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Transient quantum coherent response to a partially coherent radiation field
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10.1063/1.4864759
/content/aip/journal/jcp/140/7/10.1063/1.4864759
http://aip.metastore.ingenta.com/content/aip/journal/jcp/140/7/10.1063/1.4864759

Figures

Image of FIG. 1.
FIG. 1.

Three level system used in our numerical scheme. Population is initially in the ground state |1⟩ and is pumped to two non-degenerate excited states, |2⟩ and |3⟩. The frequency difference between the two excited states ω determines a characteristic excited state timescale τ = 2π/ω.

Image of FIG. 2.
FIG. 2.

(Top) Ensemble averaged excited state coherence (⟨ρ⟩) plotted versus perturbative coherences for a three level ladder system excited by thermally broadened CW source. (Bottom) Excited state populations for both perturbative and numerical results for the same system. τ = 60 fs and τ = 120 fs for both figures.

Image of FIG. 3.
FIG. 3.

plotted against time for three level ladder system excited by thermally broadened CW source for various level splittings at fixed τ. The values of τ used are τ = 60 fs (top), τ = 120 fs (middle), and τ = 240 fs (bottom). For large values of time, the quantity becomes smaller and as → ∞ the value approaches zero.

Image of FIG. 4.
FIG. 4.

System purity Tr(ρ2) plotted as a function of time for various excited state periods τ and radiation coherence times τ for a three level ladder system excited by thermally broadened CW source. As the excited state period τ becomes larger, the purity of the system decreases at a faster rate. The following τ times are shown: 60 fs (top), 120 fs (middle), and 240 fs (bottom).

Image of FIG. 5.
FIG. 5.

Excited state purity plotted against time for three level ladder system excited by thermally broadened CW source for various level splittings, τ at various τ. The following τ times are shown: 60 fs (top), 120 fs (middle), and 240 fs (bottom).

Image of FIG. 6.
FIG. 6.

Plot of , red regions represent highest intensity and blue regions represent lowest intensity.

Image of FIG. 7.
FIG. 7.

(Top) Coherences between the | ⟩ and | +⟩ in the toy PC645 model as a function of time for the sudden turn-on case. (Bottom) Populations of | ⟩ and | +⟩ in the toy model of PC645 as a function of time for the sudden turn-on case. Excitation frequency of the laser is in the middle of the two transitions.

Image of FIG. 8.
FIG. 8.

Plot of for a toy model of PC645 upon excitation by a collisionally broadened CW source, for parameters indicated in the text.

Image of FIG. 9.
FIG. 9.

Plot of for various excited state splittings, τ for long incoherent pulses incident on a three level ladder system. The pulse used is 1 ps in duration. τ = 120 fs. The frequency center of the pulse is chosen to be in the center of the two transitions.

Image of FIG. 10.
FIG. 10.

, the magnitude of the post pulse excited state coherence fraction of a toy model of PC645, plotted as a function of pulse duration, τ. For long pulses, it is evident that post pulse coherence is extremely small.

Image of FIG. 11.
FIG. 11.

Comparison of numerically generated (top) and numerical [Eq. (1) ] (bottom) ⟨ɛ( )ɛ( )⟩. Both plots share the same color legend. The times are in units of femtosecond.

Image of FIG. 12.
FIG. 12.

(Top) Exact contour plot of the correlation function in Eq. (2) and (bottom) numerical reproduction of correlation for the noisy pulsed source. Both plots share the same color legend. The times are in units of femtosecond.

Image of FIG. 13.
FIG. 13.

Plot of ||2 defined in Eq. (B8) using the parameters of toy PC645. Solid line is the stationary coherence as a function of τ while the dashed line represents the saturation level from Eq. (B10) .

Image of FIG. 14.
FIG. 14.

Plot of for a three level system irradiated with white noise, as a function of dimensionless time, .

Tables

Generic image for table
Table I.

Parameters used in perturbative calculations of PC645.

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/content/aip/journal/jcp/140/7/10.1063/1.4864759
2014-02-19
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Transient quantum coherent response to a partially coherent radiation field
http://aip.metastore.ingenta.com/content/aip/journal/jcp/140/7/10.1063/1.4864759
10.1063/1.4864759
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