Frequency-Dependent Sternheimer Linear-Response Formalism for Strongly Coupled Light–Matter Systems

Abstract

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.

Tunable Nonlinearity and Efficient Harmonic Generation from a Strongly Coupled Light–Matter System

“…It is important to note that the linear response spectrum computed from the displacement coordinate equally captures polaritonic features (lower and upper polariton peaks), as shown for the case of the azulene molecule. 42 Thus, it is not surprising to find photon SHG originating from polaritonic states, as shown in Figure 6. Similar to the SHG in Figure 3b,c, we have SHG from polaritonic peaks for different light−matter coupling strengths, with the only difference being in the peak intensities.…”

“…The azulene molecule has a noncentrosymmetric molecular arrangement, which is favorable for a SHG process. In the ultraviolet region of the absorption spectrum of the azulene molecule is a sharp absorption peak at 4.865 eV that corresponds to the π–π* excitation energy of the molecule . Since we are interested in harmonic generation from polaritonic states, it is intuitive to compute the spectrum for the photoabsorption cross section of the coupled system since it captures the hallmark of strong light–matter coupling (i.e., Rabi splitting between polaritons) usually identified in linear spectroscopy.…”

Transition from Lorentz to Fano Spectral Line Shapes in Nonrelativistic Quantum Electrodynamics

“…Upon increasing the coupling strength leads to an increase in the transparency window. With these results, the EIT phenomenon is now for the first time realized from first-principles using QEDFT linear-response framework and our results show the new perspectives that can be achieved with ab initio QEDFT methods. ,, We note that EIT has also been studied using a time-dependent density-functional theory (TDDFT) approach that includes a local potential which accounts for the coupling to the electromagnetic continuum …”

“…φ (rad) ℏΓ (eV) q 6.39 × 10 −5 π 0.019 −8.17 EIT phenomenon is now for the first time realized from firstprinciples using QEDFT linear-response framework and our results show the new perspectives that can be achieved with ab initio QEDFT methods. 32,34,49 We note that EIT has also been studied using a time-dependent density-functional theory (TDDFT) approach that includes a local potential which accounts for the coupling to the electromagnetic continuum. 63 It is important to note that the splitting of the absorption peak that occur at the transparency window (see Figure 6b−d) differs from the strong coupling regime that leads to the formation of polariton peaks (see Figure 7).…”

“…To study the coupled electron–photon system, we solve the stationary eigenvalue problem of eq by employing the reformulation of linear-response theory for light–matter systems within the framework of QEDFT . In particular, we use the electron–photon Casida approach introduced in ref , while noting that similar approaches, as in refs and , can be used.…”