dorsal/arxiv
View SchemaDecoherence in a driven three-level system
| Authors | A. R. P. Rau, Weichang Zhao |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307039 |
| URL | https://arxiv.org/abs/quant-ph/0307039 |
| DOI | 10.1103/PhysRevA.68.052102 |
| Journal | Phys. Rev. A 68, 052102 (2003) |
Abstract
Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics are handled through master equations for the density matrix. Master equations such as the Lindblad equation preserve the trace of this matrix. Viewing them as first-order time-dependent operator equations for the elements of the density matrix, a unitary integration procedure can be adapted to solve for these matrix elements. A simple model for decoherence preserves the hermiticity of the density matrix. A single, classical Riccati equation is the only one requiring numerical handling to obtain a full solution of the quantum evolution. The procedure is general, valid for any number of levels, but is illustrated here for a three-level system with two driving fields. For various choices of the initial state, we study the evolution of the system as a function of the amplitudes, relative frequencies and phases of the driven fields, and of the strength of the decoherence. The monotonic growth of the entropy is followed as the system evolves from a pure to a mixed state. An example is provided by the $n=3$ states of the hydrogen atom in a time-dependent electric field, such degenerate manifolds affording an analytical solution.
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"abstract": "Dissipation and decoherence, and the evolution from pure to mixed states in\nquantum physics are handled through master equations for the density matrix.\nMaster equations such as the Lindblad equation preserve the trace of this\nmatrix. Viewing them as first-order time-dependent operator equations for the\nelements of the density matrix, a unitary integration procedure can be adapted\nto solve for these matrix elements. A simple model for decoherence preserves\nthe hermiticity of the density matrix. A single, classical Riccati equation is\nthe only one requiring numerical handling to obtain a full solution of the\nquantum evolution. The procedure is general, valid for any number of levels,\nbut is illustrated here for a three-level system with two driving fields. For\nvarious choices of the initial state, we study the evolution of the system as a\nfunction of the amplitudes, relative frequencies and phases of the driven\nfields, and of the strength of the decoherence. The monotonic growth of the\nentropy is followed as the system evolves from a pure to a mixed state. An\nexample is provided by the $n=3$ states of the hydrogen atom in a\ntime-dependent electric field, such degenerate manifolds affording an\nanalytical solution.",
"arxiv_id": "quant-ph/0307039",
"authors": [
"A. R. P. Rau",
"Weichang Zhao"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.052102",
"journal_ref": "Phys. Rev. A 68, 052102 (2003)",
"title": "Decoherence in a driven three-level system",
"url": "https://arxiv.org/abs/quant-ph/0307039"
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