arXiv subjects

Florian Marquardt

Publications and source records attributed to Florian Marquardt.

At least 73 records · Page 4Linked to original sources

arXiv2021

Observing polarization patterns in the collective motion of nanomechanical arrays

In recent years, nanomechanics has evolved into a mature field, with wide-ranging impact from sensing applications to fundamental physics, and it has now reached a stage which enables the fabrication and study of ever more elaborate devices. This has led to the emergence of arrays of coupled nanomechanical resonators as a promising field of research, serving as model systems to study collective dynamical phenomena such as synchronization or topological transport. From a general point of view, the arrays investigated so far represent scalar fields on a lattice. Moving to a scenario where these could be extended to vector fields would unlock a whole host of conceptually interesting additional phenomena, including the physics of polarization patterns in wave fields and their associated topology. Here we introduce a new platform, a two-dimensional array of coupled nanomechanical pillar resonators, whose orthogonal vibration directions encode a mechanical polarization degree of freedom. We demonstrate direct optical imaging of the collective dynamics, enabling us to analyze the emerging polarization patterns and follow their evolution with drive frequency.

physics.app-ph↗

arXiv2021

Optical signatures of the coupled spin-mechanics of a levitated magnetic microparticle

We propose a platform that combines the fields of cavity optomagnonics and levitated optomechanics in order to control and probe the coupled spin-mechanics of magnetic dielectric particles. We theoretically study the dynamics of a levitated Faraday-active dielectric microsphere serving as an optomagnonic cavity, placed in an external magnetic field and driven by an external laser. We find that the optically driven magnetization dynamics induces angular oscillations of the particle with low associated damping. Further, we show that the magnetization and angular motion dynamics can be probed via the power spectrum of the outgoing light. Namely, the characteristic frequencies attributed to the angular oscillations and the spin dynamics are imprinted in the light spectrum by two main resonance peaks. Additionally, we demonstrate that a ferromagnetic resonance setup with an oscillatory perpendicular magnetic field can enhance the resonance peak corresponding to the spin oscillations and induce fast rotations of the particle around its anisotropy axis.

cond-mat.mes-hall↗

arXiv2021

Tunneling in the Brillouin Zone: Theory of Backscattering in Valley Hall Edge Channels

A large set of recent experiments has been exploring topological transport in bosonic systems, e.g. of photons or phonons. In the vast majority, time-reversal symmetry is preserved, and band structures are engineered by a suitable choice of geometry, to produce topologically nontrivial bandgaps in the vicinity of high-symmetry points. However, this leaves open the possibility of large-quasimomentum backscattering, destroying the topological protection. Up to now, it has been unclear what precisely are the conditions where this effect can be sufficiently suppressed. In the present work, we introduce a comprehensive semiclassical theory of tunneling transitions in momentum space, describing backscattering for one of the most important system classes, based on the valley Hall effect. We predict that even for a smooth domain wall effective scattering centres develop at locations determined by both the local slope of the wall and the energy. Moreover, our theory provides a quantitative analysis of the exponential suppression of the overall reflection amplitude with increasing domain wall smoothness.

cond-mat.mes-hall↗

arXiv2021

Machine Learning and Quantum Devices

These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation, image classification, convolutional networks and autoencoders. The second part is about advanced techniques like reinforcement learning (for discovering control strategies), recurrent neural networks (for analyzing time traces), and Boltzmann machines (for learning probability distributions). In the third lecture, we discuss first recent applications to quantum physics, with an emphasis on quantum information processing machines. Finally, the fourth lecture is devoted to the promise of using quantum effects to accelerate machine learning.

quant-ph↗

arXiv2021

Rapid Exploration of Topological Band Structures using Deep Learning

The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However, what is missing currently are efficient ways to rapidly explore and optimize band structures and to classify their topological characteristics, for arbitrary unit cell geometries. In this work, we show how deep learning can address this challenge. We introduce an approach where a neural network first maps the geometry to a tight-binding model. This allows us to exploit any underlying space group and predict the symmetries of Bloch waves. We demonstrate how that helps to rapidly categorize a large set of geometries in terms of their band representations, identifying designs for fragile topologies. Engineering of domain walls and optimization are also accelerated by orders of magnitude. The approach is general enough to permit future applications to the geometry discovery in other classes of materials (e.g. active and nonlinear metamaterials).

cond-mat.mes-hall↗

arXiv2021

Quantum circuit optimization with deep reinforcement learning

A central aspect for operating future quantum computers is quantum circuit optimization, i.e., the search for efficient realizations of quantum algorithms given the device capabilities. In recent years, powerful approaches have been developed which focus on optimizing the high-level circuit structure. However, these approaches do not consider and thus cannot optimize for the hardware details of the quantum architecture, which is especially important for near-term devices. To address this point, we present an approach to quantum circuit optimization based on reinforcement learning. We demonstrate how an agent, realized by a deep convolutional neural network, can autonomously learn generic strategies to optimize arbitrary circuits on a specific architecture, where the optimization target can be chosen freely by the user. We demonstrate the feasibility of this approach by training agents on 12-qubit random circuits, where we find on average a depth reduction by 27% and a gate count reduction by 15%. We examine the extrapolation to larger circuits than used for training, and envision how this approach can be utilized for near-term quantum devices.

quant-ph↗

arXiv2021

Renormalized Mutual Information for Artificial Scientific Discovery

We derive a well-defined renormalized version of mutual information that allows to estimate the dependence between continuous random variables in the important case when one is deterministically dependent on the other. This is the situation relevant for feature extraction, where the goal is to produce a low-dimensional effective description of a high-dimensional system. Our approach enables the discovery of collective variables in physical systems, thus adding to the toolbox of artificial scientific discovery, while also aiding the analysis of information flow in artificial neural networks.

cs.LG↗

arXiv2020

Topological phonon transport in an optomechanical system

Recent advances in cavity-optomechanics have now made it possible to use light not just as a passive measuring device of mechanical motion, but also to manipulate the motion of mechanical objects down to the level of individual quanta of vibrations (phonons). At the same time, microfabrication techniques have enabled small-scale optomechanical circuits capable of on-chip manipulation of mechanical and optical signals. Building on these developments, theoretical proposals have shown that larger scale optomechanical arrays can be used to modify the propagation of phonons, realizing a form of topologically protected phonon transport. Here, we report the observation of topological phonon transport within a multiscale optomechanical crystal structure consisting of an array of over $800$ cavity-optomechanical elements. Using sensitive, spatially resolved optical read-out we detect thermal phonons in a $0.325-0.34$GHz band traveling along a topological edge channel, with substantial reduction in backscattering. This represents an important step from the pioneering macroscopic mechanical systems work towards topological phononic systems at the nanoscale, where hypersonic frequency ($\gtrsim$GHz) acoustic wave circuits consisting of robust delay lines and non-reciprocal elements may be implemented. Owing to the broadband character of the topological channels, the control of the flow of heat-carrying phonons, albeit at cryogenic temperatures, may also be envisioned.

cond-mat.mes-hall↗

arXiv2020

Many-Body Dephasing in a Trapped-Ion Quantum Simulator

How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this work, we analyse and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-$1/2$ particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions even for the long-time non-integrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of many-body dephasing.

cond-mat.stat-mech↗

arXiv2020

Efficient cavity control with SNAP gates

Microwave cavities coupled to superconducting qubits have been demonstrated to be a promising platform for quantum information processing. A major challenge in this setup is to realize universal control over the cavity. A promising approach are selective number-dependent arbitrary phase (SNAP) gates combined with cavity displacements. It has been proven that this is a universal gate set, but a central question remained open so far: how can a given target operation be realized efficiently with a sequence of these operations. In this work, we present a practical scheme to address this problem. It involves a hierarchical strategy to insert new gates into a sequence, followed by a co-optimization of the control parameters, which generates short high-fidelity sequences. For a broad range of experimentally relevant applications, we find that they can be implemented with 3 to 4 SNAP gates, compared to up to 50 with previously known techniques.

quant-ph↗

arXiv2020

Nonlinear dynamics of weakly dissipative optomechanical systems

Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly rich and so far remains underexplored. Works devoted to this subject have typically focussed on dissipation constants which are substantially larger than those encountered in current experiments, such that the nonlinear dynamics of weakly dissipative optomechanical systems is almost uncharted waters. In this work, we fill this gap and investigate the regular and chaotic dynamics in this important regime. To analyze the dynamical attractors, we have extended the "Generalized Alignment Index" method to dissipative systems. We show that, even when chaotic motion is absent, the dynamics in the weakly dissipative regime is extremely sensitive to initial conditions. We argue that reducing dissipation allows chaotic dynamics to appear at a substantially smaller driving strength and enables various routes to chaos. We identify three generic features in weakly dissipative classical optomechanical nonlinear dynamics: the Neimark-Sacker bifurcation between limit cycles and limit tori (leading to a comb of sidebands in the spectrum), the quasiperiodic route to chaos, and the existence of transient chaos.

quant-ph↗

arXiv2019

Arbitrary optical wave evolution with Fourier transforms and phase masks

A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. it was shown how to build such multiport universal interferometers with a mesh of beam splitters and phase shifters, and this design became the basis for most experimental implementations in the last decades. However, the design of Reck et al. is difficult to scale up to a large number of modes, which would be required for many applications. Here we present a constructive proof that it is possible to realize a multiport universal interferometer on N modes with a succession of 6N Fourier transforms and 6N+1 phase masks, for any even integer N. Furthermore, we provide an algorithm to find the correct succesion of Fourier transforms and phase masks to realize a given arbitrary unitary transformation. Since Fourier transforms and phase masks are routinely implemented in several optical setups and they do not suffer from the scalability issues associated with building extensive meshes of beam splitters, we believe that our design can be useful for many applications in photonics.

quant-ph↗

arXiv2019

Kinetics of Many-Body Reservoir Engineering

Recent advances illustrate the power of reservoir engineering in applications to many-body systems, such as quantum simulators based on superconducting circuits. We present a framework based on kinetic equations and noise spectra that can be used to understand both the transient and long-time behavior of many particles coupled to an engineered reservoir in a number-conserving way. For the example of a bosonic array, we show that the non-equilibrium steady state can be expressed, in a wide parameter regime, in terms of a modified Bose-Einstein distribution with an energy-dependent temperature.

quant-ph↗

arXiv2019

Oscillating bound states for a giant atom

We investigate the relaxation dynamics of a single artificial atom interacting, via multiple coupling points, with a continuum of bosonic modes (photons or phonons) in a one-dimensional waveguide. In the non-Markovian regime, where the travelling time of a photon or phonon between the coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the atom, we find that a boson can be trapped and form a stable bound state. More interestingly, if the number of coupling points is more than two, the bound state can oscillate persistently by exchanging energy with the atom despite the presence of the dissipative environment. We propose several realistic experimental schemes to generate such oscillating bound states.

quant-ph↗

arXiv2019

Quench Dynamics in 1D Optomechanical Arrays

Non-equilibrium dynamics induced by rapid changes of external parameters is relevant for a wide range of scenarios across many domains of physics. For waves in spatially periodic systems, quenches will alter the bandstructure and generate new excitations. In the case of topological bandstructures, defect modes at boundaries can be generated or destroyed when quenching through a topological phase transition. Here, we demonstrate that optomechanical arrays are a promising platform for studying such dynamics, as their bandstructure can be tuned temporally by a control laser. We study the creation of nonequilibrium optical and mechanical excitations in 1D arrays, including a bosonic version of the Su-Schrieffer-Heeger model. These ideas can be transferred to other systems such as driven nonlinear cavity arrays.

quant-ph↗

arXiv2019

Dynamically Generated Synthetic Electric Fields for Photons

Static synthetic magnetic fields give rise to phenomena including the Lorentz force and the quantum Hall effect even for neutral particles, and they have by now been implemented in a variety of physical systems. Moving towards fully dynamical synthetic gauge fields allows, in addition, for backaction of the particles' motion onto the field. If this results in a time-dependent vector potential, conventional electromagnetism predicts the generation of an electric field. Here, we show how synthetic electric fields for photons arise self-consistently due to the nonlinear dynamics in a driven system. Our analysis is based on optomechanical arrays, where dynamical gauge fields arise naturally from phonon-assisted photon tunneling. We study open, one-dimensional arrays, where synthetic magnetic fields are absent. However, we show that synthetic electric fields can be generated dynamically, which, importantly, suppress photon transport in the array. The generation of these fields depends on the direction of photon propagation, leading to a novel mechanism for a photon diode, inducing nonlinear nonreciprocal transport via dynamical synthetic gauge fields.

cond-mat.mes-hall↗

arXiv2019

Perturbation theory of optical resonances of deformed dielectric spheres

We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our theory is applicable, for example, to freely levitated liquid drops or solid spheres, which are deformed by thermal surface vibrations, centrifugal forces or arbitrary surface waves. A dielectric sphere is effectively an open system whose description requires the introduction of non-Hermitian operators characterized by complex eigenvalues and not normalizable eigenfunctions. We avoid these difficulties using the Kapur-Peierls formalism which enables us to extend the popular Rayleigh-Schrödinger perturbation theory to the case of electromagnetic Debye's potentials describing the light fields inside and outside the near-spherical dielectric object. We find analytical formulas, valid within certain limits, for the deformation-induced first- and second-order corrections to the central frequency and bandwidth of a resonance. As an application of our method, we compare our results with preexisting ones finding full agreement.

physics.optics↗

arXiv2018

Cavity optomagnonics with magnetic textures: coupling a magnetic vortex to light

Optomagnonic systems, where light couples coherently to collective excitations in magnetically ordered solids, are currently of high interest due to their potential for quantum information processing platforms at the nanoscale. Efforts so far, both at the experimental and theoretical level, have focused on systems with a homogeneous magnetic background. A unique feature in optomagnonics is however the possibility of coupling light to spin excitations on top of magnetic textures. We propose a cavity-optomagnonic system with a non homogeneous magnetic ground state, namely a vortex in a magnetic microdisk. In particular we study the coupling between optical whispering gallery modes to magnon modes localized at the vortex. We show that the optomagnonic coupling has a rich spatial structure and that it can be tuned by an externally applied magnetic field. Our results predict cooperativities at maximum photon density of the order of $\mathcal{C}\approx10^{-2}$ by proper engineering of these structures.

cond-mat.mes-hall↗