Zero-Point Fluctuations and the Quenching of the Persistent Current in Normal Metal Rings

2006

We investigate quantum noise effect on the transportation of nonlocal Cooper pairs accross the realistic Andreev entangler which consists of an s-wave superconductor coupled to two small quantum dots at resonance which themselves are coupled to normal leads. The noise emerges due to voltage fluctuations felt by the electrons residing on the two dots as a result of the finite resistances in the gate leads or of any resistive lead capacitively coupled to the dots. In the ideal noiseless case, the setup provides a trustable source of mobile and nonlocal spin-entangled electrons and the transport is dominated by a two-particle Breit-Wigner resonance that allows the injection of two spin-entangled electrons into different leads at the same energy [P. Recher, E. V. Sukhorukov, and D. Loss, Phys. Rev. B 63, 165314 (2001)]. We seek to revisit the transport of those nonlocal Cooper pairs as well as the efficiency of such an Andreev entangler when including the quantum noise (decoherence).PACS numbers: 73.23. Hk, 73.40.Gk, 73.50.Td The concept of nonlocal pairwise-entangled quantum states 1 , namely the Einstein-Podolsky-Rosen (EPR) pairs 2 is extremely fundamental for testing the violation of Bell inequality 3 and at the same time is also crucial for efficient quantum communication 4 and quantum teleportation 5 for example. Tests on the entanglement of massless particles like the photons already exist 6 but not yet for massive particles such as the electrons. A concrete challenge is to realize an entangler of electrons, i.e., a device that generates spin singlets that are made out of two electrons. Recently, an interesting setup involving an s-wave superconductor weakly-coupled to two quantum dots, which themselves are coupled to normal leads has been envisioned in Ref. 7. The spin correlations of an s-wave superconductor induce a spin-singlet state between two electrons, each of which can now reside on a separate quantum dot; this results in the formation of a nonlocal Cooper pair described by the quantum statewhere d † lσ produces an electron with spin σ on the dot l and |i = |0 S |0 D |µ l (|0 S is the quasiparticle vacuum for the superconductor, |0 D means that both dot levels ǫ l are unoccupied, and |µ l defines the occupation of the leads which are filled with electrons up to the electrochemical potential µ l ) is the initial state. A prerequisite to perform such a nonlocal spin-entangled electron state is the Coulomb blockade phenomenon which typically forbids double occupancy on each quantum dot: the spin singlet coming from the Cooper pair remains preserved in this process even though the two involved partners are well separated physically because they reside on different quantum dots. More precisely, such an Andreev entangler 8 of EPR pairs has been predicted to be well efficient when 7 E/γ ≫ (k F δr) where E −1 = 1/(π∆) + 1/U , U being twice the charging energy of a given dot, ∆ the superconducting gap, δr = |δr| which might be of the order of the distance between dots denotes the distance between the poin...

“…(25). When focussing on the tunneling of a Cooper pair from the SC to the dots, hence one requires to evaluate D B | DD|…”

Section: B Discussion On Tunneling Matrix Elementsmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Decoherence of Einstein-Podolsky-Rosen pairs in a noisy Andreev entangler

Dupont

2006

“…In the neighborhood of a quantum critical point of a metallic system the finite temperature properties as a rule show non-Fermi liquid behavior 3 . In recent years, quantum phase transitions at the nanoscale have attracted much attention [4][5][6][7][8][9][10][11][12][13][14][15] . Much of the effort has been focused on the breakdown of the Kondo effect in transport of a quantum dot due to its coupling to a dissipative environment.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium quantum transport through a dissipative resonant level

Chung¹,

Finkelstein

et al. 2013

The resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the non-equilibrium transport near a quantum phase transition in a spinless dissipative resonant-level model, extending earlier work [Phys. Rev. Lett. 102, 216803 (2009)]. A detailed derivation of a rigorous mapping of our system onto an effective Kondo model is presented. A controlled energy-dependent renormalization group approach is applied to compute the non-equilibrium current in the presence of a finite bias voltage V . In the linear response regime V → 0, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the non-equilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the non-equilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for V < T , while it obeys a distinct non-equilibrium profile for V > T . We furthermore provide new signatures of the transition in the finite-frequency current noise and AC conductance via a recently developed functional renormalization group (FRG) approach. The generalization of our analysis to non-equilibrium transport through a resonant level coupled to two chiral Luttinger-liquid leads, generated by fractional quantum Hall edge states, is discussed. Our work on the dissipative resonant level has direct relevance to experiments on a quantum dot coupled to a resistive environment, such as H. Mebrahtu et al., Nature 488, 61, (2012).

“…1 is small enough such that we can only restrict ourselves to the highestoccupied level. This leads to a two-level system [4]. The gate voltage V g is fixed such that the two states in which the level is occupied (|1 ) or not (|0 ) are almost degener- ate.…”

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confidence: 99%

Unification of electromagnetic noise and Luttinger liquid via a quantum dot

2005

We investigate the effect of dissipation on a small quantum dot (resonant level) tunnel-coupled to a chiral Luttinger liquid (LL) with the LL parameter K. The dissipation stems from the coupling of the dot to an electric environment, being characterized by the resistance R, via Coulomb interactions. We show that this problem can be mapped onto a Caldeira-Leggett model where the (ohmic) bath of harmonic oscillators is governed by the effective dissipation strength α = (2K) −1 withK −1 = K −1 + 2R/RK and RK = h/e 2 the quantum of resistance. Experimental consequences are discussed and the limit K = 1/2 + is thoroughly studied at small R/RK through the spin-boson-fermion model. PACS numbers: 73.23.Hk, 71.10.Pm, 72.70.+m A quantum dot can be viewed as a simple artificial atom exhibiting charge quantization [1], and its charge can now be measured with a very high accuracy with the aid of an electrometer based on a single-electron transistor [2]. The coupling of the quantum dot to a macroscopic reservoir of electrons inevitably produces quantum charge fluctuations on the dot. This generic phenomenon has been vividly investigated theoretically both in the case of a large metallic box with a very dense spectrum [3] and in the opposite limit of a two-level system [4]. The reservoir of electrons may be a two-dimensional (2D) Fermi-liquid lead [3,5] or a 1D structure [6,7] [e.g., a fractional quantum Hall edge state (FQHES)or a quantum wire] where interacting electrons form TomonagaLuttinger liquid (LL). Some recent endeavors have been accomplished by Cedraschi et al. [4] and by one of us [8] to understand the role of dissipation-coming from the capacitive coupling of the dot to an electric environment with an ohmic resistance-on the charge quantization of a quantum dot, but with the limitation of free electrons in the reservoir lead. In this Letter, we explore dissipation effects on the small quantum dot (resonant level) coupled to a chiral LL (CLL) which has been previously introduced by Furusaki and Matveev [6]. We seek to provide a unified picture of the role of interactions in the onechannel conductor and of the zero-point fluctuations of the electric environment generalizing the case of a single junction [9]. Of interest to us is to understand the nature of the quantum phases emerging through the dissipative mesoscopic structure shown in Fig. 1 and hence to discuss physical implications for the occupation probability on the quantum dot. We highlight that the physics explored here is sufficiently appealing to experimentalists to carry out activities similar to those already existing on superconducting qubits capacitively coupled to lossy transmission lines in GaAs/AlGaAs heterostructures [10].The quantum dot of interest in Fig. 1 is small enough such that we can only restrict ourselves to the highestoccupied level. This leads to a two-level system [4]. The gate voltage V g is fixed such that the two states in which the level is occupied (|1 ) or not (|0 ) are almost degener- ate. We can thus resort to an orbital s...