Detecting topological edge states with the dynamics of a qubit

Zaimi, Meri; Boudreault, Christian; Baspin, Nouédyn; Delnour, Nicolas; Eleuch, Hichem; MacKenzie, R.; Hilke, Michael

doi:10.1016/j.physleta.2020.127035

Cited by 10 publications

(17 citation statements)

References 33 publications

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“…Therefore, the occupation-measurable via the current flowing through a quantum point contact close to the dot region [43]-constitutes a simple experimental probe and an alternative to the method presented in Ref. 31, where the decoherence of a double dot has been proposed as an edge-state detector. We note that spectral and transport characteristics of quantum dots were also used in the context of Majorana bound state detection [44][45][46][47].…”

Section: Discussionmentioning

confidence: 99%

“…Apart from the original polymer system, the SSH model was realized experimentally and the topological edge states were detected in more controllable settings such as cold atoms [20][21][22][23], electronic states in artificial atomic lattices [24] or superlattices [25], mechanical chains [26], and photonic systems [27][28][29]. Among theoretically predicted signatures of the topological edge states are effects in the entanglement entropy [30], in the decoherence of a coupled qubit [31], and in transport and noise characteristics in non-equilibrium settings where a current is driven through an SSH chain [32][33][34][35][36]. However, to the best of our knowledge, the archetypal mesoscopic setup of a quantum dot coupled to leads has not yet been studied if the latter are modeled as SSH chains.…”

Section: Introductionmentioning

confidence: 99%

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Quantum dot coupled to topological insulators: The role of edge states

Maurer,

Lin,

Kennes

et al. 2021

Preprint

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We investigate a system consisting of one or two topological-insulator leads which are tunnel coupled to a single dot level. The leads are described by the one-dimensional Su-Schrieffer-Heeger model. We show that (topological) edge states cause characteristic features in the dot spectral function, the dot occupation, and the finite-bias current across the dot. As the kinetic energy is quenched in the dot region, local two-particle interactions are of particular relevance there. This motivates us to test whether the aforementioned edge-state features are robust against such interactions; we report here that they are either robust or even enhanced. We conclude that the characteristic features can be used to determine if the leads are in their topologically non-trivial or trivial phase.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum dot coupled to topological insulators: The role of edge states

Maurer,

Lin,

Kennes

et al. 2021

Preprint

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“…which clearly shows the Θ(L 2 ) scaling for large L. Moreover, the Fock basis is an optimal measurement basis, as the ground state of SSH Hamiltonian has real coefficients in that basis [59]. Such a measurement can be performed by measuring the number operator ĉ † j,m ĉ j,m for each fermionic mode.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Free-Fermionic Topological Quantum Sensors

Sarkar,

Mukhopadhyay,

Alase

et al. 2022

Preprint

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Second order quantum phase transitions, with well-known features such as long-range entanglement, symmetry breaking, and gap closing, exhibit quantum enhancement for sensing at criticality. However, it is unclear which of these features are responsible for this enhancement. To address this issue, we investigate phase transitions in free-fermionic topological systems that exhibit neither symmetry-breaking nor long-range entanglement. We analytically demonstrate that quantum enhanced sensing is possible using topological edge states near the phase boundary. Remarkably, such enhancement also endures for ground states of such models that are accessible in solid state experiments. We illustrate the results with 1D Su-Schrieffer-Heeger chain and a 2D Chern insulator which are both experimentally accessible. While neither symmetry-breaking nor long-range entanglement are essential, gap closing remains as the major candidate for the ultimate source of quantum enhanced sensing. In addition, we also provide a fixed and simple measurement strategy that achieves near-optimal precision for sensing using generic edge states irrespective of the parameter value. This paves the way for development of topological quantum sensors which are expected to also be robust against local perturbations.

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“…. , M. In contrast, the topological edge eigenstates read[75,76] j+1 sinh[κa(M + 1 − j)] ± sinh[κaj] , ( A . 5 ) where κ fulfills v sinh[κ(M + 1)a] = w sinh[κMa] and N 0 = (w sinh(2κaM)/2v sinh(κa)) − (M + 1) is a normalization constant.…”

mentioning

confidence: 99%

Real-space effects of a quench in the Su–Schrieffer–Heeger model and elusive dynamical appearance of the topological edge states

Rossi

Dolcini

2022

New J. Phys.

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The topological phase of the Su-Schrieffer-Heeger (SSH) model is known to exhibit two edge states that are topologically protected by the chiral symmetry. We demonstrate that, for any parameter quench performed on the half-filled SSH chain, the occupancy of each lattice site remains locked to 1/2 at any time, due to the additional time-reversal and charge conjugation symmetries. In particular, for a quench from the trivial to the topological phase, no signature of the topological edge states appears in real-space occupancies, independently of the quench protocol, the temperature of the pre-quench thermal state or the presence of chiral disorder. However, a suitably designed local quench from/to a SSH ring threaded by a magnetic flux can break these additional symmetries while preserving the chiral one. Then, real-space effects of the quench do appear and exhibit different dynamical features in the topological and in the trivial phases. Moreover, when the particle filling is different from a half and the pre-quench state is not insulating, the dynamical appearance of the topological edge states is visible already in a chain, it survives time averaging and can be observed also in the presence of chiral-breaking disorder and for instantaneous quenches.

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Detecting topological edge states with the dynamics of a qubit

Cited by 10 publications

References 33 publications

Quantum dot coupled to topological insulators: The role of edge states

Quantum dot coupled to topological insulators: The role of edge states

Free-Fermionic Topological Quantum Sensors

Real-space effects of a quench in the Su–Schrieffer–Heeger model and elusive dynamical appearance of the topological edge states

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