Ab initio starke Licht-Materie Theoretischer Rahmen für Phänomene in der nichtrelativistischen Quantenelektrodynamik

In condensed matter physics, material science and quantum chemistry, recent experimental progress has laid the foundation to control and alter the properties of matter at will by coupling strongly to individual photons or even just the vacuum fluctuations of the electromagnetic field. This is usually realized by changing the photonic environment and with this the photon field, e.g., by using high-Q optical cavities or plasmonic nanostructures to which the matter system is then strongly coupled to. The ensuing strong coupling brings about novel states of matter with hybrid light-matter character known as polaritons. These hybridized systems allow to control material properties and chemistry in an unprecedented way such as altering chemical reactions, room-temperature polariton lasing, enhance charge and energy transfer, to name but a few. To better understand these intriguing effects, numerous theoretical studies have been performed, most of which are based on simple approximate models. These simplified models capture correctly the main features of the emerging novel physics but overlook important details pertaining to the coupled system. To overcome these restrictions, ab-initio methods such as quantum electrodynamical density-functional theory ( QEDFT ) that treat matter and photons on the same quantized footing have recently been developed. This method allow an in-depth modeling of the light-matter system from first principles. However, the application of these theoretical methods is so far still limited. This is, on the one hand, due to missing efficient numerical schemes to solve the resulting equations. On the other hand, it remains unclear in which cases a full ab-initio simulation would provide novel insights and uncovers new effects. This work presents a first-principles linear-response formulation of QEDFT that captures the hallmark of strong light-matter coupling (Rabi splitting between polaritons) usually identified in linear spectroscopy. Crucial in the linear-response formulation is the stability of matter. While in the usual models this issue is irrelevant, we show how answering this question can shed light on the long-lasting debate about the existence of a Dicke superradiant phase. We extend three linear-response methods for matter-only systems to the linear-response framework of QEDFT that makes the problem computationally feasible. These methods are shown to be numerically equivalent and capture excited-states properties of strongly coupled light-matter systems which is identified by the emergence of polaritonic peaks not only in the matter spectrum but also the photonic spectrum. These strong coupling features are not captured by standard many-body methods that discard the photon degrees of freedom. This opens new possibilities to investigate different situations with complex systems coupled to many photon modes such as non-perturbative first-principles calculation of lifetimes of excited-states, beyond the single molecule limit and dissipation, and Lorentz to Fano transition of lineshapes in strong coupling. Making QEDFT practical now provides a route to analyze and propose experiments at the interface between quantum chemistry, nanoplasmonics and quantum optics and present novel observables that describes the strong coupling between light and matter. Beyond the linear response, this work also highlights new avenues of the down-conversion process that become available in ab-initio simulations of coupled light-matter systems. By changing the photonic environment in an experimentally feasible way, 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 generated photons. In addition, we show that this also causes the down-conversion to occur at earlier times with potential to overcome detrimental decoherence effects. By coupling the signal modes to virtual and polaritonic states we propose an inverse (high-) harmonic generation that acts as an N-photon gun (source). Such a cavity-controlled down-conversion process will not be captured using standard non-linear optics approach since the field is treated classically and only as an external perturbation and with a quantum optics approach, it becomes less accurate due to the simplification of the matter subsystem to a few "relevant" energy levels

Ab initio starke Licht-Materie Theoretischer Rahmen für Phänomene in der nichtrelativistischen Quantenelektrodynamik

In condensed matter physics, material science and quantum chemistry, recent experimental progress has laid the foundation to control and alter the properties of matter at will by coupling strongly to individual photons or even just the vacuum fluctuations of the electromagnetic field. This is usually realized by changing the photonic environment and with this the photon field, e.g., by using high-Q optical cavities or plasmonic nanostructures to which the matter system is then strongly coupled to. The ensuing strong coupling brings about novel states of matter with hybrid light-matter character known as polaritons. These hybridized systems allow to control material properties and chemistry in an unprecedented way such as altering chemical reactions, room-temperature polariton lasing, enhance charge and energy transfer, to name but a few. To better understand these intriguing effects, numerous theoretical studies have been performed, most of which are based on simple approximate models. These simplified models capture correctly the main features of the emerging novel physics but overlook important details pertaining to the coupled system. To overcome these restrictions, ab-initio methods such as quantum electrodynamical density-functional theory ( QEDFT ) that treat matter and photons on the same quantized footing have recently been developed. This method allow an in-depth modeling of the light-matter system from first principles. However, the application of these theoretical methods is so far still limited. This is, on the one hand, due to missing efficient numerical schemes to solve the resulting equations. On the other hand, it remains unclear in which cases a full ab-initio simulation would provide novel insights and uncovers new effects. This work presents a first-principles linear-response formulation of QEDFT that captures the hallmark of strong light-matter coupling (Rabi splitting between polaritons) usually identified in linear spectroscopy. Crucial in the linear-response formulation is the stability of matter. While in the usual models this issue is irrelevant, we show how answering this question can shed light on the long-lasting debate about the existence of a Dicke superradiant phase. We extend three linear-response methods for matter-only systems to the linear-response framework of QEDFT that makes the problem computationally feasible. These methods are shown to be numerically equivalent and capture excited-states properties of strongly coupled light-matter systems which is identified by the emergence of polaritonic peaks not only in the matter spectrum but also the photonic spectrum. These strong coupling features are not captured by standard many-body methods that discard the photon degrees of freedom. This opens new possibilities to investigate different situations with complex systems coupled to many photon modes such as non-perturbative first-principles calculation of lifetimes of excited-states, beyond the single molecule limit and dissipation, and Lorentz to Fano transition of lineshapes in strong coupling. Making QEDFT practical now provides a route to analyze and propose experiments at the interface between quantum chemistry, nanoplasmonics and quantum optics and present novel observables that describes the strong coupling between light and matter. Beyond the linear response, this work also highlights new avenues of the down-conversion process that become available in ab-initio simulations of coupled light-matter systems. By changing the photonic environment in an experimentally feasible way, 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 generated photons. In addition, we show that this also causes the down-conversion to occur at earlier times with potential to overcome detrimental decoherence effects. By coupling the signal modes to virtual and polaritonic states we propose an inverse (high-) harmonic generation that acts as an N-photon gun (source). Such a cavity-controlled down-conversion process will not be captured using standard non-linear optics approach since the field is treated classically and only as an external perturbation and with a quantum optics approach, it becomes less accurate due to the simplification of the matter subsystem to a few "relevant" energy levels

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 one 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), which 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

Light–matter interaction in the long-wavelength limit: no ground-state without dipole self-energy

Most theoretical studies for correlated light–matter systems are performed within the long-wavelength limit, i.e., the electromagnetic field is assumed to be spatially uniform. In this limit the so-called length-gauge transformation for a fully quantized light–matter system gives rise to a dipole self-energy term in the Hamiltonian, i.e., a harmonic potential of the total dipole matter moment. In practice this term is often discarded as it is assumed to be subsumed in the kinetic energy term. In this work we show the necessity of the dipole self-energy term. First and foremost, without it the light–matter system in the long-wavelength limit does not have a ground-state, i.e., the combined light–matter system is unstable. Further, the mixing of matter and photon degrees of freedom due to the length-gauge transformation, which also changes the representation of the translation operator for matter, gives rise to the Maxwell equations in matter and the omittance of the dipole self-energy leads to a violation of these equations. Specifically we show that without the dipole self-energy the so-called 'depolarization shift' is not properly described. Finally we show that this term also arises if we perform the semi-classical limit after the length-gauge transformation. In contrast to the standard approach where the semi-classical limit is performed before the length-gauge transformation, the resulting Hamiltonian is bounded from below and thus supports ground-states. This is very important for practical calculations and for density-functional variational implementations of the non-relativistic QED formalism. For example, the existence of a combined light–matter ground-state allows one to calculate the Stark shift non-perturbatively

Light–Matter Response in Nonrelativistic Quantum Electrodynamics

We derive the full linear-response theory for nonrelativistic quantum electrodynamics in the long wavelength limit and provide a practical framework to solve the resulting equations by using quantum-electrodynamical density-functional theory. We highlight how the coupling between quantized light and matter changes the usual response functions and introduces cross-correlated light-matter response functions. These cross-correlation responses lead to measurable changes in Maxwell’s equations due to the quantum-matter-mediated photon–photon interactions. Key features of treating the combined matter-photon response are that natural lifetimes of excitations become directly accessible from first-principles, changes in the electronic structure due to strong light-matter coupling are treated fully nonperturbatively, and self-consistent solutions of the back-reaction of matter onto the photon vacuum and vice versa are accounted for. By introducing a straightforward extension of the random-phase approximation for the coupled matter-photon problem, we calculate the ab initio spectra for a real molecular system that is coupled to the quantized electromagnetic field. Our approach can be solved numerically very efficiently. The presented framework leads to a shift in paradigm by highlighting how electronically excited states arise as a modification of the photon field and that experimentally observed effects are always due to a complex interplay between light and matter. At the same time the findings provide a route to analyze as well as propose experiments at the interface between quantum chemistry, nanoplasmonics and quantum optics