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An Exact Scheme for the EIT for a Three-level Λ -Type Atom in a Quantum Cavity

Siamak Khademi, Ghasem Naeimi, Samira Alipour, Shoaib Mirzaei

Published Jan 1, 2015• 2 citations
OpenAlex

Abstract

Semi-quantum or full-quantum electromagnetically induced transparency has been fully studied for three-level atoms in a weak field approximation method, where probe field is very wea ker than the coupling field. The weak field approximation is no t valid in full-quantum model where the number of coupling photons is not so large. In the present article, the master equations for the interaction of two-mode photons with a three-level Λ -type atom are exactly solved and the exact dispersion and absorption spectra for the probe beam photons are also obtained analytically. The results of the exact scheme are compared with the corresponding results in the weak field approximation method in full-quantum and semi-classi cal models.

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Acta Physica Sinica•Jan 1, 2011•5 citations
Semi-quantum or full-quantum electromagnetically induced transparency has been fully studied for three-level atoms in a weak field approximation method, where probe field is very wea ker than the coupling field. The weak field approximation is no t valid in full-quantum model where the number of coupling photons is not so large. In the present article, the master equations for the interaction of two-mode photons with a three-level Λ -type atom are exactly solved and the exact dispersion and absorption spectra for the probe beam photons are also obtained analytically. The results of the exact scheme are compared with the corresponding results in the weak field approximation method in full-quantum and semi-classi cal models.
We consider a four-level atomic system in inverted-Y system and study the phenomenon of Electromagnetically Induced Transparency (EIT) in this system in interaction with three quantized fields (one probe field and two coupling fields) by full quantum model. The results indicate dependency of the interval between peaks and their altitude in absorption curve of probe field on number of coupling field photons’ that trapped inside the quantum cavity. In this paper a non-demolition photon counting method has been offered for two different kind of photons that belong to coupling fields that interact with an ensemble of four-level Inverted-Y type atoms and a quantize probe field by analytical calculation of density matrix equations.
We introduce a simple model for electromagnetically induced transparency in which all fields are treated quantum mechanically. We study a system of three separated atoms at fixed positions in a one-dimensional multimode optical cavity. The first atom serves as the source for a single spontaneously emitted photon; the photon scatters from a three-level Lambda-configuration atom which interacts with a single-mode field coupling two of the atomic levels; the third atom serves as a detector of the total transmitted field. We find an analytical solution for the quantum dynamics. From the quantum amplitude describing the excitation of the detector atom we extract information that provides exact single-photon analogs to wave delays predicted by semi-classical theories. We also find complementary information in the expectation value of the electric field intensity operator.
We study the features of electromagnetically induced transparency(EIT) in a single Λ-type three-level atom placed in a high-finesse cavity under the action of a coupling laser and a probe laser.Our calculations show that three transparency windows appear when the pump strength is large enough.This can be explained by the residual pump in the cavity mostly resulting in energy splitting.The level |3 is split into four slightly different energy levels,and interference takes place between the excitation pathways.Furthermore,it is also shown that the frequencies of the EIT windows can be tuned by changing the coupling field detuning 2,and that the reflection profile is very sensitive to the cavity field detuning △c.
We study the features of electromagnetically induced transparency (EIT) in a single Λ-type three-level atom placed in a high-finesse cavity under the action of a coupling laser and a probe laser. Our calculations show that three transparency windows appear when the pump strength is large enough. This can be explained by the residual pump in the cavity mostly resulting in energy splitting. The level |3〉 is split into four slightly different energy levels, and interference takes place between the excitation pathways. Furthermore, it is also shown that the frequencies of the EIT windows can be tuned by changing the coupling field detuning Δ 2 , and that the reflection profile is very sensitive to the cavity field detuning Δ c .
We show that a fully quantum-mechanical model consisting of a four-level atom with Y-type atomic structure inside a three-mode cavity can exhibit double cavity induced transparency (CIT). In this model, it is cavity photons that induce the transparency, and there is no need to use external classical fields. As this double-CIT model involves several atomic levels, we adapt the wavefunction approach as a quantum-jump description of dissipation to derive an analytical expression for the steady-state linear susceptibility of a weak cavity field. We then use this analytical expression to investigate the dependence of the CIT transparency windows on the detuning of the coupling fields, intensities of the cavity fields and the cavity linewidths. We also have tested the analytical results by numerically integrating the full set of optical Bloch equations for the atomic density-matrix elements.
We studied the electromagnetically induced transparency, where the three-level atom of Λ-type is put in two statistically independent squeezed vacuums. We start from the master equation containing the decay of the atom to the squeezed vacuums, and solve the non-diagonal density matrix element analytically, finding that it is strongly dependent on the squeezing degree and the phase of the squeezed vacuum. There is also a dependence on the intensity and phase of the probe beam, which would not appear in the normal vacuum case. By coupling with squeezed vacuums, the atom would not only experience electromagnetically induced transparency and slow group velocity, but also induce a fast group velocity,backward group velocity and a gain in the probe light field. Besides, the absorption and gain can be modulated by the intensity of probe light.