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

Journal of Physics B Atomic Molecular and Optical Physics

Measurement of steep dispersion associated with magnetically assisted gain in Zeeman degenerate two-level system of cold atoms

J. C. de Aquino Carvalho, Raoni S. N. Moreira, J. W. R. Tabosa

Published Feb 21, 2024• 0 citations
Publisher

Abstract

Abstract We report on the measurements of magnetically assisted dispersion and gain in a Zeeman degenerate two-level system associated with the closed D 2 hyperfine transition F g = 3 → F e = 2 cold cesium atoms. We use a Mach–Zehnder interferometer to measure the dispersive properties of this system in the presence of a magnetic field, transversal to the quantization direction, when the atomic system is excited by a coupling and probe beams with orthogonal polarizations. We have measured the spectrum of the refraction index for different magnitudes of the external magnetic field and different coupling beam intensities. A previously published theoretical model, using a simpler atomic transition F g = 1 → F e = 0 , accounts reasonably for the experimentally observed gain and dispersive lineshapes.

DOI
10.1088/1361-6455/ad2b6f

Related papers

Quasi-degenerate phase conjugation spectroscopy of cold cesium

George C. Cardoso, A. Lezama, J. W. R. Tabosa

Summary form only given. Resonant cold atomic samples are known to provide an efficient medium for the study of nonlinear optical processes such as four-wave-mixing (FWM) and phase conjugation (PC). Although this system is frequently modeled as an homogeneous sample of two-level atoms, the actual nonlinear response strongly depends on the internal structure (Zeeman degeneracy) of the atomic energy levels and consequently on the polarizations of the optical fields. We have studied the spectra of quasi-degenerate PC on the 6S/sub 1/2/(F=4)-6P/sub 3/2/(F=5) transition of cold Cs atoms for different optical polarizations. The atomic sample was obtained in a magneto-optical trap. The spectra where recorded within a 1 ms time interval during which the trapping light beams were blocked and the quadrupole magnetic field was turned off. We used a backwards FWM scheme with two counter-propagating pump beams and a probe beam. The PC signal propagates in opposite direction respect to the probe beam. Typical PC spectra as a function of frequency offset are shown for probe beam polarization parallel and perpendicular to pump polarization. Large differences are observed between these two cases demonstrating the crucial role of the Zeeman degeneracy on the atomic response. The experimental spectra are in good agreement with the theoretical predictions for FWM generation in degenerate two-level atoms.

Conference on Lasers and Electro-Optics•Aug 29, 2005•0 citations

Lasing without inversion based on magnetically assisted gain in coherently prepared cold atoms

J. C. de Aquino Carvalho, A. D. M. de Lima, J. W. R. Tabosa

We report on the observation of laser oscillation using the magnetically assisted gain in an ensemble of coherently prepared cold cesium atoms. This gain mechanism was recently demonstrated and is based on the modification of the Zeeman populations and coherences induced by a coupling and a probe beams by the presence of a transverse magnetic field. We have also investigated the enhancement of the gain due to the presence of a resonant ring cavity having different finesses. In the case of a low-finesse cavity operating below threshold, a 14-fold gain enhancement, in comparison with the single-pass gain, was measured and, finally, the system showed laser oscillation when a higher-finesse cavity was used. The present demonstration of laser oscillation constitutes an unconventional kind of lasing without inversion which is based on the manipulation of the dark state by an external magnetic field.

Physical Review A•Feb 7, 2022•9 citations

Nonlinear spectroscopy of cold atoms

Zhongliang Hu, J. W. R. Tabosa, Harry J. Kimble

Nonlinear spectroscopy of cold atoms has recently been reported for a sample of cesium atoms confined in a magnetooptical trap.1,2 In particular, we report measurements of the spectral response of the cold sample to a weak probe beam for a range of detunings and power for the saturating trapping beams. Transmission spectra for the probe beam reveal the presence of broad absorption and gain features as well as narrow resonances. The power dependence of the broad part of the spectrum can be reasonably well described by earlier work for two-level atoms in a strong field.3 However, narrow dispersive shaped features around the frequency of the trapping beams are also observed and can have appreciable single pass gain (>20%). An exploration of the correlation between the narrow spectroscopic features and the mechanical properties of the atomic sample leads to the observation of both positive and negative radiation pressure associated with stimulated absorption from and emission to the probe beam.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

Coherent two-field spectroscopy of degenerate two-level systems

A. Lezama, S. Barreiro, A. Lipsich +1 more

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, subnatural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited-state population modulation in the ${D}_{2}$ line of Rb vapor are presented in good agreement with the calculations.

Physical Review A•Dec 8, 1999•87 citations

Coherent two-field spectroscopy of degenerate two-level systems

A. Lezama

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 calculations

arXiv:quant-ph/9907002•Jul 1, 1999•0 citations

Magneto-optical effect near the D1 resonance of spin-polarized cold cesium atoms

Jai Min Choi, Jang Myun Kim, Je Hyun Lee +2 more

We report our study of the magneto-optical effect in a strictly linear regime on spin-polarized cold cesium atoms. Due to the low intensity and the short illumination period of the probe beam, less than 7.5% of the sample atoms change their states by absorbing probe photons. We produce a medium of atoms at rest in either the $6{S}_{1∕2},F=3,{m}_{F}=0$ or $6{S}_{1∕2},F=3,{m}_{F}=3$ state by optically pumping atoms trapped in a magneto-optical trap. We use the $D1$ resonance with large lower and upper state hyperfine splittings as a probe transition to avoid hyperfine mixing from the Zeeman interaction. Under this idealized situation we measure the Stokes parameters in order to find the polarization rotation and circular dichroism experienced by the probe light. We find that there are qualitative differences between the results for the ${m}_{F}=0$ and ${m}_{F}=3$ cases. While dispersion and consequent Faraday rotation play a dominant role when the atoms are in the ${m}_{F}=0$ state, it is dissipation and circular dichroism that are important when they are in the ${m}_{F}=3$ state. Similarly, while the size of the Faraday rotation and the circular dichroism for the ${m}_{F}=0$ case scales linearly with the applied magnetic field, for the ${m}_{F}=3$ case it is the shift of the probe polarization change versus frequency that is linearly proportional to the magnetic field strength.

Physical Review A•Apr 22, 2005•3 citations
Abstract We report on the measurements of magnetically assisted dispersion and gain in a Zeeman degenerate two-level system associated with the closed D 2 hyperfine transition F g = 3 → F e = 2 cold cesium atoms. We use a Mach–Zehnder interferometer to measure the dispersive properties of this system in the presence of a magnetic field, transversal to the quantization direction, when the atomic system is excited by a coupling and probe beams with orthogonal polarizations. We have measured the spectrum of the refraction index for different magnitudes of the external magnetic field and different coupling beam intensities. A previously published theoretical model, using a simpler atomic transition F g = 1 → F e = 0 , accounts reasonably for the experimentally observed gain and dispersive lineshapes.
Summary form only given. Resonant cold atomic samples are known to provide an efficient medium for the study of nonlinear optical processes such as four-wave-mixing (FWM) and phase conjugation (PC). Although this system is frequently modeled as an homogeneous sample of two-level atoms, the actual nonlinear response strongly depends on the internal structure (Zeeman degeneracy) of the atomic energy levels and consequently on the polarizations of the optical fields. We have studied the spectra of quasi-degenerate PC on the 6S/sub 1/2/(F=4)-6P/sub 3/2/(F=5) transition of cold Cs atoms for different optical polarizations. The atomic sample was obtained in a magneto-optical trap. The spectra where recorded within a 1 ms time interval during which the trapping light beams were blocked and the quadrupole magnetic field was turned off. We used a backwards FWM scheme with two counter-propagating pump beams and a probe beam. The PC signal propagates in opposite direction respect to the probe beam. Typical PC spectra as a function of frequency offset are shown for probe beam polarization parallel and perpendicular to pump polarization. Large differences are observed between these two cases demonstrating the crucial role of the Zeeman degeneracy on the atomic response. The experimental spectra are in good agreement with the theoretical predictions for FWM generation in degenerate two-level atoms.
We report on the observation of laser oscillation using the magnetically assisted gain in an ensemble of coherently prepared cold cesium atoms. This gain mechanism was recently demonstrated and is based on the modification of the Zeeman populations and coherences induced by a coupling and a probe beams by the presence of a transverse magnetic field. We have also investigated the enhancement of the gain due to the presence of a resonant ring cavity having different finesses. In the case of a low-finesse cavity operating below threshold, a 14-fold gain enhancement, in comparison with the single-pass gain, was measured and, finally, the system showed laser oscillation when a higher-finesse cavity was used. The present demonstration of laser oscillation constitutes an unconventional kind of lasing without inversion which is based on the manipulation of the dark state by an external magnetic field.
Nonlinear spectroscopy of cold atoms has recently been reported for a sample of cesium atoms confined in a magnetooptical trap.1,2 In particular, we report measurements of the spectral response of the cold sample to a weak probe beam for a range of detunings and power for the saturating trapping beams. Transmission spectra for the probe beam reveal the presence of broad absorption and gain features as well as narrow resonances. The power dependence of the broad part of the spectrum can be reasonably well described by earlier work for two-level atoms in a strong field.3 However, narrow dispersive shaped features around the frequency of the trapping beams are also observed and can have appreciable single pass gain (>20%). An exploration of the correlation between the narrow spectroscopic features and the mechanical properties of the atomic sample leads to the observation of both positive and negative radiation pressure associated with stimulated absorption from and emission to the probe beam.
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, subnatural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited-state population modulation in the D2{D}_{2}D2​ line of Rb vapor are presented in good agreement with the calculations.
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 calculations
We report our study of the magneto-optical effect in a strictly linear regime on spin-polarized cold cesium atoms. Due to the low intensity and the short illumination period of the probe beam, less than 7.5% of the sample atoms change their states by absorbing probe photons. We produce a medium of atoms at rest in either the 6S1∕2,F=3,mF=06{S}_{1∕2},F=3,{m}_{F}=06S1∕2​,F=3,mF​=0 or 6S1∕2,F=3,mF=36{S}_{1∕2},F=3,{m}_{F}=36S1∕2​,F=3,mF​=3 state by optically pumping atoms trapped in a magneto-optical trap. We use the D1D1D1 resonance with large lower and upper state hyperfine splittings as a probe transition to avoid hyperfine mixing from the Zeeman interaction. Under this idealized situation we measure the Stokes parameters in order to find the polarization rotation and circular dichroism experienced by the probe light. We find that there are qualitative differences between the results for the mF=0{m}_{F}=0mF​=0 and mF=3{m}_{F}=3mF​=3 cases. While dispersion and consequent Faraday rotation play a dominant role when the atoms are in the mF=0{m}_{F}=0mF​=0 state, it is dissipation and circular dichroism that are important when they are in the mF=3{m}_{F}=3mF​=3 state. Similarly, while the size of the Faraday rotation and the circular dichroism for the mF=0{m}_{F}=0mF​=0 case scales linearly with the applied magnetic field, for the mF=3{m}_{F}=3mF​=3 case it is the shift of the probe polarization change versus frequency that is linearly proportional to the magnetic field strength.