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Electron spins confined to quantum dots are a promising platform for scalable quantum computation. A necessary component of such a quantum processor is a microwave magnetic field (B$_1$) that implements single-qubit gate operations via electron spin resonance. A common method for generating a B$_1$ field is to place a micro-stripline close to the device. A second method is to place a micromagnet near the device and apply local voltage pulses to induce electric dipole spin resonance. Both methods involve elements that are bulky (&gt; 1 µm) compared to the scale of an individual quantum dot (~60 nm), and are placed on the surface of the chip, taking up valuable space and preventing scalable, dense packing of qubits. Furthermore, the B$_1$ produced by both methods is local, limiting single-qubit rotations to only a few quantum dots per micro-stripline or micromagnet.

We have investigated a centimeter-scale bowtie-shaped microwave resonator design that produces a global B$_1$ field with minimal electric field over a relatively large area (~mm$^2$), which could enable single-qubit rotations for thousands of qubits. The design ensures that the magnetic field is maximal near the center of the resonator, whereas the electric field is expelled towards the edges of the resonator. A minimal electric field in the active area is necessary to prevent photon-assisted tunneling of the confined electrons. The resonator can be vertically integrated above the quantum device layer, removing the need for microwave interconnects or bulky components in the device layer. Individual qubits can be tuned in and out of resonance with this global B$_1$ field using the Stark effect, wherein the electronic $g$-factor shifts slightly as a function of applied electric field. Coupling an external microwave source to the resonator is achieved by an excitation stripline on the opposite side of a dielectric substrate. The resonator and stripline dimensions are optimized for operation at ~15 GHz, corresponding to a DC magnetic field of 0.53 T for a $g=2$ electron spin. At this field and a temperature of 100 mK, the spin qubit is initialized by relaxing into its ground state with a probability of 99.9 %. Our experimental implementation of lateral quantum dots in silicon will be discussed, along with progress in testing and integrating the global B$_1$ field resonator.

2021 CAP Virtual Congress

Microwave resonators for global control of electron spins qubits

spin qubits

spintronics

quantum computing

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Electron spins confined to quantum dots are a promising platform for scalable quantum computation. A necessary component of such a quantum processor is a microwave magnetic field (B$_1$) that implements single-qubit gate operations via electron spin resonance. A common method for generating a B$_1$ field is to place a micro-stripline close to the device. A second method is to place a micromagnet near the device and apply local voltage pulses to induce electric dipole spin resonance. Both methods involve elements that are bulky (> 1 µm) compared to the scale of an individual quantum dot (~60 nm), and are placed on the surface of the chip, taking up valuable space and preventing scalable, dense packing of qubits. Furthermore, the B$_1$ produced by both methods is local, limiting single-qubit rotations to only a few quantum dots per micro-stripline or micromagnet.

We have investigated a centimeter-scale bowtie-shaped microwave resonator design that produces a global B$_1$ field with minimal electric field over a relatively large area (~mm$^2$), which could enable single-qubit rotations for thousands of qubits. The design ensures that the magnetic field is maximal near the center of the resonator, whereas the electric field is expelled towards the edges of the resonator. A minimal electric field in the active area is necessary to prevent photon-assisted tunneling of the confined electrons. The resonator can be vertically integrated above the quantum device layer, removing the need for microwave interconnects or bulky components in the device layer. Individual qubits can be tuned in and out of resonance with this global B$_1$ field using the Stark effect, wherein the electronic $g$-factor shifts slightly as a function of applied electric field. Coupling an external microwave source to the resonator is achieved by an excitation stripline on the opposite side of a dielectric substrate. The resonator and stripline dimensions are optimized for operation at ~15 GHz, corresponding to a DC magnetic field of 0.53 T for a $g=2$ electron spin. At this field and a temperature of 100 mK, the spin qubit is initialized by relaxing into its ground state with a probability of 99.9 %. Our experimental implementation of lateral quantum dots in silicon will be discussed, along with progress in testing and integrating the global B$_1$ field resonator.

poster

Autopsy studies indicate that the distribution of axons throughout the brain could differ in brains with and without schizophrenia. MRI has inferred axon diameters and distribution in the brain, typically for axons larger than 5 μm in diameter. The goal of this work is to modify these methods to adapt oscillating gradients (OG) to target small axons (1 to 2 μm range) which constitute the majority of cortical connections and shorten the data acquisition time so that the method can be used to measure axon diameters in *vivo*.
Methods to determine micron-sized axon radii using oscillating gradients were too time-consuming for in *vivo* mouse imaging. The methods use many gradient frequencies, and a geometric model called AxCaliber which uses intracellular and extracellular compartments. Through simulations, we found that fewer gradient frequencies for data provided a good fit to the intracellular model, and in some cases, fewer frequencies led to a better fit to the model than more frequencies. A moderate correlation was found between the predicted axonal radius from the model and the actual axonal radius used in the simulations. In conclusion, reducing the number of gradient frequencies and gradient strengths appears to be possible, in theory, to reduce the imaging time by a factor of 4.16 without a significant change in the precision of the inferred axon radii. The method proposed here requires *a priori* knowledge of the desired cell sizes to be inferred. Imaging data, as well as electron microscopy data, need to be collected after reopening the lab after the pandemic to verify the theoretical predictions. This work is the first step to reducing the imaging time so that OG can be used with the AxCaliber model to infer 1-2 μm axon sizes.
The authors wish to acknowledge funding from Mitacs and NSERC.

Moving toward faster measurements of micron-sized axon diameters in vivo

With advances in nanofabrication, modelling the optical properties of nanoscale systems is critical.

The optical response of nanostructures can be simulated using the bulk permittivity of the constituent materials (1). The permittivity is generally assumed time-invariant and spatially dispersionless. While these approximations are enough for the simulations of most systems, in some cases the physics must be modelled more precisely.

We present three recent projects on the modelling of complex optical properties with implications in active nanophotonics (2), ultrafast physics and nonlinear plasmonics. The algorithms we developed are unavailable in commercial or open-source software.

1.) Nonlocal models: for small nanostructures (< 10 nm) spatial dispersion cannot be neglected, and we need to account for the electron degeneracy pressure (3).

2.) Nonlinear hydrodynamics: The hydrodynamic plasma model is required to properly model conduction electron dynamics in strong optical fields (4).

3.) Time-variant permittivity: Electrodynamics combined with two-temperature modelling is required to calculate the optical response induced by nonlinearity in ITO under strong optical fields (5).

Our models combined with high-performance computing allow us to achieve accurate results and significant agreement to experiments.

References

1. Pernice, W. H. P. Finite-Difference Time-Domain Methods and Material Models for the Simulation of Metallic and Plasmonic Structures. J. Comput. Theor. Nanosci. 7, 1–14 (2010).

2. Shaltout, A. M., Shalaev, V. M. & Brongersma, M. L. Spatiotemporal light control with active metasurfaces. Science 364, eaat3100 (2019).

3. Baxter, J., Lesina, A. C. & Ramunno, L. Parallel FDTD modelling of nonlocality in plasmonics. ArXiv200506997 Phys. (2020).

4. Bin-Alam, M. S. et al. Hyperpolarizability of plasmonic meta-atoms in metasurfaces. ArXiv200705142 Phys. (2020).

5. Alam, M. Z., Schulz, S. A., Upham, J., De Leon, I. & Boyd, R. W. Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material. Nat. Photonics 12, 79–83 (2018)

Advanced modelling in computational nanophotonics

Strong field physics, femtosecond (1 fs = $10^{-15}$), and attosecond (1 as = $10^{-18}$) science require intense ultrashort laser pulses for excitation and measurement. Although fs pulses can be generated directly from a laser amplifier, durations necessary for ultrafast science require spectral broadening and compression. The most common spectral broadening technique exploits the nonlinear interaction of intense pulses focused into gas-filled hollow-core fibres [1]. These fibres allow for a long interaction length to generate octave-spanning spectra while maintaining a near Gaussian spatial distribution. However, these fibres can be 1 – 3 metres on an optical table with additional 1 m focusing and collimating optics, and require continuous backfilled gas flow. More recently, the self-phase modulation in thin crystals broadens the spectrum and uses a self-focusing relay to maintain the beam quality [2]. A combination of solids and gases to generate a supercontinuum has been used to generate attosecond extreme ultraviolet (XUV) pulses [3]. Ultrashort pulses can have a wide variety of applications, including disrupting biological processes for medical procedures, observation of electronic processes on an attosecond scale, and generating XUV and soft X-ray pulses via high harmonic generation or terahertz via difference frequency generation [4]. Here, we compare numerically and experimentally the spectral broadening in solvents and crystals to demonstrate the potential for a compact setup for generating octave spanning pulses for ultrafast experiments. 

We find that passing a beam through several cm of methanol produces a supercontinuum spectrum that can support few-fs pulses. Similar to the multi-plate thin crystal method, we place a series of 1 cm cuvettes of methanol around two foci in order to reduce self-focussing effects and to avoid filamentation within the material. We compress these pulses using dispersion compensating mirrors, and characterize the resulting pulses using frequency resolved optical gating (FROG) and a novel measurement scheme. Our simulations and models predict a sub-10 fs bandwidth-limited pulse resulting from two subsequent compressions using a total of 4 cm of methanol to generate a supercontinuum. Using this method, experimentally, we have achieved a broad spectrum capable of supporting sub-30 fs pulses.


[1] E. Haddad, R. Safaei, A. Leblanc, R. Piccoli, Y.G. Jeong, H. Ibrahim,B.E. Schmidt, R. Morandotti, L. Razzari, F. Légaré, P. Lassonde. "Molecular gases for pulse compression in hollow core fibers," Optics Express (2018).

[2] Y.-C. Cheng, C.-H. Lu, Y.-Y. Lin, and A. H. Kung, "Supercontinuum generation in a multi-plate medium," Optics Express (2016).

[3] T. J. Hammond, S. Monchocé, C. Zhang, G. Vampa, D. Klug, A. Y. Naumov, D. M. Villeneuve, and P. B. Corkum "Integrating solids and gases for attosecond pulse generation," Nature Photonics (2017).

[4] M. Cheng, A. Reynolds, H. Widgren, and M. Khalil, "Generation of tunable octave-spanning mid-infrared pulses by filamentation in gas media," Optics Letters (2012).

Novel Methods for Pulse Compression

From cytoskeleton to centriole, we investigate the photonic inner workings of the living cell. The cytoskeleton provides the structural organization of the cell, as the supporting architecture for all known forms of life. A major structural unit of this architecture is the cellular “microtubule,” a hollow tubular body composed of individual units of the protein “tubulin” organized in an array of spiral-shaped components. Recently, it was proposed that microtubules may exhibit useful photonic properties, as well as a myriad of known structural features. In this work, we explore the role that photonic super-radiance may play in facilitating excitonic transport and communication within the cellular architecture, from the cytoskeleton to the eukaryotic centriole—and beyond.

Photonic Cooperativity and Coherence in Tubulin Architectures

When a chemical bond breaks, all valence electrons in the bond will re-arrange and transfer as the nuclei are separating. The dynamical information of such electronic re-arrangement processes will be encoded in the kinetic energy of the ions if the breaking neutral molecule is ionized, allowing us to follow the entire electronic re-arrangement process by only observing the ions. Here, using Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) and a pump-probe experiment in the bromine molecule. we show how the single ionization reveals the bond breaking while the double ionization measures the separation distance of the neutral dissociating bromine molecule. In addition, we also studied the vibrational wave packet dynamics of bromine single ion, which is pumped by a strong 800nm pulse and probed by another weak 400nm pulse.

Light-induced dissociation dynamics of Br2

The connection between quantum entanglement and classical chaos has puzzled physicists for decades. To understand chaos in the quantum context, it is necessary to explore signatures of chaos in the deep quantum regime, where the quantum-classical correspondence cannot be invoked. A common approach is to study the quantum kicked top, which is a finite-dimensional quantum system that displays chaotic dynamics in the classical limit. Few experimental realizations of the quantum kicked top have been achieved for small number of time steps and low chaoticity parameters. However, the problem of accurate experimental realization of long-term dynamics and large range of chaoticity parameter in the quantum kicked top is still unsolved. In this work we propose and demonstrate an exact simulation of the 2-qubit quantum kicked top on a universal quantum computer. Our proposal allows for arbitrary time steps and chaoticity parameter without compromising experimental fidelity. Using the IBM 5-qubit quantum chip we physically demonstrate the theoretical connection between delocalization and entanglement. We obtain a phase space plot of time-averaged entanglement in the deep quantum regime, which surprisingly reflects the classical phase space structure. Since chaos is known to generate entanglement in the quantum kicked top, our proposed method could be useful in Quantum Information Processing.

Quantum Simulation of the Quantum Kicked Top

Simple Measurement for Field Reconstruction

The temporal resolution of pump-probe experiments is determined by the duration of the excitation and measurement pulses. A major constraint on femtosecond ($1$ fs = $10^{-15}$ s) and attosecond ($1$ as = $10^{-18}$ s) science is how well we can control and compress these pulses. However, such ultrashort pulses require a broad spectrum with careful phase control across its bandwidth to minimize the duration. The temporal characterization of these pulses is crucial in establishing ultrafast experiments. For this reason, several pulse characterizing techniques have been developed, each with their own strengths and weaknesses [1].

In this paper, we discuss a new optical measurement technique that can directly measure the electric field that constitutes the laser pulse. We find that compared to other techniques for electric field measurements, our method is relatively inexpensive and robust in characterizing pulses up to 100 fs in duration. This method requires only a commercially available CCD camera as opposed to spectrometers or other expensive instruments and provides the ability to reconstruct the field without ambiguities [2]. In this way, we can directly measure the temporal evolution of the field amplitude and phase [3]. We find that the measurement is in good agreement with established characterization techniques.

References

[1] J. C. Diels and W. Rudolph. Ultrashort Laser Pulse Phenomena, chapter Diagnostic Techniques,pages 452–466. Elsevier, 2006.

[2] T. J. Hammond, A. Korobenko, Y. Naumov, M. Villeneuve, P. B. Corkum and D. H. Ko. Near-field imaging for single-shot wave form measurements.Journal of Physics, 51, February 2018

[3] E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. West-erwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher and F. Krausz. Direct measurement of light waves.Science, 305(5688):1267–1269, August 2004.

Simple Measurement for Field Reconstruction

Trapped ions can offer a functional platform for quantum simulation of many-body Hamiltonians modeled by spin-systems. Programmable, arbitrary and precise control over each ion is required in order to tune ion-ion interactions, which translate to diverse parameters of the system under study. Current technologies suffer from scalability issues to large ion chains, and from ``cross-talk'' due to micron-level inter-ion separation. Here, we report our development of a holographic optical ion-addressing setup for Yb$^+$ ions ($\lambda = 369.5$ nm) using a Digital Micromirror Device (DMD). This technique uses a reprogrammable hologram to modulate the wavefront of the addressing beam and thus engineer the amplitude and phase profile of light across the ion ensemble to better than $\lambda/20$. We implement a novel Iterative Fourier Transform Algorithm (IFTA) to compute the desired hologram. This algorithm efficiently compensates for optical aberrations and produces $<10^{-4}$ intensity cross-talk error in arbitrary pair-wise addressing profiles, suitable for over fifty ions. This scheme relies on standard commercial hardware, can be readily extended to over a hundred ions, and adapted to other ion-species and quantum platforms. Such high-precision optical control will enable the simulation of arbitrary and dynamic lattice geometries of spins to be realized in a 1D chain of ions. This technique will also allow us to investigate problems in quantum quench, quantum phase transitions, and physics of higher dimensional systems such as the creation of topological states. 

We acknowledge financial support from University of Waterloo, US ARO, NSERC Discovery and NFRF grants, TQT (CFREF), and the Ontario Government.

Holographic optical manipulation of trapped ions for quantum simulation

In the past few decades, scientists discovered that TiO2 was capable of purifying polluted water without any addition of strong oxidants. Active hydroxyl radicals can be produced through photodegradation process when TiO2 is illuminated under water, and such process is viewed as a favorable method for on-site decomposition of organic compounds. However, the main drawback of this process suffers from the range of wavelength TiO2 can absorb, which lies in Ultraviolet region. In previous studies, Fe (III) doping was used to broaden the band gap of titania and allow the material of absorb into the visible region. Yet, in our own work, the doping of TiO2 with iron does not provide the expected improvement during methylene blue photodegradation under simulated sun light illumination.

In this study, we characterized pure and Fe(III) doped TiO2 nanopowders using SEM, EDS, XRD, valence band XPS and UPS, to learn about the phase, particle size, chemical composition, and more importantly the influence of Fe (III) dopants on the valence band structure of TiO2 nanoparticles synthesized through Sol-Gel method. The relationship between the valence band structure and the material’s photocatalytic properties will be discussed.

Electronic properties of pure and iron(III) doped TiO2 nanomaterials

Hydrogen terminated silicon has seen a recent resurgence in popularity due to several works demonstrating its use for ultra-dense memory, atomic electronics, and quantum devices. On this surface, individual hydrogen atoms can be removed with atomic precision through STM pulses, leaving a dangling bond (DB) behind. DBs are quantum dot-like entities that can hold either 0, 1, or 2 electrons, with their discrete energy levels in the bandgap. We are studying DBs to achieve true random number generators (RNG) on the atomic scale. Two DBs patterned in close proximity to each other on a highly n-doped crystal host a net extra electron, which can quantum mechanically tunnel to reside on either side. Through measurement of the extra electrons’ spatial location in the pair, it is expected that the electron will be found on either side with equal probability in the absence of any biasing effects. This opens the possibility of using the system as a true RNG, where the bits are generated by probing the electrons’ spatial location. Quantum processes are most desired for RNG because the randomness can be such that no common naturally occurring or imposed noise will alter the number generation. We study these DB pairs by DFT methods to establish the effect of geometry, external fields, and nearby dopants on charge localization and consequent RNG bit generation.
![Image abstract.][1]


[1]: https://i.ibb.co/jhvjz07/Image-Abstract.png

Microwave resonators for global control of electron spins qubits

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