A rotating tokamak plasma can interact resonantly with the external helical magnetic perturbations, also known as error fields. This can lead to locking and then to disruptions. We leverage machine learning (ML) methods to predict the locking events. We use a coupled third-order nonlinear ordinary differential equation model to represent the interaction of the magnetic perturbation and the plasma rotation with the error field. This model is sufficient to describe qualitatively the locking and unlocking bifurcations. We explore using ML algorithms with the simulation data and experimental data, focusing on the methods that can be used with sparse datasets. These methods lead to the possibility of the avoidance of locking in real-time operations. We describe the operational space in terms of two control parameters: the magnitude of the error field and the rotation frequency associated with the momentum source that maintains the plasma rotation. The outcomes are quantified by order parameters that completely characterize the state, whether locked or unlocked. We use unsupervised ML methods to classify locked/unlocked states and note the usefulness of a certain normalization of the order parameters. Three supervised ML classifiers are used in suite to estimate the probability of locking in the region of control parameter space with hysteresis, i.e., the set of control parameters for which both locked and unlocked states can exist. The results show that a neural network gives the best estimate of the locking probability. An analogy of the present locking model with the van der Waals equation of state is also provided.

We derive general conditions for the emergence of singlet Feshbach molecules in the presence of artificial Zeeman fields for arbritary mixtures of Rashba and Dresselhaus spin-orbit orbit coupling in two or three dimensions. We focus on the formation of two-particle bound states resulting from interactions between ultra-cold spin-1/2 fermions, under the assumption that interactions are shortranged and occur only in the s-wave channel. In this case, we calculate explicitly binding energies of Feshbach molecules and analyze their dependence on spin-orbit couplings, Zeeman fields, interactions and center of mass momentum, paying particular attention to the experimentally relevant case of spin-orbit couplings with equal Rashba and Dresselhaus (ERD) amplitudes. The effects of spin-orbit interactions is ubiquitous in nature, from the macroscopic scale of the Earth-Moon complex in astronomy and astrophysics, to the microscopic scale of the electron in the hydrogen atom in atomic physics. The interest in spin-orbit coupled systems has been revived in condensed matter physics due the emergence of non-trivial topological properties of insulators and superconductors subject to Rashba spinorbit fields [1,2], and in atomic physics due to the creation of artificial spin-orbit coupling in ultra-cold atoms [3], which made possible the study of special quantum phase transitions in bosonic systems.This new tool in the toolbox of atomic physics was experimentally developed first to study interacting bosonic atoms where an equal Rashba-Dresselhaus (ERD) artificial spin-orbit coupling was created [3]. It was suggested that interacting fermions could be studied using the same technique [3,4]. Estimulated by the dense literature of the effects of Rashba spin-orbit coupling (SOC) encountered in condensed matter physics [1,2], several theoretical groups investigated the effects of Rashba SOC for interacting ultra-cold fermions using mean field theories [5][6][7][8] or for interacting bosons [9,10]. Unfortunately, the experimental study of Rashba SOC requires more lasers and further developments are necessary to overcome several difficulties [11]. Thus, presently, artificial Rashba SOC has not yet been created in the context of ultra-cold atoms. However, simultaneous theoretical studies of superfluidity for the experimentally relevant ERD spin-orbit coupling were performed for ultra-cold bosons by others [12,13] and for ultra-cold fermions by our group [14][15][16].One of the benchmarks of experimental studies of Fermi superfluidity of cold atoms without artificial spinorbit coupling was the emergence of molecular bound states via the use of Feshbach resonances [17], which lead to the formation of molecules [18] To address the important issue of the emergence of Feshbach molecules for interacting fermions in the presence of artificial SOC and Zeeman fields, we start from the Hamiltonian for two non-interacting fermionswritten as the sum of two contributions, which have the generic form (withh = 1)The term containing h R = v R k x e y −k ...

We discuss the implementation of quantum algorithms for lattice Φ 4 theory on circuit quantum electrodynamics (cQED) system. The field is represented on qudits in a discretized field amplitude basis. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates. Considering the set of universal gates formed by the single-qudit phase gate and the displacement gate, we address initial state preparation and single-qudit gate synthesis with variational methods.

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We describe how color superfluidity is modified in the presence of color-flip and color-orbit fields in the context of ultra-cold atoms, and discuss connections between this problem and that of color superconductivity in quantum chromodynamics. We study the case of s-wave contact interactions between different colors, and we identify several superfluid phases, with five being nodal and one being fully gapped. When our system is described in a mixed color basis, the superfluid order parameter tensor is characterized by six independent components with explicit momentum dependence induced by color-orbit coupling. The nodal superfluid phases are topological in nature, and the low temperature phase diagram of color-flip field versus interaction parameter exhibits a pentacritical point, where all five nodal color superfluid phases converge. These results are in sharp contrast to the case of zero color-flip and color-orbit fields, where the system has perfect U(3) symmetry and possesses a superfluid phase that is characterized by fully gapped quasiparticle excitations with a single complex order parameter with no momentum dependence and by inert unpaired fermions representing a non-superfluid component. In the latter case, just a crossover between a Bardeen-Cooper-Schrieffer and a Bose-Einstein-Condensation superfluid occurs. Furthermore, we analyse the order parameter tensor in a total pseudo-spin basis, investigate its momentum dependence in the singlet, triplet and quintet sectors, and compare the results with the simpler case of spin-1/2 fermions in the presence of spin-flip and spin-orbit fields, where only singlet and triplet channels arise. Finally, we analyse in detail spectroscopic properties of color superfluids in the presence of color-flip and color-orbit fields, such as the quasiparticle excitation spectrum, momentum distribution, and density of states to help characterize all the encountered topological quantum phases, which can be realized in fermionic isotopes of Lithium, Potassium and Ytterbium atoms with three internal states trapped.

We also introduce the scaled condensate wave function for the solution of the GPE: Φ(r, t) = L −3/2 0

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