Readout of Majorana bound states via Landau-Zener transition

Zhang, Zhentao; Liu, Dong E.

doi:10.1103/physrevb.103.195401

Cited by 9 publications

(4 citation statements)

References 55 publications

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“…These are formed by the Majorana bound states that reside in topological superconducting systems. A realization of this could be an rf superconducting quantum interference device (SQUID) with a topological JJ that is formed by a onedimensional nanowire with spin-orbit coupling, quantum spin-Hall edge states, or ferromagnetic atomic chains (Feng et al, 2018;Huang et al, 2015;Wang et al, 2018;Zhang and Liu, 2021). The energy level structure is controlled by an external magnetic flux.…”

Section: B Driven Few-level Systemsmentioning

confidence: 99%

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Ivakhnenko¹,

Shevchenko²,

Nori³

2022

Preprint

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H. Comparison of different methods IV. Interferometry A. Superconducting circuits B. Semiconductor quantum dots C. Donors and impurities (atomic qubits) D. Graphene E. Microscopic systems F. Other systems G. Multilevel systems V. Quantum control A. Coherent control of microscopic and mesoscopic structures B. Universal single-and two-qubit control C. Shortcuts to adiabaticity D. Adiabatic quantum computation VI. Related classical coherent phenomena VII. Conclusion 1. With near-adiabatic limit (Landau) 2. With parabolic cylinder functions (Zener) 3. With contour integrals (Majorana) 4. With WKB approximation and phase integral method (Stückelberg) 5. Duration of the LZSM transition B. Description of a periodically driven two-level system 1. Adiabatic-impulse model a. Adiabatic evolution b. Multiple-passage evolution 2. Rotating-wave approximation (RWA) 3. Floquet theory 4. Rate equation and white noise approach a. Transition rate b. Rate equation c. From Bessel to Airy d. Double-passage regime ReferencesAbbreviations and most-often-used symbols Because this review article is quite long, for the readers' convenience, we present the main abbreviations used. This list also includes some of the topics covered.

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Section: B Driven Few-level Systemsmentioning

confidence: 99%

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Ivakhnenko¹,

Shevchenko²,

Nori³

2022

Preprint

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“…Turning to possible measurements these observations can lead to, there have been multiple proposals to detect the presence of MBSs in Josephson junctions in nanowires 42 . Some proposals attempt to take advantage of the non-local parity of MBSs and its manifestation in a number of measurable physical phenomena [47][48][49][50] . Alongside these methods, electron parity may also be directly detected through quantum dots and single-electron transistors (SETs).…”

Section: Locating the Majoranasmentioning

confidence: 99%

Signatures of Majorana bound states and parity effects in two-dimensional chiral p-wave Josephson junctions

Abboud,

Subramanyan,

Sun

et al. 2022

Preprint

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We characterize topological features of Josephson junctions formed by coupled mesoscopic chiral p-wave superconducting islands. Through analytic and numerical studies of the low-lying BdG (Bogoliubov-deGennes) spectrum, we identify localized MBS (Majorana bound states) nucleated in Josephson vortices by the application of a perpendicular magnetic field. Additionally, we demonstrate the existence of an extended MBS that is delocalized around the outer perimeter of the coupled islands, which has measurable consequences on the Josephson supercurrent and phase dynamics of the junction. In particular, we predict a change in the critical current diffraction pattern in which the odd integer-flux nodes are lifted in a fermion parity-dependent fashion. We model the competing stochastic effects of thermal noise and macroscopic quantum tunneling within the RCSJ framework and show the emergence of a bimodal critical current distribution. We demonstrate that increasing the parity transition rate suppresses the bimodal nature of the distribution, thus strongly emphasizing the non-trivial parity dependent nature of the many-body ground state. Finally, we consider a trijunction geometry with three islands and discuss possible schemes to braid Majorana bound states by moving the Josephson vortices to which they are bound.

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“…There has been considerable interest in nonequilibrium dynamics of quantum systems (see e.g., refs. [1,2]) over the last couple of decades that surged again recently in connection with quantum information problems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. These include the dynamical discrete-state Bardeen-Cooper-Shriffer (BCS) pairing models [5,[20][21][22][23][24][25][26][27][28][29][30][31][32][33], where for example the interaction strength can be made time dependent, and various multi-level Landau-Zenner tunneling models and their many body generalizations [34][35][36][37][38][39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations

Sedrakyan

Babujian

2022

J. High Energ. Phys.

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We consider a set of non-stationary quantum models. We show that their dynamics can be studied using links to Knizhnik-Zamolodchikov (KZ) equations for correlation functions in conformal field theories. We specifically consider the boundary Wess-Zumino-Novikov-Witten model, where equations for correlators of primary fields are defined by an extension of KZ equations and explore the links to dynamical systems. As an example of the workability of the proposed method, we provide an exact solution to a dynamical system that is a specific multi-level generalization of the two-level Landau-Zenner system known in the literature as the Demkov-Osherov model. The method can be used to study the nonequilibrium dynamics in various multi-level systems from the solution of the corresponding KZ equations.

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Readout of Majorana bound states via Landau-Zener transition

Cited by 9 publications

References 55 publications

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Signatures of Majorana bound states and parity effects in two-dimensional chiral p-wave Josephson junctions

Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations

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