Dynamical Signatures of Quasiparticle Interactions in Quantum Spin Chains.

We study the transverse dynamical susceptibility of an antiferromagnetic spin-1/2 chain in the presence of a longitudinal Zeeman field. In the low magnetization regime in the gapless phase, we show that the marginally irrelevant backscattering interaction between the spinons creates a nonzero gap between two branches of excitations at small momentum. We further demonstrate how this gap varies upon introducing a second neighbor antiferromagnetic interaction, vanishing in the limit of a noninteracting "spinon gas." In the high magnetization regime, as the Zeeman field approaches the saturation value, we uncover the appearance of two-magnon bound states in the transverse susceptibility. This bound state feature generalizes the one arising from string states in the Bethe ansatz solution of the integrable case. Our results are based on numerically accurate, unbiased matrix-product-state techniques as well as analytic approximations.

Emergent Fermi Surface in a Triangular-Lattice SU(4) Quantum Antiferromagnet.

Motivated by multiple possible physical realizations, we study the SU(4) quantum antiferromagnet with a fundamental representation on each site of the triangular lattice. We provide evidence for a gapless liquid ground state of this system with an emergent Fermi surface of fractionalized fermionic partons coupled with a U(1) gauge field. Our conclusions are based on numerical simulations using the density matrix renormalization group method, which we support with a field theory analysis.

Three-Magnon Bound State in the Quasi-One-Dimensional Antiferromagnet α-NaMnO_{2}.

Here we report on the formation of a three-magnon bound state in the quasi-one-dimensional antiferromagnet α-NaMnO_{2}, where the single-ion, uniaxial anisotropy inherent to the Mn^{3+} ions in this material provides a binding mechanism capable of stabilizing higher order magnon bound states. While such states have long remained elusive in studies of antiferromagnetic chains, neutron scattering data presented here demonstrate that higher order n>2 composite magnons exist, and, specifically, that a weak three-magnon bound state is detected below the antiferromagnetic ordering transition of NaMnO_{2}. We corroborate our findings with exact numerical simulations of a one-dimensional Heisenberg chain with easy-axis anisotropy using matrix-product state techniques, finding a good quantitative agreement with the experiment. These results establish α-NaMnO_{2} as a unique platform for exploring the dynamics of composite magnon states inherent to a classical antiferromagnetic spin chain with Ising-like single ion anisotropy.

Evidence of topological superconductivity in planar Josephson junctions.

Majorana zero modes-quasiparticle states localized at the boundaries of topological superconductors-are expected to be ideal building blocks for fault-tolerant quantum computing1,2. Several observations of zero-bias conductance peaks measured by tunnelling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor-semiconductor nanowires3-8. On the other hand, two-dimensional systems offer the alternative approach of confining Majorana channels within planar Josephson junctions, in which the phase difference φ between the superconducting leads represents an additional tuning knob that is predicted to drive the system into the topological phase at lower magnetic fields than for a system without phase bias9,10. Here we report the observation of phase-dependent zero-bias conductance peaks measured by tunnelling spectroscopy at the end of Josephson junctions realized on a heterostructure consisting of aluminium on indium arsenide. Biasing the junction to φ ≈ π reduces the critical field at which the zero-bias peak appears, with respect to φ = 0. The phase and magnetic-field dependence of the zero-energy states is consistent with a model of Majorana zero modes in finite-size Josephson junctions. As well as providing experimental evidence of phase-tuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures11 and are scalable to the complex geometries needed for topological quantum computing9,12,13.

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

Inducing time-reversal-invariant topological superconductivity and fermion parity pumping in quantum wires.

We propose a setup to realize time-reversal-invariant topological superconductors in quantum wires, proximity coupled to conventional superconductors. We consider a model of quantum wire with strong spin-orbit coupling and proximity coupling to two s-wave superconductors. When the relative phase between the two superconductors is ϕ=π a Kramers pair of Majorana zero modes appears at each edge of the wire. We study the robustness of the phase in the presence of both time-reversal-invariant and time-reversal-breaking perturbations. In addition, we show that the system forms a natural realization of a fermion parity pump, switching the local fermion parity of both edges when the relative phase between the superconductors is changed adiabatically by 2π.

Single-ion quantum lock-in amplifier.

Quantum metrology uses tools from quantum information science to improve measurement signal-to-noise ratios. The challenge is to increase sensitivity while reducing susceptibility to noise, tasks that are often in conflict. Lock-in measurement is a detection scheme designed to overcome this difficulty by spectrally separating signal from noise. Here we report on the implementation of a quantum analogue to the classical lock-in amplifier. All the lock-in operations--modulation, detection and mixing--are performed through the application of non-commuting quantum operators to the electronic spin state of a single, trapped Sr(+) ion. We significantly increase its sensitivity to external fields while extending phase coherence by three orders of magnitude, to more than one second. Using this technique, we measure frequency shifts with a sensitivity of 0.42 Hz Hz(-1/2) (corresponding to a magnetic field measurement sensitivity of 15 pT Hz(-1/2)), obtaining an uncertainty of less than 10 mHz (350 fT) after 3,720 seconds of averaging. These sensitivities are limited by quantum projection noise and improve on other single-spin probe technologies by two orders of magnitude. Our reported sensitivity is sufficient for the measurement of parity non-conservation, as well as the detection of the magnetic field of a single electronic spin one micrometre from an ion detector with nanometre resolution. As a first application, we perform light shift spectroscopy of a narrow optical quadrupole transition. Finally, we emphasize that the quantum lock-in technique is generic and can potentially enhance the sensitivity of any quantum sensor.