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Вестник Санкт-Петербургского университета. Серия 4. Физика. Химия

Formation and control of dark states in hyperfine levels of Na atoms

Dmitry K. Efimov, Martins Bruvelis, Nikolai N. Bezuglov, K. Miculis, Aigars Ekers

Published Jan 1, 2013• 0 citations
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Hyperfine interaction in the Autler-Townes effect: The formation of bright, dark, and chameleon states

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This paper is devoted to clarifying the implications of hyperfine (HF) interaction in the formation of adiabatic (i.e., ``laser-dressed'') states and their expression in the Autler-Townes (AT) spectra. We first use the Morris-Shore model [J. R. Morris and B. W. Shore, Phys. Rev. A 27, 906 (1983)] to illustrate how bright and dark states are formed in a simple reference system where closely spaced energy levels are coupled to a single state with a strong laser field with the respective Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{S}$. We then expand the simulations to realistic hyperfine level systems in Na atoms for a more general case when non-negligible HF interaction can be treated as a perturbation in the total system Hamiltonian. A numerical analysis of the adiabatic states that are formed by coupling of the $3{p}_{3/2}$ and $4{d}_{5/2}$ states by the strong laser field and probed by a weak laser field on the $3{s}_{1/2}\ensuremath{-}3{p}_{3/2}$ transition yielded two important conclusions. Firstly, the perturbation introduced by the HF interaction leads to the observation of what we term ``chameleon'' states---states that change their appearance in the AT spectrum, behaving as bright states at small to moderate ${\mathrm{\ensuremath{\Omega}}}_{S}$, and fading from the spectrum similarly to dark states when ${\mathrm{\ensuremath{\Omega}}}_{S}$ is much larger than the HF splitting of the $3{p}_{3/2}$ state. Secondly, excitation by the probe field from two different HF levels of the ground state allows one to address orthogonal sets of adiabatic states; this enables, with appropriate choice of ${\mathrm{\ensuremath{\Omega}}}_{S}$ and the involved quantum states, a selective excitation of otherwise unresolved hyperfine levels in excited electronic states.

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By imaging the dark states that are due to coherent population trapping in Na atomic vapor, we have succeeded in depicting a spatially inhomogeneous magnetic field. Highly resolved dark lines represent cross sections of the surfaces of constant magnetic fields, and they agree well with the predicted hyperfine Zeeman splitting and the two-photon selection rules of the Na atom. Mapping was made two dimensionally in real time, but extension to three dimensions is straightforward. Furthermore, unlike the previous techniques based on optical pumping, this method can be used for any magnetic-field directions.

Optics Letters•Jul 1, 2003•15 citations

Quantum Coherence in a Double Λ - Type Five - Level System

Tang Huijuan

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.

International Conference on Measuring Technology and Mechatronics Automation (ICMTMA)•Jan 1, 2017•0 citations
This paper is devoted to clarifying the implications of hyperfine (HF) interaction in the formation of adiabatic (i.e., ``laser-dressed'') states and their expression in the Autler-Townes (AT) spectra. We first use the Morris-Shore model [J. R. Morris and B. W. Shore, Phys. Rev. A 27, 906 (1983)] to illustrate how bright and dark states are formed in a simple reference system where closely spaced energy levels are coupled to a single state with a strong laser field with the respective Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{S}$. We then expand the simulations to realistic hyperfine level systems in Na atoms for a more general case when non-negligible HF interaction can be treated as a perturbation in the total system Hamiltonian. A numerical analysis of the adiabatic states that are formed by coupling of the 3p3/23{p}_{3/2}3p3/2​ and 4d5/24{d}_{5/2}4d5/2​ states by the strong laser field and probed by a weak laser field on the $3{s}_{1/2}\ensuremath{-}3{p}_{3/2}$ transition yielded two important conclusions. Firstly, the perturbation introduced by the HF interaction leads to the observation of what we term ``chameleon'' states---states that change their appearance in the AT spectrum, behaving as bright states at small to moderate ${\mathrm{\ensuremath{\Omega}}}_{S}$, and fading from the spectrum similarly to dark states when ${\mathrm{\ensuremath{\Omega}}}_{S}$ is much larger than the HF splitting of the 3p3/23{p}_{3/2}3p3/2​ state. Secondly, excitation by the probe field from two different HF levels of the ground state allows one to address orthogonal sets of adiabatic states; this enables, with appropriate choice of ${\mathrm{\ensuremath{\Omega}}}_{S}$ and the involved quantum states, a selective excitation of otherwise unresolved hyperfine levels in excited electronic states.
By imaging the dark states that are due to coherent population trapping in Na atomic vapor, we have succeeded in depicting a spatially inhomogeneous magnetic field. Highly resolved dark lines represent cross sections of the surfaces of constant magnetic fields, and they agree well with the predicted hyperfine Zeeman splitting and the two-photon selection rules of the Na atom. Mapping was made two dimensionally in real time, but extension to three dimensions is straightforward. Furthermore, unlike the previous techniques based on optical pumping, this method can be used for any magnetic-field directions.
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.