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Acta Sinica Quantum Optica

Normal and Anomalous Dispersion in Three-level Cascade Media

Xiangming Hu

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

We suggest that a three-level cascade medium be used to achieve the switching from normal dispersion to anomalous dispersion. In the cascade medium, two dipole-allowed transitions are coupled by two different coherent fields, respectively. A probe field is applied either to the upper transition or to the lower transition. The equations for density matrix elements are transformed into a set of equations with time-independent coefficients in the steady state via harmonic expansion, which are solved by matrix inversion. By the solutions we obtain the absorption and dispersion spectra. It is shown that for each case, the medium exhibits either normal or anomalous dispersion at the same frequency regime. The switching from normal dispersion to anomalous dispersion is obtained by varying the intensity from couple to probe transition. The two differences lie between the proposed cascade system and the Λ and V systems. Firstly, near degenerate levels are required for the Λ and V systems when the probe field is simultaneously coupled to the two transitions to achieve dispersion switching. The present scheme is based on an equivalent realization of near degeneracy in the dressed picture, and the interval is controlled by the corresponding field. Secondly, dispersion switching does not occur in the Λ and V systems when the probe field is only coupled to either of two transitions and the decoupled state plays a dominant role. In contrast, the present scheme does not involve the decoupled state.

Related papers

Double switching from normal to anomalous dispersion via trichromatic phase manipulation of electromagnetically induced transparency

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We present a theoretical analysis of trichromatic phase manipulation of electromagnetically induced transparency and show that it is possible to obtain double switching, in which switching from normal to anomalous dispersion occurs in two separate frequency regimes. In particular, a four-level system in the N configuration is considered, in which electromagnetically induced transparency is established in the $\ensuremath{\Lambda}$ subsystem and the additional transition is connected to the probe transition and is coupled by a trichromatic field. It is shown that the sum of the relative phases of the sideband components compared to that of the central component plays a crucial role in the absorption and dispersion spectra. Normal dispersion with negligible absorption or anomalous dispersion with small gain can be achieved in multiple-frequency regimes by varying the sum of the relative phases. When the sum phase is changed from 0 to $\ensuremath{\pi}$, switching from normal to anomalous dispersion occurs in the two different frequency regimes. On the other hand, so long as we fix the sum of two relative phases, the absorption and dispersion spectra keep their own features unchanged no matter how we vary the respective relative phases.

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Switching from positive to negative dispersion in a three-level V system driven by a single coherent field

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The Absorption and Dispersion Properties in the Four-level System with Two Controlling Fields

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Coherent control of the refractive index using optical bistability

H. Aswath Babu, Harshawardhan Wanare

Refractive index and absorption experienced by a probe field propagating through a three-level atomic medium can be effectively manipulated by the bistable behavior of a control field. The probe field couples the lower transition of the atom in a ladder configuration and experiences normal or anomalous dispersion depending on the control field being in the upper or lower bistable state, respectively. We also obtain nonlinear dynamical instability in the form of periodic self-pulsing as the lower bistable branch becomes unstable, quite unlike earlier demonstrations of an unstable regime in the upper branch. Consequently, the susceptibility experienced by the probe field varies periodically in time as dictated by the control field self-pulsing.

arXiv:1209.1891•Physical Review A•Mar 19, 2013•6 citations
We suggest that a three-level cascade medium be used to achieve the switching from normal dispersion to anomalous dispersion. In the cascade medium, two dipole-allowed transitions are coupled by two different coherent fields, respectively. A probe field is applied either to the upper transition or to the lower transition. The equations for density matrix elements are transformed into a set of equations with time-independent coefficients in the steady state via harmonic expansion, which are solved by matrix inversion. By the solutions we obtain the absorption and dispersion spectra. It is shown that for each case, the medium exhibits either normal or anomalous dispersion at the same frequency regime. The switching from normal dispersion to anomalous dispersion is obtained by varying the intensity from couple to probe transition. The two differences lie between the proposed cascade system and the Λ and V systems. Firstly, near degenerate levels are required for the Λ and V systems when the probe field is simultaneously coupled to the two transitions to achieve dispersion switching. The present scheme is based on an equivalent realization of near degeneracy in the dressed picture, and the interval is controlled by the corresponding field. Secondly, dispersion switching does not occur in the Λ and V systems when the probe field is only coupled to either of two transitions and the decoupled state plays a dominant role. In contrast, the present scheme does not involve the decoupled state.
We present a theoretical analysis of trichromatic phase manipulation of electromagnetically induced transparency and show that it is possible to obtain double switching, in which switching from normal to anomalous dispersion occurs in two separate frequency regimes. In particular, a four-level system in the N configuration is considered, in which electromagnetically induced transparency is established in the $\ensuremath{\Lambda}$ subsystem and the additional transition is connected to the probe transition and is coupled by a trichromatic field. It is shown that the sum of the relative phases of the sideband components compared to that of the central component plays a crucial role in the absorption and dispersion spectra. Normal dispersion with negligible absorption or anomalous dispersion with small gain can be achieved in multiple-frequency regimes by varying the sum of the relative phases. When the sum phase is changed from 0 to $\ensuremath{\pi}$, switching from normal to anomalous dispersion occurs in the two different frequency regimes. On the other hand, so long as we fix the sum of two relative phases, the absorption and dispersion spectra keep their own features unchanged no matter how we vary the respective relative phases.
We study the absorption and dispersion in the near-degenerate closed three-level V system, in which a single coherent driving field is tuned resonant with the average frequency of two dipole-allowed transitions. Firstly, the switching from positive to negative dispersion can be achieved simply by increasing the driving field intensity. This is the same as in the driven Λ system. Secondly, the common feature originates from the fact that both V and Λ systems have the same transitions in terms of atomic dressed states under given conditions. These dressed transitions interfere destructively in the central spectrum while the sideband resonance transitions determine the possible appearance of two pairs of absorption doublet lines and two pairs of gain doublet lines in the sideband spectrum. Thirdly, there are two minor differences between these two systems. For large driving field intensity, a narrow steep structure is always present in the central negative dispersion spectrum in the V system but it disappears in the Λ system. The driving field intensity for the appearance of the outer sideband absorption or gain peaks is larger in the V system than in the Λ system.
The absorption and dispersion properties of the probe field were investigated along with the parameters of the coupling field and the microwave field by numerically solving the density matrix equation of the quasi-Λ-four-level system. It is shown that as the microwave field Rabi frequency increasing,the probe field absorption of the resonance frequency position decreased gradually,and the dispersion property was also influenced which the switching from anomalous dispersion to normal dispersion can be observed. Both microwave field and coupling field were strong fields,the effect of two fields on the probe absorption and dispersion can be obtained by changing the parameters of two fields.
We study the propagation of a bichromatic field in three-level and four-level media. In the case of a three-level medium, we consider the \ensuremath{\Lambda} configuration and demonstrate that if the upper level is not empty there is a critical value for the low-frequency coherence such that below this threshold and for intense fields, coherent bleaching occurs. This implies a sharp reduction of the field absorption and the fluorescence emission whereas above this threshold a parametric instability takes place. It corresponds to an amplification of the field that does not need a population inversion between the optical transitions. Finally we prove that the field alone cannot create a low-frequency coherence exceeding this threshold. Therefore we analyze the double-\ensuremath{\Lambda} configuration involving a four-level medium in which the upper and lower pairs of atomic levels have a low-frequency separation while optical transitions take place between the two pairs of states. An intense bichromatic field that is resonant with one upper state and the lower levels and a weak bichromatic field resonant with the other upper state and the same two lower states are sent into the medium. We analyze the limit in which the low-frequency coherence created between the lower pair of states has a relaxation time which is large. Then there will be population trapping in the lower states leading to coherent bleaching if there is no inversion between the upper levels but there will be amplification if there is inversion between the upper levels. In this way amplification at the optical transitions without population inversion between these states is realized.
Abstract The manipulation of the group velocity of light is very important in further information processing and quantum network. It is well known that subluminal and superluminal light propagation can be obtained by controlling the dispersion property of the experimental medium. In order to realize the switching from normal dispersion to anomalous dispersion at the same frequency, we investigate the dispersion and absorption properties of a four-level atomic system. By adjusting the intensity of an incoherent pump, we get transparent normal dispersion and lossless anomalous dispersion, which lead to subluminal and superluminal light propagation respectively. For a strong incoherent pump, the intensity of the coherent coupling field also can be used to realize a similar switching effect.
Refractive index and absorption experienced by a probe field propagating through a three-level atomic medium can be effectively manipulated by the bistable behavior of a control field. The probe field couples the lower transition of the atom in a ladder configuration and experiences normal or anomalous dispersion depending on the control field being in the upper or lower bistable state, respectively. We also obtain nonlinear dynamical instability in the form of periodic self-pulsing as the lower bistable branch becomes unstable, quite unlike earlier demonstrations of an unstable regime in the upper branch. Consequently, the susceptibility experienced by the probe field varies periodically in time as dictated by the control field self-pulsing.