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Manuscript Title: A Maxwell-Schrödinger solver for quantum optical few-level systems
Authors: Robert Fleischhaker, Jörg Evers
Program title: msprop
Catalogue identifier: AEHR_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 182(2011)739
Programming language: C (C99 standard), Mathematica, bash script, gnuplot script.
Computer: Tested on x86 architecture.
Operating system: Unix/Linux environment.
RAM: less than 30 MB
Keywords: Maxwell-Schrödinger equation, quantum optical few-level system, crosscoupling, magnetic field component, second order Lax-Wendroff algorithm, Adams predictor.
PACS: 42.50.Gy, 42.65.Sf, 42.65.An.
Classification: 2.5.

External routines: Standard C math library, accompanying bash script uses gnuplot, bc (basic calculator), and convert (ImageMagick)

Nature of problem:
We consider a system of quantum optical few-level atoms exposed to several near-resonant continuous-wave or pulsed laser fields. The complexity of the problem arises from the combination of the coherent and incoherent time evolution of the atoms and its dependence on the spatially varying fields. In systems with a coupling to the electric and magnetic field component the simultaneous treatment of both field components poses an additional challenge. Studying the system dynamics requires solving the quantum optical master equation coupled to the wave equations governing the spatio-temporal dynamics of the fields [1,2].

Solution method:
We numerically integrate the equations of motion using a second order Adams predictor method for the time evolution of the atomic density matrix and a second order Lax-Wendroff scheme for iterating the fields in space [3]. For the Lax-Wendroff scheme, the source function is adapted such that a simultaneous coupling to the polarization and the magnetization of the medium can be taken into account.

The evolution of the fields is treated in slowly varying envelope approximation [2] such that variations of the fields in space and time must be on a scale larger than the wavelength and the optical cycle. Propagation is restricted to the forward direction and to one dimension. Concerning the description of the atomic system, only a finite number of basis states can be treated and the laser-driven transitions have to be near-resonant such that the rotating-wave approximation can be applied [2].

Unusual features:
The program allows the dipole interaction of both the electric and the magnetic component of a laser field to be taken into account at the same time. Thus, a system with a phase-dependent cross coupling of electric and magnetic field component can be treated (see Sec. 4.2 and [4]). Concerning the implementation of the data structure, it has been optimized for faster memory access. Compared to using standard memory allocation methods, shorter run times are achieved (see Sec. 3.2).

Additional comments:
Three examples are given. They each include a readme file, a mathematica notebook to generate the C-code form of the quantum optical master equation, a parameter file, a bash script which runs the program and converts the numerical data into a movie, two gnuplot scripts, and all files that are produced by running the bash script.

Running time:
For the first two examples the running time is less than a minute, the third example takes about 12 minutes. On a Pentium 4 (3 GHz) system, a rough estimate can be made with a value of 1 second per million grid points and per field variable.

[1] Z. Ficek and S. Swain, Quantum Interference and Coherence: Theory and Experiments (Springer, Berlin, 2005).
[2] M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
[3] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge University Press, Cambridge, 1992).
[4] R. Fleischhaker and J. Evers, Phys. Rev. A 80 (2009) 063816