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Chinese Physics B

Quantum coherence in Λ-three-level system driven by bichromatic coupling field

Yang Li-Jun, Zhao Min, Lianshui Zhang, Xiaomin Feng, Xiaoli Li, Wei Chang-Jiang

Published Aug 1, 2010• 3 citations
Publisher

Abstract

We present a theoretical study of quantum coherent effects in a Λ-three-level system with a strong bichromatic coupling field and a weak probe field. When one component of the strong bichromatic coupling field is resonant with a corresponding transition and the other is detuning with an integer fraction of the Rabi frequency of the resonant field, the absorption spectrum exhibits a series of symmetrical doublets. While two frequencies of the strong bichromatic coupling field are symmetrically detuned from the transition, the position and the relative intensity of the absorption peak are both affected by the coupling field intensity and detuning. An explanation of the spectrum is given in term of the dressed-state formalism.

DOI
10.1088/1674-1056/19/8/084204

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Physical Review A•Dec 23, 2005•39 citations
We present a theoretical study of quantum coherent effects in a Λ-three-level system with a strong bichromatic coupling field and a weak probe field. When one component of the strong bichromatic coupling field is resonant with a corresponding transition and the other is detuning with an integer fraction of the Rabi frequency of the resonant field, the absorption spectrum exhibits a series of symmetrical doublets. While two frequencies of the strong bichromatic coupling field are symmetrically detuned from the transition, the position and the relative intensity of the absorption peak are both affected by the coupling field intensity and detuning. An explanation of the spectrum is given in term of the dressed-state formalism.
The probe absorption spectrum of the Λ-three-level system driven by bichromatic coupling field and weak probe field is investigated. We obtain the probe absorption spectra for different frequency detunings of coupling field by solving the density matrix equation and numerical analysis. Three electromagnetically induced absorption (EIA) peaks are simultaneously observed in the absorption profile of probe field. We report the dependence of position and relative intensity of EIA on the frequency detuning of the bichromatic coupling field. The results show that central EIA always appears at the resonant frequency of probe field, with the constant intensity. The position of the secondary EIA vary with the frequency detuning of coupled field, and the intensity of the absorption peaks decrease with the increasing detuning.
Transparency and absorption overlaping with Mollow profile in a lambda three-level scheme driven by two coupling fields was investigated. There are two degenerate hyperfine levels within ground state. A strong coupling field and a probing field interact with the same optical transition between the excited state level and the first ground state hyperfine level, and an additional weak coupling field interacts with the excited state level and the second ground state hyperfine level, which is named double coupling lambda three-level scheme. It can be seen that when the strong coupling field is off-resonant, there is the superposition of Mollow profile with EIT, EIA and other quantum coherent phenomena, namely, Mollow profile with seven peaks. The dependence of the position of the EIT or EIA on Rabi frequency and frequency detuning of the strong coupling field was investigated. The results can be accounted for by dressed-state formalism.
The possibility of obtaining strong negative dispersion without absorption in the central resonance structure of the spectrum of a bichromatically driven two-level system is investigated. A nonlinear analysis is performed using the technique of continued fractions with respect to the dressedstate basis of a strong pumping laser. We discuss the transition between the two regimes of the monochromatic driving case with a weak probing laser and of nearly equally strong lasers in terms of the contributions from coherences and populations of these dressed states. In contrast with the strong dependence of the Rabi side bands on probe field intensity, we find a remarkable stability of the negative dispersion in the central resonance structure.
The transparency and absorption of the Λ-type three-level scheme driven by two coupling fields were investigated.Mollow profile was obtained in a two-level scheme where a strong coupling field and a probing field were applied on the same optical transition between excited state and ground state.There was another coupling field which drived excited state to another ground states hyperfine level in this paper.The Λ-type three-level scheme driven by two coupling fields was introduced,and some new quantum coherent phenomena were given.It can be seen that there is superposition of Mollow profile and electromagnetically induced transparency(EIT) or electromagnetically induced absorption(EIA).The dependence of the position of EIT or EIA on Rabi frequencies and frequency detunings of two coupling fields is investigated.The results can be explained by dressed-state formalism.
We examine the radiative properties of a two-level atom driven by a strong bichromatic field with frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{0}$-${\mathrm{\ensuremath{\delta}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{0}$+${\mathrm{\ensuremath{\delta}}}_{2}$, which can be asymmetrically placed about the atomic transition frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ and can have different Rabi frequencies ${\mathrm{\ensuremath{\Omega}}}_{1}$ and ${\mathrm{\ensuremath{\Omega}}}_{2}$. Applying the optical Bloch equations for the bichromatic excitation, we derive an infinite set of equations of motion for the time evolution of the atomic variables. The equations are solved numerically by matrix inversion and Laplace transforms. Using the quantum regression theorem, we then solve for the steady-state total fluorescence intensity, and the resonance-fluorescence and absorption spectra. The spectra are found to depend on the frequency difference 2\ensuremath{\delta}=${\mathrm{\ensuremath{\delta}}}_{1}$+${\mathrm{\ensuremath{\delta}}}_{2}$, the average detuning \ensuremath{\Delta}=${\mathrm{\ensuremath{\omega}}}_{0}$-1/2(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$), and the Rabi frequencies of the driving fields. For ${\mathrm{\ensuremath{\Omega}}}_{1}$=${\mathrm{\ensuremath{\Omega}}}_{2}$=\ensuremath{\Omega}, the total fluorescent intensity displays a series of maxima for \ensuremath{\Delta}=\ifmmode\pm\else\textpm\fi{}n\ensuremath{\delta}\ensuremath{\mp}${\mathrm{\ensuremath{\Omega}}}^{2}$/4\ensuremath{\delta}, where the n are the odd integers. The intensity-dependent shift from the resonances n\ensuremath{\delta} is explained as an analog of the generalized Bloch-Siegert shift. The resonance-fluorescence spectrum for \ensuremath{\Delta}\ensuremath{\ne}0 appears to contain more peaks than that for \ensuremath{\Delta}=0.This is due to the splitting of the central peak and the even sidebands into doublets. The absorption spectrum of a weak-probe beam for \ensuremath{\Delta}=0 and equal Rabi frequencies consists of a symmetric series of dispersionlike sidebands separated from ${\mathrm{\ensuremath{\omega}}}_{0}$ by integer multiples of \ensuremath{\delta}, together with a central absorption peak at ${\mathrm{\ensuremath{\omega}}}_{0}$, whose amplitude oscillates with \ensuremath{\Omega}. For \ensuremath{\Delta}\ensuremath{\ne}0 and/or ${\mathrm{\ensuremath{\Omega}}}_{1}$\ensuremath{\ne}${\mathrm{\ensuremath{\Omega}}}_{2}$, the odd sidebands remain dispersionlike, while the central peak and the even sidebands split into absorption-emission doublets. A simple physical interpretation of the spectral features is given in terms of the dressed-atom model.
Electromagnetically induced transparency (EIT) resonance in a $\ensuremath{\Lambda}$ configuration is obtained when the frequencies of two fields are close to resonance with two of the transitions and their frequency difference matches the frequency of the third transition. In this situation the spectrum of one swept field as a probe gives a simple transparency feature. However, when an additional field drives the third transition the EIT feature associated with the probe is split. This perturbed EIT is illustrated for both single and bichromatic driving fields. In the single-driving-field case a density matrix treatment is shown to be in reasonable agreement with experiment, and in both single and bichromatic cases the structure in the spectrum can be explained using the dressed-state formalism. The dressed states can also be used to account for subharmonic resonances observed in the strong-probe regime.