Cavity quantum electrodynamics provides an ideal platform to engineer and control light-matter interactions with polariton quasiparticles. In this work, we investigate collective phenomena in a system of many particles in a harmonic trap coupled to a homogeneous quantum cavity field. The system couples collectively to the cavity field, through its center of mass, and collective polariton states emerge. The cavity field mediates pairwise long-range interactions and enhances the effective mass of the particles. This leads to an enhancement of localization in the matter ground state density, which features a maximum when light and matter are on resonance, and demonstrates a Dicke-like, collective behavior with the particle number. The light-matter interaction also modifies the photonic properties of the polariton system, as the ground state is populated with bunched photons. In addition, it is shown that the diamagnetic $\mathbf{A}^2$ term is necessary for the stability of the system, as otherwise the superradiant ground state instability occurs. We demonstrate that coherent transfer of polaritonic population is possbile with an external magnetic field and by monitoring the Landau-Zener transition probability.
Recent studies of quantum phase transitions in coupled atom-cavity arrays have focused on the similarities between such systems and the Bose-Hubbard model. However, the bipartite nature of the atom-cavity systems that make up the array introduces some differences. In order to examine the unique features of the coupled-cavity system, the behavior of a simple two-site model is studied over a wide range of parameters. Four regions are identified, in which the ground state of the system may be classified as either a polaritonic insulator, a photonic superfluid, an atomic insulator, or a polaritoni…
The interaction of quantum light with matter like that inside a cavity is known to give rise to mixed light-matter states called polaritons. We discuss the impact of rotation of the cavity on the polaritons. It is shown that the number of polaritons increases due to this rotation. The structure of the original polaritons is modified and new ones are induced by the rotation that strongly depend on the angular velocity and the choice of axis of rotation. In molecules the rotation can change the number of light-induced conical intersections and their dimensionality and hence strongly impact their…
We demonstrate a scheme for quantum communication between the ends of an array of coupled cavities. Each cavity is doped with a single two level system (atoms or quantum dots) and the detuning of the atomic level spacing and photonic frequency is appropriately tuned to achieve photon blockade in the array. We show that in such a regime, the array can simulate a dual rail quantum state transfer protocol where the arrival of quantum information at the receiving cavity is heralded through a fluorescence measurement. Communication is also possible between any pair of cavities of a network of conne…
We consider molecules confined to a microcavity whose dimensions are such that an excitation of the molecule is nearly resonant with a cavity mode. We investigate the situation where the excitation energies of the molecules are randomly distributed with a mean value of $ε_a$ and variance $σ$. For this case, we find a solution that approaches the exact result for large values of the number density $\mathscr{N}$ of the molecules. We find the conditions for the existence of the polaritonic states, as well as expressions for their energies. The polaritonic states are quite stable against disorder.…
We present a full analysis of the mode spectrum in a cavity formed by two parallel plates, one of which is a magneto-dielectric, e.g. a metamaterial, while the other one is metallic, and obtain dispersion relations in closed form. The optical properties of the cavity walls are described in terms of realistic models for the effective permittivity and the permeability. Surface polaritons, i.e. electromagnetic modes that have at least partly an evanescent character, are shown to dominate the Casimir interaction at small separations. We analyze in detail the s-polarized polaritons, which are a cha…
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 H…
The electromagnetic field in an optical cavity can dramatically modify and even control chemical reactivity via vibrational strong coupling (VSC). Since the typical vibration and cavity frequencies are considerably higher than thermal energy, it is essential to adopt a quantum description of cavity-catalyzed adiabatic chemical reactions. Using quantum transition state theory (TST), we examine the coherent nature of adiabatic reactions and derive the cavity-induced changes in eigen frequencies, zero-point-energy, and quantum tunneling. The resulting quantum TST calculation allows us to explain …
Bipartite entanglement entropies are calculated for the ground state of the two-excitation subspace in a two-site coupled cavity model. Each region in the phase diagram (atomic insulator, polaritonic insulator, photonic superfluid, and polaritonic superfluid) is found to be characterized by unique entanglement properties. In particular, the polaritonic superfluid region exhibits multipartite entanglement among the two atoms and two cavity fields. This system provides a toy model in which a number of intriguing aspects of entanglement can be studied, such as the relationship of entanglement to …
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 metho…
I investigate the tunneling decay rate of a polaritonic system formed by a strong coupling between a vacuum cavity mode and $N$ metastable systems. Using a simple model potential, I find the instanton solutions controlling the low-temperature tunneling rate. The resulting rate modification due to the cavity is proportional to the mean of the second power of the light-matter coupling. No collective effect that would enhance the rates by a factor of $\sqrt{N}$ is present, which is in line with the results in the thermal activation regime.
Recent experiments have demonstrated an open system realization of the Dicke quantum phase transition in the motional degrees of freedom of an optically driven Bose-Einstein condensate in a cavity. Relevant collective excitations of this light-matter system are polaritonic in nature, allowing access to the quantum critical behavior of the Dicke model through light leaking out of the cavity. This opens the path to using photodetection based quantum optical techniques to study the dynamics and excitations of this elementary quantum critical system. We first discuss the photon flux observed at th…
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, being distinct from the previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effecti…
It has been experimentally demonstrated that reaction rates for molecules embedded in microfluidic optical cavities are altered when compared to rates observed under "ordinary" reaction conditions. However, precise mechanisms of how strong coupling of an optical cavity mode to molecular vibrations affect the reactivity and how resonance behavior emerges are still under dispute. In the present work, we approach these mechanistic issues from the perspective of a thermal model reaction, the inversion of ammonia along the umbrella mode, in presence of a single cavity mode of varying frequency and …
Nonadiabatic phenomena are investigated in the rovibrational motion of molecules confined in an infrared cavity. Conical intersections (CIs) between vibrational polaritons, similar to CIs between electronic polaritonic surfaces, are found. The spectral, topological, and dynamic properties of the vibrational polaritons show clear fingerprints of nonadiabatic couplings between molecular vibration, rotation and the cavity photonic mode. Furthermore, it is found that for the investigated system, composed of two rovibrating HCl molecules and the cavity mode, breaking the molecular permutational sym…
The exact time-dependent potential energy surface driving the nuclear dynamics was recently shown to be a useful tool to understand and interpret the coupling of nuclei, electrons, and photons, in cavity settings. Here we provide a detailed analysis of its structure for exactly-solvable systems that model two phenomena: cavity-induced suppression of proton-coupled electron transfer and its dependence on the initial state, and cavity-induced electronic excitation. We demonstrate the inadequacy of simply using a weighted average of polaritonic surfaces to determine the dynamics. Such a weighted …
The photon blockade (PB) effect in emitter-cavity systems depends on the anharmonicity of the ladder of dressed energy eigenstates. The recent developments in color center photonics are leading toward experimental demonstrations of multi-emitter-cavity solid-state systems with an expanded set of energy levels compared to the traditionally studied single-emitter systems. We focus on the case of N = 2 nonidentical quasi-atoms strongly coupled to a nanocavity in the bad cavity regime (with parameters within reach of the color center systems), and discover three PB mechanisms: polaritonic, subradi…
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 …
We study the collective effects of an ensemble of organic molecules confined in an optical cavity based on Holstein-Tavis-Cummings model. By using the quantum Langevin approach and adiabatically eliminating the degree of freedom of the vibrational motion, we analytically obtain the expression of the cavity transmission spectrum to analyze the features of polaritonic states. As an application, we show that the dependence for the frequency shift of the lower polaritonic state on the number of molecules can be used in the detection of the ultra-cold molecules. We also numerically analyze the fluo…
We investigate theoretically the coupling of a cavity mode to a continuous distribution of emitters. We discuss the influence of the emitters inhomogeneous broadening on the existence and on the coherence properties of the polaritonic peaks. We find that their coherence depends crucially on the shape of the distribution and not only on its width. Under certain conditions the coupling to the cavity protects the polaritonic states from inhomogeneous broadening, resulting in a longer storage time for a quantum memory based on emitters ensembles. When two different ensembles of emitters are couple…
We study the interplay between disorder and light-matter coupling by considering a disordered one-dimensional chain of lossy dipoles coupled to a multimode optical cavity, through a microscopically derived Hamiltonian. Such a system, hosting polaritonic excitations, may be realized experimentally in a wide range of platforms under strong light-matter coupling. By analyzing both the eigenspectrum and the driven-dissipative transport properties of our system, we find that in the strong-coupling regime, increasing disorder leads almost uncoupled dark states to acquire a photonic part, allowing th…
Competing pathways in polaritonic chemistry and general harmonic environments
University of Copenhagen（哥本哈根大学）；Niels Bohr Institute, University of Copenhagen（尼尔斯·玻尔研究所，哥本哈根大学）；Flatiron Institute（平顿研究所）；Bates College（贝茨学院）；City College of New York（纽约市立学院）；The Graduate Center, City University of New York（纽约市立大学研究生院）
We show that polaritons in an array of interacting micro-cavities with strong atom-photon coupling can form a two-component Bose-Hubbard model. Both polariton species are thereby protected against spontaneous emission as their atomic part is stored in two ground states of the atoms. The parameters of the effective model can be tuned via the driving strength of external lasers. We also describe a method to measure the number statistics in one cavity for each polariton species independently.
Strong coupling between vibrational transitions in molecules within a resonant optical microcavity leads to the formation of collective, delocalized vibrational polaritons. There are many potential applications of "polaritonic chemistry," ranging from modified chemical reactivity to quantum in-formation processing. One challenge in obtaining the polaritonic response is to remove a background contribution due to the uncoupled molecules that generate an ordinary 2D-IR spectrum whose amplitude is filtered by the polariton transmission spectrum. We show that most features in 2D-IR spectra of vibra…
Rayleigh scattering is usually considered to be the elastic scattering of photons from sub-wavelength physical objects, such as small particles or molecules. Here, we present the spectroscopic study of the scattering properties of molecules embedded in an optical cavity under strong coupling conditions, where the collective interaction between the molecules and the cavity gives rise to composite light-matter excitations known as cavity polaritons. We show that the polaritonic states exhibit strong resonant Rayleigh scattering, reaching 25% efficiency. Since the polaritonic wavefunctions in suc…
We study the collective emission of a beam of atomic dipoles into an optical cavity. Our focus lies on the effect of a finite detuning between the atomic transition frequency and the cavity resonance frequency. By developing a theoretical description of the coupled atom-cavity dynamics we analyze the stationary atomic configurations including a superradiant phase where the atoms undergo continuous monochromatic collective emission. In addition, we derive an analytical formula for the cavity pulling coefficient which characterizes the displacement of the emission frequency towards the cavity fr…
We consider an ensemble of diatomic molecules resonantly coupled to an optical cavity under strong coupling conditions at normal incidence. Photodissociation dynamics is examined via direct numerical integration of the coupled Maxwell-Schrodinger equations with molecular ro-vibrational degrees of freedom explicitly taken into account. It is shown that the dissociation is significantly affected (slowed down) when the system is driven at its polaritonic frequencies. The observed effect is demonstrated to be of transient nature and has no classical analog. An intuitive explanation of the dissocia…
We study the case of two polaritonic qubits localized in two separate cavities coupled by a fiber/additional cavity. We show that surprisingly enough, even a coherent classical pump in the intermediate cavity/fiber can lead to the creation of entanglement between the two ends in the steady state. The stationary nature of this entanglement and its survival under dissipation opens possibilities for its production under realistic laboratory conditions. To facilitate the verification of the entanglement in an experiment we also construct the relevant entanglement witness measurable by accessing on…
We show that photon number measurement can be used to detect superfluidity for a two-band Bose-Hubbard model coupled to a cavity field. The atom-photon coupling induces transitions between the two internal atomic levels and results in entangled polaritonic states. In the presence of a cavity field, we find different photon numbers in the Mott-insulating versus superfluid phases, providing a method of distinguishing the atomic phases by photon counting. Furthermore, we examine the dynamics of the photon field after a rapid quench to zero atomic hopping by increasing the well depth. We find a ro…
We propose a mechanism to realize high-yield molecular formation from ultracold atoms. Atom pairs are continuously excited by a laser, and a collective decay into the molecular ground state is induced by a coupling to a lossy cavity mode. Using a combination of analytical and numerical techniques, we demonstrate that the molecular yield can be improved by simply increasing the number of atoms, and can overcome efficiencies of state-of-the-art association schemes. We discuss realistic experimental setups for diatomic polar and nonpolar molecules, opening up collective light matter interactions …
We investigate the single-photon transport properties of a one-dimensional coupled cavity array (CCA) containing a single qubit in its central site by coupling the CCA to two transmission lines supporting propagating bosonic modes with linear dispersion. We find that even in the nominally weak light-matter coupling regime, the transmission through a long array exhibits two ultra-narrow resonances corresponding to long-lived self-protected polaritonic states localized around the site containing the qubit. The lifetime of these states is found to increase exponentially with the number of array s…
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-ma…
Advances in nanophotonics, quantum optics, and low-dimensional materials have enabled precise control of light-matter interactions down to the nanoscale. Combining concepts from each of these fields, there is now an opportunity to create and manipulate photonic matter via strong coupling of molecules to the electromagnetic field. Towards this goal, here we introduce a first principles framework to calculate polaritonic excited-state potential-energy surfaces for strongly coupled light-matter systems. In particular, we demonstrate the applicability of our methodology by calculating the polarito…
A lattice of locally bistable driven-dissipative cavity polaritons is found theoretically to effectively simulate the Ising model, also enabling an effective transverse field. We benchmark the system performance for spin glass problems, and study the scaling of the ground state energy deviation and success probability as a function of system size. As particular examples we consider NP-hard problems embedded in the Ising model, namely graph partitioning and the knapsack problem. We find that locally bistable polariton networks act as classical simulators for solving optimization problems, which…
Chirality routing non-polaritonic vacuum correlations in Landau polaritons
College of Physical Sciences and Engineering, University Mohammed VI Polytechnic（物理科学与工程学院，穆罕默德六世polytechnic大学）；Jülich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum Jülich（于利希超级计算中心，高级模拟研究所，于利希研究中心）；Institut für Theoretische Physik, Universität Tübingen（理论物理研究所，蒂宾根大学）；Department of Chemistry, Princeton University（化学系，普林斯顿大学）
