As a consequence of degeneracies arising from crystal symmetries, it is possible for electron states at band-edges ('valleys') to have additional spin-like quantum numbers. An important question is whether coherent manipulation can be performed on such valley pseudospins, analogous to that implemented using true spin, in the quest for quantum technologies. Here, we show that valley coherence can be generated and detected. Because excitons in a single valley emit circularly polarized photons, linear polarization can only be generated through recombination of an exciton in a coherent superposition of the two valley states. Using monolayer semiconductor WSe2 devices, we first establish the circularly polarized optical selection rules for addressing individual valley excitons and trions. We then demonstrate coherence between valley excitons through the observation of linearly polarized luminescence, whose orientation coincides with that of the linearly polarized excitation, for any given polarization angle. In contrast, the corresponding photoluminescence from trions is not observed to be linearly polarized, consistent with the expectation that the emitted photon polarization is entangled with valley pseudospin. The ability to address coherence, in addition to valley polarization, is a step forward towards achieving quantum manipulation of the valley index necessary for coherent valleytronics.

http://depts.washington.edu/xulab/wordpress/wp-content/uploads/2012/03/nnano.2013.151.pdf

Optical generation of excitonic valley coherence in monolayer WSe2

Realizing topological superconductivity and Majorana zero modes in the laboratory is a major goal in condensed-matter physics. In this Review, we survey the current status of this rapidly developing field, focusing on proposals for the realization of topological superconductivity in semiconductor–superconductor heterostructures. We examine materials science progress in growing InAs and InSb semiconductor nanowires and characterizing these systems. We then discuss the observation of robust signatures of Majorana zero modes in recent experiments, paying particular attention to zero-bias tunnelling conduction measurements and Coulomb blockade experiments. We also outline several next-generation experiments probing exotic properties of Majorana zero modes, including fusion rules and non-Abelian exchange statistics. Finally, we discuss prospects for implementing Majorana-based topological quantum computation.

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Majorana zero modes in superconductor–semiconductor heterostructures

The isolation of qubits from noise sources, such as surrounding nuclear spins and spin–electric susceptibility
 1–4
 , has enabled extensions of quantum coherence times in recent pivotal advances towards the concrete implementation of spin-based quantum computation. In fact, the possibility of achieving enhanced quantum coherence has been substantially doubted for nanostructures due to the characteristic high degree of background charge fluctuations
 5–7
 . Still, a sizeable spin–electric coupling will be needed in realistic multiple-qubit systems to address single-spin and spin–spin manipulations
 8–10
 . Here, we realize a single-electron spin qubit with an isotopically enriched phase coherence time (20 μs)
 11,12
 and fast electrical control speed (up to 30 MHz) mediated by extrinsic spin–electric coupling. Using rapid spin rotations, we reveal that the free-evolution dephasing is caused by charge noise—rather than conventional magnetic noise—as highlighted by a 1/f spectrum extended over seven decades of frequency. The qubit exhibits superior performance with single-qubit gate fidelities exceeding 99.9% on average, offering a promising route to large-scale spin-qubit systems with fault-tolerant controllability.

A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9.

The spin of an electron or a nucleus in a semiconductor naturally implements the unit of quantum information--the qubit In addition, because semiconductors are currently used in the electronics industry, developing qubits in semiconductors would be a promising route to realize scalable quantum information devices The solid-state environment, however, may provide deleterious interactions between the qubit and the nuclear spins of surrounding atoms, or charge and spin fluctuations arising from defects in oxides and interfaces For materials such as silicon, enrichment of the spin-zero (28)Si isotope drastically reduces spin-bath decoherence Experiments on bulk spin ensembles in (28)Si crystals have indeed demonstrated extraordinary coherence times However, it remained unclear whether these would persist at the single-spin level, in gated nanostructures near amorphous interfaces Here, we present the coherent operation of individual (31)P electron and nuclear spin qubits in a top-gated nanostructure, fabricated on an isotopically engineered (28)Si substrate The (31)P nuclear spin sets the new benchmark coherence time (>30 s with Carr-Purcell-Meiboom-Gill (CPMG) sequence) of any single qubit in the solid state and reaches >9999% control fidelity The electron spin CPMG coherence time exceeds 05 s, and detailed noise spectroscopy indicates that--contrary to widespread belief--it is not limited by the proximity to an interface Instead, decoherence is probably dominated by thermal and magnetic noise external to the device, and is thus amenable to further improvement

Storing quantum information for 30 seconds in a nanoelectronic device

Realizing topological superconductivity and Majorana zero modes in the laboratory is one of the major goals in condensed matter physics. We review the current status of this rapidly-developing field, focusing on semiconductor-superconductor proposals for topological superconductivity. Material science progress and robust signatures of Majorana zero modes in recent experiments are discussed. After a brief introduction to the subject, we outline several next-generation experiments probing exotic properties of Majorana zero modes, including fusion rules and non-Abelian exchange statistics. Finally, we discuss prospects for implementing Majorana-based topological quantum computation in these systems.

Realizing Majorana zero modes in superconductor-semiconductor heterostructures

Although electron spins in III–V semiconductor quantum dots have shown great promise as qubits1,2,3, hyperfine decoherence remains a major challenge in these materials. Group IV semiconductors possess dominant nuclear species that are spinless, allowing qubit coherence times4,5,6 up to 2 s. In carbon nanotubes, where the spin–orbit interaction allows for all-electrical qubit manipulation7,8,9,10, theoretical predictions of the coherence time vary by at least six orders of magnitude and range up to 10 s or more11,12. Here, we realize a qubit encoded in two nanotube valley–spin states, with coherent manipulation via electrically driven spin resonance2,3 mediated by a bend in the nanotube. Readout uses Pauli blockade leakage current through a double quantum dot13,14,15. Arbitrary qubit rotations are demonstrated and the coherence time is measured for the first time via Hahn echo, allowing comparison with theoretical predictions. The coherence time is found to be ∼65 ns, probably limited by electrical noise. This shows that, even with low nuclear spin abundance, coherence can be strongly degraded if the qubit states are coupled to electric fields. A qubit based on a valley–spin state can be realized in a carbon nanotube quantum dot.

A valley-spin qubit in a carbon nanotube

It has recently been recognised that the strong spin-orbit interaction present in solids can lead to new phenomena, such as materials with non-trivial topological order. Although the atomic spin-orbit coupling in carbon is weak, the spin-orbit coupling in carbon nanotubes can be significant due to their curved surface. Previous works have reported spin-orbit couplings in reasonable agreement with theory, and this coupling strength has formed the basis of a large number of theoretical proposals. Here we report a spin-orbit coupling in three carbon nanotube devices that is an order of magnitude larger than previously measured. We find a zero-field spin splitting of up to 3.4 meV, corresponding to a built-in effective magnetic field of 29 T aligned along the nanotube axis. Although the origin of the large spin-orbit coupling is not explained by existing theories, its strength is promising for applications of the spin-orbit interaction in carbon nanotubes devices.

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Large spin-orbit coupling in carbon nanotubes

We measure the mechanical resonances of an as-grown suspended carbon nanotube, detected via electrical mixing in the device. A sequence of modes extending to 39 GHz is observed with a quality factor of 35 000 in the highest mode. This unprecedentedly high combination corresponds to a thermal excited state probability below 10–8 and a relaxation time of 140 ns with microsecond relaxation times for lower modes. The effect of electron tunneling on the mechanical resonance is found to depend on frequency as the tunneling time becomes comparable to the vibration period.

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A High Quality Factor Carbon Nanotube Mechanical Resonator at 39 GHz

The bandgap of a low-disorder, bent carbon nanotube is exploited to achieve Pauli blockade and spin resonance.

Valley–spin blockade and spin resonance in carbon nanotubes

Ballistic electron transport is a key requirement for existence of a topological phase transition in proximitized InSb nanowires. However, measurements of quantized conductance as direct evidence of ballistic transport have so far been obscured due to the increased chance of backscattering in one-dimensional nanowires. We show that by improving the nanowire–metal interface as well as the dielectric environment we can consistently achieve conductance quantization at zero magnetic field. Additionally we study the contribution of orbital effects to the sub-band dispersion for different orientation of the magnetic field, observing a near-degeneracy between the second and third sub-bands.

Fei Pei

Papers

A valley-spin qubit in a carbon nanotube

Large spin-orbit coupling in carbon nanotubes

A High Quality Factor Carbon Nanotube Mechanical Resonator at 39 GHz

Valley–spin blockade and spin resonance in carbon nanotubes

Conductance quantization at zero magnetic field in InSb nanowires