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The open-source code FESTIM (Finite Element Simulation of Tritium In Materials) is a powerful user-friendly software for hydrogen transport simulations. Up to now, it was capable of addressing various hydrogen transport problems with surface processes dependent on the concentration of solute species. However, the kinetics of surface hydrogen concentration should be considered under certain conditions. The recent 1.3 release of FESTIM introduced a new kinetic surface model, implemented in a flexible way for various applications. The correctness of the implementation is first proven using the method of manufactured solutions. Then, reliability of the model is demonstrated by reproducing four experimental cases on dynamics of hydrogen isotope retention in different materials. An additional cross-code comparison with two other simulation packages, MHIMS and TESSIM-X, shows an excellent agreement and strengthens the validity of the model., Comment: 13 pages, 9 figures

We study the case where phase modulation of the harmonic signal is used to obtain the error signal for the frequency stabilization to a reference atomic transition. High-frequency modulation, or analog of the Pound-Drever-Hall regime, is considered. We demonstrate that for coherent population trapping, the maximal error-signal slope retains at a certain level with growth in the modulation frequency, while for other types of resonances it drops steadily. The investigation of the low-frequency modulation regime reveals the stationarity effect. We show that in this case, the maximal steepness of the error signal does not depend on the modulation frequency and is reached at a fixed value of the frequency deviation.

Emergent strongly-correlated electronic phenomena in atomically-thin transition metal dichalcogenides are an exciting frontier in condensed matter physics, with examples ranging from bilayer superconductivity~\cite{zhao2023evidence} and electronic Wigner crystals~\cite{smolenski2021signatures,zhou2021bilayer} to the ongoing quest for exciton condensation~\cite{wang2019evidence,ma2021strongly,shi2022bilayer}. Here, we experimentally investigate the properties of indirect excitons in naturally-grown MoS$_2$-homobilayer, integrated in a dual-gate device structure allowing independent control of the electron density and out-of-plane electric field. Under conditions when electron tunneling between the layers is negligible~\cite{pisoni2019absence}, upon electron doping the sample, we observe that the two excitons with opposing dipoles hybridize, displaying unusual behavior distinct from both conventional level crossing and anti-crossing. We show that these observations can be explained by static random coupling between the excitons, which increases with electron density and decreases with temperature. We argue that this phenomenon is indicative of a spatially fluctuating order parameter in the form of interlayer electron coherence, a theoretically predicted many-body state~\cite{zheng1997exchange} that has yet to be unambiguously established experimentally outside of the quantum Hall regime~\cite{sarma2008perspectives,spielman2000resonantly,kellogg2004vanishing,kellogg2002observation,spielman2001observation,fertig1989energy,shi2022bilayer}. Implications of our findings for future experiments and quantum optics applications are discussed.

Excitons in transition metal dichalcogenides (TMDs) have emerged as a promising platform for novel applications ranging from optoelectronic devices to quantum optics and solid state quantum simulators. While much progress has been made towards characterizing and controlling excitons in TMDs, manipulating their properties during the course of their lifetime - a key requirement for many optoelectronic device and information processing modalities - remains an outstanding challenge. Here we combine long-lived interlayer excitons in angle-aligned MoSe$_2$/WSe$_2$ heterostructures with fast electrical control to realize dynamical control schemes, in which exciton properties are not predetermined at the time of excitation but can be dynamically manipulated during their lifetime. Leveraging the out-of-plane exciton dipole moment, we use electric fields to demonstrate dynamical control over the exciton emission wavelength. Moreover, employing a patterned gate geometry, we demonstrate rapid local sample doping and toggling of the radiative decay rate through exciton-charge interactions during the exciton lifetime. Spatially mapping the exciton response reveals charge redistribution, offering a novel probe of electronic transport in twisted TMD heterostructures. Our results establish the feasibility of dynamical exciton control schemes, unlocking new directions for exciton-based information processing and optoelectronic devices, and the realization of excitonic phenomena in TMDs., Comment: 37 pages, 4 figures in main text, 6 figures in supplemental materials; (v2) corrected funding acknowledgements

The phase diagram of an interacting two-dimensional electron system in a high magnetic field is enriched by the varying form of the effective Coulomb interaction, which depends strongly on the Landau level index. While the fractional quantum Hall states that dominate in the lower energy Landau levels have been explored experimentally in a variety of two-dimensional systems, much less work has been done to explore electron solids owing to their subtle transport signatures and extreme sensitivity to disorder. Here we use chemical potential measurements to map the phase diagram of electron solid states in $N=2$, $N=3$, and $N=4$ Landau levels in monolayer graphene. Direct comparison between our data and theoretical calculations reveals a cascade of density-tuned phase transitions between electron bubble phases up to two, three or four electrons per bubble in the N=2, 3 and 4 Landau levels respectively. Finite temperature measurements are consistent with melting of the solids for T$\approx$1K., Comment: 5 pages, 4 figures in main text, 7 pages, 3 figures in supplementary material

We propose to use local electromagnetic noise spectroscopy as a versatile and noninvasive tool to study Wigner crystal phases of strongly-interacting two-dimensional electronic systems. In-plane imaging of the local noise is predicted to enable single-site resolution of the electron crystal when the sample-probe distance is less than the inter-electron separation. At larger sample-probe distances, noise spectroscopy encodes information about the low-energy Wigner crystal phonons, including the dispersion of the transverse shear mode, the pinning resonance due to disorder, and optical modes emerging, for instance, in bilayer crystals. We discuss the potential utility of local noise probes in analyzing the rich set of phenomena expected to occur in the vicinity of the melting transition.

We investigate the effect of buffer gases on the coherent population trapping resonance induced by a $\sigma$-polarized optical field in $^{87}$Rb atoms. Our experimental results show that inert gases, which depolarize the excited state of the alkali-metal atoms, provide higher contrast than nitrogen that effectively quenches their fluorescence. We also demonstrate that elimination of the spontaneous radiation does not significantly decrease the width at moderate temperatures of an atomic medium. Therefore, a mixture of inert gases can be preferable over a mixture with nitrogen for atomic clocks.

The development of two-dimensional materials has resulted in a diverse range of novel, high-quality compounds with increasing complexity. A key requirement for a comprehensive quantitative theory is the accurate determination of these materials' band structure parameters. However, this task is challenging due to the intricate band structures and the indirect nature of experimental probes. In this work, we introduce a general framework to derive band structure parameters from experimental data using deep neural networks. We applied our method to the penetration field capacitance measurement of trilayer graphene, an effective probe of its density of states. First, we demonstrate that a trained deep network gives accurate predictions for the penetration field capacitance as a function of tight-binding parameters. Next, we use the fast and accurate predictions from the trained network to automatically determine tight-binding parameters directly from experimental data, with extracted parameters being in a good agreement with values in the literature. We conclude by discussing potential applications of our method to other materials and experimental techniques beyond penetration field capacitance., Comment: (v2): 12 pages, 6 figures, close to published version; (v1): 11 pages, 4 figures

Techniques to mold the flow of light on subwavelength scales enable fundamentally new optical systems and device applications. The realization of programmable, active optical systems with fast, tunable components is among the outstanding challenges in the field. Here, we experimentally demonstrate a few-pixel beam steering device based on electrostatic gate control of excitons in an atomically thin semiconductor with strong light-matter interactions. By combining the high reflectivity of a MoSe2 monolayer with a graphene split-gate geometry, we shape the wavefront phase profile to achieve continuously tunable beam deflection with a range of 10$^\circ$, two-dimensional beam steering, and switching times down to 1.6 nanoseconds. Our approach opens the door for a new class of atomically thin optical systems, such as rapidly switchable beam arrays and quantum metasurfaces operating at their fundamental thickness limit.

This work demonstrates the effectiveness of the high-pressure method for the production of graphite and diamond with a high degree of boron doping using adamantanecarborane mixture as a precursor. At 8 GPa and $1700 ^{o}C$, graphite is obtained from adamantane $C_{10}H_{16}$, whereas microcrystals of boron-doped diamond (2{\div}2.5 at.% of boron) are synthesized from a mixture of adamantane and ortho-carborane $C_{2}B_{10}H_{12}$ (atomic ratio B:C = 5:95). This result shows convincingly the catalytical activity of boron in the synthesis of diamond under high pressure. At pressures lower than 7 GPa, only graphite is synthesized from the adamantane and carborane mixture. Graphitization starts at quite low temperatures (below $1400 ^{o}C$) and an increase in temperature simultaneously increases boron content and the quality of the graphite crystal lattice. Thorough study of the material structure allows us to assume that the substitutional boron atoms are distributed periodically and equidistantly from each other in the graphite layers at high boron concentrations (>1 at.%). The theoretical arguments and model ab initio calculations confirm this assumption and explain the experimentally observed boron concentrations.

We propose nanoscale magnetometry via isolated single-spin qubits as a probe of superconductivity in two-dimensional materials. We characterize the magnetic field noise at the qubit location, arising from current and spin fluctuations in the sample and leading to measurable polarization decay of the qubit. We show that the noise due to transverse current fluctuations studied as a function of temperature and sample-probe distance can be used to extract useful information about the transition to a superconducting phase and the pairing symmetry of the superconductor. Surprisingly, at low temperatures, the dominant contribution to the magnetic noise arises from longitudinal current fluctuations and can be used to probe collective modes such as monolayer plasmons and bilayer Josephson plasmons. We also characterize the noise due to spin fluctuations, which allows probing the spin structure of the pairing wave function. Our results provide a non-invasive route to probe the rich physics of two-dimensional superconductors., Comment: 15 + 14 pages, 7 figures; (v2) Minor edits

A single-spin qubit placed near the surface of a conductor acquires an additional contribution to its $1/T_1$ relaxation rate due to magnetic noise created by electric current fluctuations in the material. We analyze this technique as a wireless probe of superconductivity in atomically thin two dimensional materials. At temperatures $T \lesssim T_c$, the dominant contribution to the qubit relaxation rate is due to transverse electric current fluctuations arising from quasiparticle excitations. We demonstrate that this method enables detection of metal-to-superconductor transitions, as well as investigation of the symmetry of the superconducting gap function, through the noise scaling with temperature. We show that scaling of the noise with sample-probe distance provides a window into the non-local quasi-static conductivity of superconductors, both clean and disordered. At low temperatures the quasiparticle fluctuations get suppressed, yet the noise can be substantial due to resonant contributions from collective longitudinal modes, such as plasmons in monolayers and Josephson plasmons in bilayers. Potential experimental implications are discussed., Comment: 5 + 2 pages, 3 figures; (v2) minor edits

We have found that the error-signal frequency corresponding to the coherent population trapping resonance can be displaced from that of "$0-0$" transition unperturbed by the optical field, although the frequency is not sensitive to changes in its intensity. We consider the double $\Lambda$-system of levels interacting with the asymmetric polychromatic optical field to demonstrate that this effect arises due to intensity nonlinearity of the error-signal frequency shift. The experiment with $^{87}$Rb atoms in Ar-N$_2$ buffer gas atomic cell shows how the displacement value depends on different parameters. The possible influence of the effect on the clocks' frequency stability and reproducibility are discussed.

We have grown and characterized three samples of Co doped MnSi and studied their physical properties (magnetization and magnetic susceptibility, heat capacity and electrical resistance). All three samples show non-Fermi liquid physical properties. From literature data and current results follow that impurities (Co and Fe) eliminate the first order phase transition peaks and spread the fluctuation maxima in such a way that its low temperature part effectively reaches the zero temperature, where the fluctuations inevitably become quantum. The behavior of low temperature branches of the heat capacity of the samples suggests that a gradual transition from classical to quantum fluctuations can be described by a simple power function of temperature with the exponent less than one. The $d\rho/dT$ data generally support this suggestion. The values of the heat capacity exponents immediately lead to the diverging ratio $C_p/T$ and hence to the diverging effective electron mass. We found out that at large concentration of the dopant there are no distinct phase transition points. What we observe is a cloud of the helical fluctuations spreading over a significant range of concentrations and temperatures, which become quantum close to 0~K., Comment: 5 hages, 12 figures

We describe an experimental technique to measure the chemical potential, $\mu$, in atomically thin layered materials with high sensitivity and in the static limit. We apply the technique to a high quality graphene monolayer to map out the evolution of $\mu$ with carrier density throughout the N=0 and N=1 Landau levels at high magnetic field. By integrating $\mu$ over filling factor, $\nu$, we obtain the ground state energy per particle, which can be directly compared with numerical calculations. In the N=0 Landau level, our data show exceptional agreement with numerical calculations over the whole Landau level without adjustable parameters, as long as the screening of the Coulomb interaction by the filled Landau levels is accounted for. In the N=1 Landau level, comparison between experimental and numerical data reveals the importance of valley anisotropic interactions and the presence of valley-textured electron solids near odd filling., Comment: 14 pages, 11 figures

We report on the first study of the noncentrosymmetric ternary carbide YbCoC$_{2}$. Our magnetization, specific heat, resistivity and neutron diffraction measurements consistently show that the system behaves as a heavy-fermion compound, displaying an amplitude-modulated magnetic structure below the N\'eel temperature reaching $T_{N}$ = 33 K under pressure. Such a large value, being the highest among the Yb-based systems, is explained in the light of our ab initio calculations, which show that the 4f electronic states of Yb have a dual nature -- i.e., due to their strong hybridization with the 3d states of Co, 4f states expose both localized and itinerant properties., Comment: 25 pages, 8 figures, includes supplement

A method of dynamic continuous-wave spectroscopy of coherent population trapping (CPT) resonances using phase modulation of the jump type is developed. The time evolution of the spectroscopic signal is investigated. A method for the formation of an error signal for frequency stabilization is proposed. We show that our approach has a reduced sensitivity to the lineshape asymmetry of the CPT resonance. The experimental results are in good qualitative agreement with theoretical predictions based on a mathematical model of a three-level $\Lambda$ system in a bichromatic field. This method can be used in atomic frequency standards (including chip-scale atomic clocks)., Comment: 10 pages, 15 figures

Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging, since such states are extremely fragile. Using a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states, we demonstrate the deterministic generation of 'Schr\"odinger cat' states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits. Our approach is based on engineering the energy spectrum and using optimal control of the many-body system. We further demonstrate entanglement manipulation by using GHZ states to distribute entanglement to distant sites in the array, establishing important ingredients for quantum information processing and quantum metrology., Comment: 6 pages, 4 figures + Supplementary Materials (8 pages, 9 figures, 1 table)

Photon-mediated interactions between quantum systems are essential for realizing quantum networks and scalable quantum information processing. We demonstrate such interactions between pairs of silicon-vacancy (SiV) color centers strongly coupled to a diamond nanophotonic cavity. When the optical transitions of the two color centers are tuned into resonance, the coupling to the common cavity mode results in a coherent interaction between them, leading to spectrally-resolved superradiant and subradiant states. We use the electronic spin degrees of freedom of the SiV centers to control these optically-mediated interactions. Our experiments pave the way for implementation of cavity-mediated quantum gates between spin qubits and for realization of scalable quantum network nodes., Comment: 8 pages and 4 figures. Supplementary Material, 23 pages and 9 figures, available as an ancillary file

We report on structural, magnetic and transport properties of a new set of the high-pressuresynthesized compounds Mn$_{1-x}$Rh$x$Ge ($0 \leq x \leq 1$) with the chiral magnetic ordering. The magnetic and transport properties depend substantially on the concentration of rhodium (x) and the pressure. The saturation magnetic moment corresponds to a known high-spin value for pristine MnGe (x = 0) and decreases almost linearly with increasing concentration $x$. In addition, XMCD spectra taken at 10 K and 2 T indicate magnetic polarization of the Rh 4d electron states and Ge $4p$ states, which decreases with $x$, too. In rhodium rich compounds ($x \geq 0.5$) the temperature of the magnetic ordering increases significantly with pressure, whereas in manganese rich compounds ($x < 0.5$) the temperature decreases. Three different tendencies are also found for several structural and transport properties. In the intermediate range ($0.3 \leq x \leq 0.7$) samples are semiconducting in the paramagnetic phase, but become metallic in the magnetically ordered state. We carried out ab initio density-functional calculations of Mn$_{1-x}$Rh$_x$Ge at various concentrations $x$ and traced the evolution of electronic and magnetic properties. The calculation results are in good agreement with the measured magnetic moments and qualitatively explain the observed trends in transport properties.

Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities associated with such Rydberg excitations. We report progress towards high-fidelity quantum control of Rydberg atom qubits. Enabled by a reduction in laser phase noise, our approach yields a significant improvement in coherence properties of individual qubits. We further show that this high-fidelity control extends to the multi-particle case by preparing a two-atom entangled state with a fidelity exceeding 0.97(3), and extending its lifetime with a two-atom dynamical decoupling protocol. These advances open up new prospects for scalable quantum simulation and quantum computation with neutral atoms., Comment: 9 pages, 4 figures

We report on quantum capacitance measurements of high quality, graphite- and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned features in the electronic compressibility associated with changes in Fermi surface topology. At high displacement field and low density, strong trigonal warping gives rise to emergent Dirac gullies centered near the corners of the hexagonal Brillouin and related by three fold rotation symmetry. At low magnetic fields of $B=1.25$~T, the gullies manifest as a change in the degeneracy of the Landau levels from two to three. Weak incompressible states are also observed at integer filling within these triplets Landau levels, which a Hartree-Fock analysis indicates are associated with Coulomb-driven nematic phases that spontaneously break rotation symmetry., Comment: Main text: 5 pages, 3 Figures. Supplements: 8 pages, 5 figures

Magnetic fields quench the kinetic energy of two dimensional electrons, confining them to highly degenerate Landau levels. In the absence of disorder, the ground state at partial Landau level filling is determined only by Coulomb interactions, leading to a variety of correlation-driven phenomena. Here, we realize a quantum Hall analog of the Ne\'el-to-valence bond solid transition within the spin- and sublattice- degenerate monolayer graphene zero energy Landau level by experimentally controlling substrate-induced sublattice symmetry breaking. The transition is marked by unusual isospin transitions in odd denominator fractional quantum Hall states for filling factors $\nu$ near charge neutrality, and the unexpected appearance of incompressible even denominator fractional quantum Hall states at $\nu=\pm1/2$ and $\pm1/4$ associated with pairing between composite fermions on different carbon sublattices., Comment: High resolution figures and additional information available at afylab.com

Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on classical approaches. Here we demonstrate a method for creating controlled many-body quantum matter that combines deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. We realize a programmable Ising-type quantum spin model with tunable interactions and system sizes of up to 51 qubits. Within this model, we observe phase transitions into spatially ordered states that break various discrete symmetries, verify the high-fidelity preparation of these states and investigate the dynamics across the phase transition in large arrays of atoms. In particular, we observe robust manybody dynamics corresponding to persistent oscillations of the order after a rapid quantum quench that results from a sudden transition across the phase boundary. Our method provides a way of exploring many-body phenomena on a programmable quantum simulator and could enable realizations of new quantum algorithms., Comment: 17 pages, 13 figures

Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional filling of topologically non-trivial "Chern" bands. Here, we report the observation of gapped states at fractional filling of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene/hexagonal boron nitride heterostructure. We observe new phases at fractional filling of bands with Chern indices $\mathcal{C} = -1, \pm 2,$ and $\pm 3$. Some of these, in $\mathcal{C}=-1$ and $\mathcal{C}=2$ bands, are characterized by fractional Hall conductance---they are `fractional Chern insulators' and constitute a new example of topological order beyond Landau levels., Comment: EMS and AAZ contributed equally to this work. We have corrected a factor of two error in the area of the superlattice unit cell and updated the analysis and calculations accordingly

Nonabelian anyons offer the prospect of storing quantum information in a topological qubit protected from decoherence, with the degree of protection determined by the energy gap separating the topological vacuum from its low lying excitations. Originally proposed to occur in quantum wells in high magnetic fields, experimental systems thought to harbor nonabelian anyons range from p-wave superfluids to superconducting systems with strong spin orbit coupling. However, all of these systems are characterized by small energy gaps, and despite several decades of experimental work, definitive evidence for nonabelian anyons remains elusive. Here, we report the observation of arobust, incompressible even-denominator fractional quantum Hall phase in a new generation of dual-gated, hexagonal boron nitride encapsulated bilayer graphene samples. Numerical simulations suggest that this state is in the Pfaffian phase and hosts nonabelian anyons, and the measured energy gaps are several times larger than those observed in other systems. Moreover, the unique electronic structure of bilayer graphene endows the electron system with two new control parameters. Magnetic field continuously tunes the effective electron interactions, changing the even-denominator gap non-monotonically and consistent with predictions that a transition between the Pfaffian phase and the composite Fermi liquid (CFL) occurs just beyond the experimentally explored magnetic field range. Electric field, meanwhile, tunes crossings between levels from different valleys. By directly measuring the valley polarization, we observe a continuous transition from an incompressible to a compressible phase at half-filling mediated by an unexpected incompressible, yet polarizable, intermediate phase. Valley conservation implies this phase is an electrical insulator with gapless neutral excitations., Comment: Considerably expanded and rewritten. New experimental data from two additional devices, including transport data and thermodynamic gap measurements up to 35T. Theoretical model updated to include screening from filled Landau levels. Experimental and numerical methods section greatly expanded. Paper, including Methods and supplementary data totals 27 pages with 20 figures, 3 tables

We report a high-pressure high-temperature synthesis of several millimeter-sized samples of bulk graphanes with the composition C-H(D) from benzene and graphene-derivative C-H-N$_{0.2}$ from pyridine. X-ray diffraction, transmission electron microscopy, and infrared spectroscopy of new materials reveal relatively large (several nanometers in size) crystalline grains of an sp3-bonded graphane lattice (3-cycle-4-step, the orthorhombic structure with Pbca space group and parameters a = 9.5-9.8, b = 8.9-9.1, c = 17.1-17.3 $\AA$). The main hydrogen groups in samples are C-H groups connected by aliphatic bonds. The synthesized graphanes at atmospheric pressure are stable up to 500 C. The macroscopic density of CH samples is 1.5-1.57 g cm$^{-3} $ and the refractive index is 1.78-1.80. The absorption spectra of samples with a high degree of crystallization exhibits a weak absorption maximum at 2.8 eV, which is responsible for the yellow-orange color, large absorption maximum at 4 eV and an absorption edge associated with the width of the optical gap at 5.2 eV. The bulk modulus (30-37 GPa) and shear modulus (15-18 GPa) of the fabricated samples, as well as their hardness (1-1.5 GPa), are about twice as high as the respective values for polycrystalline graphite. The solution of metalorganic complexes in benzene and pyridine makes it possible to obtain doped graphanes, which can have extraordinary electron transport and magnetic properties.

Strongly interacting two dimensional electron systems (2DESs) host a complex landscape of broken symmetry states. The possible ground states are further expanded by internal degrees of freedom such as spin or valley-isospin. While direct probes of spin in 2DESs were demonstrated two decades ago, the valley quantum number has only been probed indirectly in semiconductor quantum wells, graphene mono- and bilayers, and transition-metal dichalcogenides. Here, we present the first direct experimental measurement of valley polarization in a two dimensional electron system, effected via the direct mapping of the valley quantum number onto the layer polarization in bilayer graphene at high magnetic fields. We find that the layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital polarization. Our data can be fit by a model that captures both single particle and interaction induced orbital, valley, and spin anisotropies, providing the most complete model of this complex system to date. Among the newly discovered phases are theoretically unanticipated orbitally polarized states stabilized by skew interlayer hopping. The resulting roadmap to symmetry breaking in bilayer graphene paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two dimensional materials where layer polarization maps to the valley or spin quantum numbers, providing an essential direct probe that is a prerequisite for manipulating these new quantum degrees of freedom., Comment: This version (v3) updates a large portion of the theoretical treatment in previous versions and consequently has new Figs. 3 and 4 of the main text and a significant overhaul of the Supplementary Material