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 Modern Optics

Refractive index enhancement in three-levelΛ-type atom with a saturation field: a dressed state analysis

C. Yang, Ying Gu, Lulu Wang, Qihuang Gong

Published Dec 15, 2006• 0 citations
Publisher

Abstract

The paper reports investigations of refractive index enhancement (RIE) with zero absorption in a three-level Λ-type atom subject to a drive field, a saturation field and a probe field. As RIEs lie in the alternate points between emission and absorption peaks, one can predict their positions by employing dressed state theory and optical Bloch equations. The numerical calculations with dressed state analysis indicate that high refractive index enhancement appears mainly at two conditions: (i) off-resonance detuning of drive and saturation frequencies have the opposite sign; (ii) the saturation Rabi frequency is larger than the drive Rabi frequency. The analysis can be extended to multi-field multi-level atomic systems.

DOI
10.1080/09500340600872804

Related papers

Stimulated emission and multi-peaked absorption in a four level N-type atom

Wang Kai, Ying Gu, Gong Qi-Huang

Absorption and refraction of the inner transition F2↔F3 of the closed four level N-type atom have been investigated under a weak field. The outer transitions F1↔F3 and F2↔F4 are resonantly interacted with drive field with frequency ωc and Rabi frequency Ωc, and saturation field with ωs and Ωs, respectively. For the suitable Rabi frequencies Ωc and Ωs, we obtain the Mollow absorption spectrum of probe field. The reason is that the drive field excites the atom to the upper level F3 and simultaneously the saturation field takes the atom out of the lower level F2, leading to the stimulated emission. Meanwhile, due to the dynamic energy splitting induced by the drive and saturation fields, the two- and four-peaked absorption spectra are observed. At the zero off-resonance detuning of probe field, we also find the transfer of dispersion from negative to positive with an increment of Ωs. Finally, the refractive index enhancement is predicted for a wide spectral region.

Chinese Physics•Dec 20, 2006•21 citations

Coherent control of refractive index in far-detuned Λ systems

Chris O’Brien, Petr M. Anisimov, Yuri V. Rostovtsev +1 more

Enhancement and control of the index of refraction in a mixture of two three-level atomic species that form a pair of far-detuned $\ensuremath{\Lambda}$ schemes under two-photon resonance has been studied. We employ the density-matrix approach to properly take population relaxation into account and to describe the interaction of each $\ensuremath{\Lambda}$ system with the electromagnetic fields. Both $\ensuremath{\Lambda}$ systems are driven by a corresponding far-detuned coherent field at one atomic transition and are probed by the same weak field. In the dressed-state basis, it represents a superposition of effective two-level subsystems with the positions, widths, and amplitudes of the resonances controlled by the driving fields and allows for efficient control of the susceptibility of the total system; leading to refractive index (RI) enhancement with vanishing absorption in the absence of amplification. We analyze the experimental implementation of such a system in a cell of Rb atoms with a natural abundance of isotopes. An upper limit estimate of the RI enhancement is obtained.

Physical Review A•Dec 15, 2011•26 citations

Multiple electromagnetically induced transparency in a quasi-Λ type four-level atomic system

Xiangwei Wang, Xiangyang Zhang

Using density matrix eqution, the absorption and dispersion properties of a A-type four-level system driven by coherent fields are investigated. The result obtained by means of numerical method indicates that by adjusting the intensity of Rabi frequencies of the coherent field in the steady state, three, double or single electromagnetically induced transparency (EIT) can appear explicitly in this system. And the explanations of these phenomena are given by using the dressed states. In the three EIT, the location of transparent windows can be manipulated by controlling the detuning of the driving field. What's more, it is also found that the medium shows a large refractive index at each transparency window, and the group velocity of the probe laser can be enhanced.

Chinese Journal of Quantum Electronics•Jan 1, 2010•0 citations

Time-dependent dressed-states analysis of lasing without population inversion in a three-level ladder scheme

Doron Braunstein, R. Shuker

A dressed-state study of lasing without population inversion from a three-level atom interacting with a bichromatic laser field in the ladder configuration is being formulated. The system is allowed to be dressed by both laser-field photons (double dressing). The temporal behavior of the system under consideration is being explored numerically. Although the use of dressed-basis density matrix equations introduces major complexity into the equations, this procedure has crucial importance to the understanding of the atomic spectrum and the underlying physics of the processes involved. The system is found to possess a gain without population inversion, as well as a regular gain with inversion for various transitions, both in the transient and steady-state regimes. Enhancement of the refractive index accompanied by vanishingly small absorption was also found. The frequency response of various transitions is explored via numerical Fourier analysis. Some transitions are found to exhibit a dispersion-like line shape, clear evidence of a quantum-coherent interference effect. The spectrum consists of two distinct quintets centered about the coupling and probe-laser frequencies. The spectral features consisting of each quintet are located symmetrically (at resonance conditions only) around the line center at positions shifted from the center by the generalized Rabi and double Rabi frequencies.

Laser Physics•Mar 1, 2008•4 citations

Saturation of optical susceptibilities in strong amplitude-modulated fields

G. S. Agarwal, N. Nayak

Optical non-linearities and spectroscopy in fields that are strongly modulated and also intense are examined by obtaining the solution of the optical Bloch equations in modulated fields as a matrix continued fraction. Numerical results for emission and absorption in such fields are presented. The saturation optical susceptibilities and the different types of spectra show resonances at the Rabi frequency if the modulation index is small. With increase in this index, additional resonant features appear at submultiples of the Rabi frequency. These additional features become more and more prominent as the modulation index increases further. For modulated fields on resonance, a dressed-atom formulation is developed to explain the results obtained from the numerical evaluation of the continued fraction. The results are also applicable to non-linear spectroscopic measurements such as Raman gain when the probe field is modulated.

Journal of Physics B Atomic and Molecular Physics•Oct 28, 1986•32 citations

Maximal atomic coherence via selective trapping of dressed states

Xiangming Hu, Jie‐Peng Zhang, Zhizhan Xu

We consider strong-field index enhancement in three-level systems in which there is a strong spontaneous decay from an auxiliary level into either of two states that the probe field couples. A control field is detuned resonant with the transition between the auxiliary level and one of the dressed states produced by the strong probe field. It is shown that it is possible to achieve maximal atomic coherence, which characterizes an ultralarge index of refraction and vanishing absorption. This scheme is based on selective dressed population trapping, which is established by relying on the control field and the strong decay to transfer population from one dressed state to another through the auxiliary level. An advantage of the present scheme is that the conditions for its realization are accessible experimentally.

Physical Review A•Jun 13, 2002•7 citations
The paper reports investigations of refractive index enhancement (RIE) with zero absorption in a three-level Λ-type atom subject to a drive field, a saturation field and a probe field. As RIEs lie in the alternate points between emission and absorption peaks, one can predict their positions by employing dressed state theory and optical Bloch equations. The numerical calculations with dressed state analysis indicate that high refractive index enhancement appears mainly at two conditions: (i) off-resonance detuning of drive and saturation frequencies have the opposite sign; (ii) the saturation Rabi frequency is larger than the drive Rabi frequency. The analysis can be extended to multi-field multi-level atomic systems.
Absorption and refraction of the inner transition F2↔F3 of the closed four level N-type atom have been investigated under a weak field. The outer transitions F1↔F3 and F2↔F4 are resonantly interacted with drive field with frequency ωc and Rabi frequency Ωc, and saturation field with ωs and Ωs, respectively. For the suitable Rabi frequencies Ωc and Ωs, we obtain the Mollow absorption spectrum of probe field. The reason is that the drive field excites the atom to the upper level F3 and simultaneously the saturation field takes the atom out of the lower level F2, leading to the stimulated emission. Meanwhile, due to the dynamic energy splitting induced by the drive and saturation fields, the two- and four-peaked absorption spectra are observed. At the zero off-resonance detuning of probe field, we also find the transfer of dispersion from negative to positive with an increment of Ωs. Finally, the refractive index enhancement is predicted for a wide spectral region.
Enhancement and control of the index of refraction in a mixture of two three-level atomic species that form a pair of far-detuned $\ensuremath{\Lambda}$ schemes under two-photon resonance has been studied. We employ the density-matrix approach to properly take population relaxation into account and to describe the interaction of each $\ensuremath{\Lambda}$ system with the electromagnetic fields. Both $\ensuremath{\Lambda}$ systems are driven by a corresponding far-detuned coherent field at one atomic transition and are probed by the same weak field. In the dressed-state basis, it represents a superposition of effective two-level subsystems with the positions, widths, and amplitudes of the resonances controlled by the driving fields and allows for efficient control of the susceptibility of the total system; leading to refractive index (RI) enhancement with vanishing absorption in the absence of amplification. We analyze the experimental implementation of such a system in a cell of Rb atoms with a natural abundance of isotopes. An upper limit estimate of the RI enhancement is obtained.
Using density matrix eqution, the absorption and dispersion properties of a A-type four-level system driven by coherent fields are investigated. The result obtained by means of numerical method indicates that by adjusting the intensity of Rabi frequencies of the coherent field in the steady state, three, double or single electromagnetically induced transparency (EIT) can appear explicitly in this system. And the explanations of these phenomena are given by using the dressed states. In the three EIT, the location of transparent windows can be manipulated by controlling the detuning of the driving field. What's more, it is also found that the medium shows a large refractive index at each transparency window, and the group velocity of the probe laser can be enhanced.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bichromatic laser field in the ladder configuration is being formulated. The system is allowed to be dressed by both laser-field photons (double dressing). The temporal behavior of the system under consideration is being explored numerically. Although the use of dressed-basis density matrix equations introduces major complexity into the equations, this procedure has crucial importance to the understanding of the atomic spectrum and the underlying physics of the processes involved. The system is found to possess a gain without population inversion, as well as a regular gain with inversion for various transitions, both in the transient and steady-state regimes. Enhancement of the refractive index accompanied by vanishingly small absorption was also found. The frequency response of various transitions is explored via numerical Fourier analysis. Some transitions are found to exhibit a dispersion-like line shape, clear evidence of a quantum-coherent interference effect. The spectrum consists of two distinct quintets centered about the coupling and probe-laser frequencies. The spectral features consisting of each quintet are located symmetrically (at resonance conditions only) around the line center at positions shifted from the center by the generalized Rabi and double Rabi frequencies.
Optical non-linearities and spectroscopy in fields that are strongly modulated and also intense are examined by obtaining the solution of the optical Bloch equations in modulated fields as a matrix continued fraction. Numerical results for emission and absorption in such fields are presented. The saturation optical susceptibilities and the different types of spectra show resonances at the Rabi frequency if the modulation index is small. With increase in this index, additional resonant features appear at submultiples of the Rabi frequency. These additional features become more and more prominent as the modulation index increases further. For modulated fields on resonance, a dressed-atom formulation is developed to explain the results obtained from the numerical evaluation of the continued fraction. The results are also applicable to non-linear spectroscopic measurements such as Raman gain when the probe field is modulated.
We consider strong-field index enhancement in three-level systems in which there is a strong spontaneous decay from an auxiliary level into either of two states that the probe field couples. A control field is detuned resonant with the transition between the auxiliary level and one of the dressed states produced by the strong probe field. It is shown that it is possible to achieve maximal atomic coherence, which characterizes an ultralarge index of refraction and vanishing absorption. This scheme is based on selective dressed population trapping, which is established by relying on the control field and the strong decay to transfer population from one dressed state to another through the auxiliary level. An advantage of the present scheme is that the conditions for its realization are accessible experimentally.