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 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.
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.
We initially discuss the theory of three-level systems using the dressed state formalism. One of the dressed states, containing a ground state and a Rydberg state, does not couple with the probe laser; thus, the medium becomes transparent to the latter. This phenomenon is known as electro- magnetically induced transparency (EIT) and this dressed state is known as a Rydberg dark state. We show that EIT can be used to extract the reduced dipole matrix element for transitions to a Rydberg state. However, a prob- lem with three-level Rydberg EIT in a vapour cell is the occurrence of space charges caused by photoelectric ionisation of Rb metal deposited inside the cell. To avoid this problem, we consider adding a third laser resonant with a fourth level. This is to avoid using the laser whose wavelength is less than the threshold wavelength. In cold atoms, the effect of the third laser is to split the usual EIT resonance into a doublet. In thermal atoms, we observe narrow features due to electromagnetically induced absorption and electro- magnetically induced transparency in the Doppler-free configuration. Next we consider the action of a far off-resonance radio frequency (rf) field in the three-level system. We demonstrate the formation of rf-dressed EIT reso- nances in a thermal Rb vapour and show that such states exhibit enhanced sensitivity to dc electric fields compared to their bare counterparts. Fitting the corresponding EIT profile enables precise measurements of the dc field in- dependent of laser frequency fluctuations. We further investigate the theory of rf-dressed Rydberg EIT using the Floquet approach in order to understand the formation of the sideband structure of the Rydberg state. We find that if the time scale of the rf interaction is much shorter than that of the system evolution and decoherence, the sideband structure is well resolved. We also show that the intermediate state exhibits a sideband structure, induced by the Rydberg state, when the Rabi frequency of coupling laser is larger than twice the modulation frequency. Finally we consider resonant microwave cou- pling between the Rydberg states which leads to an Autler-Townes splitting of the EIT resonance in cold atoms. This splitting can be employed to vary the group index by ±10^5 allowing independent control of the absorptive and dispersive properties of the medium, i.e., one can switch the transparency of the medium or control the group velocity of a pulse propagation by tuning on and off the microwave field.
We study laser-induced transparency and dark-line effects in a two-level atomic system where the upper transition level is coupled by a laser field to a dressed system consisting of two lower-energy metastable states mixed by a second laser field (\ensuremath{\Pi} configuration). We show that the emission (absorption) spectrum of the two-level system develops two dynamic dark lines (transparency holes) with tunable central frequencies equal to the Rabi frequency of the second field with positive and negative signs, and widths proportional to that of the first field. The detailed evolution of these effects at low- and high-field intensities and the role of quantum interferences are discussed by presenting a model based on laser-induced continuum structure and adopting a dressed-state picture. We discuss various nonlinear processes in this system and show how the dynamics of emission and absorption spectra are determined by one- and two-photon coupling processes.
In this paper, a two-Λ-type five-level system is constructed by using the Zeeman energy level of the lithium atom's hyperfine structure and interacting with two optical fields which have different polarization directions. The quantum coherence effect of the system is studied under the condition of two photon resonance. Firstly, we construct the Hamiltonian of the system under the rotation frame, and get the dark state of the system by solving the eigenvalues and eigenstates of the Hamiltonian. Then, a new coupled representation is constructed by the dark state, and the preparation of the dark state of the five-level system is further studied. Finally, the density matrix motion equations of the five-level system are established, and the numerical solution is solved by program. Through numerical simulation, we give the curve of the signal light absorption intensity with its changed detuning, and from this curve. We can see that there is a transparent window near the zero of the signal light detuning, accompanied by a normal dispersion curve. The position of the transparent window corresponds to the dark state condition for the formation of the system, that is, the system is prepared to the dark state under the two-photon resonance condition, and the atoms in the dark state do not interact with the light field, so the incident signal light appears transparent.
We investigate the steady optical response of a coherently driven five-level M-type atomic system in three different situations. When all three coupling fields have the same zero detuning, we just find one deep transparency window accompanied by a steep normal dispersion in the probe absorption and dispersion spectra. When two coupling fields are detuned from the relevant transitions to the same extent, however, a second deep transparency window may be observed in the presence of a narrow absorption line of linewidth ∼ 50 kHz. In this case, two single-photon far-detuned transitions can be replaced by a two-photon resonant transition, so the five-level M system in fact reduces into a four-level quasi-Λ system. Finally, we note that no deep transparency windows and no narrow absorption lines can be found when all three coupling fields have unequal detunings.
As a rule the thermal motion removes the dark resonance from the spectrum of a three-level system driven by two strong fields. An example has been found where, conversely, the dark resonance manifests itself even after averaging over the velocities. The four-level system is studied with a closed cycle of four resonant fields, when two relatively strong fields interact with opposite transitions. If Rabi frequencies exceed relaxation constants, then the frequency dependence of the nonlinear susceptibility consists of several narrow peaks. Each peak corresponds to a ‘turning point’, the resonant frequency with zero derivative with respect to the velocity. It is shown that two peaks disappear when non-absorbing states coincide with the turning points. The coincidence occurs for equal Rabi frequencies of relatively weak fields.