Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPhoton assisted braiding of Majorana fermions in a cavity
97
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the dynamical process of braiding Majorana bound states in the presence of the coupling to photons in a microwave cavity. We show theoretically that the $pi/4$ phase associated with the braiding of Majoranas, as well as the parity of the ground state are imprinted into the photonic field of the cavity, which can be detected by dispersive readouts techniques. These manifestations are purely dynamical, they occur in the absence of any splitting of the MBS that are exchanged, and they disappear in the static setups studied previously. Conversely, the cavity can affect the braiding phase, which in turn should allow for cavity controlled braiding.
rate research
Read More
We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are charge-neutral quasiparticles (equal to their own antiparticle), they have an effective long-range interaction through the even-odd electron number dependence of the superconducting ground state. The flux through a split Josephson junction controls this interaction via the ratio of Josephson and charging energies, with exponential sensitivity. By switching the interaction on and off in neighboring segments of a Josephson junction array, the non-Abelian braiding statistics can be realized without the need to control tunnel couplings by gate electrodes. This is a solution to the problem how to operate on topological qubits when gate voltages are screened by the superconductor.
We show how a quantum dot with a ballistic single-channel point contact to a superconductor can be created by means of a gate electrode at the edge of a quantum spin Hall insulator (such as an InAs/GaSb quantum well). A weak perpendicular magnetic field traps a Majorana zero-mode, so that it can be observed in the gate-voltage-averaged differential conductance <dI/dV> as a 4e^2/h zero-bias peak above a (2/3{pi}^2 - 4)e^2/h background. The one-dimensional edge does not permit the braiding of pairs of Majorana fermions, but this obstacle can be overcome by coupling opposite edges at a constriction, allowing for a demonstration of non-Abelian statistics.
The non-Abelian braiding of Majorana fermions is one of the most promising operations providing a key building block for the realization of topological quantum computation. Recently, the chiral Majorana fermions were observed in a hybrid junction btween a quantum anomalous Hall insulator and an s-wave superconductor. Here we show that if a quantum dot or Majorana zero mode couples to the chiral Majorana fermions, the resulting resonant exchange of chiral Majorana fermions can lead to the non-Abelian braiding. Remarkably, any operation in the braid group can be achieved by this scheme. We further propose electrical transport experiments to observe the braiding of four chiral Majorana fermions and demonstrate the non-Abelian braiding statistics in four-terminal devices of the hybrid junctions. Both a conductance peak due to the braiding and the braiding-order dependent conductance are predicted. These findings pave a way to perform any braiding operation of chiral Majorana fermions by electrically controllable quantum dots.
It has been argued that fluctuations of fermion parity are harmful for the demonstration of non-Abelian anyonic statistics. Here, we demonstrate a striking exception in which such fluctuations are actively used. We present a theory of coherent electron transport from a tunneling tip into a Corbino geometry Josephson junction where four Majorana bound states (MBSs) rotate. While the MBSs rotate, electron tunneling happens from the tip to one of the MBSs thereby changing the fermion parity of the MBSs. The tunneling events in combination with the rotation allow us to identify a novel braiding operator that does not commute with the braiding cycles in the absence of tunneling, revealing the non-Abelian nature of MBSs. The time-averaged tunneling current exhibits resonances as a function of the tip voltage with a period that is a direct consequence of the interference between the non-commuting braiding operations. Our work opens up a possibility for utilizing parity non-conserving processes to control non-Abelian states.
A trijunction made of three topological semiconducting wires, each supporting a Majorana bound state at its two extremities, appears as one of the simplest geometry in order to perform braiding of Majorana fermions. By embedding the trijunction into a microwave cavity allows to study the intricate dynamics of the low-energy Majorana bound states (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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
