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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Creation and measurement of coherent superposition states in multilevel atoms

Gagik P. Djotyan, N. Sandor, Joseph S. Bakos, Zs. Sörlei, Wojciech Gawlik, Adam M. Wojciechowski, Jerzy Zachorowski, Szymon Pustelny, Gagik Yu. Kryuchkyan

Published Oct 29, 2010• 1 citation
Publisher

Abstract

We propose and analyze a scheme for creation of coherent superposition of meta-stable states in a multilevel atom. The scheme is based on interaction of a frequency modulated (chirped) laser pulse and a pulse of a constant carrier frequency with the atom having two meta-stable (ground) states and multiple excited states. The negligible excitation of the atoms is a priority in the proposed scheme to eliminate the de-coherence processes caused by the decay of the excited states. The scheme is applied to create coherent superposition of magnetic sublevels of ground states of the 87Rb atom taking into account all allowed electric-dipole transitions between magnetic sublevels of the 5 2S1/2 - 52P3/2 transition (D2 line). In addition to the theoretical analysis we consider possible experimental realizations of the proposed coherence creation scheme and discuss their feasibilities and constraints. We concentrate on a detection of the superposition state in the Faraday-rotation experiment. Such detection reduces technical laser noise background and offers high sensitivity of the coherence detection. Moreover, it allows extra control of the atomic sample and the interaction dynamics by external magnetic field.

DOI
10.1117/12.890857

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We propose and analyze a scheme for creation of coherent superposition of meta-stable states in a multilevel atom. The scheme is based on interaction of a frequency modulated (chirped) laser pulse and a pulse of a constant carrier frequency with the atom having two meta-stable (ground) states and multiple excited states. The negligible excitation of the atoms is a priority in the proposed scheme to eliminate the de-coherence processes caused by the decay of the excited states. The scheme is applied to create coherent superposition of magnetic sublevels of ground states of the 87Rb atom taking into account all allowed electric-dipole transitions between magnetic sublevels of the 5 2S1/2 - 52P3/2 transition (D2 line). In addition to the theoretical analysis we consider possible experimental realizations of the proposed coherence creation scheme and discuss their feasibilities and constraints. We concentrate on a detection of the superposition state in the Faraday-rotation experiment. Such detection reduces technical laser noise background and offers high sensitivity of the coherence detection. Moreover, it allows extra control of the atomic sample and the interaction dynamics by external magnetic field.
Traditional schemes for coherent population transfer or generation of coherent superposition states in multilevel atoms or molecules usually utilize two or more laser beams with radiation bandwidth smaller than the frequency interval between the working levels. We show the possibility of creation of the coherent superposition of three metastable states of a four-level atom with tripodlike level structure using a single short frequency-chirped laser pulse. The bandwidth of the pulse envelope (without chirp) must be comparable to or exceed the frequency distance between the two metastable levels. No appreciable excitation of the atom takes place during the creation of the coherent superposition state, thus diminishing significantly the effect of decoherence due to the spontaneous decay of the excited state. The proposed method of creation of superposition states is robust against variations in the laser pulse parameters. Since this method does not require maintaining steady resonance with the atomic transitions (owing to the frequency chirp of the laser pulse), it is effective both in homogeneously and inhomogeneously broadened media.
We propose and analyze a scheme for creation of coherent superposition of meta-stable states in a tripod-structured atom using frequency-chirped laser pulses with negligible excitation of the atoms. The underlying physics of the scheme is explained using the formalism of adiabatic states. We show that the proposed scheme may be equally efficient in homogeneously and Doppler-broadened media. By numerically solving master equation for the density matrix operator, we analyze the influence of relaxation processes on the efficiency of the creation of superposition states. We show that the proposed scheme is robust against small-to-medium variations of the laser field's parameters.
We present a scheme of population transfer between two metastable (ground) states of the $\ensuremath{\Lambda}$ atom without considerable excitation of the atom using single frequency-chirped laser pulses. The physics of the process is generation of the ``trapped'' superposition of the ground states by the laser pulse at sufficiently high laser peak intensity. The main conditions for realization of this regime are the following: The width of the transform-limited laser pulse envelope frequency spectrum (without chirp) must be smaller and the peak Rabi frequency of the pulse must be larger than the frequency interval between the two ground states of the $\ensuremath{\Lambda}$ atom. During the frequency chirp, the laser pulse must first come into resonance with the transition from the initially occupied ground state to the excited state and after that with the transition between the excited and second initially empty ground states. In the case when the envelope frequency spectrum width (without chirp) of the pulse exceeds the frequency interval between the two ground states, we show a possibility of controllable generation of superposition of the ground states with a controllable excitation of the $\ensuremath{\Lambda}$ atom.
We propose and analyze a scheme for adiabatic creation of maximum coherence of 0.5 with a controllable phase between a ground state and the excited state in a model Λ-structured atom using two short laser pulses. One of the pulses has constant carrier frequency quasi-resonant with transition between an initially empty ground and the excite states. The frequency of the second pulse is swept through the resonance with the adjacent transition between the initially populated ground state and the common excited state of the atom. We demonstrate high degree of robustness of the scheme against variation of parameters of the laser radiation in relatively broad region of values. The proposed scheme may find practical applications in the field of multi-photon ionization, high-order harmonics and Raman sideband generation, as well as in nonlinear wave mixing in coherently prepared media.
A simple method for measuring the parameters of a completely or partially coherent superposition of multiple atomic states is proposed. The method, which can be applied in principle to a superposition of arbitrary energy states, is described in the case of a superposition of magnetic sublevels of a degenerate ground level. It is based upon coupling the sublevels involved in the superposition to the sublevels of a degenerate excited level by using a single elliptically polarized laser pulse. Such an interaction maps the parameters of the initial superposition onto the populations of the excited sublevels. By measuring the subsequent fluorescence from the excited sublevels for several suitably chosen laser polarizations one can deduce unambiguously the parameters of the initial superposition.
We demonstrate experimental techniques for creating and measuring a coherent superposition of two degenerate atomic states with equal amplitudes in metastable neon. Starting from state (3)P(0), we create adiabatically a coherent superposition of the magnetic sublevels M=+/-1 of the state (3)P(2) using a tripod stimulated Raman adiabatic passage scheme. The measurement is based on the coupling of the levels (3)P(2)<-->(3)P(1) by a linearly polarized laser, followed by the detection of the population in the (3)P(2)(M=+/-2) states as a function of the polarization angle of that laser.