We consider the effect of electron-electron interactions on a voltage biased quantum point contact in the tunneling regime used as a detector of a nearby qubit. We model the leads of the quantum point contact as Luttinger liquids, incorporate the effects of finite temperature and analyze the detection-induced decoherence rate and the detector efficiency, Q. We find that interactions generically reduce the induced decoherence along with the detector's efficiency, and strongly affect the relative strength of the decoherence induced by tunneling and that induced by interactions with the local density. With increasing interaction strength, the regime of quantum-limited detection (Q → 1) is shifted to increasingly lower temperatures or higher bias voltages respectively. For small to moderate interaction strengths, Q is a monotonously decreasing function of temperature as in the non-interacting case. Surprisingly, for sufficiently strong interactions we identify an intermediate temperature regime where the efficiency of the detector increases with rising temperature.

The problem of resonant transport of strongly interacting electrons through a one-dimensional single-level vibrating quantum dot is being considered. In this paper, we generalize the Komnik and Gogolin model 13 for the single-electron transistor with g = 1/2-Luttinger liquid leads to the case of strong electron-vibron interaction in a quantum dot. The effective transmission coefficient and differential conductance of the system has been derived for the general case of asymmetric tunnel barriers. The main result obtained is that, in the zero-temperature limit, the resonant polaronassisted tunneling with perfect transmission is possible. This resonant tunneling is of the novel (Andreev-like) type due to a special electron-electron interaction in the leads. As a result, a strong domination of resonant polaron-assisted electron transport at low temperatures has been found. Additional narrowing due to electron-electron interaction in the leads, is roughly the same for all polaron-assisted resonances.

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The low-temperature regime 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. Earlier results on related problems were approximate, up to the second order in small electrostatic coupling between chargequbit and QPC. However, here it is shown that in low-(and zero-)temperature limit the respective perturbative decoherence-and acquisition of information timescales both tend to diverge, thus, shadowing a true picture of low-temperature quantum detection for such quantum systems. Here it is shown, that one can successfully circumvent these difficulties in order to restore complete and exact picture of low-temperature decoherence and quantum detection for charge-qubit being measured by arbitrary Luttinger liquid QPC. To do this, here I prove two general mathematical statements (S-theorem and S-lemma) about exact re-exponentiation of Keldysh-contour ordered T-exponent for arbitrary Luttinger liquid tunnel Hamiltonian. The resulting exact formulas are believed to be important in a wide range of those Luttinger liquid problems, where real-time quantum field dynamic is crucial. As the result, decoherence-and acquisition of information time-scales as well as QPC quantum detector efficiency rate are calculated exactly and are shown to have a dramatic dependence on repulsive interaction between electrons in 1D leads of QPC. In particular, it is found that at temperatures close to zero there exists a certain well-defined threshold value g ≈ gcr(T ) of Luttinger liquid correlation parameter g (0 < g ≤ 1) which serves as a sharp boundary between region of good (or even perfect) quantum detection at g < gcr and the region of quantum detection breakdown for g > gcr. Moreover, discovered abrupt decrease of QPC quantum detector efficiency Q with the increase of g in the close vicinity of value gcr represents a fingerprint of interactiondependent instability of all the quantum detection procedure for any Luttinger liquid QPC quantum detector at definite low enough temperatures Tcr(g). The reasons behind these effects are discussed. Also, it is shown that such the low-temperature detection instability effect is able to explain a large unclear mismatch between expected and observed decoherence timescales in two recent experiments ( J.Gorman, D.G.Hasko, D.A.Williams, Phys.Rev.Lett., 95, 090502, (2005) and K.D.Petersson, J.R.Petta, H.Lu, A.C.Gossard, Phys.Rev.Lett., 105, 246804 (2010) ) on charge-qubit quantum dynamics.PACS numbers: