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ω-3 ω双色场相干控制电离与高次谐波

吴海涛, 龚尚庆, 冯勋立, 徐至展

Published Jan 1, 2001• 0 citations
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Abstract

通过数值求解一维含时薛定谔方程 ,研究了原子在双色场作用下的电离和高次谐波及它们的相互关系。通过讨论两种不同的电离机制 :隧穿电离机制和过势垒电离机制 ,发现电离变化的规律很相似 ,但高次谐波谱的变化规律却很不同。研究说明利用双色场对原子过程进行相位控制是可行的

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Canadian Journal of Physics•Dec 1, 1981•16 citations
通过数值求解一维含时薛定谔方程 ,研究了原子在双色场作用下的电离和高次谐波及它们的相互关系。通过讨论两种不同的电离机制 :隧穿电离机制和过势垒电离机制 ,发现电离变化的规律很相似 ,但高次谐波谱的变化规律却很不同。研究说明利用双色场对原子过程进行相位控制是可行的
行列の定式化による特別な場合に相当する量子ウォークモデルが採用されているとみること もできる,さらに,グラフ理論的な視点では,グラフの辺を被覆するクリーク分割の概念を用 いた Staggered walk [7] が提案されており,幾つかの量子ウォークモデルの包含関係などにつ いて議論されている.さらに舞台をグラフから単体複体上への拡張を提案することも可能である [6].ここでは,これらの様々な量子ウォークモデルを含むような,Partition-based walk という自然な拡張モデルを通じて,各量子ウォークモデルの傭磁を試みる.そして,実はこれらのほとんどすべての量子ウオークモデルがこのPartition-based walk とユニタリ同値とな ることをが示されることを説明する. 2 Partition-based walk 離散集合 \Omega=\{\omega_{1}, \omega_{2}, . . .\} 上の,同値関係 \pi_{1}, \pi 2 から誘導される以下の二種類の分割を定義 する.\Omega/\pi _{ 1} \Ri ght arrow\{ [ \omega] _{ \pi _{ 1} } | \omega\i n\Omega\} , \Omega/\pi _{2}=\{[\omega]_{\pi _{2}}| \omega\i n\Omega\}_{7} 但し, [\omega]_{\pi _{j }}=\{\omega' \i n\Omega| \omega' \si m\pi , \omega\}(j =1, 2) は \omega の同値類.商集合\Omega/\pi _{ 1} の各元を C_{i}, \Omega/\pi _{ 2} の各元を D_{j} で記述し.C_{i}, D_{j} に含まれる \Omega の元は有限とする.離散集合 \Omega から誘導されるヒルベルト空間は \mat hcal { H} =l ^{ 2} ( \Omega) =\{ \psi .` \Omegaar r ow \mat hbb{ C} 1\sum_{ \pr i me} | \psi ( \omega) 1^{ 2} <\i nf t y\} \omega\i n\Omega
We consider the excitation spectrum of a three-level atom interacting with an electromagnetic field whose two initially populated modes ω a and ω b are in resonance with two atomic transition frequencies while the remaining unpopulated modes are simultaneously coupled to the atomic states. It is found that at high photon densities, the Green's functions describing the lower and upper systems corresponding to the transition frequencies ω a and ω b respectively are-independent of each other. The spectral functions for the lower and upper systems consist of seven lorentzian lines describing the central peak and three pairs of sidebands where each pair is symmetrically located with respect to the transition frequency. For the lower system, the lines are peaked at frequencies ω = ω a , ω = ω a ± Ω a , ω = ω a ± Ω b and ω = ω a ± Ω ab with radiative widths γa 0/2, 3γa 0/4, (γa 0 + γb 0)/4 and (γa 0 + 3γb 0)/4 respectively, where Ω a and Ω b are the energy shifts of the populated modes ω a and ω b , Ω ab 2 = Ω b 2 + Ω a 2/4 and γa 0/2 is equal to the natural width of a photon spontaneously emitted from an isolated atom. For the upper system, the lines occur at ω = ω b , ω = ω b ± Ω b , ω = ω b ± Ω a and ω = ω b ± Ω ba with radiative widths (γa 0 + γb 0)/2, (γa 0 + 3γb 0)/4, (γa 0 + 2γb 0)/4, and 3γa 0/4 respectively. Relations between Ω a and Ω b are derived for which the heights of the lorentzian lines of the corresponding bands become positive or negative indicating attenuation or amplification of the signal field respectively. It is also shown that when certain relations exist between Ω a and Ω b , the signal field is attenuated in the lower system while it is simultaneously amplified in the upper system at different frequencies and vice versa. Spectral functions of the lower and upper systems are derived and discussed for equally spaced levels and equally populated modes Ω a = Ω b , as well as for the limiting case when Ω b 2 = 3Ω a 2/4 or Ω a 2 = 3Ω b 2/4.
We have studied the excitation spectrum arising from the optical mixing of the frequencies of a strong bichromatic field interacting with a three-level atom, where the two initially populated modes ωa and ωb are equal to the two atomic transition frequencies, respectively. In the limit of high photon densities, the excitation spectrum near the frequency ω = ωa – 2ωb has been calculated as a function of the parameter η = Ωa2/Ωb2, where Ωa and Ωb are the Rabi frequencies of the two laser fields, respectively. For [Formula: see text] and for weak fields for which [Formula: see text], the spectral function describes a Lorentzian line peaked at the frequency ω = ωa – 2ωb and has a width of the order of γ0, where γ0/2 is the natural width for a two-level atom. When Ωb2 > γ02 and [Formula: see text], the band at ω = ωa – 2ωb splits into two bands described by two Lorentzian lines peaked at ω = ωa – 2ωb ± Ωb/√2 and have spectral widths of the order of 3γ0/4. The ratio of the height of the band ω = ωa – 2ωb to the height ω = ωa – 2ωb ± Ωb/2 is 3:2. The probability amplitudes for both bands take large negative values indicating that optical amplification of the signal field may be expected to occur at these frequencies. When Ωa = Ωb = Ω, η = 1, and for Ω2 < γ02, the spectral function describes a single band at ω = ωa – 2ωb while for Ω2 > γ02, the single band splits into five pairs of bands which are separated from the frequency ω = ωa – 2ωb by frequency shifts which are equal to: ± Ω/√2, [Formula: see text], ± Ω, ± Ω√2, and ± Ω√3, respectively, and have spectral widths of the order of 3γ0/4. For [Formula: see text] and for laser fields for which Ωa2 > γ02 and Ωb2 > γ02, the spectral function consists of three pairs of bands. The probability amplitudes for these bands vary linearly with η and may take large values for [Formula: see text]. A complete discussion of the excitation spectrum as well as a graphical representation of the derived results has been given.