Dr. Michael Reitz

Linear optical elements based on cooperative subwavelength emitter arrays

Nico S. Baßler, Michael Reitz, Kai P. Schmidt, Claudiu Genes

We describe applications of two-dimensional subwavelength quantum emitter<br>arrays as efficient optical elements in the linear regime. For normally<br>incident light, the cooperative optical response, stemming from emitter-emitter<br>dipole exchanges, allows the control of the array's transmission, its resonance<br>frequency, and bandwidth. Operations on fully polarized incident light, such as<br>generic linear and circular polarizers as well as phase retarders can be<br>engineered and described in terms of Jones matrices. Our analytical approach<br>and accompanying numerical simulations identify optimal regimes for such<br>operations and reveal the importance of adjusting the array geometry and of the<br>careful tuning of the external magnetic fields amplitude and direction.<br>

Cooperative subwavelength molecular quantum emitter arrays

Raphael Holzinger, Sue Ann Oh, Michael Reitz, Helmut Ritsch, Claudiu Genes

Dipole-coupled subwavelength quantum emitter arrays respond cooperatively to<br>external light fields as they may host collective delocalized excitations (a<br>form of excitons) with super- or subradiant character. Deeply subwavelength<br>separations typically occur in molecular ensembles, where in addition to<br>photon-electron interactions, electron-vibron couplings and vibrational<br>relaxation processes play an important role. We provide analytical and<br>numerical results on the modification of super- and subradiance in molecular<br>rings of dipoles including excitations of the vibrational degrees of freedom.<br>While vibrations are typically considered detrimental to coherent dynamics, we<br>show that molecular dimers or rings can be operated as platforms for the<br>preparation of long-lived dark superposition states aided by vibrational<br>relaxation. In closed ring configurations, we extend previous predictions for<br>the generation of coherent light from ideal quantum emitters to molecular<br>emitters, quantifying the role of vibronic coupling onto the output intensity<br>and coherence.<br>

Cooperative quantum phenomena in light-matter platforms

Michael Reitz, Christian Sommer, Claudiu Genes

Quantum cooperativity is evident in light-matter platforms where quantum-emitter ensembles are interfaced<br>with confined optical modes and are coupled via the ubiquitous electromagnetic quantum vacuum.<br>Cooperative effects can find applications, among other areas, in topological quantum optics, in quantum<br>metrology, or in quantum information. This tutorial provides a set of theoretical tools to tackle the behavior<br>responsible for the onset of cooperativity by extending open quantum system dynamics methods, such as<br>the master equation and quantum Langevin equations, to electron-photon interactions in strongly coupled<br>and correlated quantum-emitter ensembles. The methods are illustrated on a wide range of current research<br>topics such as the design of nanoscale coherent-light sources, highly reflective quantum metasurfaces, or<br>low intracavity power superradiant lasers.

Molecular polaritonics in dense mesoscopic disordered ensembles

Christian Sommer, Michael Reitz, Francesca Mineo, Claudiu Genes

We study the dependence of the vacuum Rabi splitting (VRS) on frequency disorder, vibrations, near-field effects, and density in molecular polaritonics. In the mesoscopic limit, static frequency disorder alone can already introduce a loss mechanism from polaritonic states into a dark state reservoir, which we quantitatively describe, providing an analytical scaling of the VRS with the level of disorder. Disorder additionally can split a molecular ensemble into donor-type and acceptor-type molecules and the combination of vibronic coupling, dipole-dipole interactions, and vibrational relaxation induces an incoherent FRET (Förster resonance energy transfer) migration of excitations within the collective molecular state. This is equivalent to a dissipative disorder and has the effect of saturating and even reducing the VRS in the mesoscopic, high-density limit. Overall, this analysis allows to quantify the crucial role played by dark states in cavity quantum electrodynamics with mesoscopic, disordered ensembles.

Floquet engineering of molecular dynamics via infrared coupling

Michael Reitz, Claudiu Genes

We discuss Floquet engineering of dissipative molecular systems through periodic driving of an infrared-active vibrational transition, either directly or via a cavity mode. Following a polaron quantum Langevin equations approach, we derive correlation functions and stationary quantities showing strongly modified optical response<br>of the infrared-dressed molecule. The coherent excitation of molecular vibrational modes, in combination with the modulation of electronic degrees of freedom due to vibronic coupling can lead to both enhanced<br>vibronic coherence as well as control over vibrational sideband amplitudes. The additional coupling to an infrared cavity allows for the controlled suppression of undesired sidebands, an effect stemming from the Purcell enhancement of vibrational relaxation rates.

Molecule-photon interactions in phononic environments

Michael Reitz, Christian Sommer, Burak Gürlek, Vahid Sandoghdar, Diego-Martin Cano, Claudiu Genes

Molecules constitute compact hybrid quantum optical systems that can interface photons, electronic degrees of freedom, localized mechanical vibrations, and phonons. In particular, the strong vibronic interaction between electrons and nuclear motion in a molecule resembles the optomechanical radiation pressure Hamiltonian. While molecular vibrations are often in the ground state even at elevated temperatures, one still needs to get a handle on decoherence channels associated with phonons before an efficient quantum optical network based on optovibrational interactions in solid-state molecular systems could be realized. As a step towards a better understanding of decoherence in phononic environments, we take here an open quantum system approach to the nonequilibrium dynamics of guest molecules embedded in a crystal, identifying regimes of Markovian versus non-Markovian vibrational relaxation. A stochastic treatment, based on quantum Langevin equations, predicts collective vibron-vibron dynamics that resembles processes of sub- and super-radiance for radiative transitions. This in turn leads to the possibility of decoupling intramolecular vibrations from the phononic bath, allowing for enhanced coherence times of collective vibrations. For molecular polaritonics in strongly confined geometries, we also show that the imprint of optovibrational couplings onto the emerging output field results in effective polariton cross-talk rates for finite bath occupancies.

Langevin Approach to Quantum Optics with Molecules

Michael Reitz, Christian Sommer, Claudiu Genes

We investigate the interaction between light and molecular systems modeled as quantum emitters coupled to a multitude of vibrational modes via a Holstein-type interaction. We follow a quantum Langevin equations approach that allows for analytical derivations of absorption and fluorescence profiles of molecules driven by classical fields or coupled to quantized optical modes. We retrieve analytical expressions for the modification of the radiative emission branching ratio in the Purcell regime and for the asymmetric cavity transmission associated with dissipative cross talk between upper and lower polaritons in the strong coupling regime. We also characterize the Förster resonance energy transfer process between donor-acceptor molecules mediated by the vacuum or by a cavity mode.

Enhanced collective Purcell effect of coupled quantum emitter systems

David Plankensteiner, Christian Sommer, Michael Reitz, Helmut Ritsch, Claudiu Genes

Cavity-embedded quantum emitters show strong modifications of free space radiation properties such as an enhanced decay known as the Purcell effect. The central parameter is the cooperativity C - the ratio of the square of the coherent cavity coupling strength over the product of cavity and emitter decay rates. For a single emitter, C is independent of the transition dipole moment and dictated by geometric cavity properties such as finesse and mode waist. In a recent work Phys. Rev. Lett. 119, 093601 (2017) we have shown that collective excitations in ensembles of dipole-dipole coupled quantum emitters show a disentanglement between the coherent coupling to the cavity mode and spontaneous free space decay. This leads to a strong enhancement of the cavity cooperativity around certain collective subradiant antiresonances. Here, we present a quantum Langevin equations approach aimed at providing results beyond the classical coupled dipoles model. We show that the subradiantly enhanced cooperativity imprints its effects onto the cavity output field quantum correlations while also strongly increasing the cavity-emitter system's collective Kerr nonlinear effect.

Energy transfer and correlations in cavity-embedded donor-acceptor configurations

Michael Reitz, Francesca Mineo, Claudiu Genes

The rate of energy transfer in donor-acceptor systems can be manipulated via the common interaction with the confined electromagnetic modes of a micro-cavity. We analyze the competition between the near-field short range dipole-dipole energy exchange processes and the cavity mediated long-range interactions in a simplified model consisting of effective two-level quantum emitters that could be relevant for molecules in experiments under cryogenic conditions. We find that free-space collective incoherent interactions, typically associated with sub-and superradiance, can modify the traditional resonant energy transfer scaling with distance. The same holds true for cavity-mediated collective incoherent interactions in a weak-coupling but strong-cooperativity regime. In the strong coupling regime, we elucidate the effect of pumping into cavity polaritons and analytically identify an optimal energy flow regime characterized by equal donor/acceptor Hopfield coefficients in the middle polariton. Finally we quantify the build-up of quantum correlations in the donor-acceptor system via the two-qubit concurrence as a measure of entanglement.