Creation of a Dirac monopole-antimonopole pair in a spin-1 Bose-Einstein condensate

We theoretically demonstrate that a pair of Dirac monopoles with opposite synthetic charges can be created within a single spin-1 Bose-Einstein condensate by steering the spin degrees of freedom by external magnetic fields. Although the net synthetic magnetic charge of this configuration vanishes, both the monopole and the antimonopole are accompanied by vortex filaments carrying opposite angular momenta. Such a Dirac dipole can be realized experimentally by imprinting a spin texture with a nonlinear magnetic field generated by a pair of coils in a modified Helmholtz configuration. We also investigate the case where the initial state for the dipole-creation procedure is pierced by a quantized vortex line with a winding number kappa. It is shown that if kappa = -1, the resulting monopole and antimonopole lie along the core of a singly quantized vortex whose sign is reversed at the locations of the monopoles. For kappa = -2, the monopole and antimonopole are connected by a vortex line segment carrying two quanta of angular momentum, and hence the dipole as a whole is an isolated configuration. In addition, we simulate the long-time evolution of the dipoles in the magnetic field used to create them. For kappa = 0, each of the semi-infinite doubly quantized vortices splits into two singly quantized vortices, as in the case of a single Dirac monopole. For kappa = -1 and kappa = -2, the initial vortices deform into a vortex with a kink and a vortex ring, respectively.Peer reviewe

Correcting non-independent and non-identically distributed errors with surface codes

A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern multi-qubit devices are typically neither independent nor identical across qubits. In this work, we develop and investigate the properties of topological surface codes adapted to a known noise structure by Clifford conjugations. We show that the surface code locally tailored to non-uniform single-qubit noise in conjunction with a scalable matching decoder yields an increase in error thresholds and exponential suppression of sub-threshold failure rates when compared to the standard surface code. Furthermore, we study the behaviour of the tailored surface code under local two-qubit noise and show the role that code degeneracy plays in correcting such noise. The proposed methods do not require additional overhead in terms of the number of qubits or gates and use a standard matching decoder, hence come at no extra cost compared to the standard surface-code error correction

High-fidelity multi-photon-entangled cluster state with solid-state quantum emitters in photonic nanostructures

We propose a complete architecture for deterministic generation of entangled multiphoton states. Our approach utilizes periodic driving of a quantum-dot emitter and an efficient light-matter interface enabled by a photonic crystal waveguide. We assess the quality of the photonic states produced from a real system by including all intrinsic experimental imperfections. Importantly, the protocol is robust against the nuclear spin bath dynamics due to a naturally built-in refocussing method reminiscent to spin echo. We demonstrate the feasibility of producing Greenberger-Horne-Zeilinger and one-dimensional cluster states with fidelities and generation rates exceeding those achieved with conventional 'fusion' methods in current state-of-the-art experiments. The proposed hardware constitutes a scalable and resource-efficient approach towards implementation of measurement-based quantum communication and computing

Three-dimensional skyrmions in spin-2 Bose-Einstein condensates

We introduce topologically stable three-dimensional skyrmions in the cyclic and biaxial nematic phases of a spin-2 Bose-Einstein condensate. These skyrmions exhibit exceptionally high mapping degrees resulting from the versatile symmetries of the corresponding order parameters. We show how these structures can be created in existing experimental setups and study their temporal evolution and lifetime by numerically solving the three-dimensional Gross-Pitaevskii equations for realistic parameter values. Although the biaxial nematic and cyclic phases are observed to be unstable against transition towards the ferromagnetic phase, their lifetimes are long enough for the skyrmions to be imprinted and detected experimentally.Peer reviewe

Entangling a Hole Spin with a Time-Bin Photon: A Waveguide Approach for Quantum Dot Sources of Multi-Photon Entanglement

Deterministic sources of multi-photon entanglement are highly attractive for quantum information processing but are challenging to realize experimentally. In this paper, we demonstrate a route towards a scaleable source of time-bin encoded Greenberger-Horne-Zeilinger and linear cluster states from a solid-state quantum dot embedded in a nanophotonic crystal waveguide. By utilizing a self-stabilizing double-pass interferometer, we measure a spin-photon Bell state with $(67.8\pm0.4)\%$ fidelity and devise steps for significant further improvements. By employing strict resonant excitation, we demonstrate a photon indistinguishability of $(95.7\pm0.8)\%$, which is conducive to fusion of multiple cluster states for scaling up the technology and producing more general graph states.Comment: Manuscript: 7 pages, 3 figures. Supplementary information: 23 pages, 12 figure

Quantum Knots and Monopoles

Bose–Einstein condensation is a quantum statistical phase transition that occurs in a system consisting of bosons when a single-particle quantum state becomes macroscopically occupied. This peculiar state of matter was first predicted in 1925 and finally realized seventy years later in vapours of weakly-interacting alkali-metal atoms. Since then, Bose–Einstein condensates have been one of the most fascinating research fields in modern physics.  The gaseous condensates offer a robust platform to accurately study interacting many-particle systems from the first principles. Experimentally, the possibility to precisely control a condensate with external fields and directly image its order parameter provides unforeseen opportunities to obtain deep insight into phenomena across different subfields of physics. In particular, gaseous condensates can emulate complicated models that arise in atomic, condensed-matter, and even particle physics, allowing realizations of exotic phenomena that are elusive in their original contexts. An outstanding example is the existence of various topological defects in ultacold quantum gases with internal degrees of freedom.  In this thesis, we investigate the creation, stability, and dynamical properties of various topological defects in spinor Bose–Einstein condensates. The majority of the theoretical results is obtained by numerically solving the dynamics using Gross–Pitaevskii equations for spin-1 condensates. Many theoretical predictions are confirmed by the very good agreement with experiments.  The first experimental observations of a topological point defect in an order parameter describing the quantum gas are presented. Such a point defect is reminiscent to the magnetic monopole particle appearing in grand unified theories. Therefore, the discovery of monopoles in quantum gases further encourages the quest for finding magnetic monopoles in natural electromagnetic fields, a search largely initiated by Paul Dirac almost a century ago.  Subsequently, the fine structure and decay dynamics of the point defect are studied numerically and verified in experiments. The created monopole is gradually destroyed during the polar-to-ferromagnetic quantum phase transition, which results in the spontaneous emergence of a Dirac monopole in synthetic magnetic field. In addition to the singular point defect, the first experimental realization of a knot soliton in the context of quantum field is reported. This thesis lays the foundation for studies of the dynamics and stability of three-dimensional topological structures in quantum systems

Fidelity of time-bin entangled multi-photon states from a quantum emitter

We devise a mathematical framework for assessing the fidelity of multi-photon entangled states generated by a single solid-state quantum emitter, such as a quantum dot or a nitrogen-vacancy center. Within this formalism, we theoretically study the role of imperfections present in real systems on the generation of time-bin encoded Greenberger-Horne-Zeilinger and one-dimensional cluster states. We consider both fundamental limitations, such as the effect of phonon-induced dephasing, interaction with the nuclear spin bath, and second-order emissions, as well as technological imperfections, such as branching effects, non-perfect filtering, and photon losses. In a companion paper, we consider a particular physical implementation based on a quantum dot emitter embedded in a photonic crystal waveguide and apply our theoretical formalism to assess the fidelities achievable with current technologies

Evolution of an isolated monopole in a spin-1 Bose-Einstein condensate

We simulate the decay dynamics of an isolated monopole defect in the nematic vector of a spin-1 Bose-Einstein condensate during the polar-to-ferromagnetic phase transition of the system. Importantly, the decay of the monopole occurs in the absence of external magnetic fields and is driven principally by the dynamical instability due to the ferromagnetic spin-exchange interactions. An initial isolated monopole is observed to relax into a polar-core spin vortex, thus demonstrating the spontaneous transformation of a point defect of the polar order parameter manifold to a line defect of the ferromagnetic manifold. We also investigate the dynamics of an isolated monopole pierced by a quantum vortex line with winding number κ. It is shown to decay into a coreless Anderson-Toulouse vortex if κ=1 and into a singular vortex with an empty core if κ=2. In both cases, the resulting vortex is also encircled by a polar-core vortex ring.Peer reviewe

Synthetic electromagnetic knot in a three-dimensional skyrmion

Classical electromagnetism and quantum mechanics are both central to the modern understanding of the physical world and its ongoing technological development. Quantum simulations of electromagnetic forces have the potential to provide information about materials and systems that do not have conveniently solvable theoretical descriptions, such as those related to quantum Hall physics, or that have not been physically observed, such as magnetic monopoles. However, quantum simulations that simultaneously implement all of the principal features of classical electromagnetism have thus far proved elusive. We experimentally realize a simulation in which a charged quantum particle interacts with the knotted electromagnetic fields peculiar to a topological model of ball lightning. These phenomena are induced by precise spatiotemporal control of the spin field of an atomic Bose-Einstein condensate, simultaneously creating a Shankar skyrmion—a topological excitation that was theoretically predicted four decades ago but never before observed experimentally. Our results reveal the versatile capabilities of synthetic electromagnetism and provide the first experimental images of topological three-dimensional skyrmions in a quantum system.peerReviewe