Fermion parity measurement and control in Majorana circuit quantum electrodynamics

Yavilberg, Konstantin; Ginossar, Eran; Grosfeld, Eytan

doi:10.1103/physrevb.92.075143

Cited by 52 publications

(65 citation statements)

References 44 publications

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“…A possible avenue for exploring parity effects would involve coupling the Majorana wire to a charge sensitive system, such as a quantum dot, a single electron transistor, or a scanning tunneling microscope(STM) tip 25,89,[98][99][100][101][102] . Other methods which have gained prominence in the Majorana mode context include coupling to microwave cavity, circuit quantum electrodynamics, cooper pair boxes and Transmon systems seem to show promise and have gained much attention, especially as they directly couple to the parity sectors arising from the Majorana modes 92,[103][104][105][106][107][108][109] . There have also been several proposals for realization of topological systems hosting Majorana modes in cold atomic systems [110][111][112] .…”

Section: Discussionmentioning

confidence: 99%

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

Hegde¹,

Vishveshwara²

2016

Phys. Rev. B

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We study the decay and oscillations of Majorana fermion wavefunctions and ground state (GS) fermion parity in one-dimensional topological superconducting lattice systems. Using a Majorana transfer matrix method, we find that Majorana wavefunction properties are encoded in the associated Lyapunov exponent, which in turn is the sum of two independent components: a 'superconducting component' which characterizes the gap induced decay, and the 'normal component', which determines the oscillations and response to chemical potential configurations. The topological phase transition separating phases with and without Majorana end modes is seen to be a cancellation of these two components. We show that Majorana wavefunction oscillations are completely determined by an underlying non-superconducting tight-binding model and are solely responsible for GS fermion parity switches in finite-sized systems. These observations enable us to analytically chart out wavefunction oscillations, the resultant GS parity configuration as a function of parameter space in uniform wires, and special parity switch points where degenerate zero energy Majorana modes are restored in spite of finite size effects. For disordered wires, we find that band oscillations are completely washed out leading to a second localization length for the Majorana mode and the remnant oscillations are randomized as per Anderson localization physics in normal systems. Our transfer matrix method further allows us to i) reproduce known results on the scaling of mid-gap Majorana states and demonstrate the origin of its log-normal distribution, ii) identify contrasting behavior of disorder-dependent GS parity switches for the cases of even versus odd number of lattice sites, and iii) chart out the GS parity configuration and associated parity switch points as a function of disorder strength.

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Section: Discussionmentioning

confidence: 99%

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

Hegde¹,

Vishveshwara²

2016

Phys. Rev. B

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“…Secondly we discuss readout in the dispersive regime, see [34,35] for similar models and discussion of Majorana systems coupled to microwave resonators. Depending on experimental details, operation of the resonator and readout devices either in the strong-coupling or dispersive regime may be more practical.…”

Section: B3 Charge Reflectometry Readoutmentioning

confidence: 99%

Majorana box qubits

et al. 2017

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Quantum information protected by the topology of the storage medium is expected to exhibit long coherence times. Another feature are topologically protected gates generated through braiding of Majorana bound states. However, braiding requires structures with branched topological segments which have inherent difficulties in the semiconductor-superconductor heterostructures now believed to host Majorana bound states. In this paper, we construct quantum bits taking advantage of the topological protection and non-local properties of Majorana bound states in a network of parallel wires, but without relying on braiding for quantum gates. The elementary unit is made from three topological wires, two wires coupled by a trivial superconductor and the third acting as an interference arm. Coulomb blockade of the combined wires spawns a fractionalized spin, non-locally addressable by quantum dots used for single-qubit readout, initialization, and manipulation. We describe how the same tools allow for measurement-based implementation of the Clifford gates, in total making the architecture universal. Proof-of-principle demonstration of topologically protected qubits using existing techniques is therefore within reach.

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“…Hence, the direct electric coupling between Majorana bound states and cavity photons has raised a lot of attention recently [44][45][46][47][48] . The indirect coupling of Majorana fermions to cavities through a superconducting quantum bit also raises interest for quantum computation purposes [194][195][196][197][198][199][200][201][202][203] .…”

Section: Majorana Nanocircuitsmentioning

confidence: 99%

Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena

Cottet¹,

Dartiailh²,

Desjardins³

et al. 2017

J. Phys.: Condens. Matter

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Circuit QED techniques have been instrumental to manipulate and probe with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices where the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of Mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the Circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments consists in using cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.

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Fermion parity measurement and control in Majorana circuit quantum electrodynamics

Cited by 52 publications

References 44 publications

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

Majorana box qubits

Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena

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