Lossy Cavity Research Articles

Thermal disorder prevents the suppression of ultra-fast photochemistry in the strong light-matter coupling regime

Strong coupling between molecules and confined light modes of optical cavities to form polaritons can alter photochemistry, but the origin of this effect remains largely unknown. While theoretical models suggest a suppression of photochemistry due to the formation of new polaritonic potential energy surfaces, many of these models do not account for the energetic disorder among the molecules, which is unavoidable at ambient conditions. Here, we combine simulations and experiments to show that for an ultra-fast photochemical reaction such thermal disorder prevents the modification of the potential energy surface and that suppression is due to radiative decay of the lossy cavity modes. We also show that the excitation spectrum under strong coupling is a product of the excitation spectrum of the bare molecules and the absorption spectrum of the molecule-cavity system, suggesting that polaritons can act as gateways for channeling an excitation into a molecule, which then reacts normally. Our results therefore imply that strong coupling provides a means to tune the action spectrum of a molecule, rather than to change the reaction.

Extracting kinetic information from short-time trajectories: relaxation and disorder of lossy cavity polaritons

Abstract The emerging field of molecular cavity polaritons has stimulated a surge of experimental and theoretical activities and presents a unique opportunity to develop the many-body simulation methodology. This paper presents a numerical scheme for the extraction of key kinetic information of lossy cavity polaritons based on the transfer tensor method (TTM). Steady state, relaxation timescales, and oscillatory phenomena can all be deduced directly from a set of transfer tensors without the need for long-time simulation. Moreover, we generalize TTM to disordered systems by sampling dynamical maps and achieve fast convergence to disordered-averaged dynamics using a small set of realizations. Together, these techniques provide a toolbox for characterizing the interplay of cavity loss, disorder, and cooperativity in polariton relaxation and allow us to predict unusual dependences on the initial excitation state, photon decay rate, strength of disorder, and the type of cavity models. Thus, using the example of cavity polaritons, we have demonstrated significant potential in the use of the TTM toward both the efficient computation of long-time polariton dynamics and the extraction of crucial kinetic information about polariton relaxation from a small set of short-time trajectories.

Incorporation of Empirical Gain and Loss Mechanisms in Open Quantum Systems through Path Integral Lindblad Dynamics.

Path integrals offer a robust approach for simulating open quantum dynamics with advancements transcending initial system size limitations. However, accurately modeling systems governed by mechanisms that do not conserve the number of quantum particles, such as lossy cavity modes, remains a challenge. We present a method to incorporate such empirical source and drain mechanisms within a path integral framework using quantum master equations. This technique facilitates rigorous inclusion of bath degrees of freedom while accommodating empirical time scales via Lindbladian dynamics. Computational costs are primarily driven by the path integral method with minimal overhead from Lindbladian terms. We use it to study exciton transport in a four-site Fenna-Matthews-Olson model, examining the potential loss of the exciton to the reaction center. This path integral Lindblad method promises an enhanced ability to simulate dynamics and will be fundamental to simulation of spectra in diverse quantum processes in open systems.

Non-Hermitian molecular dynamics simulations of exciton-polaritons in lossy cavities.

The observation that materials can change their properties when placed inside or near an optical resonator has sparked a fervid interest in understanding the effects of strong light-matter coupling on molecular dynamics, and several approaches have been proposed to extend the methods of computational chemistry into this regime. Whereas the majority of these approaches have focused on modeling a single molecule coupled to a single cavity mode, changes to chemistry have so far only been observed experimentally when very many molecules are coupled collectively to multiple modes with short lifetimes. While atomistic simulations of many molecules coupled to multiple cavity modes have been performed with semi-classical molecular dynamics, an explicit description of cavity losses has so far been restricted to simulations in which only a very few molecular degrees of freedom were considered. Here, we have implemented an effective non-Hermitian Hamiltonian to explicitly treat cavity losses in large-scale semi-classical molecular dynamics simulations of organic polaritons and used it to perform both mean-field and surface hopping simulations of polariton relaxation, propagation, and energy transfer.

Molecular optomechanics in the anharmonic regime: from nonclassical mechanical states to mechanical lasing

Cavity optomechanics aims to establish optical control over vibrations of nanoscale mechanical systems, to heat, cool or to drive them toward coherent, or nonclassical states. This field was recently extended to encompass molecular optomechanics: the dynamics of THz molecular vibrations coupled to the optical fields of lossy cavities via Raman transitions. The molecular platform should prove suitable for demonstrating more sophisticated optomechanical effects, including engineering of nonclassical mechanical states, or inducing coherent molecular vibrations. We propose two schemes for implementing these effects, exploiting the strong intrinsic anharmonicities of molecular vibrations. First, to prepare a nonclassical mechanical state, we propose an incoherent analogue of the mechanical blockade, in which the molecular anharmonicity and optical response of hybrid cavities isolate the two lowest-energy vibrational states. Secondly, we show that for a strongly driven optomechanical system, the anharmonicity can suppress the mechanical amplification, shifting and reshaping the onset of coherent mechanical oscillations. Our estimates indicate that both effects should be within reach of existing platforms for Surface Enhanced Raman Scattering.

Singly-excited resonant open quantum system Tavis-Cummings model with quantum circuit mapping

Tavis-Cummings (TC) cavity quantum electrodynamical effects, describing the interaction of N atoms with an optical resonator, are at the core of atomic, optical and solid state physics. The full numerical simulation of TC dynamics scales exponentially with the number of atoms. By restricting the open quantum system to a single excitation, typical of experimental realizations in quantum optics, we analytically solve the TC model with an arbitrary number of atoms with linear complexity. This solution allows us to devise the Quantum Mapping Algorithm of Resonator Interaction with N Atoms (Q-MARINA), an intuitive TC mapping to a quantum circuit with linear space and time scaling, whose N+1 qubits represent atoms and a lossy cavity, while the dynamics is encoded through 2N entangling gates. Finally, we benchmark the robustness of the algorithm on a quantum simulator and superconducting quantum processors against the quantum master equation solution on a classical computer.

Unconventional saturation effects at intermediate drive in a lossy cavity coupled to few emitters

Unconventional saturation effects at intermediate drive in a lossy cavity coupled to few emitters

Molecular Chemistry in Cavity Strong Coupling.

The coherent exchange of energy between materials and optical fields leads to strong light-matter interactions and so-called polaritonic states with intriguing properties, halfway between light and matter. Two decades ago, research on these strong light-matter interactions, using optical cavity (vacuum) fields, remained for the most part the province of the physicist, with a focus on inorganic materials requiring cryogenic temperatures and carefully fabricated, high-quality optical cavities for their study. This review explores the history and recent acceleration of interest in the application of polaritonic states to molecular properties and processes. The enormous collective oscillator strength of dense films of organic molecules, aggregates, and materials allows cavity vacuum field strong coupling to be achieved at room temperature, even in rapidly fabricated, highly lossy metallic optical cavities. This has put polaritonic states and their associated coherent phenomena at the fingertips of laboratory chemists, materials scientists, and even biochemists as a potentially new tool to control molecular chemistry. The exciting phenomena that have emerged suggest that polaritonic states are of genuine relevance within the molecular and material energy landscape.

Optical Spectra of Plasmon–Exciton Core–Shell Nanoparticles: A Heuristic Quantum Approach

Light–matter coupling in plasmonic nanocavities has been widely studied in the past years. Yet, for core–shell particles, popular electromagnetic models that use the classical Lorentz oscillator to describe the shell predict extinction spectra with three maxima, if the plasmon and the shell absorption are in resonance. In contrast, experiments exhibit only two peaks, as also expected from simple quantum models of hybrid states. In order to reconcile the convenient and widely used classical electromagnetic description with experimental data, we connect it to the quantum world by conceiving a heuristic quantum model. Our model is based on the permittivity of a two-level system in a classical electric field derived from the optical Bloch equations. The light–matter coupling is included via the collective vacuum Rabi frequency Ω0. Using our model, we obtain excellent agreement with a series of experimental extinction spectra of particles with various coupling strengths due to a systematic size variation. The suppression of the third maximum, which mainly stems from the absorption in the shell, can be interpreted as a vacuum induced power broadening, which may occur in lossy (plasmonic) cavities below the strong-coupling regime.

Transverse impedance studies of 2D azimuthally symmetric devices of finite length

The accurate calculation of the beam coupling impedance for particle accelerators is necessary to carefully assess the machine stability against impedance-driven collective effects. A first order evaluation of the beam coupling impedance is often done by means of analytical formulas and/or 2D numerical codes. The infinite length approximation is often used to simplify the calculation of the beam coupling impedance of accelerator elements. This is expected to be a reasonable assumption for devices whose length is greater than the transverse dimension but may be a less accurate approximation for segmented devices. In this work, we present the application of the mode matching method to the calculation of the transverse dipolar impedance of a cylindrical cavity loaded with a toroidal insert. By choosing different insert electromagnetic properties (permittivity, permeability, and conductivity) and dimensions, the model can represent a beam pipe, a thin insert, a lossy cavity, or a collimator for which the effect of the finite length is investigated. The method is successfully benchmarked against available analytical formulas, field-matching codes, and 3D commercial solvers. The proposed model allows for performing wide parametric scans and reaching accurate results, therefore becoming an essential tool for the impedance evaluation of accelerator devices.

Modeling the frequency response of an acoustic cavity using the method of images

We demonstrate the ability of a simple algorithm based on the venerable method of images (MOIs), to accurately model the detailed frequency response of a multidimensional, rectangular, lossy resonant cavity. The convergence properties of the model's infinite series solution are shown to be determined by the cavity's quality factor Q. A 1D example demonstrates that the MOI series converges to the exact solution. Next, a comparison to precisely measure 2D cavity data confirms that a straightforward extension of the 1D algorithm to multiple dimensions provides accurate results. The algorithm is short, easily understandable by undergraduate students and relatively undemanding to code. An example using ®mathematica is provided.

Multilevel domain uncertainty quantification in computational electromagnetics

We continue our study [R. Aylwin, C. Jerez-Hanckes, C. Schwab and J. Zech, Domain uncertainty quantification in computational electromagnetics, SIAM/ASA J. Uncertain. Quant. 8 (2020) 301–341] of the numerical approximation of time-harmonic electromagnetic fields for the Maxwell lossy cavity problem for uncertain geometries. We adopt the same affine-parametric shape parametrization framework, mapping the physical domains to a nominal polygonal domain with piecewise smooth maps. The regularity of the pullback solutions on the nominal domain is characterized in piecewise Sobolev spaces. We prove error convergence rates and optimize the algorithmic steering of parameters for edge-element discretizations in the nominal domain combined with: (a) multilevel Monte Carlo sampling, and (b) multilevel, sparse-grid quadrature for computing the expectation of the solutions with respect to uncertain domain ensembles. In addition, we analyze sparse-grid interpolation to compute surrogates of the domain-to-solution mappings. All calculations are performed on the polyhedral nominal domain, which enables the use of standard simplicial finite element meshes. We provide a rigorous fully discrete error analysis and show, in all cases, that dimension-independent algebraic convergence is achieved. For the multilevel sparse-grid quadrature methods, we prove higher order convergence rates free from the so-called curse of dimensionality. Numerical experiments confirm our theoretical results and verify the superiority of the sparse-grid methods.

Nonclassical correlations in lossy cavity optomechanics with intensity-dependent coupling

In this paper, we describe a double-optomechanical system which contains two lossy cavities, where each cavity includes a single-mode quantized field coupled to a single vibrational mode of a flexible membrane. There exists an interaction between a two-level atom and the cavity mode in the rotating wave approximation, with degenerate multi-photon transition in the presence of intensity-dependent coupling. Furthermore, we consider the effect of different sources of dissipation consisting of cavity decay, losses of cavity mirror, and spontaneous emission from the atom. We then start with the master equation to study the dynamics of considered quantum system. Afterward, we show that under some circumstances, the solution of the complicated problem via the master equation is reduced to the determination of the state vector in the time-dependent Schrödinger equation, with the help of an effective non-Hermitian Hamiltonian. Obtaining the explicit form of the state vector of the entire system, we study the nonclassical correlations of two atoms by means of geometric discord. We also examine the roles of intensity-dependent nonlinearity function, number of photons contributed to atomic transition, number of photons in the Fock states, and different sources of dissipation in the dynamics of geometric discord of the atoms. The numerical results indicate that the steady-state value of geometric discord can be revealed, and can appropriately be controlled via the mentioned-above effects. It can be found that the existence of spontaneous emission not only protects the nonclassical correlations of the atoms but also tends the geometric discord to a steady-state value.

Tuning and Enhancing Quantum Coherence Time Scales in Molecules via Light-Matter Hybridization.

Protecting quantum coherences in matter from the detrimental effects introduced by its environment is essential to employ molecules and materials in quantum technologies and develop enhanced spectroscopies. Here, we show how dressing molecular chromophores with quantum light in the context of optical cavities can be used to generate quantum superposition states with tunable coherence time scales that are longer than those of the bare molecule, even at room temperature and for molecules immersed in solvent. For this, we develop a theory of decoherence rates for molecular polaritonic states and demonstrate that quantum superpositions that involve such hybrid light-matter states can survive for times that are orders of magnitude longer than those of the bare molecule while remaining optically controllable. Further, by studying these tunable coherence enhancements in the presence of lossy cavities, we demonstrate that they can be enacted using present-day optical cavities. The analysis offers a viable strategy to engineer and increase quantum coherence lifetimes in molecules.

Simulation of thermal fragility of vacuum squeezing in two photon lossy cavity

In this research, squeezing fragility due to thermal bath, in quantum squeezed state generation, is simulated. For this purpose, single mode dissipative cavity with non-zero second-order susceptibility is used. Cavity nonlinear medium is driving by laser pump with known frequency, and pairs of identical photons are created, with one-half frequency of driving pump. This process known as degenerate parametric down conversion. In the absence of any dissipation, simulation shows linear time dependent squeezing parameter, which is in agreement with theoretical results. In two photon loss of cavity in contact with cold reservoir, competition between gain and two photon loss, results in stable squeezing of initial vacuum, in steady state of system. At the end, has been shown that, non-zero thermal reservoir, omits the squeezing and leads the final cavity field to the thermal mixture of Fock states.

Radio-frequency sheath excitation at the extremities of scrape-off layer plasma filaments, mediated by resonant high harmonic fast wave scattering

Resonant filament-assisted mode conversion (FAMC) scattering of high harmonic fast waves (HHFW) by cylindrical field-aligned density inhomogeneities can efficiently redirect a fraction of the launched HHFW power flux into the parallel direction. Within a simplified analytic approach, this contribution compares the parallel propagation, reflection and dissipation of nearly resonant FAMC modes for three magnetic field line geometries in the scrape-off layer, in the presence of radio-frequency (RF) sheaths at field line extremities and phenomenological wave damping in the plasma volume. When a FAMC mode, excited at the HHFW antenna parallel location and guided along the open magnetic field lines, impinges onto a boundary at normal incidence, we show that it can excite sheath RF oscillations, even toroidally far away from the HHFW launcher. The RF sheaths then dissipate part of the power flux carried by the incident mode, while another part reflects into the FAMC mode with the opposite wave vector parallel to the magnetic field. The reflected FAMC mode in turn propagates and can possibly interact with the sheath at the opposite field line boundary. The two counter-propagating modes then form in the bounded magnetic flux tube a lossy cavity excited by the HHFW scattering. We investigate how the presence of field line boundaries affects the total HHFW power redirected into the filament, and its splitting between sheath and volume losses, as a function of relevant parameters in the model.

F-deformed cavity mode coupled to a Λ-type atom in the presence of dissipation and Kerr nonlinearity

In this paper, the dynamics of a system consisting of a three-level atom, which interacts with a single-mode quantized field in a lossy cavity, is studied in the presence of the dependence of atom–field coupling and third-order nonlinear susceptibility on the intensity of light. The system contains a Λ -type atom coupled to a single-mode radiation field, with a degenerate multi-photon transition in the intensity-dependent regime. Also, the nonlinearity of the medium due to Kerr and intensity-dependent Kerr effects, and the detuning parameters are considered. Furthermore, to see the effects of dissipation such as photon absorption and scattering by the cavity mirrors and spontaneous emission of the atom, a non-Hermitian Hamiltonian is introduced, which results in obtaining the state vector of the whole system by applying the time-dependent Schrödinger equation. Thereupon, the dynamics of entanglement, coherence, photon statistics, and quadrature squeezing are numerically investigated. In each case, the roles of the intensity-dependent nonlinearity function, Kerr and intensity-dependent Kerr nonlinearity, different sources of dissipation, and detuning parameters are discussed. The numerical results indicate that the nonclassicality can remarkably be revealed, and can appropriately be controlled via the above-mentioned effects. It can be found that the presence of dissipation not only does not weaken the physical properties but also can enhance and protect the nonclassicality of the system.

Simple way to incorporate loss when modeling multimode-entangled-state generation

We show that the light generated via spontaneous four-wave mixing or parametric down conversion in multiple, coupled, lossy cavities is a multimode squeezed thermal state. Requiring this state to be the solution of the Lindblad master equation results in a set of coupled first-order differential equations for the time-dependent squeezing parameters and thermal photon numbers of the state. The benefit of this semianalytic approach is that the number of coupled equations scales linearly with the number of modes and is independent of the number of photons generated. With this analytic form of the state, correlation variances are easily expressed as analytic functions of the time-dependent mode parameters. Thus, our solution makes it computationally tractable and relatively straightforward to calculate the generation and evolution of multimode entangled states in multiple coupled, lossy cavities, even when there are a large number of modes and/or photons.

Steady states of Λ-type three-level systems excited by quantum light with various photon statistics in lossy cavities

The interaction between quantum light and matter is being intensively studied for systems that are enclosed in high-Q cavities which strongly enhance the light–matter coupling. Cavities with low Q-factors are generally given less attention due to their high losses that quickly destroy quantum systems. However, bad cavities can be utilized for several applications, where lower Q-factors are required, e.g., to increase the spectral width of the cavity mode. In this work, we demonstrate that low-Q cavities can be beneficial for preparing specific electronic steady states when certain quantum states of light are applied. We investigate the interaction between quantum light with various statistics and matter represented by a Λ-type three-level system in lossy cavities, assuming that cavity losses are the dominant loss mechanism. We show that cavity losses lead to non-trivial electronic steady states that can be controlled by the loss rate and the initial statistics of the quantum fields. We discuss the mechanism of the formation of such steady states on the basis of the equations of motion and present both analytical expressions and numerical simulations for such steady states.

Supersolid gap soliton in a Bose-Einstein condensate and optical ring cavity coupling system.

The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation, and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usual BEC gap solitons in static optical lattices.