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Journal of Experimental and Theoretical Physics

Multiquantum Transitions Between Excited Nonequidistant Atomic Sublevels

V. G. Pokazan'ev, L. I. Yakub, G. V. Skrotskiǐ

Published Jul 1, 1967• 1 citation
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We present a technique to identify exact analytic expressions for the multiquantum eigenstates of a linear chain of coupled qubits. A choice of Hilbert subspaces is described that allows an exact solution of the stationary Schr\"odinger equation without imposing periodic boundary conditions and without neglecting end effects, fully including the dipole-dipole nearest-neighbor interaction between the atoms. The treatment is valid for an arbitrary coherent excitation in the atomic system, any number of atoms, any size of the chain relative to the resonant wavelength and arbitrary initial conditions of the atomic system. The procedure we develop is general enough to be adopted for the study of excitation in an arbitrary array of atoms including spin chains and one-dimensional Bose-Einstein condensates.

arXiv:quant-ph/0505206•Physical Review A•Jun 29, 2005•6 citations
A method to excite multiquantum transitions in a two-level system by application of continuous irradiation with a four-frequency microwave field is presented. The generated signal is composed of many intermodulation sidebands at different frequencies, which arise from the multiquantum transitions. These processes involve an odd number of photons, that are absorbed from, or emitted to two, three, or four fields. The correspondence between the frequency spectrum of the signal and possible pathways of multiquantum processes is found with recourse to the many mode Floquet theory. The reported experiments demonstrate the multiquantum origin of the detected intermodulation sidebands and their properties.
It is experimentally demonstrated that use of an extremely thin cell (ETC) with the thickness of a Rb atomic vapor column of ∼400 nm allows one to resolve a large number of individual transitions between Zeeman sublevels of the D1 line of 87Rb and 85Rb in the sub-Doppler fluorescence excitation spectra in an external magnetic field of ∼200 G. It is revealed that due to the peculiarities of the Zeeman effect for different hyperfine levels of Rb, all allowed transitions between magnetic sublevels can be clearly resolved for 87RbF_g = 1 --> F_e = 1, 2 and F_g = 2 --> F_e = 1, 2 fluorescence excitation. Also, relatively good spectral resolution can be achieved for 85RbF_g = 2 --> F_e = 2, 3 fluorescence excitation. Some partial resolution of transitions between magnetic sublevels is achieved for 85RbF_g = 3 --> F_e = 2, 3 fluorescence excitation. The spectral resolution of individual transitions allows one to easily observe both linear and nonlinear Zeeman effects in the fluorescence excitation spectra obtained with the help of the ETC. In the fluorescence spectra of a cell of usual length there is no evidence of a spectral resolution of individual transitions at B ∼ 200 G. A simple magnetometer based on ETC with Rb with a submicrometer spatial resolution is described.
We present a technique to identify exact analytic expressions for the multiquantum eigenstates of a linear chain of coupled qubits. A choice of Hilbert subspaces is described that allows an exact solution of the stationary Schr\"odinger equation without imposing periodic boundary conditions and without neglecting end effects, fully including the dipole-dipole nearest-neighbor interaction between the atoms. The treatment is valid for an arbitrary coherent excitation in the atomic system, any number of atoms, any size of the chain relative to the resonant wavelength and arbitrary initial conditions of the atomic system. The procedure we develop is general enough to be adopted for the study of excitation in an arbitrary array of atoms including spin chains and one-dimensional Bose-Einstein condensates.