Tiger Team Projects

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Tiger Team: tt-dicke-modell

Dissipative Dynamik eines abgebildeten Dicke Modells

A Dicke model [1] can be realized in a new hybrid architecture, where a cloud of cold atoms is brought close to a superconducting microwave resonator. The influence of the environment demands for a dissipative extension of the model. Dissipation is incorporated by the quantum jump method [2]. Within this framework, numerical simulations are feasible even for hundreds of atoms in various non-equilibrium scenarios of interest. Exemplary, we study the influence of the dissipative part of the model on the signatures of a quantum phase transition of the (finite size) system for different coupling ignitions.

For the actual time evolution (and the realization of the quantum jump method), one has to discretize the time parameter sufficiently fine and apply a Trotter decomposing on the time evolution operator, yielding a potential (position) and a kinetic (momentum) part. Thus the dynamics can be accomplished serially by alternating between position and momentum space and this alternation is performed by a Fourier transform, numerically realized as a fast Fourier transform.

The original version of the code implemented the Fourier transforms in-code with support for FFTW compiled with the GCC compiler. The resulting binaries executed substantially below peak performance in many situations. After consideration of options and in cooperation with the competence center for computational chemistry the code was modified and linked against Intel's code-mapping wrappers for the FFTW library. Benchmarks for different mesh sizes running either on 1 or 16 core showed speedups up to a factor of 2.4 compared with the FFTW/GCC compiled binary. The average speedup has been found to be between 1.7 for 1-core jobs and 1.3 for 16 core jobs.

[1] R.H. Dicke, Coherence in Spontaneous Radiation Processes, Physical Review, Vol. 93, Iss. 1, 1954.
[2] Klaus Mølmer and Yvan Castin, Monte Carlo wavefunctions in quantum optics, Quantum and Semiclassical Optics: Journal of the European Optical Society Part B, Vol. 8, Nb. 1, 1996.

Mitglieder des Tiger-Teams/Members of the Tiger-Team: Institut für komplexe Quantensysteme, Universität Ulm; Kompetenzzentrum für computergestützte Chemie und Quantenwissenschaften, Universität Ulm

Status: abgeschlossen.