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Non-Hermitian wave packet approximation of Bloch optical equations
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10.1063/1.4774056
/content/aip/journal/jcp/138/2/10.1063/1.4774056
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/2/10.1063/1.4774056
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Transmission T(E) (a), (d), and (g); reflection R(E) (b), (e), and (h); and absorption A(E) (c), (f), and (i) spectra of an atomic layer of thickness Δz = 400 nm as a function of the incident photon energy E. The atomic density is n = 2.5 × 1025 m−3 in the first column, n = 2.5 × 1026 m−3 in the second column, and n = 2.5 × 1027 m−3 in the last column. The decay rate and pure dephasing rate are Γ = 1012 s−1 and γ* = 1015 s−1, respectively. The atomic transition energy is ℏω B = 2 eV and the transition dipole moment is 2 D. The solution of Maxwell-Liouville-von Neumann equations is shown as a blue solid line, while the open red squares are from the solution of our approximate non-Hermitian Schrödinger model.

Image of FIG. 2.
FIG. 2.

Log-log plot of the maximum excited state population (red solid line with circles) and the relative error (blue lines with squares) in the calculation of the absorption spectrum A(E) at the transition energy E B = ℏω B using the Schrödinger approximation, when compared to the solution of the full Liouville-von Neumann equation as a function of the incident field intensity in atomic units. The blue solid line is for the lowest atomic density n = 2.5 × 1025 m−3 and the blue dashed line is for the highest atomic density n = 2.5 × 1027 m−3. All other parameters are as in Fig. 1 .

Image of FIG. 3.
FIG. 3.

Reflection probability R(E) of an atomic layer of thickness Δz = 400 nm as a function of the incident photon energy E. The atomic density is n = 2.5 × 1027 m−3. The solution of Maxwell-Liouville-von Neumann equations is shown as a blue solid line, while the dotted line with red squares is from the solution of our approximate non-Hermitian Schrödinger model. The exciting field amplitude is chosen such that the maximum excited state population reaches 35%. All other parameters are as in Fig. 1 .

Image of FIG. 4.
FIG. 4.

Population dynamics: (a) excited state population as a function of time, (b) squared modulus of the system's coherence as a function of time, (c) effective ground state gain rate γ0(t) as a function of time, and (d) real part of the system's coherence as a function of time. The results obtained from the solution of Liouville-von Neumann equations are shown with a blue solid line, while the results obtained from the non-Hermitian Schrödinger approach are shown using red dashed lines. The atomic density is n = 2.5 × 1027 m−3. All other parameters are as in Fig. 1 .

Image of FIG. 5.
FIG. 5.

Absorption spectra A(E) of a Li2 molecular layer of thickness Δz = 400 nm as a function of the incident photon energy E. The molecular density is n = 2.5 × 1025 m−3 in the left column (panels (a) and (b)) and n = 2.5 × 1027 m−3 in the right column (panels (c) and (d)). The solutions of Maxwell-Liouville-von Neumann equations are shown as blue solid lines in the first row (panels (a) and (c)) while the red solid lines (inverted spectra, panels (b) and (d)) are from the solutions of our approximate non-Hermitian Schrödinger model. All other parameters are as in Fig. 1 .

Image of FIG. 6.
FIG. 6.

Computation process time necessary on a Intel Xeon E5-1650 processor for the calculation of the absorption spectrum of a Li2 molecular nano-layer of thickness Δz = 400 nm as a function of the number of quantum levels included in the calculation. The blue line with circles is for the solution obtained from Maxwell-Liouville-von Neumann equations, while the red line with squares is for our proposed Schrödinger-type approximation. The spatial grid has a total size of 2560 nm with a spatial step of 1 nm. The time propagation is performed on a temporal grid of total size 1.7 ps with a time step of 1.7 as.

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/content/aip/journal/jcp/138/2/10.1063/1.4774056
2013-01-11
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Non-Hermitian wave packet approximation of Bloch optical equations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/2/10.1063/1.4774056
10.1063/1.4774056
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