Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculationsSpectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations

arXiv:quant-ph/9907002Jul 1, 19990 citations

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

T. Zigdon, A. D. Wilson‐Gordon, Harry Friedmann

We study the pump and probe absorption spectra, as a function of the probe detuning, in a degenerate two-level atomic system, for the case where the probe intensity is high enough to affect the pump absorption. The theory is valid for any ${F}_{g}\ensuremath{\rightarrow}{F}_{e}$ alkali-metal transition interacting with an arbitrarily intense pump and probe (with general Rabi frequencies ${\ensuremath{\Omega}}_{1,2}$) which are perpendicularly polarized with either ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ or $\ensuremath{\pi}$ polarization. We have constructed a computer program that can calculate the spectra without requiring one to write out the Bloch equations explicitly. We show that, when the pump is ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ polarized and the probe $\ensuremath{\pi}$ polarized, or vice versa, the pump and probe absorptions depend on the Zeeman coherences between the nearest-neighboring ground or excited Zeeman sublevels, whereas when the pump is ${\ensuremath{\sigma}}_{+}$ polarized and the probe ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized, or vice versa, the Zeeman coherences that directly determine the absorption are between next-nearest neighbors. We report calculations of the pump and probe absorption spectra for the cycling ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition in the ${D}_{2}$ line of $^{87}\text{R}\text{b}$ , interacting with a resonant ${\ensuremath{\sigma}}_{+}$-polarized pump and either a $\ensuremath{\pi}$- or a ${\ensuremath{\sigma}}_{\ensuremath{-}}$- polarized probe. The probe and pump absorption spectra are analyzed by considering the contributions that derive from the individual ${m}_{g}\ensuremath{\rightarrow}{m}_{e}$ transitions. We then show how these contributions depend on the ground- and excited-state populations and Zeeman coherences, and investigate the role played by transfer of coherence from the excited to the ground hyperfine state. We show that the pump and probe absorption spectra are mirror images of each other when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}>\ensuremath{\Gamma}$, and have the same behavior at line center and complementary behavior in the wings, when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}<\ensuremath{\Gamma}$ ($\ensuremath{\Gamma}$ is the rate of spontaneous decay from ${F}_{e}$ to ${F}_{g}$ ).We study the pump and probe absorption spectra, as a function of the probe detuning, in a degenerate two-level atomic system, for the case where the probe intensity is high enough to affect the pump absorption. The theory is valid for any ${F}_{g}\ensuremath{\rightarrow}{F}_{e}$ alkali-metal transition interacting with an arbitrarily intense pump and probe (with general Rabi frequencies ${\ensuremath{\Omega}}_{1,2}$) which are perpendicularly polarized with either ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ or $\ensuremath{\pi}$ polarization. We have constructed a computer program that can calculate the spectra without requiring one to write out the Bloch equations explicitly. We show that, when the pump is ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ polarized and the probe $\ensuremath{\pi}$ polarized, or vice versa, the pump and probe absorptions depend on the Zeeman coherences between the nearest-neighboring ground or excited Zeeman sublevels, whereas when the pump is ${\ensuremath{\sigma}}_{+}$ polarized and the probe ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized, or vice versa, the Zeeman coherences that directly determine the absorption are between next-nearest neighbors. We report calculations of the pump and probe absorption spectra for the cycling ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition in the ${D}_{2}$ line of $^{87}\text{R}\text{b}$, interacting with a resonant ${\ensuremath{\sigma}}_{+}$-polarized pump and either a $\ensuremath{\pi}$- or a ${\ensuremath{\sigma}}_{\ensuremath{-}}$- polarized probe. The probe and pump absorption spectra are analyzed by considering the contributions that derive from the individual ${m}_{g}\ensuremath{\rightarrow}{m}_{e}$ transitions. We then show how these contributions depend on the ground- and excited-state populations and Zeeman coherences, and investigate the role played by transfer of coherence from the excited to the ground hyperfine state. We show that the pump and probe absorption spectra are mirror images of each other when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}>\ensuremath{\Gamma}$, and have the same behavior at line center and complementary behavior in the wings, when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}<\ensuremath{\Gamma}$ ($\ensuremath{\Gamma}$ is the rate of spontaneous decay from ${F}_{e}$ to ${F}_{g}$).

Physical Review AMar 19, 200818 citations

Absorption spectra of driven degenerate two-level atomic systems

A. Lipsich, S. Barreiro, A. M. Akulshin +1 more

The absorption properties of degenerate two-level atomic systems tested by a weak probe field in the presence of an intense pump field have been analyzed. The theoretical model previously presented in Phys. Rev. A 61, 013801 (1999) that appears to be suitable for arbitrary choices of the pump intensity, level angular momenta, and pump and probe polarizations, was used for the calculation of the spectra for several basic configurations. Experimental absorption spectra obtained on a Rb atomic beam for different pump and probe field polarizations show good agreement with the calculation. The spectra are in general essentially different from and more complex than the classical Mollow absorption triplet.The absorption properties of degenerate two-level atomic systems tested by a weak probe field in the presence of an intense pump field have been analyzed. The theoretical model previously presented in Phys. Rev. A 61, 013801 (1999) that appears to be suitable for arbitrary choices of the pump intensity, level angular momenta, and pump and probe polarizations, was used for the calculation of the spectra for several basic configurations. Experimental absorption spectra obtained on a Rb atomic beam for different pump and probe field polarizations show good agreement with the calculation. The spectra are in general essentially different from and more complex than the classical Mollow absorption triplet.

Physical Review AApr 10, 2000102 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.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 SPIEMar 2, 20072 citations

Coherent spectroscopy of degenerate two-level systems in Cs

C. Andreeva, S. Cartaleva, Yordanka V. Dancheva +6 more

Coherent spectroscopy of degenerate two-level systems of the Doppler-broadened ${D}_{2}$ cesium line has been performed in vacuum and in buffer gas cells. Subnatural-width (SNW) electromagnetically induced transparency and electromagnetically induced absorption (EIA) resonances have been observed with single-frequency laser excitation for different light polarizations and collision regimes. SNW-EIA resonances with linearly polarized excitation of the ${F}_{g}=4$ level are observed, and they increase their contrast with power density increase and reach a contrast of 20% at $200 \mathrm{mW}{\mathrm{cm}}^{\ensuremath{-}2}.$ A theoretical model has been elaborated, taking into account the Doppler broadening of the transitions, the linewidth of the laser light, and the experimental conditions for observation of the fluorescence. Here the theoretical results are in agreement with those of the experiment. In a buffer gas cell, the SNW resonances in the fluorescence, in degenerate two-level systems are observed for the first time and they are only obtained with circularly polarized light. A theoretical explanation of this result is proposed. At the expense of contrast, in the presence of a buffer gas the coherent resonances are significantly narrower than in a vacuum cell for the same power density. The observation of SNW resonances in buffer gas is significantly less sensitive to the laser frequency drift than in a vacuum cell, which could be advantageous for applications in metrology and in the measurement of weak magnetic fields.Coherent spectroscopy of degenerate two-level systems of the Doppler-broadened ${D}_{2}$ cesium line has been performed in vacuum and in buffer gas cells. Subnatural-width (SNW) electromagnetically induced transparency and electromagnetically induced absorption (EIA) resonances have been observed with single-frequency laser excitation for different light polarizations and collision regimes. SNW-EIA resonances with linearly polarized excitation of the ${F}_{g}=4$ level are observed, and they increase their contrast with power density increase and reach a contrast of 20% at $200 \mathrm{mW}{\mathrm{cm}}^{\ensuremath{-}2}.$ A theoretical model has been elaborated, taking into account the Doppler broadening of the transitions, the linewidth of the laser light, and the experimental conditions for observation of the fluorescence. Here the theoretical results are in agreement with those of the experiment. In a buffer gas cell, the SNW resonances in the fluorescence, in degenerate two-level systems are observed for the first time and they are only obtained with circularly polarized light. A theoretical explanation of this result is proposed. At the expense of contrast, in the presence of a buffer gas the coherent resonances are significantly narrower than in a vacuum cell for the same power density. The observation of SNW resonances in buffer gas is significantly less sensitive to the laser frequency drift than in a vacuum cell, which could be advantageous for applications in metrology and in the measurement of weak magnetic fields.

Physical Review AJul 11, 200296 citations

Degenerate four-wave mixing spectra in a two-level atomic system with phase-modulated time-delayed coherent fields

Arthur K. Mills, Daniel S. Elliott

We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the $3s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}$ , $F=2$ , ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, $F=3$ , ${m}_{F}=3$ transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the $3s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}$, $F=2$, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, $F=3$, ${m}_{F}=3$ transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.

Physical Review AAug 12, 20052 citations

{D}_{2}

line of Rb vapor are presented in good agreement with the calculations.

{D}_{2}

line of

^{87}\text{R}\text{b}

, interacting with a resonant ${\ensuremath{\sigma}}_{+}$-polarized pump and either a $\ensuremath{\pi}$- or a ${\ensuremath{\sigma}}_{\ensuremath{-}}$- polarized probe. The probe and pump absorption spectra are analyzed by considering the contributions that derive from the individual ${m}_{g}\ensuremath{\rightarrow}{m}_{e}$ transitions. We then show how these contributions depend on the ground- and excited-state populations and Zeeman coherences, and investigate the role played by transfer of coherence from the excited to the ground hyperfine state. We show that the pump and probe absorption spectra are mirror images of each other when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}>\ensuremath{\Gamma}$, and have the same behavior at line center and complementary behavior in the wings, when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}<\ensuremath{\Gamma}$ ($\ensuremath{\Gamma}$ is the rate of spontaneous decay from

{F}_{e}

{F}_{g}

Coherent spectroscopy of degenerate two-level systems of the Doppler-broadened

{D}_{2}

cesium line has been performed in vacuum and in buffer gas cells. Subnatural-width (SNW) electromagnetically induced transparency and electromagnetically induced absorption (EIA) resonances have been observed with single-frequency laser excitation for different light polarizations and collision regimes. SNW-EIA resonances with linearly polarized excitation of the

{F}_{g}=4

level are observed, and they increase their contrast with power density increase and reach a contrast of 20% at $200 \mathrm{mW}{\mathrm{cm}}^{\ensuremath{-}2}.$ A theoretical model has been elaborated, taking into account the Doppler broadening of the transitions, the linewidth of the laser light, and the experimental conditions for observation of the fluorescence. Here the theoretical results are in agreement with those of the experiment. In a buffer gas cell, the SNW resonances in the fluorescence, in degenerate two-level systems are observed for the first time and they are only obtained with circularly polarized light. A theoretical explanation of this result is proposed. At the expense of contrast, in the presence of a buffer gas the coherent resonances are significantly narrower than in a vacuum cell for the same power density. The observation of SNW resonances in buffer gas is significantly less sensitive to the laser frequency drift than in a vacuum cell, which could be advantageous for applications in metrology and in the measurement of weak magnetic fields.

We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the

3s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}

F=2

, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$,

F=3

{m}_{F}=3

transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.