Browsing by Subject "Two-level approximation"
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Item Open Access Non-Markovian decoherence: A critique of the two-level approximation(Elsevier B.V., 2006) Hakioǧlu T.; Savran, K.; Sevinçli, H.; Meşe, E.The environmental decoherence in multilevelled systems in the context of two-level approximation is examined. It is found that the environmental temperature plays a minor role in the magnitudes of the decoherence rates whereas, the system-environment coupling and the environmental energy spectrum are dominant. Particularly, the latter is important in zero temperature quantum fluctuations and/or the nonequilibrium noise sources due to the large range of energies present in the environmental modes. Decoherence is found to be dominated by the short time nonresonant processes and this observation severely questions the use of the two-levelled models on decoherence.Item Open Access The off-resonant aspects of decoherence and a critique of the two-level approximation(IOP Institute of Physics, 2006) Savran, K.; Hakioǧlu T.; Mese, E.; Sevinçli, H.Conditions 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.Item Open Access Quantum information processing in solid states: A critique of two-level approximation(World Scientific Publishing Co., 2005) Savran K.; Hakioğlu T.We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a non-ideal two level subspace, identified as the qubit and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model that we use is an rf-SQUID under macroscopic quantum coherence and coupled inductively to a flux noise characterized by an environmental spectrum. The model interaction can generate dipole couplings which can be appreciable for a number of high levels. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system’s reduced density matrix. We numerically examine the relaxation and dephasing times as the environmental frequency spectrum, and the multilevel system parameters are varied at zero temperature. We observe that, these time scales receive contribution from all available energies in the noise spectrum (even well above the system’s energy scales) stressing the dominant role played by the non-resonant (virtual) transitions. The relaxation and dephasing times calculated, strongly depend on the number of levels within the range of levels for which appreciable couplings are produced. Under the influence of these effects, we remark that the validity of the two level approximation is restricted not by the temperature but by these dipole couplings as well as the availability of the environmental modes at low temperatures. © 2005 by World Scientific Publishing Co. Pte. Ltd.