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Physical Review A

Optical dark resonance in multilevel systems with a treelike configuration

H. Kanokogi, Kenji Sakurai

Published Sep 1, 1996• 1 citation
Publisher

Abstract

Optical dark resonance in systems with arbitrary multilevels and multiphotons is studied theoretically. When the system configuration is treelike (the term of graph theory), all the coherence terms in the system can be categorized into several groups on dark resonance. It is proved for generic system configurations with arbitrary multilevels that the resonance conditions can be obtained successively by setting the determinant of the submatrix of the Hamiltonian with respect to each group to zero. We calculate, as one of the practical examples, all the conditions of dark resonance of potassium atoms with two laser fields and one rf field mixing one excited state and eight ground states in the hyperfine structure. Although the system configuration is very complicated, the condition is easily obtained in an analytic form and verified by the result of a numerical simulation. Furthermore, our theory can reveal the fine structure of dark lines with power broadening in the observed light-induced-fluorescence spectra and numerical calculations. In addition, the dark lines with the complicated splitting pattern observed in experiments can be assigned to the relevant level configuration and transitions by the present theory. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.2334

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The optical dark resonance in a symmetric five-level system with two lasers and two rf (or microwave) fields is studied theoretically. We obtain the analytic steady-state solution for the density matrix of the system. We find that some manifolds of narrower dark resonance due to rf fields appear at the positions that depend on the Rabi frequencies and the detuning frequencies of rf fields. The exact expression of the resonance position, the line shape, and the resonance width are obtained. The resonance width of the dark lines with rf-dressed atoms is proved to be narrower than that of the ordinary three-level \ensuremath{\Lambda} system and is desirable for trapping atoms. As the dark lines can simultaneously trap atoms with a nonzero velocity as well as those with a zero velocity, they can be used for the collision experiments. \textcopyright{} 1996 The American Physical Society.

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Electromagnetically induced transparency and dark fluorescence in a cascade three-level diatomic lithium system

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Optical dark resonance in systems with arbitrary multilevels and multiphotons is studied theoretically. When the system configuration is treelike (the term of graph theory), all the coherence terms in the system can be categorized into several groups on dark resonance. It is proved for generic system configurations with arbitrary multilevels that the resonance conditions can be obtained successively by setting the determinant of the submatrix of the Hamiltonian with respect to each group to zero. We calculate, as one of the practical examples, all the conditions of dark resonance of potassium atoms with two laser fields and one rf field mixing one excited state and eight ground states in the hyperfine structure. Although the system configuration is very complicated, the condition is easily obtained in an analytic form and verified by the result of a numerical simulation. Furthermore, our theory can reveal the fine structure of dark lines with power broadening in the observed light-induced-fluorescence spectra and numerical calculations. In addition, the dark lines with the complicated splitting pattern observed in experiments can be assigned to the relevant level configuration and transitions by the present theory. \textcopyright{} 1996 The American Physical Society.
The optical dark resonance in a symmetric five-level system with two lasers and two rf (or microwave) fields is studied theoretically. We obtain the analytic steady-state solution for the density matrix of the system. We find that some manifolds of narrower dark resonance due to rf fields appear at the positions that depend on the Rabi frequencies and the detuning frequencies of rf fields. The exact expression of the resonance position, the line shape, and the resonance width are obtained. The resonance width of the dark lines with rf-dressed atoms is proved to be narrower than that of the ordinary three-level \ensuremath{\Lambda} system and is desirable for trapping atoms. As the dark lines can simultaneously trap atoms with a nonzero velocity as well as those with a zero velocity, they can be used for the collision experiments. \textcopyright{} 1996 The American Physical Society.
The dark-state effect, caused by destructive quantum interference, is an important physical effect in atomic physics and quantum optics. It not only deepens the understanding of light-atom interactions, but also has wide applications in quantum physics and quantum information. Therefore, how to efficiently and conveniently determine the number and form of the dark states in multilevel quantum systems with complex transitions is an important and interesting topic in this field. In this work, we present a general theory for determining the dark states in multilevel quantum systems with any coupling configuration using the arrowhead-matrix method. To confirm the dark states in a multilevel system, we first define the upper- and lower-state subspaces, and then diagonalize the Hamiltonians restricted within the two subspaces to obtain the dressed upper and lower states. By further expressing the transitions between the dressed upper and lower states, we can map the multilevel system to a bipartite-graph network, in which the nodes and links are acted by the dressed states and transitions, respectively. Based on the coupling configurations of the network, we can determine the lower dark states with respect to the upper-state subspace. As examples, we analyze the dark states in three-, four-, and five-level quantum systems, for all possible configurations through the classification of the numbers of upper and lower states. Furthermore, we extend the framework to multilevel quantum systems and discuss the existence of dark states in some typical configurations. We also recover the results of the dark-state polaritons in driven three-level systems with the arrowhead-matrix method. Our theory paves the way for manipulating and utilizing the dark states of multilevel quantum systems in atomic physics and quantum optics.
A universal theory for calculating coherent population trapping resonances in multilevel atoms is suggested. The theory allows arbitrary schemes of multilevel atoms and their excitations to be calculated taking into account the influence of relaxation effects in atoms, applied magnetic field, and the Doppler effect. The experimental data obtained by high-precision diode spectroscopy of coherent dark resonances in samarium vapor are systematically analyzed using the suggested theory. In the absence of a magnetic field, the model of samarium is based on consideration of a degenerate Λ system of the 4f 66s 2(7 F 0) ↔ 4f 6(7 F)6s6p(3 P 0)9 F 1 0 ↔4f 66s 2(7 F 1) active transitions. If the fourth 4f 66s 2(7 F 2) level is taken into account, this Λ system becomes open. Numerical simulation of coherent population trapping resonances shows that the open character of the system decreases the contrast of resonance curves in absorption spectra without changing resonance widths. The system under applied external longitudinal and transverse magnetic fields is correctly described by 7-and 12-level models of atomic transitions, respectively.
Summary form only given. In a three-level system, two resonant optical fields can excite spin coherence on the ground states via two-photon resonance. One of the two-superposition states created by the atom-field interactions is decoupled from the excited state. Thus, the population can be trapped in that state showing non-absorption resonance. The essential feature of this decoupled state is dark resonance. Therefore, the existence of the dark resonance is a basis of non-absorption resonance, coherent population trapping, and electromagnetically induced transparency. In a four-level system, however, the two-laser induced spin coherence can be broken when a third laser is applied. At the same time, new coherence between the third laser and one of the pre-existed lasers is created. This phenomenon is useful for optical switching owing to annihilation and creation of the dark resonance in the four-level system. It is noted that the switching time depends on the dark resonance build-up time, which is inversely proportional to the applied Rabi frequency. Numerical simulations are shown for potentially ultrahigh-speed optical switches. Each diffracted four-wave mixing signal is proportional to the spin coherence strength. For a preliminary experiment, a spectral hole-burning crystal is used. The intensity of the diffracted signals is reversed at line center. This coherence switching effect is based on the dark resonance interactions.
Theoretical study and computer modeling results of the spectra of coherent dark resonances resulted from excitation of Zeeman sublevels of the Fg=2→Fe=1 transition of the D1 line in 87Rb atoms by a frequency-modulated laser field are presented and discussed in detail. The influence of the nonlinear Zeeman effect on the structure of the coherent dark resonances is observed. It is shown that calculated for different values of the magnetic field spectra are in a good agreement with the experimental data.
Following our previous brief report [Phys. Rev. Lett. 88, 173003 (2002)], we report here a detailed study of electromagnetically induced transparency (EIT) and dark fluorescence in a cascade three-level diatomic lithium system using optical-optical double resonance (OODR) spectroscopy for both resonance and off resonance coupling. When a strong coupling laser couples the intermediate state $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(v=13,J=14)$ to the upper state $G\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}_{g}(v=11,J=14)$ of 7Li2^{7}\mathrm{Li}_{2}7Li2​, the fluorescence from both $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ and $G\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}_{g}$ states was drastically reduced as the weak probe laser was tuned through the resonance transition between the ground state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}(v=4,J=15)$ and the excited state $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(v=13,J=14)$. The strong coupling laser makes an optically thick medium transparent for the probe transition. In addition, the fact that fluorescence from the upper state $G\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}_{g}(v=11,J=14)$ was also dark when both lasers were tuned at resonance implies that the molecules were trapped in the ground state. We used density matrix methods to simulate the response of an open molecular three-level system to the action of a strong coupling field and a weak probe field. The analytical solutions were obtained under the steady-state condition. We have incorporated the magnetic sublevel (M)(M)(M) degeneracy of the rotational levels in the line shape analysis and report $\ensuremath{\mid}M\ensuremath{\mid}$ dependent line shape splitting. Our theoretical calculations are in excellent agreement with the observed fluorescence spectra. We show that the coherence is remarkably preserved even when the coupling field was detuned far from the resonance.