Accurate Lindblad-Form Master Equation for Weakly Damped Quantum Systems Across All Regimes
| Autor: | Denys I. Bondar, Kurt Jacobs, Benjamin Cruikshank, Gavin McCauley |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Density matrix
Quantum Physics Computer Networks and Communications Degenerate energy levels Complex system System identification FOS: Physical sciences Statistical and Nonlinear Physics 01 natural sciences lcsh:QC1-999 lcsh:QA75.5-76.95 010305 fluids & plasmas Quantum technology Computational Theory and Mathematics 0103 physical sciences Master equation Computer Science (miscellaneous) Dissipative system lcsh:Electronic computers. Computer science Statistical physics 010306 general physics Quantum Physics (quant-ph) Quantum lcsh:Physics |
| Zdroj: | npj Quantum Information, Vol 6, Iss 1, Pp 1-14 (2020) |
| DOI: | 10.48550/arxiv.1906.08279 |
| Popis: | Realistic models of quantum systems must include dissipative interactions with an environment. For weakly-damped systems the Lindblad-form Markovian master equation is invaluable for this task due to its tractability and efficiency. This equation only applies, however, when the frequencies of any subset of the system's transitions are either equal (degenerate), or their differences are much greater than the transitions' linewidths (far-detuned). Outside of these two regimes the only available efficient description has been the Bloch-Redfield (B-R) master equation, the efficacy of which has long been controversial due to its failure to guarantee the positivity of the density matrix. The ability to efficiently simulate weakly-damped systems across all regimes is becoming increasingly important, especially in the area of quantum technologies. Here we solve this long-standing problem. We discover that a condition on the slope of the spectral density is sufficient to derive a Lindblad form master equation that is accurate for all regimes. We further show that this condition is necessary for weakly-damped systems to be described by the B-R equation or indeed any Markovian master equation. We thus obtain a replacement for the B-R equation over its entire domain of applicability that is no less accurate, simpler in structure, completely positive, allows simulation by efficient quantum trajectory methods, and unifies the previous Lindblad master equations. We also show via exact simulations that the new master equation can describe systems in which slowly-varying transition frequencies cross each other during the evolution. System identification tools, developed in systems engineering, play an important role in our analysis. We expect these tools to prove useful in other areas of physics involving complex systems. Comment: Revtex4-1, 16 pages, 7 png figures. v2: contains significant new material |
| Databáze: | OpenAIRE |
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