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Michael Ruggenthaler

Publications and source records attributed to Michael Ruggenthaler.

At least 55 records · Page 3Linked to original sources
arXiv2023

A protected spin-orbit induced absorption divergence in distorted Landau levels

The effect of spin-orbit (and Darwin) interaction on a 2D electron gas subject to a radial symmetric, inhomogeneous $1/r$-magnetic field is discussed analytically in a perturbative and non-perturbative manner. For this purpose, we investigate the radial Hall conductivity that emerges from an additional homogeneous electric field perturbation perpendicular to the 2D electron gas, which solely interacts via spin-orbit coupling. Numerical calculations of the absorptive spin-orbit spectra show for an ideal InSb electron gas a behaviour that is dominated by the localized (atomic) part of the distorted Landau levels. In contrast, however, we also find analytically that a (non-local) divergent static response emerges for Fermi energies close to the ionization energy in the thermodynamic limit. The divergent linear response implies that the external electric field is entirely absorbed outside the 2D electron gas by induced radial spin-orbit currents, as it would be the case inside a perfect conductor. This spin-orbit induced polarization mechanism depends on the effective $g^*$-factor of the material for which it shows a critical behaviour at $g^*_c=2$, where it abruptly switches direction. The diverging absorption relies on the presence of degenerate energies with allowed selection rules that are imposed by the radial symmetry of our inhomogeneous setup. We show analytically the presence of a discrete Rydberg-like band structure that obeys these symmetry properties. In a last step, we investigate the robustness of the spectra by solving analytically the Dirac equation expanded up to order $1/(mc)^2$. We find that the distorted Landau-levels, and thus the divergent spin-orbit polarization, remain protected with respect to slow changes of the applied $1/r$-magnetic field.

cond-mat.mes-hall↗
arXiv2022

Understanding polaritonic chemistry from ab initio quantum electrodynamics

In this review we present the theoretical foundations and first principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime. Having a rigorous and fully quantized description of interacting photons, electrons and nuclei/ions, from weak to strong light-matter coupling regimes, is pivotal for a detailed understanding of the emerging fields of polaritonic chemistry and cavity materials engineering. The use of rigorous first principles avoids ambiguities and problems stemming from using approximate models based on phenomenological descriptions of light, matter and their interactions. By starting from fundamental physical and mathematical principles, we first review in great detail non-relativistic QED, which allows to study polaritonic systems non-perturbatively by solving a Schrödinger-type equation. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of computational methods, such as quantum-electrodynamical density functional theory, QED coupled cluster or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key-ideas behind those novel ab initio QED methods, we explain their benefits for a better understanding of photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods we identify the open theoretical questions and how a so far missing mechanistic understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first principles QED and address the open questions that need to be solved in the next years both from a theoretical as well as experimental viewpoint.

quant-ph↗
arXiv2022

Exact Solution for A Real Polaritonic System Under Vibrational Strong Coupling in Thermodynamic Equilibrium: Absence of Zero Temperature and Loss of Light-Matter Entanglement

The first exact quantum simulation of a real molecular system (HD$^+$) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (Bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our exact simulations reveal the absence of a zero temperature for the strongly coupled matter and light subsystems, due to cavity induced non-equilibrium conditions. Furthermore, we explore the temperature dependency of light-matter quantum entanglement, which emerges for the groundstate, but is quickly lost already in the deep cryogenic regime, opposing predictions from phenomenological models (Jaynes-Cummings). Distillable molecular light-matter entanglement of ro-vibrational states may open interesting perspectives for quantum technological applications. Moreover, we find that the dynamics (fluctuations) of matter remains modified by the quantum nature of the thermal and vacuum field fluctuations for significant temperatures, e.g. at ambient conditions. These observations (loss of entanglement and coupling to quantum fluctuations) has far reaching consequences for the understanding and control of polaritonic chemistry and materials science, since a semi-classical theoretical description of light-matter interaction becomes feasible, but the typical canonical equilibrium assumption for the nuclear dynamics remains broken. This opens the door for quantum fluctuations induced stochastic resonance phenomena under vibrational strong coupling. A plausible theoretical mechanism to explain the experimentally observed resonance phenomena in absence of periodic driving, which have not yet been understood.

quant-ph↗
arXiv2022

Polaritonic Hofstadter Butterfly and Cavity-Control of the Quantized Hall Conductance

In a previous work [Phys. Rev. Lett. 123, 047202 (2019)] a translationally invariant framework called quantum-electrodynamical Bloch (QED-Bloch) theory was introduced for the description of periodic materials in homogeneous magnetic fields and strongly coupled to the quantized photon field in the optical limit. For such systems, we show that QED-Bloch theory predicts the existence of fractal polaritonic spectra as a function of the cavity coupling strength. In addition, for the energy spectrum as a function of the relative magnetic flux we find that a terahertz cavity can modify the standard Hofstadter butterfly. In the limit of no quantized photon field, QED-Bloch theory captures the well-known fractal spectrum of the Hofstadter butterfly and can be used for the description of 2D materials in strong magnetic fields, which are of great experimental interest. As a further application, we consider Landau levels under cavity confinement and show that the cavity alters the quantized Hall conductance and that the Hall plateaus are modified as $σ_{xy}=e^2ν/h(1+η^2)$ by the light-matter coupling $η$. Most of the aforementioned phenomena should be experimentally accessible and corresponding implications are discussed.

cond-mat.mes-hall↗
arXiv2022

A perspective on ab initio modeling of polaritonic chemistry: The role of non-equilibrium effects and quantum collectivity

This perspective provides a brief introduction into the theoretical complexity of polaritonic chemistry, which emerges from the hybrid nature of strongly coupled light-matter states. To tackle this complexity, the importance of ab initio methods is highlighted. Based on those, novel ideas and research avenues are developed with respect to quantum collectivity, as well as for resonance phenomena immanent in reaction rates under vibrational strong coupling. Indeed, fundamental theoretical questions arise about the mesoscopic scale of quantum-collectively coupled molecules, when considering the depolarization shift in the interpretation of experimental data. Furthermore, to rationalise recent findings based on quantum electrodynamical density-functional theory (QEDFT), a simple, but computationally efficient, Langevin framework is proposed, based on well-established methods from molecular dynamics. It suggests the emergence of cavity induced non-equilibrium nuclear dynamics, where thermal (stochastic) resonance phenomena could emerge in the absence of external periodic driving. Overall, we believe the latest ab initio results indeed suggest a paradigmatic shift for ground-state chemical reactions under vibrational strong coupling, from the collective quantum interpretation towards a more local, (semi)-classically and non-equilibrium dominated perspective. Finally, various extensions towards a refined description of cavity-modified chemistry are introduced in the context of QEDFT and future directions of the field are sketched.

physics.chem-ph↗
arXiv2022

New Class of Landau Levels and Hall Phases in a 2D Electron Gas Subject to an Inhomogeneous Magnetic Field: An Analytic Solution

An analytic closed form solution is derived for the bound states of electrons subject to a static, inhomogeneous ($1/r$-decaying) magnetic field, including the Zeeman interaction. The solution provides access to many-body properties of a two-dimensional, non-interacting, electron gas in the thermodynamic limit. Radially distorted Landau levels can be identified as well as magnetic field induced density and current oscillations close to the magnetic impurity. These radially localised oscillations depend strongly on the coupling of the spin to the magnetic field, which give rise to non-trivial spin currents. Moreover, the Zeeman interaction introduces a lowest flat band for $E_F=0^+$ assuming a spin $g_s$-factor of two. Surprisingly, in this case the charge and current densities can be computed analytically in the thermodynamic limit. Numerical calculations show that the total magnetic response of the electron gas remains diamagnetic (similar to Landau levels) independent of the Fermi energy. However, the contribution of certain, infinitely degenerate energy levels may become paramagnetic. Furthermore, numerical computations of the Hall conductivity reveal asymptotic properties of the electron gas, which are driven by the anisotropy of the vector potential instead of the magnetic field, i.e. become independent of spin. Eventually, the distorted Landau levels give rise to different Hall conductivity phases, which are characterized by sharp sign flips at specific Fermi energies. Overall, our work merges "impurity" with Landau-level physics, which provides novel physical insights, not only locally, but also in the asymptotic limit. This paves the way for a large number of future theoretical as well as experimental investigations.

cond-mat.mes-hall↗
arXiv2022

Frequency-dependent Sternheimer linear-response formalism for strongly coupled light-matter systems

The rapid progress in quantum-optical experiments especially in the field of cavity quantum electrodynamics and nanoplasmonics, allows to substantially modify and control chemical and physical properties of atoms, molecules and solids by strongly coupling to the quantized field. Alongside such experimental advances has been the recent development of ab-initio approaches such as quantum electrodynamical density-functional theory (QEDFT) that is capable of describing these strongly coupled systems from first-principles. To investigate response properties of relatively large systems coupled to a wide range of photon modes, ab-initio methods that scale well with system size become relevant. In light of this, we extend the linear-response Sternheimer approach within the framework of QEDFT to efficiently compute excited-state properties of strongly coupled light-matter systems. Using this method, we capture features of strong light-matter coupling both in the dispersion and absorption properties of a molecular system strongly coupled to the modes of a cavity. We exemplify the efficiency of the Sternheimer approach by coupling the matter system to the continuum of an electromagnetic field. We observe changes in the spectral features of the coupled system as Lorentzian line shapes turn into Fano resonances when the molecule interacts strongly with the continuum of modes. This work provides an alternative approach for computing efficiently excited-state properties of large molecular systems interacting with the quantized electromagnetic field.

physics.chem-ph↗
arXiv2021

Making ab initio QED functional(s): Non-perturbative and photon-free effective frameworks for strong light-matter coupling

Strong light-matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first-principles. However, combining the quantized nature of light with this ab initio tool set is challenging and merely developing, as the coupled light-matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a non-perturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods. The present formulation is an extension of quantum mechanics that recovers the exact results of QED for the zero- and infinite-coupling limit, the infinite-frequency as well as the homogeneous limit and we can constructively increase its accuracy. We show how this formulation can be used to devise approximations for quantum-electrodynamical density-functional theory (QEDFT), which in turn also allows to extend the ansatz to the full minimal-coupling problem and to non-adiabatic situations. Finally, we provide a simple local-density-type functional that takes the strong coupling to the transverse photon-degrees of freedom into account and includes the correct frequency and polarization dependence. This is the first QEDFT functional that accounts for the quantized nature of light while remaining computationally simple enough to allow its application to a large range of systems. All approximations allow the seamless application to periodic systems.

quant-ph↗
arXiv2021

The Free Electron Gas in Cavity Quantum Electrodynamics

Cavity modification of material properties and phenomena is a novel research field largely motivated by the advances in strong light-matter interactions. Despite this progress, exact solutions for extended systems strongly coupled to the photon field are not available, and both theory and experiments rely mainly on finite-system models. Therefore a paradigmatic example of an exactly solvable extended system in a cavity becomes highly desireable. To fill this gap we revisit Sommerfeld's theory of the free electron gas in cavity quantum electrodynamics (QED). We solve this system analytically in the long-wavelength limit for an arbitrary number of non-interacting electrons, and we demonstrate that the electron-photon ground state is a Fermi liquid which contains virtual photons. In contrast to models of finite systems, no ground state exists if the diamagentic $\textbf{A}^2$ term is omitted. Further, by performing linear response we show that the cavity field induces plasmon-polariton excitations and modifies the optical and the DC conductivity of the electron gas. Our exact solution allows us to consider the thermodynamic limit for both electrons and photons by constructing an effective quantum field theory. The continuum of modes leads to a many-body renormalization of the electron mass, which modifies the fermionic quasiparticle excitations of the Fermi liquid and the Wigner-Seitz radius of the interacting electron gas. Lastly, we show how the matter-modified photon field leads to a repulsive Casimir force and how the continuum of modes introduces dissipation into the light-matter system. Several of the presented findings should be experimentally accessible.

quant-ph↗
arXiv2021

Down-conversion processes in ab-initio non-relativistic quantum electrodynamics

The availability of efficient photon sources with specific properties is important for quantum-technological applications. However, the realization of such photon sources is often challenging and hence alternative perspectives that suggest new means to enhance desired properties while suppressing detrimental processes are valuable. In this work we highlight that ab-initio simulations of coupled light-matter systems can provide such new avenues. We show for a simple model of a quantum ring that by treating light and matter on equal footing we can create and enhance novel pathways for down-conversion processes. By changing the matter subsystem as well as the photonic environment in experimentally feasible ways, we can engineer hybrid light-matter states that enhance at the same time the efficiency of the down-conversion process and the non-classicality of the created photons. Furthermore we show that this also leads to a faster down-conversion, potentially avoiding detrimental decoherence effects.

quant-ph↗
arXiv2021

Approximations based on density-matrix embedding theory for density-functional theories

Recently a novel approach to find approximate exchange-correlation functionals in density-functional theory (DFT) was presented (U. Mordovina et. al., JCTC 15, 5209 (2019)), which relies on approximations to the interacting wave function using density-matrix embedding theory (DMET). This approximate interacting wave function is constructed by using a projection determined by an iterative procedure that makes parts of the reduced density matrix of an auxiliary system the same as the approximate interacting density matrix. If only the diagonal of both systems are connected this leads to an approximation of the interacting-to-non-interacting mapping of the Kohn-Sham approach to DFT. Yet other choices are possible and allow to connect DMET with other DFTs such as kinetic-energy DFT or reduced density-matrix functional theory. In this work we give a detailed review of the basics of the DMET procedure from a DFT perspective and show how both approaches can be used to supplement each other. We do so explicitly for the case of a one-dimensional lattice system, as this is the simplest setting where we can apply DMET and the one that was originally presented. Among others we highlight how the mappings of DFTs can be used to identify uniquely defined auxiliary systems and auxiliary projections in DMET and how to construct approximations for different DFTs using DMET inspired projections. Such alternative approximation strategies become especially important for DFTs that are based on non-linearly coupled observables such as kinetic-energy DFT, where the Kohn-Sham fields are no longer simply obtainable by functional differentiation of an energy expression, or for reduced density-matrix functional theories, where a straightforward Kohn-Sham construction is not feasible.

physics.chem-ph↗
arXiv2020

Polaritonic Chemistry: Collective Strong Coupling Implies Strong Local Modification of Chemical Properties

Polaritonic chemistry has become a rapidly developing field within the last few years. A multitude of experimental observations suggest that chemical properties can be fundamentally altered and novel physical states appear when matter is strongly coupled to resonant cavity modes, i.e. when hybrid light-matter states emerge. Up until now, theoretical approaches to explain and predict these observations were either limited to phenomenological quantum optical models, suited to describe collective polaritonic effects, or alternatively to ab initio approaches for small system sizes. The later methods were particularly controversial since collective effects could not be explicitly included due to the intrinsically low particle numbers, which are computationally accessible. Here, we demonstrate for a nitrogen dimer chain of variable size that any impurity present in a collectively coupled chemical ensemble (e.g. temperature fluctuations or reaction process) induces local modifications in the polaritonic system. From this we deduce that a novel dark state is formed, whose local chemical properties are modified considerably at the impurity due to the collectively coupled environment. Our simulations unify theoretical predictions from quantum optical models (e.g. formation of collective dark states and different polaritonic branches) with the single molecule quantum chemical perspective, which relies on the (quantized) redistribution of local charges. Moreover, our findings suggest that the recently developed QEDFT method is suitable to access these locally scaling polaritonic effects and it is a useful tool to better understand recent experimental results and to even design novel experimental approaches. All of which paves the way for many novel discoveries and applications in polaritonic chemistry.

cond-mat.mes-hall↗
arXiv2020

Virial relations for electrons coupled to quantum field modes

In this work we present a set of virial relations for many electron systems coupled to field modes, described by the Pauli--Fierz Hamiltonian in dipole approximation and using length gauge. Currently, there is growing interest in solutions of this Hamiltonian due to its relevance for describing molecular systems strongly coupled to photonic modes in cavities, and in the possible modification of chemical properties of such systems compared to the ones in free space. The relevance of such virial relations is demonstrated by showing a connection to mass renormalization and by providing an exact way to obtain total energies from potentials in the framework of Quantum Electrodynamical Density Functional Theory.

quant-ph↗
arXiv2020

Chemistry in Quantum Cavities: Exact Results, the Impact of Thermal Velocities and Modified Dissociation

In recent years tremendous progress in the field of light-matter interactions has unveiled that strong coupling to the modes of an optical cavity can alter chemistry even at room temperature. Despite these impressive advances, many fundamental questions of chemistry in cavities remain unanswered. This is also due to a lack of exact results that can be used to validate and benchmark approximate approaches. In this work we provide such reference calculations from exact diagonalisation of the Pauli-Fierz Hamiltonian in the long-wavelength limit with an effective cavity mode. This allows us to investigate the reliability of the ubiquitous Jaynes-Cummings model not only for electronic but also for the case of ro-vibrational transitions. We demonstrate how the commonly ignored thermal velocity of charged molecular systems can influence chemical properties, while leaving the spectra invariant. Furthermore, we show the emergence of new bound polaritonic states beyond the dissociation energy limit.

physics.chem-ph↗
arXiv2020

Light-matter hybrid-orbital-based first-principles methods: the influence of the polariton statistics

A detailed understanding of strong matter-photon interactions requires first-principle methods that can solve the fundamental Pauli-Fierz Hamiltonian of non-relativistic quantum electrodynamics efficiently. A possible way to extend well-established electronic-structure methods to this situation is to embed the Pauli-Fierz Hamiltonian in a higher-dimensional light-matter hybrid auxiliary configuration space. In this work we show the importance of the resulting hybrid Fermi-Bose statistics of the polaritons, which are the new fundamental particles of the ``photon-dressed'' Pauli-Fierz Hamiltonian for systems in cavities. We show that violations of these statistics can lead to unphysical results. We present an efficient way to ensure the proper symmetry of the underlying wave functions by enforcing representability conditions on the dressed one-body reduced density matrix. We further present a general prescription how to extend a given first-principles approach to polaritons and as an example introduce polaritonic Hartree-Fock theory. While being a single-reference method in polariton space, polaritonic Hartree-Fock is a multi-reference method in the electronic space, i.e. it describes electronic correlations. We also discuss possible applications to polaritonic QEDFT. We apply this theory to a lattice model and find that the more delocalized the bound-state wave function of the particles is, the stronger it reacts to photons. The main reason is that within a small energy range many states with different electronic configurations are available as opposed to a strongly bound (and hence energetically separated) ground-state wave function. This indicates that under certain conditions coupling to the quantum vacuum of a cavity can indeed modify ground state properties.

quant-ph↗
arXiv2020

Relevance of the quadratic diamagnetic and self-polarization terms in cavity quantum electrodynamics

Experiments at the interface of quantum-optics and chemistry have revealed that strong coupling between light and matter can substantially modify chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on non-relativistic quantum electrodynamics, which contains quadratic light-matter coupling terms, it is commonplace to disregard these terms and restrict to purely bilinear couplings. In this work we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically we demonstrate its relevance by showing that neglecting it leads to the loss of gauge invariance, basis-set dependence, disintegration (loss of bound states) of any system in the basis set-limit, unphysical radiation of the ground state and an artificial dependence on the static dipole. Besides providing important guidance for modeling strongly coupled light-matter systems, the presented results do also indicate under which conditions those effects might become accessible.

quant-ph↗
arXiv2019

Force Balance Approach for Advanced Approximations in Density Functional Theories

We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent setting. This avoids, besides differentiability and causality issues, the optimized-effective-potential procedure of orbital-dependent functionals. We provide straightforward exchange-type approximations for different density functional theories that for a homogeneous system and no external vector potential reduce to the exchange-only local-density and Slater X$α$ approximations.

physics.chem-ph↗