Dynamics of a Majorana Trijunction in a Microwave Cavity

Abstract

A trijunction made of three topological semiconducting wires, each supporting a Majorana bound state (MBS) at its two extremities, appears as one of the simplest geometries in order to perform braiding of Majorana fermions. Embedding the trijunction into a microwave cavity allows to study the intricate dynamics of the low‐energy MBSs coupled to the cavity electric field under a braiding operation. Extending a previous work [Phys. Rev. Lett. 2019, 122, 236803], the full time evolution of the density matrix of the low‐energy states, including various relaxation channels, is computed both in the adiabatic regime, as well as within the Floquet formalism in the case of periodic driving. It turns out that in the stationary state the observables of the system depend on both the parity of the ground state and on the non‐Abelian Berry phase acquired during braiding. The average photon number and the second‐order photon coherence function g(2)(0) are explicitly evaluated and reveal the accumulated non‐Abelian Berry phase during the braiding process.

Ground-state quantum geometry in superconductor–quantum dot chains

“…More recently, multiterminal Josephson junctions (MJJs) consisting of many superconducting terminals have been theoretically investigated and shown to exhibit topologically nontrivial physics [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. In such multiterminal systems, topology emerges in the synthetic space of superconducting phases and the integer-valued Chern number can manifest itself in a quantized transconductance between two terminals [22][23][24][25][26][27][28]32,34].…”

“…In such multiterminal systems, topology emerges in the synthetic space of superconducting phases and the integer-valued Chern number can manifest itself in a quantized transconductance between two terminals [22][23][24][25][26][27][28]32,34]. The advantage of these systems is that, in principle, an arbitrary number of synthetic dimensions can be implemented by simply increasing the number of superconducting leads and that building blocks can be conventional materials, although also topological superconductors hosting Majorana zero modes have been studied in this context [27,[32][33][34]. Moreover, it has been recently suggested to use microwave spectroscopy to measure the more fundamental quantum geometric tensor of ABS, which provides both the information about the geometry of the state manifold and the topological information contained in the Berry curvature [30].…”

Statistical properties of linear Majorana fermions

“…In fact, once we understand the behavior of these particles better, we are able to comprehensively understand some physical phenomena, for example, the dynamic of quantum spin liquid which has been widely studied [40][41][42][43] to understand spin transports in quantum spin systems and are applied in spintronic contexts [44]. In addition, to understand the properties of Majorana's fermions allow us to know a little more about the thermodynamics associated with topological insulators and the Majorana's superconductivity [45], which can leads to semiconductor nanowires [46] and to a revolution in the industry of electrical devices [47].…”