Zero temperature decoherence of interacting electrons: theend of the story?

Pritiraj Mohanty

Gleb A. Skorobagatko

The low-temperature limit of charge qubit decoherence due to its Coulomb interaction with electrons tunneling through Luttinger liquid quantum-point contact (QPC) is investigated. The study is focused on quantum detector properties of Luttinger liquid QPC. Efficiency of Luttinger liquid qurrent-carrying quantum point-contact (QPC) as quantum detector for the coupled charge qubit quantum state is characterized by the ratio of decoherence time and the acquisition of information time and how both depend on electron-electron interaction has remained an interesting open question. Here this question is answered in its most challenging zero- (and near zero-) temperature realization where the latter two characteristic time-scales, both tends to zero shadowing true picture of quantum detection in the zero-temperature limit. In order to resolve this difficulty two important mathematical statements (S-theorem and S-lemma) have been proven here for the first time. As the result, it was established here that low-temperature properties of QPC quantum detector with 1D electrodes are defined explicitly by the competition between two different time-scales those reflecting two different types of physical processes in the system. These processes are: i) the orthogonality catastrophe-type decoherence of charge-qubit, one is analogous to the decay of Kondo-resonance narrowed by QPC plasmons; ii) Kane-Fisher suppression of the electron tunneling through Luttinger liquid QPC resulting in the divergence of electron tunneling time. In particular, it has been found that at temperatures close to zero there exists a certain well-defined threshold value $ g=g_{cr} $ of Luttinger liquid correlation parameter which serves as a sharp boundary between region of good (or even perfect) quantum detection at $ g<g_{cr} $ and the region of quantum detector break down where $ g>g_{cr} $.

Maxim Vavilov, Vinay Ambegaokar

We point out that even at the absolute zero of temperature environmental decoherence limits the destructive interference between time-reversed paths for an electron in a disordered metal, and thus causes the leading (`weak localization') quantum correction to the conductivity to saturate at T=0. Our calculation, which is intended to be illustrative rather than complete, uses a model in which an electron interacts with the fluctuations of the mean voltage in the sample. The average of the fluctuations produces the steady damping well known in Brownian motion, introduces a direction of time, ensures that arbitrarily long time-reversed electron paths lose phase coherence, and is consistent with the experimental observation of a finite low temperature phase-breaking lifetime.

Pritiraj Mohanty

G. W. Ford, Robert F. O’Connell

Efforts to achieve quantum computation, teleportation, and communication depend on minimizing decoherence, which is the destruction of a quantum interference pattern. Here, we examine effects arising from the universal zero-point (temperature T = 0) oscillations of the electromagnetic field on a free electron in a Schrödinger cat superposition state. A unique conclusion is that the spreading of an electron wavepacket and the rate of decay of decoherence depend on the bare mass m of the electron. However, only for m = 0 does decoherence occur and the fact that it occurs almost instantly is ruled out by electron interference experiments. For m ≠ 0, the electron essentially behaves as a free particle.

Cruz I. Velasco, Valerio Di Giulio, F. Javier Garcı́a de Abajo