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 A

Rabi resonances in the Λ excitation scheme

Aldo Godone, Salvatore Micalizio, Filippo Levi

Published Dec 16, 2002• 31 citations
Publisher

Abstract

We consider the interaction of a three-level system with phase-modulated resonant fields in the \ensuremath{\Lambda} excitation scheme. We treat theoretically the case of a sinusoidal phase modulation, a phase step perturbation, and a stochastic phase modulation. The appearance of a Rabi resonance both in the spectrum of the optical transmitted signal (electromagnetically induced transparency) and in the spectrum of the microwave emission (coherent population trapping maser) is considered in detail. All the theoretical results are compared with the analogous ones reported for the two-level system and with our experimental observations obtained for the case of rubidium in a buffer gas.

DOI
10.1103/physreva.66.063807

Related papers

Rabi resonance in coherent population trapping: microwave mixing scheme

Xiaochi Liu, Ya-Nan Lv, Songbai Kang +4 more

Coherent population trapping (CPT) resonance signals have promise in a wide range of applications involving precision sensing. Generally, the CPT phenomenon occurs in a three-level Λ system with a bichromatic phase-coherent light fields. We theoretically and experimentally studied an Rb vapor-cell-based atomic system involving bichromatic CPT optical fields and an external microwave (MW) field simultaneously. In such a mixing scheme, the coherence of the ground states could be controlled either by the Rabi frequency of the microwave field or by the relative phase between the optical fields and the MW field. Moreover, we investigated the Rabi resonance in this mixing scheme. The Rabi frequency of the MW field can be measured SI (International System of Units)-traceably based on the Rabi resonance lineshape, and thus holds the potential to realize intensity stabilization of the optical field in this system. Simple theoretical models and numerical calculations are also presented to explain the experimental results. There is scope to use the proposed technique in future development of SI-traceable optical field strength standards.

Optics Express•Jan 1, 2021•13 citations

Propagation and density effects in the coherent-population-trapping maser

Aldo Godone, Filippo Levi, Salvatore Micalizio

The coherent microwave emission from an optically thick atomic ensemble in a cavity under coherent population trapping is analyzed. Transient and continuous operations are theoretically examined within the frame of a closed three-level system in the Dicke regime. The effects related to the atomic density and to the propagation in the active medium are examined with particular reference to the subnatural linewidth, the low group velocity and the shifts of the maser emission profile from the unperturbed atomic transition. The case of alkali-metal atoms submitted to a \ensuremath{\Lambda} excitation scheme is addressed in view of applications in the atomic frequency standard field. Experimental observations in agreement with the theoretical predictions are reported for the case of rubidium in a buffer gas. Apparent superluminal propagation is also reported and briefly discussed.

Physical Review A•Feb 4, 2002•22 citations

Slow light and superluminality in the coherent population trapping maser

Aldo Godone, Filippo Levi, Salvatore Micalizio

The propagation of a band-limited light pulse through an atomic medium under a \ensuremath{\Lambda} excitation scheme is theoretically analyzed in this paper. We consider in particular the case where the light pulse is detected through the coherent microwave emission of the atomic ensemble (coherent population trapping maser). Significant differences are predicted with respect to the more usual optical detection (electromagnetically induced transparency signal) and found in agreement with the experimental results. Higher signal delays were observed in the microwave emission than in the optical signal with an equivalent group velocity of 6 m/s as well as highly superluminal propagation under a proper modulation scheme. The experiments were performed with a thermal ${}^{87}\mathrm{Rb}$ vapor in buffer gas.

Physical Review A•Oct 7, 2002•21 citations

Observation of the Rabi-resonance spectrum

James C. Camparo, R. P. Frueholz

By use of a double-resonance technique, a spectrum of Rabi resonances has been observed. These resonances are enhancements in the dynamic response of a quantum system's population to rapid changes in the phase of a perturbing electromagnetic field. Theoretically, it is shown that the appearance of a spectrum, as opposed to a single Rabi resonance, is due to the fact that the phase of the field changes discretely by \ensuremath{\pi} radians, rather than sinusoidally. In the presence of \ensuremath{\pi}-radian phase changes, the quantum system's dynamic response is found to be similar to a damped harmonic oscillator driven by a \ensuremath{\delta}-function force term. In this harmonic-oscillator approximation the Rabi-resonance spectrum arises naturally, resulting from a resonant enhancement of the atomic coherence.

Physical Review A•Dec 1, 1988•20 citations

Frequency-modulated excitation of a two-level atom

Michael W. Noel, W. M. Griffith, Thomas F. Gallagher

We present a detailed experimental study of the frequency-modulated excitation of a two-level atom, using a microwave field to drive transitions between two Rydberg Stark states of potassium. In the absence of a modulation the interaction is the standard model of the Rabi problem, producing sinusoidal oscillations of the population between the two states. In the presence of a frequency modulation of the interacting field, however, the time evolution of the system is significantly modified, producing square wave oscillations of the population, sinusoidal oscillations at a different frequency, or even sinusoidal oscillations built up in a series of stair steps. The three responses described above are each found in a different regime for the frequency of the modulation with respect to the unmodulated Rabi frequency: the low-, high-, and intermediate-frequency regimes, respectively.

Physical Review A•Sep 1, 1998•62 citations

Theory of the coherent population trapping maser: A strong-field self-consistent approach

Aldo Godone, Filippo Levi, Salvatore Micalizio +1 more

The phenomenon of coherent microwave stimulated emission in a cavity is analyzed for the case of alkali atoms such as Cs and Rb under coherent population trapping (CPT) in a \ensuremath{\Lambda} scheme. The calculations are made in transient and in continuous operation within the framework of a three level model. The coupling of the atoms to the microwave field generated inside the cavity by the atomic ensemble, is fully taken into account; it introduces radiation damping and an imbalance in the populations of the ground-state hyperfine levels, decreasing the intrinsic symmetry of the \ensuremath{\Lambda} scheme. The effect leads also to a broadening and to a frequency shift of the microwave emission profile. A comparison is made with the optically pumped alkali atom maser, allowing a deeper understanding of the CPT stimulated emission phenomenon.

Physical Review A•Oct 12, 2000•24 citations
We consider the interaction of a three-level system with phase-modulated resonant fields in the \ensuremath{\Lambda} excitation scheme. We treat theoretically the case of a sinusoidal phase modulation, a phase step perturbation, and a stochastic phase modulation. The appearance of a Rabi resonance both in the spectrum of the optical transmitted signal (electromagnetically induced transparency) and in the spectrum of the microwave emission (coherent population trapping maser) is considered in detail. All the theoretical results are compared with the analogous ones reported for the two-level system and with our experimental observations obtained for the case of rubidium in a buffer gas.
Coherent population trapping (CPT) resonance signals have promise in a wide range of applications involving precision sensing. Generally, the CPT phenomenon occurs in a three-level Λ system with a bichromatic phase-coherent light fields. We theoretically and experimentally studied an Rb vapor-cell-based atomic system involving bichromatic CPT optical fields and an external microwave (MW) field simultaneously. In such a mixing scheme, the coherence of the ground states could be controlled either by the Rabi frequency of the microwave field or by the relative phase between the optical fields and the MW field. Moreover, we investigated the Rabi resonance in this mixing scheme. The Rabi frequency of the MW field can be measured SI (International System of Units)-traceably based on the Rabi resonance lineshape, and thus holds the potential to realize intensity stabilization of the optical field in this system. Simple theoretical models and numerical calculations are also presented to explain the experimental results. There is scope to use the proposed technique in future development of SI-traceable optical field strength standards.
The coherent microwave emission from an optically thick atomic ensemble in a cavity under coherent population trapping is analyzed. Transient and continuous operations are theoretically examined within the frame of a closed three-level system in the Dicke regime. The effects related to the atomic density and to the propagation in the active medium are examined with particular reference to the subnatural linewidth, the low group velocity and the shifts of the maser emission profile from the unperturbed atomic transition. The case of alkali-metal atoms submitted to a \ensuremath{\Lambda} excitation scheme is addressed in view of applications in the atomic frequency standard field. Experimental observations in agreement with the theoretical predictions are reported for the case of rubidium in a buffer gas. Apparent superluminal propagation is also reported and briefly discussed.
The propagation of a band-limited light pulse through an atomic medium under a \ensuremath{\Lambda} excitation scheme is theoretically analyzed in this paper. We consider in particular the case where the light pulse is detected through the coherent microwave emission of the atomic ensemble (coherent population trapping maser). Significant differences are predicted with respect to the more usual optical detection (electromagnetically induced transparency signal) and found in agreement with the experimental results. Higher signal delays were observed in the microwave emission than in the optical signal with an equivalent group velocity of 6 m/s as well as highly superluminal propagation under a proper modulation scheme. The experiments were performed with a thermal 87Rb{}^{87}\mathrm{Rb}87Rb vapor in buffer gas.
By use of a double-resonance technique, a spectrum of Rabi resonances has been observed. These resonances are enhancements in the dynamic response of a quantum system's population to rapid changes in the phase of a perturbing electromagnetic field. Theoretically, it is shown that the appearance of a spectrum, as opposed to a single Rabi resonance, is due to the fact that the phase of the field changes discretely by \ensuremath{\pi} radians, rather than sinusoidally. In the presence of \ensuremath{\pi}-radian phase changes, the quantum system's dynamic response is found to be similar to a damped harmonic oscillator driven by a \ensuremath{\delta}-function force term. In this harmonic-oscillator approximation the Rabi-resonance spectrum arises naturally, resulting from a resonant enhancement of the atomic coherence.
We present a detailed experimental study of the frequency-modulated excitation of a two-level atom, using a microwave field to drive transitions between two Rydberg Stark states of potassium. In the absence of a modulation the interaction is the standard model of the Rabi problem, producing sinusoidal oscillations of the population between the two states. In the presence of a frequency modulation of the interacting field, however, the time evolution of the system is significantly modified, producing square wave oscillations of the population, sinusoidal oscillations at a different frequency, or even sinusoidal oscillations built up in a series of stair steps. The three responses described above are each found in a different regime for the frequency of the modulation with respect to the unmodulated Rabi frequency: the low-, high-, and intermediate-frequency regimes, respectively.
The phenomenon of coherent microwave stimulated emission in a cavity is analyzed for the case of alkali atoms such as Cs and Rb under coherent population trapping (CPT) in a \ensuremath{\Lambda} scheme. The calculations are made in transient and in continuous operation within the framework of a three level model. The coupling of the atoms to the microwave field generated inside the cavity by the atomic ensemble, is fully taken into account; it introduces radiation damping and an imbalance in the populations of the ground-state hyperfine levels, decreasing the intrinsic symmetry of the \ensuremath{\Lambda} scheme. The effect leads also to a broadening and to a frequency shift of the microwave emission profile. A comparison is made with the optically pumped alkali atom maser, allowing a deeper understanding of the CPT stimulated emission phenomenon.