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arXiv:1609.07281 · Physical review. B./Physical review. B

Effect of interactions on quantum-limited detectors

Gleb A. Skorobagatko, Anton Bruch, Silvia Viola Kusminskiy, Alessandro Romito

Published May 1, 2017• 4 citations
arXivHTMLPDF

Abstract

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 ($Q\ensuremath{\rightarrow}1$) 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 noninteracting case. Surprisingly, for sufficiently strong interactions we identify an intermediate temperature regime where the efficiency of the detector increases with rising temperature.

DOI
10.1103/physrevb.95.205402

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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, QQQ. 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\ensuremath→1Q\ensuremath{\rightarrow}1Q\ensuremath→1) is shifted to increasingly lower temperatures or higher bias voltages respectively. For small to moderate interaction strengths, QQQ is a monotonously decreasing function of temperature as in the noninteracting case. Surprisingly, for sufficiently strong interactions we identify an intermediate temperature regime where the efficiency of the detector increases with rising temperature.
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 TTT 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 ggg ($0<g\ensuremath{\le}1$) which serves as a sharp boundary between the region of good (or even perfect) quantum detection at g<gcrg<{g}_{cr}g<gcr​ and the region of quantum detection breakdown for g>gcrg>{g}_{cr}g>gcr​. Moreover, this abrupt decrease of QPC quantum detector efficiency QQQ with the increase of ggg in the close vicinity of value gcr{g}_{cr}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){T}_{cr}(g)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} $.
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.
We study how electron-electron interactions renormalize tunneling into a Luttinger liquid beyond the lowest order of perturbation in the tunneling amplitude. We find that the conventional fixed point has a finite basin of attraction only in the point contact model, but a finite size of the contact makes it generically unstable to the tunneling-induced breakup of the liquid into two independent parts. In the course of renormalization to the nonperturbative-in-tunneling fixed point, the tunneling conductance may show a nonmonotonic behavior with temperature or bias voltage.
We consider a biased quantum point contact between two Luttinger liquids measuring a quantum-mechanical system (oscillator). There are three main physical results. First, we find that for voltages higher than the oscillator level spacing, the effect of the measurement is equivalent to coupling to a heat bath, with an effective temperature that only depends on the device $I\ensuremath{-}V$ characteristic. Second, we find that this heating changes the $I\ensuremath{-}V$ characteristics on the junction. Finally, we predict a modulation of the tunneling current at the oscillator frequency. Also, we find that a generalized nonequilibrium fluctuation-dissipation relation connects the decoherence and dissipation of the oscillator to the current-voltage characteristics of the device.
Recent experiments performed on weakly pinched quantum point contacts have shown a resistance that tends to decrease at low source drain voltage. We show that enhanced Coulomb interactions, prompted by the presence of the point contact, may lead to anomalously large multiple-particle scattering at finite bias voltage. These processes tend to decrease at low voltage, and thus may account for the observed reduction of the resistance. We concentrate on the case of a normal point contact, and model it by a spinful interacting Tomonaga-Luttinger liquid, with a single impurity, connected to noninteracting leads. We find that sufficiently strong Coulomb interactions enhance two-electron scatterings, which dominate the conductance. Our calculation shows that the effective charge, probed by the shot noise of such a system, approaches a value proportional to e∗=2e{e}^{*}=2ee∗=2e at a sufficiently large backscattering current. This distinctive hallmark may be tested experimentally. We discuss possible applications of this model to experiments conducted on Hall bars.