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

Slow light and superluminality in the coherent population trapping maser

Aldo Godone, Filippo Levi, Salvatore Micalizio

Published Oct 7, 2002• 21 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.66.043804

Related papers

Slow light and superluminality in the coherent population trapping maserAldo Godone, Filippo Levi, and Salvatore Micalizio

Aldo Godone, Filippo Levi, Salvatore Micalizio

The propagation of a band-limited light pulse through an atomic medium under a Λ 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 vapor in buffer gas.

•Jan 1, 2002•0 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

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

Slow and stopped light by light-matter coherence control

Jonas Tidström

In this thesis we study light-matter coherence phenomena related to the interaction of a coherent laser field and the so-called Λ-system, a three-level quantum system (e.g., an atom). We observe electromagnetically induced transparency (EIT), slow and stored light in hot rubidium vapor. For example, a 6 μs Gaussian pulse propagate at a velocity of ~1 km/s (to be compared with the normal velocity of 300 000 km/s). Dynamic changes of the control parameter allows us to slow down a pulse to a complete stop, store it for ~100 μs, and then release it. During the storage time, and also during the release process, some properties of the light pulse can be changed, e.g., frequency chirping of the pulse is obtained by means of Zeeman shifting the energy levels of the Λ-system. If, bichromatic continuous light fields are applied we observe overtone generation in the beating signal, and a narrow `dip' in overtone generation efficiency on two-photon resonance, narrower than the `coherent population trapping' transparency. The observed light-matter coherence phenomena are explained theoretically from first principles, using the Lindblad master equation, in conjunction with the Maxwell's equations. Furthermore, we analyze an optical delay-line based on EIT and show that there is in principle (besides decoherence) no fundamental limitation, but the usefulness today is scant. The combination of EIT and a photonic crystal cavity is inquired into, and we show that the quality value of a small resonator (area of 2.5λ×2.5λ with a missing central rod) can be enhanced by a factor of 500 due to the increased modal density close to two-photon resonance. Open system effects (decoherence effects) are thoroughly investigated using a coherence vector formalism, furthermore, a vector form of the Lindblad equation is derived. Specifically we find an open system channel that lead to slow light and gain.

•Jan 1, 2009•0 citations

Rabi resonances in the Λ excitation scheme

Aldo Godone, Salvatore Micalizio, Filippo Levi

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.

Physical Review A•Dec 16, 2002•31 citations

Detection of atomic entanglement and electromagnetically induced transparency in velocity-selective coherent population trapping

Martin Kiffner, Karl-Peter Marzlin

This work demonstrated theoretically that the entangled coherences of an atomic velocity-selective coherent population trapping (VSCPT) gas give rise to a distinctive optical signal, a backscattered beam of light, when the VSCPT gas is probed with a weak signal laser pulse. If the probe pulse and the pump beams are simultaneously applied the VSCPT gas also exhibits the phenomenon of electromagnetically induced transparency (EIT).

European Quantum Electronics Conference (EQEC)•Jan 18, 2006•0 citations
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.
The propagation of a band-limited light pulse through an atomic medium under a Λ 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 vapor in buffer gas.
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 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.
In this thesis we study light-matter coherence phenomena related to the interaction of a coherent laser field and the so-called Λ-system, a three-level quantum system (e.g., an atom). We observe electromagnetically induced transparency (EIT), slow and stored light in hot rubidium vapor. For example, a 6 μs Gaussian pulse propagate at a velocity of ~1 km/s (to be compared with the normal velocity of 300 000 km/s). Dynamic changes of the control parameter allows us to slow down a pulse to a complete stop, store it for ~100 μs, and then release it. During the storage time, and also during the release process, some properties of the light pulse can be changed, e.g., frequency chirping of the pulse is obtained by means of Zeeman shifting the energy levels of the Λ-system. If, bichromatic continuous light fields are applied we observe overtone generation in the beating signal, and a narrow `dip' in overtone generation efficiency on two-photon resonance, narrower than the `coherent population trapping' transparency. The observed light-matter coherence phenomena are explained theoretically from first principles, using the Lindblad master equation, in conjunction with the Maxwell's equations. Furthermore, we analyze an optical delay-line based on EIT and show that there is in principle (besides decoherence) no fundamental limitation, but the usefulness today is scant. The combination of EIT and a photonic crystal cavity is inquired into, and we show that the quality value of a small resonator (area of 2.5λ×2.5λ with a missing central rod) can be enhanced by a factor of 500 due to the increased modal density close to two-photon resonance. Open system effects (decoherence effects) are thoroughly investigated using a coherence vector formalism, furthermore, a vector form of the Lindblad equation is derived. Specifically we find an open system channel that lead to slow light and gain.
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.