2πc/ω2 = 881 nm, γ1 = 2π 78.8 MHz, γ2 = 2π 2.2 MHz). A minimum temperature of 38 μK is predicted. This temperature is lower than the Doppler temperature of the lower and upper transitions, TD = γ/k = 1.9 mK and 49 μK respectively. Due to the asymmetric absorption profile of the dressed atom, there is a remarkable increase in the damping coefficient (α) associated with the narrow transition, in comparison with the broad transition (two-level cooling). The cooling and damping times, inversely proportional to α, are reduced by the same amount. Since the curve for the diffusion coefficient (D) has the same shape as the curve for the absorption coefficient or the population of the intermediate state, D is also reduced with respect to the broad resonance, We analyze situations previously implemented experimentally in alkaline-Earth atoms using cascade transitions, and also discuss prospects for Aand V-type three-level systems.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•0 citations

Atoms in strong laser fields

J P Connerade

Multiphoton spectroscopy The subject of multiphoton excitation spectroscopy began in 1931 when Göppert-Mayer [450] wrote a theoretical paper in which she calculated the transition rate for an atom in the presence of two photons rather than just one. At the time, the process seemed rather exotic, and it was reassuring that the calculated rate was so low as to guarantee that it could not readily be observed in the laboratory with conventional sources. This conclusion was reassuring because it implies that a simple perturbative theory (one photon per transition is the weak-field limit) is adequate for most purposes. The subject came to life with the advent of lasers, when it became easy to create intense beams of light. Since the probability of excitation by two photons grows as the square of the photon density, whereas the probability of single-photon excitation grows only linearly with photon density, two-photon transitions gain in relative strength with increasing intensity despite the small value of the rate coefficient. The development of multiphoton spectroscopy has followed that of lasers: as the available power has increased, so has the number of photons involved in individual transitions. More significantly, it has become apparent that the physics of the interaction between radiation and matter is not the same at high laser powers as under weak illumination, i.e. that there is a qualitative change which sets in at strong laser fields. This is normally expressed by saying that perturbative approximations break down.

Cambridge University Press eBooks•May 7, 1998•2 citations

Two-photon excitation of Ho3+ in the Ca F2 , Sr F2 , and Cd F2 lattices

D. Narayana Rao, Jagdish Prasad, Paras N. Prasad

The observation of two-photon absorption by a very efficient up-converted emission is reported for ${\mathrm{Ho}}^{3+}$ in Ca${\mathrm{F}}_{2}$, Sr${\mathrm{F}}_{2}$, and Cd${\mathrm{F}}_{2}$ with both cw- and pulse-laser excitations. The two-photon excitation spectra are found to be highly structured and consist of two bands: The band $A$ is excited by the dye-laser photons of frequencies 15 400-15 700 ${\mathrm{cm}}^{\ensuremath{-}1}$: The band $B$ is excited by the dye-laser photons of frequencies 15 800-16 400 ${\mathrm{cm}}^{\ensuremath{-}1}$. No one-photon absorption is observed for ${\mathrm{Ho}}^{3+}$ in the above lattices at twice these frequencies. Studies of concentration dependence, temperature dependence, and dependence on the pulse repetition rate are used for the assignment of the band. The investigation shows that the two bands $A$ and $B$ arise from two different modes of two-photon excitation. The band $A$ is assigned to arise from a sequential (stepwise) two-photon excitation $^{5}I_{8}\ensuremath{\rightarrow}^{5}F_{5}\ensuremath{\rightarrow}^{5}D_{2}$. The band $B$ is assigned to arise from the direct two-photon absorption $^{5}I_{8}\ensuremath{\rightarrow}^{3}L_{8}$. Our results are in agreement with the prediction of the Judd-Ofelt theory of lanthanide transition intensities.

Physical review. B, Condensed matter•Jul 1, 1983•22 citations
The theory of one- and two-photon transitions between a given pair of impurity levels of the same parity is developed. As is well known, lattice vibrations assist the otherwise forbidden one-photon transition, increasing its intensity with temperature. The two-photon transition rate is shown to have a complementary decrease with increasing temperature. A measurement of both temperature dependences determines the effective frequency and coupling constant for the interaction. The formalism is applied to predicting the two-photon transition rate for the 4d10\ensuremath−4d95s4{d}^{10}\ensuremath{-}4{d}^{9}5s4d10\ensuremath−4d95s transition of the silver ion in NaCl:Ag. For an experiment using a ruby laser and an ultraviolet beam the maximum absorption coefficient predicted for the ultraviolet beam is 3.2\ifmmode×\else\texttimes\fi10\ensuremath−48FN3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}48}\mathrm{FN}3.2\ifmmode×\else\texttimes\fi10\ensuremath−48FN cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1 at low temperatures, where FFF is the flux (photons/cm2{\mathrm{cm}}^{2}cm2 sec) of the laser and NNN is the Ag+{\mathrm{Ag}}^{+}Ag+ concentration. This should be within reach of present experimental techniques.
A theory of resonance two-photon absorption, which describes this effect as a combination of two-stage and two-photon processes, is developed in a unified mathematical formalism. Expressions for the transition probabilities and kinetic equations are derived, the absorption coefficient is determined for different and identical frequencies, and the shift of the maximum of the resonance two-photon absorption line is obtained. Investigations are made of the intensity dependences of these expressions and of the kinetics of resonance two-photon transitions. The results are compared with available experimental data.
A new possibility of laser cooling of Calcium atoms using a two-photon transition is analyzed We investigate the possibility of Doppler cooling of Calcium using its two-photon (4s 2 ) 1 S0 - (4s5s) 1 S0 transition, with excitation in near resonance with the (4s4p) 1 P1 level. The two-photon absorption of l aser beams at 423 and 1 034 nm greatly increases the two-photon rate, allowing an effective transfer of momentum. The ex perimental i mplementation o f t his technique is discussed a nd we show that two-photon cooling can be used to achieve a temperature limit of about 1/7 of the onephoton Doppler limit reached in a conventional MOT.
Symmetry adaptation techniques are applied to the determination of the intensity of two-photon absorption transitions, between Stark levels of configurations with opposite parities, for transition ions in finite symmetry environments. The equivalence between third-order mechanisms and second- plus first-order mechanisms is clearly established. A compact formula is derived for the intensity of a two-photon transition between two levels with well-defined symmetries. A set of (selection) rules which controls the number of intensity parameters for inter-configurational transitions is given. The formalism is illustrated with the case of an ion with 4f configuration in tetragonal symmetry.
Summary form only given. We consider laser cooling of free atoms with simultaneous two-color excitation of three-level cascade transitions [1], [2], [3], [4], [5], [6] finding theoretically that temperatures below the Doppler limits associated with each one of the individual transitions are obtained. We use standard laser cooling analysis [7], [8] and the dressed state picture in order to identify different cooling regions, and determining optimum parameters for guiding further experiments. These new “sub-Doppler” limits are reached at the two-photon resonance where a significant increase of the damping coefficient and decrease of the diffusion take place. In the dressed state picture, this point corresponds to a crossing of the narrow and a (partially) dark state.Figure 1 shows a plot of temperature (normalized to the Doppler limit for cooling only on the lower transition) as function of single-photon detunings, for the 1S0-1P1-1D2 transition of Magnesium, in which the lower 1S0-1P1 transition is the usual cooling one (λ1 = 2πc/ω1 = 285 nm, λ2 = 2πc/ω2 = 881 nm, γ1 = 2π 78.8 MHz, γ2 = 2π 2.2 MHz). A minimum temperature of 38 μK is predicted. This temperature is lower than the Doppler temperature of the lower and upper transitions, TD = γ/k = 1.9 mK and 49 μK respectively. Due to the asymmetric absorption profile of the dressed atom, there is a remarkable increase in the damping coefficient (α) associated with the narrow transition, in comparison with the broad transition (two-level cooling). The cooling and damping times, inversely proportional to α, are reduced by the same amount. Since the curve for the diffusion coefficient (D) has the same shape as the curve for the absorption coefficient or the population of the intermediate state, D is also reduced with respect to the broad resonance, We analyze situations previously implemented experimentally in alkaline-Earth atoms using cascade transitions, and also discuss prospects for Aand V-type three-level systems.
Multiphoton spectroscopy The subject of multiphoton excitation spectroscopy began in 1931 when Göppert-Mayer [450] wrote a theoretical paper in which she calculated the transition rate for an atom in the presence of two photons rather than just one. At the time, the process seemed rather exotic, and it was reassuring that the calculated rate was so low as to guarantee that it could not readily be observed in the laboratory with conventional sources. This conclusion was reassuring because it implies that a simple perturbative theory (one photon per transition is the weak-field limit) is adequate for most purposes. The subject came to life with the advent of lasers, when it became easy to create intense beams of light. Since the probability of excitation by two photons grows as the square of the photon density, whereas the probability of single-photon excitation grows only linearly with photon density, two-photon transitions gain in relative strength with increasing intensity despite the small value of the rate coefficient. The development of multiphoton spectroscopy has followed that of lasers: as the available power has increased, so has the number of photons involved in individual transitions. More significantly, it has become apparent that the physics of the interaction between radiation and matter is not the same at high laser powers as under weak illumination, i.e. that there is a qualitative change which sets in at strong laser fields. This is normally expressed by saying that perturbative approximations break down.
The observation of two-photon absorption by a very efficient up-converted emission is reported for Ho3+{\mathrm{Ho}}^{3+}Ho3+ in CaF2{\mathrm{F}}_{2}F2​, SrF2{\mathrm{F}}_{2}F2​, and CdF2{\mathrm{F}}_{2}F2​ with both cw- and pulse-laser excitations. The two-photon excitation spectra are found to be highly structured and consist of two bands: The band AAA is excited by the dye-laser photons of frequencies 15 400-15 700 ${\mathrm{cm}}^{\ensuremath{-}1}$: The band BBB is excited by the dye-laser photons of frequencies 15 800-16 400 ${\mathrm{cm}}^{\ensuremath{-}1}$. No one-photon absorption is observed for Ho3+{\mathrm{Ho}}^{3+}Ho3+ in the above lattices at twice these frequencies. Studies of concentration dependence, temperature dependence, and dependence on the pulse repetition rate are used for the assignment of the band. The investigation shows that the two bands AAA and BBB arise from two different modes of two-photon excitation. The band AAA is assigned to arise from a sequential (stepwise) two-photon excitation $^{5}I_{8}\ensuremath{\rightarrow}^{5}F_{5}\ensuremath{\rightarrow}^{5}D_{2}$. The band BBB is assigned to arise from the direct two-photon absorption $^{5}I_{8}\ensuremath{\rightarrow}^{3}L_{8}$. Our results are in agreement with the prediction of the Judd-Ofelt theory of lanthanide transition intensities.