The off-resonant aspects of decoherence and a critique of the two-level approximation

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dc.citation.epage363en_US
dc.citation.issueNumber2en_US
dc.citation.spage345en_US
dc.citation.volumeNumber18en_US
dc.contributor.authorSavran, K.en_US
dc.contributor.authorHakioǧlu T.en_US
dc.contributor.authorMese, E.en_US
dc.contributor.authorSevinçli, H.en_US
dc.date.accessioned2016-02-08T10:20:30Z
dc.date.available2016-02-08T10:20:30Z
dc.date.issued2006en_US
dc.departmentDepartment of Physicsen_US
dc.description.abstractConditions in favour of a realistic multilevelled description of a decohering quantum system are examined. In this regard the first crucial observation is that the thermal effects, contrary to the conventional belief, play a minor role at low temperatures in the decoherence properties. The system-environment coupling and the environmental energy spectrum dominantly affect the decoherence. In particular, zero temperature quantum fluctuations or non-equilibrium sources can be present and influential on the decoherence rates in a wide energy range allowed by the spectrum of the environment. A crucial observation against the validity of the two-level approximation is that the decoherence rates are found to be dominated not by the long time resonant but the short time off-resonant processes. This observation is demonstrated in two stages. Firstly, our zero temperature numerical results reveal that the calculated short time decoherence rates are Gaussian-like (the time dependence of the density matrix is led by the second time derivative at t ≤ 0). Exact analytical results are also permitted in the short time limit, which, consistent with our numerical results, reveal that this specific Gaussian-like behaviour is a property of the non-Markovian correlations in the environment. These Gaussian-like rates have no dependence on any spectral parameter (position and the width of the spectrum) except, in totality, the spectral area itself. The dependence on the spectral area is a power law. Furthermore, the Gaussian-like character at short times is independent of the number of levels (N), but the numerical value of the decoherence rates is a monotonic function of N. In this context, we demonstrate that leakage, as a characteristic multilevel effect, is dominated by the non-resonant processes. The long time behaviour of decoherence is also examined. Since our spectral model allows Markovian environmental correlations at long times, the decoherence rates in this regime become exponential independently from the number of levels. The latter and the coupling strengths play the major role in the quantitative values of the rates and the rates are independent of the other spectral parameters. The validity of the presented results is restricted only by their reliance on the Born-Oppenheimer approximation. This approximation is strongly dependent on the external observational time and its reliability depends on an additional timescale. In the rest of the work, the crossover between the short and the long time behaviour of the density matrix of the multilevelled system is examined using an intuitive argument. It is shown that the Born approximation weakens as the resonant couplings become more effective at long times. This implies that, in calculations made with this approximation in the long time regime, a need for a justification arises for the reliability of the results. This justification is made for the present work.en_US
dc.identifier.doi10.1088/0953-8984/18/2/001en_US
dc.identifier.eissn2331-8228
dc.identifier.issn0953-8984
dc.identifier.urihttp://hdl.handle.net/11693/23871
dc.language.isoEnglishen_US
dc.publisherIOP Institute of Physicsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1088/0953-8984/18/2/001en_US
dc.source.titleJournal of Physics Condensed Matteren_US
dc.subjectApproximation theoryen_US
dc.subjectCorrelation methodsen_US
dc.subjectFunctionsen_US
dc.subjectMatrix algebraen_US
dc.subjectResonanceen_US
dc.subjectThermal effectsen_US
dc.subjectBorn-Oppenheimer approximationen_US
dc.subjectDecoherenceen_US
dc.subjectQuantum systemen_US
dc.subjectTwo-level approximationen_US
dc.subjectQuantum theoryen_US
dc.titleThe off-resonant aspects of decoherence and a critique of the two-level approximationen_US
dc.typeArticleen_US
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