We propose a method of measuring the fermion parity lifetime of Majorana fermion modes due to quasiparticle poisoning. We model quasiparticle poisoning by coupling the Majorana modes to electron reservoirs, explicitly breaking parity conservation in the system. This poisoning broadens and shortens the resonance peak associated with Majorana modes. In a two lead geometry, the poisoning decreases the correlation in current noise between the two leads from the maximal value characteristic of crossed Andreev reflection. The latter measurement allows for calculation of the poisoning rate even if temperature is much higher than the resonance width.The promise of topologically robust quantum computation has been a major motivation in condensed matter physics over the past decade. In such schemes quantum information is not stored locally but is stored in a global state of the system. In this way systems are protected against decoherence by local perturbations. A simple and potentially realizable platform for non-local quantum information storage is in systems with Majorana fermions, which split a single fermionic mode into two spatially separated Majorana bound states. Systems with Majorana qubits are only protected under perturbations that preserve fermion parity; that is, they only involve the transfer of Cooper pairs [13]. Perturbations that switch the fermion parity of the system, involving unpaired electrons, dubbed quasiparticle poisoning, will change the state of a Majorana qubit. The time scale of this poisoning rate is then a limiting factor for performing quantum computations. Recent theoretical calculations show that this poisoning rate may be problematically large for performing adiabatic gate operations [14].In light of this challenge, it is essential to be able to measure this poisoning rate. There have been several proposals to measure the rate based on SQUIDs in topological superconductor/superconductor heterosturctures [4,15], a quantum dot coupled to a topological superconducting wire [16], or direct measurement of parity relax- ation times [17]. In this article we propose a relatively simple experimental setup that doesn't require an interference measurement, based on the two lead transport experiments proposed by Nilsson et al.[18] and Liu et al. [19]. Our proposed measurement gives a direct probe of the breakdown of non-locality due to quasiparticle poisoning.We consider the same experimental geometry as in [18] and [19]: we have a grounded topological superconducting wire, with each Majorana bound state coupled to a normal lead. We model quasiparticle poisoning by coupling fermion reservoirs to each Majorana mode. We consider the limit with k B T, eV ∆, so that the Majorana modes are the only modes accessible to electrons tunneling from the leads. Explicitly, our effective Hamiltonian is(1) Heregives the lead and bath Hamiltonian, E M gives the splitting of the coupled Majorana modes, t α gives the coupling to the leads with electron creation operators c † α at the interface, and δ α gives the co...

We propose an experiment to use the magneto-optical Faraday effect to probe the dynamic Hall conductivity of spin-liquid candidates. Theory predicts that an external magnetic field will generate an internal gauge field. If the source of conductivity is in spinons with a Fermi surface, a finite Faraday rotation angle is expected. We predict the angle to scale as the square of the frequency rather than display the standard cyclotron resonance pattern. Furthermore, the Faraday effect should be able to distinguish the ground state of the spin liquid, as we predict no rotation for massless Dirac spinons. We give a semiquantitative estimate for the magnitude of the effect and find that it should be experimentally feasible to detect in both κ-(ET) 2 Cu 2 (CN) 3 and, if the spinons form a Fermi surface, herbertsmithite. We also comment on the magneto-optical Kerr effect and show that the imaginary part of the Kerr angle (circular dichroism) may be measurable.