The second quantum revolution has prompted not only research in quantum science, but also research on how best to teach students who may enter this burgeoning field. Much of this conversation has focused around students’ conceptual learning or skills desired by potential employers, while research on how lab experiments can contribute to undergraduate quantum education has been largely absent. In a recent survey of instructors using lab experiments with single and entangled photons, one of the most important learning goals was to "'see' quantum mechanics in real life." To better understand this goal, we investigate what seeing quantum mechanics means to instructors and why they believe it is an important part of students’ education. We present emergent themes coming from a qualitative coding analysis of 15 instructor interviews, which begin to elucidate the role quantum lab experiments may play in undergraduate education.

What Does it Mean to See Quantum Mechanics?

The von Neumann theory of quantum measurement involves uniquely entangling the eigenstates of a self-adjoint operator with the pointer states of the experimental apparatus. Then, either wavefunction collapse, or decoherence (due to the macroscopic pointer states) fixes the measurement of the apparatus. Unfortunately, most, if not all, quantum experiments don't operate that way. Instead they are counting experiments, where properties are often inferred from the geometrical set-up of the experiment. In this talk, I will focus on how momentum is actually measured, which usually follows a time-of-flight strategy, that infers the momentum by measuring the position. I will provide examples for how this works and explain why we need to teach a proper measurement theory within undergraduate quantum mechanics classes. Only in this fashion, can we properly prepare our students for future careers in the quantum-enabled workforce, particularly in the area of quantum sensing.

Teaching Measurement to Prepare for Quantum Sensing

Jupyter has become a widely used tool in recent years especially for computational physics. Nbgrader is an extension for Jupyter that assists in building, managing, and grading assignments using Jupyter. This talk will discuss specific ways I use nbgrader to improve assignments in computational and theoretical physics.

Improving Assignments using the Nbgrader Extension for Jupyter

I will provide quantitative data on the improvement in student success rates caused by the use of a Student Success Coach at a large two-year college. The College of DuPage (COD) received a five-year grant from the National Science Foundation’s Scholarships in Science, Technology, Engineering and Mathematics (S-STEM) program to provide support to approximately twenty STEM students per year. Selected students received full tuition scholarships, access to summer internships, guided study groups and STEM activities on campus. In addition, a key element of the support is the assignment of a Student Success Coach who provided close, personal attention to these particular students. In what is sometimes referred to as “intrusive advising”, the Success Coach worked to intervene early before small issues become larger ones. COD has completed this first grant and is applying for a second grant to expand the program to part-time students. (NSF DUE Award #1564720)

Using Intrusive Advising to Improve Student Success

This presentation synthesizes several strands of quantitative analysis of the relation of membership in a demographic group underrepresented in physics classes on course outcomes (course grades and Force and Motion Conceptual Evaluation post-test scores) as well as university outcomes (graduation). Differences are explored by gender, underrepresented ethnic or racial minority status, status as a first-generation college student, and rural or urban status. Mediation and moderation analysis show that many differences in course outcomes are largely explained by prior preparation (with some important exceptions), but that the factors influencing differences are not the same for all groups. Survival analysis shows that the patterns of risk of negative college outcomes are not the same for all groups suggesting retention efforts need to be tailored for different demographic groups to maximally retain all students.

The Effect of Prior Preparation on Students Underrepresented in Physics

The quantum dot with electron correlations attached to superconducting leads displays a local quantum phase transition from a spin-singlet (zero phase) to a spin-doublet (pi phase) ground state. We recently showed that one needs to apply an external magnetic field to distinguish the physical properties of the two phases [1]. Most of the properties of the superconducting quantum dot, including the zero-pi transition, can be qualitatively correctly described by a mean-field theory with a two-particle self-consistency [1]. The mean-field description of magnetic fluctuations with static self-energy fails, however, at non-zero temperatures. Linear response theory in the external magnetic field is broken with field-induced poles in the mean-field dynamical transversal susceptibility. Poles in the dynamical susceptibility generate, however, non-analytic singular contributions to the self-energy when going beyond the mean-field approximation. The renormalization of the electron propagators must hence be made dynamical and in the spin-polarized state in order to smooth the singularities in the perturbation expansion and to keep the self-energy and Green functions analytic. The dynamical renormalization due to the electron correlations leads to the broadening of the energies of the in-gap states into bands filling the superconducting gap with increasing temperature even in the limit to zero magnetic field. We demonstrate this behavior on a single impurity Anderson model attached to superconducting leads.

![](https://assets.underline.io/uploads/markdown_image/1/image/61769d37767a655ec56ea1ced4f971aa.jpg)

Thermodynamically induced broadening of the energies of the in-gap states of the superconducting single-impurity Anderson model with the Coulomb repulsion U=Δ, the strength of the hybridization of the dot to the superconducting leads Γ=Δ, and the superconducting gap of the dot (-Δ,Δ) at different temperatures T and zero magnetic field in the energy scale Δ =1.

Failure of the mean-field description of magnetic fluctuations in the superconducting quantum dot

Skyrmions and antiskyrmions are topologically protected spin structures with opposite vorticities. Particularly in coexisting phases, these two types of magnetic quasiparticles may show fascinating physics and potential for spintronic devices. While skyrmions are observed in a wide range of materials until now antiskyrmions were exclusive to materials with D2d symmetry [1]. In our recent work, we have shown first and second-order antiskyrmions stabilized by magnetic dipole-dipole interaction in Fe/Gd-based multilayers [2]. Using Lorentz transmission electron microscopy imaging, we observed coexisting first and second-order antiskyrmions, Bloch skyrmions, and type-2 bubbles (Fig. 1) and determine the range of material properties and magnetic fields where the different spin objects form and dissipate. Phase diagrams of the spin objects were created in dependence on the magnetic out-of-plane field, temperature, saturation magnetization, and uniaxial magnetic anisotropy. We performed micromagnetic simulations to obtain more insight into the studied system and conclude that low values of saturation magnetization and uniaxial magnetic anisotropy lead to the existence of this zoo of different spin objects and that they are primarily stabilized by dipole-dipole interaction. Further, we investigated the nucleation process of antiskyrmions experimentally and theoretically revealing the necessity of a crossing point of three magnetic stripe domains to form an isolated antiskyrmion with an out-of-plane magnetic field. The previous unobserved second-order antiskyrmions and the disclosed coexistence of antiskyrmions and skyrmions potentially reachable for a whole range of different materials provide great potential for further studies on quasi-particle interactions, spin dynamics as well as for possible future applications in spintronics.

![](https://assets.underline.io/uploads/markdown_image/1/image/50c16dd6974021e442524cdd7ed4e0a3.jpg)

Fig. 1. Underfocused LTEM image of [Fe/Ir/Gd]2/[Fe/Gd]76/[Fe/Ir/Gd]2 showing five different coexisting spin objects (a). Bloch skyrmion with counter- (b) and with clockwise rotation (c), type-2 bubble (d), first-order antiskyrmion (e), and second-order antiskyrmion (f). Zoomed-in spin objects (b-f, I) and simulated LTEM contrast (b-f, II) caused by the theoretical spin textures (b-f, III).

Dipolar-Stabilized First and Second-Order Antiskyrmions in Ferrimagnetic Multilayers

Skyrmions are topological spin textures that exhibit particle-like dynamics under current-driven forces such as spin-orbit torques (SOT). In frustrated magnets, competing exchange interactions along with the Dzyaloshinskii-Moriya interaction (DMI) can aid in stabilizing textures of different topologies, like skyrmions and antiskyrmions [1], which exhibit different motion under SOT, such as trochoidal trajectories and skyrmion-antiskyrmion pair generation, in addition to the usual rectilinear motion. Such behavior results from a departure from the frozen-core limit, where additional dynamics in the (anti)skyrmion helicity couples to the core position [2]. Here, we discuss the role of thermally driven helicity dynamics in the Brownian motion of skyrmions under weak DMI and SOT. Depending on the magnitude of the DMI, which governs the strength of the restoring force experienced by the helicity, with respect to kBT, the thermal drift of the skyrmion core under weak SOT can differ greatly from the dynamics at 0 K (Fig. 1). This behavior arises from the thermal drift and diffusion of the helicity under SOT, which is analogous to the well-known problem of Brownian motion in a tilted washboard potential, where the helicity can be assimilated to an oscillator phase in a periodic potential with a linear force term. Under weak SOT or strong DMI, we recover a ''phase-locked'' solution in which the helicity is pinned, resulting in rectlinear drift. For strong SOT or weak DMI, we find a ''free-running'' solution, where the helicity varies continuously in time and results in an amplified Brownian diffusion of the skyrmion core. In between these two regimes, thermally-activated hopping of the helicity between energy minima occurs. These results highlight the importance of helicity dynamics and may have bearing on dipole-stabilized bubbles for which drive-dependent skyrmion Hall angles [3] and low drift velocities have been reported [4].

![](https://assets.underline.io/uploads/markdown_image/1/image/4499995d079e5c36223e0c31052e4788.jpg)


Fig. 1. Comparison between SOT-driven skyrmion motion at 0 K (black line) and 50 different realisations of the Brownian motion at 10 K (colored lines), along with the average thermal drift at 10 K (purple line).

Anomalous thermal drift of skyrmions in frustrated magnets under spin-orbit torques

In order to develop energy efficient race track memory devices, it is crucial to create and controllably move chiral spin textures, namely, skyrmions in magnetic nanotrack. In recent time, intense efforts have been dedicated to understand the mechanism of domain wall pair to skyrmion conversion in different junction geometry that may fit into the memory applications [1,2]. Here, we study the mechanism of DW pair to skyrmion conversion in a typical junction geometry which consists of the combination of two narrow nanotracks (length – 800 nm, thickness – 1 nm, width varying from 20 nm to 60 nm in steps of 20 nm) and a wide track (width 200 nm). The separation between narrow channels are selected as 10 nm, 30 nm and 50 nm. The micromagnetic simulations have been performed using Ubermag to investigate the magnetization dynamics and the Zhang-Li torque evolver is implemented in Landau Lifshitz Gibert equation to drive the DWs using spin polarized current [3]. For a fixed Gilbert damping parameter (α = 0.3) and different values of non-adiabatic spin torque parameter (β = 0.2, 0.3 and 0.5) we investigate the DW to skyrmion conversion in these nanotracks. Interestingly, under the influence of spin torque, the DW pair gets converted to skyrmion only if the geometrical constraints allow the favorable instability to set in at the junction between optimally separated narrow channels and wide channel (cf. Fig. 1(a-d)) [4]. For certain width and separation between the narrow channels, the DW pair to skyrmion conversion cannot be observed for sufficiently large time scale (cf. Fig. 2(a-d)). We believe these results will be helpful in designing the skyrmion based racetrack memory where the controlled creation of skyrmion is expected to play crucial role.

![](https://assets.underline.io/uploads/markdown_image/1/image/af3301ae9ac634fc6c9411eabcfd6b01.jpg)

Fig 1: Snapshot of DW pair to skyrmions conversion from two narrow channels for α = β = 0.3, width of the narrow nanochannel = 60 nm, separation between the narrow channel = 30 nm

![](https://assets.underline.io/uploads/markdown_image/1/image/ed5b1617a9c98ac080b569cc57b93e0f.jpg)

Fig 2: DW dynamics from two channels for α = β = 0.3, width of the narrow nanochannel = 40 nm, separation between the narrow channel = 10 nm


Influence of Geometry on Domain-Wall Pair to Skyrmion Conversion in Typical Magnetic Nanochannel

For their applications in spintronics, skyrmions need to be controlled one by one, and therefore appear as excitations over a uniform ground state. This is why in most demonstrations, the application of an external field is required. In this study, we show by fine-tuning the micromagnetic parameters, through their control by the ferromagnetic layer thickness, multilayers can be optimized to host zero field skyrmion excitations. We study Pt/Co/Au based heterostructures with varying Co thickness t. Close to the spin reorientation transition (t = 1.6 nm), the domain wall energy vanishes and the ground state is a stripe phase. To favor the uniform state, t is reduced to increase the magnetic anisotropy, until samples show a 100% remanence. Below 1.45 nm, skyrmions could be obtained and stabilized during the magnetization reversal process, and remain stable at zero field. This bistable situation offers a perfect playground to study current-induced nucleation in zero field, which we study in the vicinity of a point contact. Starting from a uniform state, current pulses lead to the formation of magnetic textures. However, to avoid the formation of elongated structures, similar to stripes, Co thickness needs to be further reduced. At 1.2 nm, the magnetic anisotropy is sufficiently large to cut elongated structures into well-defined skyrmions, which could be obtained with good reproducibility. Their topological nature is proven through the observation of the skyrmion Hall effect: depending on the orientation of the initial state, skyrmions are deflected in one or the other directions. Velocities of about 50 m/s induced by SOT, using a current density of 3.7 x 1012 A/m2 in 1µm wide tracks were also observed. This opens an important perspective towards skyrmionic devices at zero field, in particular concerning stacks that are not sensitive to external fields such as ferrimagnets and antiferromagnets. Figure: Zero field MFM images of 3 µm wide magnetic nanotracks, after successive application of 3.7 x 1012 A/m2, 3 ns long current pulses starting from a saturated track. In the first serie (a-c) the sample is initially magnetized downward, in the second one (d-f), it is magnetized upward, evidencing the gyrotropic deflection.

![](https://assets.underline.io/uploads/markdown_image/1/image/15d074009eea6ac625bfde657bff2eb1.jpg)

Figure: Zero field MFM images of 3 µm wide magnetic nanotracks, after successive application of 3.7 x 1012 A/m2, 3 ns long current pulses starting from a saturated track. In the first serie (a-c) the sample is initially magnetized downward, in the second one (d-f), it is magnetized upward, evidencing the gyrotropic deflection.

Current induced skyrmion nucleation at zero field

Magnetic skyrmions present interesting and unique pseudo-particle behaviors which arises from their topological protection [1-2]. Key among these behaviors is their resonant dynamics, under microwave fields, which include both breathing and gyration modes. Due to their small size, and magnetic-only contrast of skyrmions, coupled with high frequency dynamics – in the GHz regime – it is challenging to do in-situ measurements on these excitations. This work reports the use of small angle neutron scattering (SANS) to capture the dynamics of hybrid skyrmions stabilized in Fe/Gd multilayers by means of dipolar interactions. Using perpendicular DC fields and in-plane RF fields, we explored the gyration modes of hybrid skyrmions away, below, at, and above resonance [Fig.1(a-d)]. We find the dynamic modes of hybrid skyrmions contribute to the SANS signal in two ways: first, the scattered neutrons incur additional transverse momentum as a result of scattering from a moving source, and second, the gyration skyrmions disrupt ordering of the lattice giving rise to enhancement form-factor scattering. Ferromagnetic resonance measurements confirm the RF and DC field conditions for these gyration modes. Our results offer new insights into the nanoscale dynamics of magnetic skyrmions and present a unique use of SANS to probe magnetization dynamics.

![](https://assets.underline.io/uploads/markdown_image/1/image/a7eefda0d3ae85f8c787ee1cd94ec130.jpg)

Fig.1 2D SANS pattern of magnetic skyrmions under different magnetic fields and excitation frequencies: (a) Static state (H=0, RF=0), (b) below-resonance state (H=150 mT, RF=1.2 GHz), (c) at-resonance state (H=150 mT, RF=1.3 GHz) and (d) above-resonance state (H=150 mT, RF=1.4 GHz). All 2D images are plotted with the same intensity scale.

In-situ GHz Dynamics of Skyrmions Probed with SANS

Skyrmions have clear advantages for future spintronic devices over domain walls in terms of information carrying and storage, however there are still many open questions left and inherent challenges in the transition to applications. Here we study the effect of an additional interfacial spin-transfer torque (ISTT) [1], as well as the well-established spin-orbit torque (SOT), on skyrmion collections [2] – group of skyrmions dense enough that they are not isolated from one another – in magnetic multilayers, by comparing modelling using Boris [3], with experimental results. We show that skyrmion collective motion has additional effects not reproduced when compared to modelled isolated skyrmions [1]. In particular, as the skyrmion collection density increases the effect of local disorder is reduced, leading to reduced threshold current densities, and a sharper dependence of skyrmion Hall Angle (SkHA) on velocity in the depinning regime, in agreement with experimental results. When including both the ISTT and SOT, the small SkHA observed in experiment are in good agreement, also explaining the observed diameter-independent SkHA [4], as seen in Figure 1. Contrary to the model which considers the SOT as the only driving torque, and which predicts a monotonically increasing SkHA with decreasing diameter, inclusion of ISTT results in SkHA closely aligned to experimental results, particularly when the effect of local disorder and skyrmion-skyrmion interactions are taken into account. Our results shed further light on collective current-driven skyrmion motion in magnetic multilayers and highlight the significance of the ISTT in understanding current-driven skyrmion motion in magnetic multilayers.

![](https://assets.underline.io/uploads/markdown_image/1/image/219d9cf02b4f240924efc702e30f317a.jpg)

Figure 1. Collective SkHA dependence on skyrmion diameter for (a) N = 50 Sk/µm2 and (b) N = 100 Sk/µm2. (c) Experimentally obtained SkHA from skyrmion collections with a range of diameters with an average current density of 2×1011 A/m2. The overlaid dashed and solid lines show the ideal isolated skyrmion case – independent of current density – for the SOT and ISTT+SOT, respectively. The solid blue line in panel (b) represents a Savitzky-Golay fit to the simulated skyrmion motion, for a current density of Jc = 2×1011 A/m2.

Underline digital video library

What Does it Mean to See Quantum Mechanics?

Teaching Measurement to Prepare for Quantum Sensing

Improving Assignments using the Nbgrader Extension for Jupyter

Using Intrusive Advising to Improve Student Success

The Effect of Prior Preparation on Students Underrepresented in Physics

Failure of the mean-field description of magnetic fluctuations in the superconducting quantum dot

Dipolar-Stabilized First and Second-Order Antiskyrmions in Ferrimagnetic Multilayers

Anomalous thermal drift of skyrmions in frustrated magnets under spin-orbit torques

Influence of Geometry on Domain-Wall Pair to Skyrmion Conversion in Typical Magnetic Nanochannel

Current induced skyrmion nucleation at zero field

In-situ GHz Dynamics of Skyrmions Probed with SANS

Collective Skyrmion Motion Under the Influence of an Additional Interfacial Spin-Transfer Torque

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