Strongly correlated transport of interacting electrons through the one-dimensional tunnel contact is considered within the Luttinger liquid model of one-dimensional electrodes on arbitrary time scales t>ħ/Λg. Using previous results, namely, the Self-equilibration theorem proven in Ref. [20] the exact distribution functions P(N,t) for the probabilities of N electrons to tunnel through the contact by the time t are derived and plotted as 3D intensity graphs called real-time tunneling maps in a whole available region of Luttinger liquid correlation parameter values, bias voltages, and temperatures. The tunneling maps being obtained reveal tunneling anomalies - unusually high tunneling probabilities for the small numbers of electrons on the short-time scales beyond the steady state regime of electron tunnel transport. Especially, this concerns the case of strong short-range electron-electron interaction in the leads at g≲1/2. The effect being found can be treated as the direct consequence of the self-equilibration phenomenon. It is shown that features of such an anomalous electron tunneling beyond the steady state regime can be used for precise experimental measurements of small differences between Luttinger liquid correlation parameter values in different one-dimensional quantum-point contacts.
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 charge qubit and QPC. However, here it is shown that in low- (and zero-) temperature limits 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 a complete and exact picture of low-temperature decoherence and quantum detection for charge qubits measured by arbitrary Luttinger liquid QPC. To do this, here I prove two general mathematical statements [summation (S) theorem and (S) lemma] about exact re-exponentiation of Keldysh-contour ordered
T exponent for an 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 timescales 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 one-dimensional (1D) leads of QPC. In particular, it is found that at temperatures close to zero there exists a certain well-defined threshold value $g\ensuremath{\approx}{g}_{cr}(T)$ of Luttinger liquid correlation parameter
g ($0<g\ensuremath{\le}1$) which serves as a sharp boundary between the region of good (or even perfect) quantum detection at
g<gcr and the region of quantum detection breakdown for
g>gcr. Moreover, this abrupt decrease of QPC quantum detector efficiency
Q with the increase of
g in the close vicinity of value
gcr represents evidence of interaction-dependent instability of all the quantum detection procedures for any Luttinger liquid QPC quantum detector at sufficiently low temperatures
Tcr(g). The reasons behind these effects are discussed. Also, it is shown that the low-temperature detection instability effect is able to explain the large mismatch between expected and observed decoherence timescales in two recent experiments [Gorman et al., Phys. Rev. Lett. 95, 090502 (2005); Petersson et al., Phys. Rev. Lett. 105, 246804 (2010)] on charge-qubit quantum dynamics.
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} $.
We study equilibration of quantum Hall edge states at integer filling factors, motivated by experiments involving point contacts at finite bias. Idealizing the experimental situation and extending the notion of a quantum quench, we consider time evolution from an initial nonequilibrium state in a translationally invariant system. We show that electron interactions bring the system into a steady state at long times. Strikingly, this state is not a thermal one: Its properties depend on the full functional form of the initial electron distribution and not simply on the initial energy density. Further, we demonstrate that measurements of the tunneling density of states at long times can yield either an overestimate or an underestimate of the energy density, depending on details of the analysis, and discuss this finding in connection with an apparent energy loss observed experimentally. More specifically, we treat several separate cases: for filling factor $\ensuremath{\nu}=1$ we discuss relaxation due to finite-range or Coulomb interactions between electrons in the same channel, and for filling factor $\ensuremath{\nu}=2$ we examine relaxation due to contact interactions between electrons in different channels. In both instances we calculate analytically the long-time asymptotics of the single-particle correlation function. These results are supported by an exact solution at arbitrary time for the problem of relaxation at $\ensuremath{\nu}=2$ from an initial state in which the two channels have electron distributions that are both thermal but with unequal temperatures, for which we also examine the tunneling density of states.
We (re)consider in this paper the problem of tunnelling through an impurity in a quantum wire with arbitrary Luttinger interaction parameter. By combining the integrable approach developed in the case of quantum Hall edge states with the introduction of radiative boundary conditions to describe the adiabatic coupling to the reservoirs, we are able to obtain the exact equilibrium and non-equilibrium current. One of the most striking features observed is the appearance of negative differential conductances out of equilibrium in the strongly interacting regime g ⩽0.2. In spite of the various charging effects, a remarkable form of duality is still observed. New results on the computation of transport properties in integrable impurity problems are gathered in the appendices. In particular, we prove that the TBA results satisfy a remarkable relation, originally derived using the Keldysh formalism, between the order T 2 correction to the current out of equilibrium and the second derivative of this current at T = 0 with respect to the voltage: this is the first direct link between the TBA approach out of equilibrium and the traditional Keldysh one