Lossless Cavity Research Articles

Practical guide to the statistical mechanics of molecular polaritons

A theoretical approach aimed at the quantum statistical mechanics of a molecular ensemble coupled to a lossless cavity mode is presented. A canonical ensemble is considered and an approximate formula is devised for the Helmholtz free energy correction due to cavity-molecule coupling, which enables the derivation of experimentally measurable thermodynamic quantities. The frequency of the cavity mode is assumed to lie in the infrared range. Therefore, the cavity couples to molecular vibrations and our treatment is restricted to the electronic ground state of the molecule. The method is tested for an analytically solvable model system of one-dimensional harmonic oscillators coupled to the cavity. The performance of the approximation and its range of validity are discussed in detail. It is shown that the leading-order correction to the Helmholtz free energy is proportional to the square of the collective coupling strength. We also demonstrate that the cavity mode does not have a significant impact on the thermodynamic properties of the system in the collective ultrastrong coupling regime (the collective coupling strength is comparable to the frequency of the cavity mode).

Phase space perspective on a model for isomerization in an optical cavity.

Explanation for the modification of rates and mechanism of reactions carried out in optical cavities still eludes us. Several studies indicate that the cavity-mediated changes in the nature of vibrational energy flow within a molecule may play a significant role. Here, we study a model polaritonic system, proposed and analyzed earlier by Fischer et al., J. Chem. Phys. 156, 154305 (2022), comprising a one-dimensional isomerization mode coupled to a single photon mode in a lossless cavity. We show that the isomerization probability in the presence of virtual photons, for specific cavity-system coupling strengths and cavity frequencies, can exhibit suppression or enhancement for different choices of the initial reactant vibropolariton wavepacket. We observe a qualitative agreement between the classical and quantum average isomerization probabilities in the virtual photon case. A significant part of the effects due to coupling to the cavity can be rationalized in terms of a "chaos-order-chaos" transition of the classical phase space and the phase space localization nature of the polariton states that dominantly participate in the quantum isomerization dynamics. On the other hand, for initial states with zero photons (i.e., a "dark cavity"), the isomerization probability is suppressed when the cavity frequency is tuned near to the fundamental frequency of the reactive mode. The classical-quantum correspondence in the zero photon case is unsatisfactory. In this simple model, we find that the suppression or enhancement of isomerization arises due to the interplay between cavity-system energy flow dynamics and quantum tunneling.

Loss-induced Purcell enhancement in PT-broken whispering gallery microcavities.

Parity-time (PT)-symmetry brings various opportunities for electromagnetic field manipulation and light-matter interaction, such as modification of spontaneous emission. However, previous works mainly focused on the behavior of spontaneous emission at exceptional points or in the PT-symmetry situation. Here, we theoretically demonstrate loss-induced Purcell enhancement in PT-broken whispering gallery microcavities. In the PT-broken phase, one of the supermodes decays slowly thereby playing a leading role in spontaneous emission. As the loss increases, the quality factor of this supermode is higher and the mode volume is smaller, so that the Purcell factors will be larger if the emitter is placed near the lossless cavity. Our findings indicate that loss can enhance the interaction between light and matter, which could be applied to single photon emission, non-Hermitian photonic devices, etc.

Quantum Simulations of Vibrational Strong Coupling via Path Integrals.

A quantum simulation of vibrational strong coupling (VSC) in the collective regime via thermostated ring-polymer molecular dynamics (TRPMD) is reported. For a collection of liquid-phase water molecules resonantly coupled to a single lossless cavity mode, the simulation shows that as compared with a fully classical calculation, the inclusion of nuclear and photonic quantum effects does not lead to a change in the Rabi splitting but does broaden polaritonic line widths roughly by a factor of 2. Moreover, under thermal equilibrium, both quantum and classical simulations predict that the static dielectric constant of liquid water is largely unchanged inside vs outside the cavity. This result disagrees with a recent experiment demonstrating that the static dielectric constant of liquid water can be resonantly enhanced under VSC, suggesting either limitations of our approach or perhaps other experimental factors that have not yet been explored.

Entanglement of two dipole-coupled qubits induced by a thermal field of one-mode lossless cavity with Kerr medium

We studied the dynamics of two qubits interacting with one-mode thermal quantum electromagnetic field of microwave cavity with Kerr medium. Using the exact solution for considered model we derived the qubit-qubit negativity for separa coherent initial qubits states. We showed that initial qubits coherencee interaction can greatly enhance the degree of qubits entanglement in the presence of the Kerr nonlinearity and dipole-dipole interactionyeven for high thermal field intensities.

Atom–atom entanglement via coherent photons in a nonlinear optical cavity

In the present article, dynamics of entanglement between two different two-level atoms, as nonidentical qubits, via monochromatic coherent photons is explored. The atoms are embedded in an optical lossless cavity filled with a centrosymmetric dielectric. A conserved (Casimir) operator, i.e. a dynamic integral of motion, is introduced to decompose the matrix representation of the total atom–photon Hamiltonian into direct sum of irreducible blocks. Using the eigenvalues and eigenvectors of the blocks, the time evolution unitary operator of the system is computed. The time-dependent atomic density operator is then calculated by partial tracing of atom–field density operator over photonic states for both initially separable and maximally entangled atomic states. The partially transposed atomic density operator, with respect to one of the atomic subsystems, is finally used to determine the negativity as an entanglement quantifier. Our results indicate that the robust entanglement is observed when the initial maximally atomic entangled state is applied. Furthermore, as Kerr-type coupling (arising from the third-order susceptibility of the centrosymmetric dielectric) increases it is shown that the entanglement enhances. In addition, effects of the initial atomic state preparation, the atom–photon structure parameters as well as field intensity on the entanglement birth and death are also addressed.

Dark state semilocalization of quantum emitters in a cavity

We study a disordered ensemble of quantum emitters collectively coupled to a lossless cavity mode. The latter is found to modify the localization properties of the "dark" eigenstates, which exhibit a character of being localized on multiple, noncontiguous sites. We denote such states as semi-localized and characterize them by means of standard localization measures. We show that those states can very efficiently contribute to coherent energy transport. Our paper underlines the important role of dark states in systems with strong light-matter coupling.

The dynamics of an atom-field system with degenerate atomic levels and a polarization-degenerate mode of the quantised field in a damped micro-cavity

The master equation for the atom-field system with degenerate atomic levels and two polarization modes of the quantized field in a damped micro-cavity is obtained in the basis of eigenvectors of the interaction operator. The solution for the lossless cavity is obtained. The analytic expressions for the probability of emission of the photon in the cavity by an excited atom and of the photon polarization matrix are derived in the ‘strong coupling’ and ‘bad cavity’ approximations for arbitrary values of angular momenta of atomic levels. The dependence of the photon polarization on the polarization of the short excitation pulse is studied.

Thermal free entanglement of a [formula omitted] -type three-level atom and bimodal photons in an optical cavity

Quantum entanglement is usually affected by the temperature and surrounding environment, thus it has been observed at low temperatures. The creation and manipulation of entanglement at finite temperatures is of crucial interest. To fulfill creating robust free (distillable) entanglement at finite temperatures, in this article, thermally-induced free entanglement of a Λ-type three-level atom and bimodal photons amid an optical lossless cavity, is investigated. We assume that the system is in thermal equilibrium with an environment thus the probabilities for finding the system in either of its eigenvalues are associated with the Boltzmann distribution. Introducing a conserved (Casimir) operator, a standard and effective procedure is then developed to calculate analytically the eigenvalues and eigenstates of the Hamiltonian, and thereby, to compute the thermal density operator and its partial transpose over atomic states. To justify the behavior of free (distillable) atom–photon entanglement, the quantitative form of Peres–Horodecki criteria, i.e. the negativity, is calculated. The analytical calculations show that the negativity vanishes at zero temperature, approaches to its maximum at a specific temperature and subsequently decreases asymptotically to zero. Furthermore, it is also illustrated that the maximum is larger for stronger atom–photon coupling while it decreases for greater atom–photon detuning. In addition, it is deduced from the representative figures that how the atom–photon structure parameters influence on the negativity.

Experimental Microwave Scattering in Polygonal Billiards

Fluctuations in the one-port scattering and normalized impedance matrices in three polygonal and one chaotic time-reversal invariant microwave billiards are experimentally investigated, in several levels of coupling and absorption, at room temperature and at 77 K. The observed distributions of reflection coefficient, phase of the scattering matrix, resistance and reactance exhibit no fingerprint of a given geometry. At low frequencies, the results are consistent with earlier theoretical models by López, Mello and Seligman and by Zheng, Antonsen and Ott, who independently predicted that the scattering fluctuations might be the same for the Wigner and Poisson level spacing distributions in the lossless cavity. The uniqueness of the observed scattering statistics at higher absorption levels is discussed with respect to inherent limitations posed by the experimental technique.

Atom-atom entanglement in a not-resonant two-photon Tavis-Cummings model

The entanglement between two two-level atoms (qubits) interacting not-resonantly with a one mode of thermal field in a lossless cavity via effective degenerate two-photon transitions is investigated. Based on the exact solution for the time-dependent density matrix of the system under consideration, negativity is calculated as a measure of the entanglement of atoms. The influence of a detuning on the dynamics of entanglement of atoms for separable and entangled initial atomic states and thermal cavity state is investigated.

Entanglement between artificial atoms and photons of lossless cavities

We investigated the dynamics of atom-field entanglement for two natural or artificial two-level atoms interacting with a one-mode quantum electromagnetic field by means of multiphoton transitions in a lossless cavity. Tavis-Cummings model is used to describe the interaction of the atoms and real microwave coplanar cavity field. We carried out the mathematical modeling of the dynamics of the system under consideration for various initial states of the atomic subsystem and an intensive coherent field of the cavity. We showed that for small multiplicities, the atoms and the field, which were initially in a pure separable state, can return to this state during the evolution. We also found that for large multiplicities the atoms and the field are in the entangled atom-field state in the process of the system evolution with the exception of the initial time instant. These results can be used in the theory of quantum networks.

Thermal Entanglement Between a Jaynes-Cummings Atom and an Isolated Atom

We studied the entanglement of a quantum system consisting of a Jaynes-Cummings atom, thermal lossless cavity and an isolated atom. The analytical expressions of the atom-atom negativity for separable and entangled initial atomic states were obtained. The influence of a detuning between the atomic transition frequency and the field frequency and direct dipole-dipole interaction on an atom-atom entanglement is examined. We showed that for a separable initial atomic states a detuning might cause high atom-atom entanglement in the presence of the dipole-dipole interaction. We also obtained that for an entangled initial atomic state a detuning causes a stabilization of an entanglement oscillations both for model with dipole-dipole interaction and model without such interaction.

Entanglement of two dipole-coupled qubits induced by a detuned thermal field

In this paper we have investigated the dynamics of entanglement of two identical qubits non-resonantly interacting with one mode of a vacuum or a thermal electromagnetic field in lossless cavity in the presence of a direct dipole-dipole interaction. Based on the exact solution to the equation used in this analysis, the Peres-Horodecki entanglement parameter (negativity) for qubits has been found. Numerical simulation of the negativity for various model parameters has been carried out. It has been shown that the interactions of qubits with a thermal field in a cavity can lead to their entanglement. It has been established that the detuning and dipole-dipole interaction of qubits can be used to manipulate and control the amount of atomic entanglement.

Effects of cavity–cavity interaction on the entanglement dynamics of a generalized double Jaynes–Cummings model

We consider a generalized double Jaynes–Cummings model consisting of two isolated two-level atoms, each contained in a lossless cavity that interact with each other through a controlled photon-hopping mechanism. We analytically show that at low values of such a mediated cavity–cavity interaction, the temporal evolution of entanglement between the atoms, under the effects of cavity perturbation, exhibits the well-known phenomenon of entanglement sudden death (ESD). Interestingly, for moderately large interaction values, a complete preclusion of ESD is achieved, irrespective of its value in the initial atomic state. Our results provide a model to sustain entanglement between two atomic qubits, under the adverse effect of cavity induced perturbation, by introducing a non-intrusive inter-cavity photon exchange that can be physically realized through cavity-QED setups in contemporary experiments.

Single-block pulse-on electro-optic Q-switch made of LiNbO3

A novel LiNbO3 (lithium niobate, LN) electro-optic (EO) Q-switch that can independently operate in the pulse-on regime without the assistance of a quarter-wave plate (QWP) or analyzer was designed and demonstrated. By theoretical analysis and calculations, the proper orientation of the LN was determined to be θ = 1.7° and φ = ±45°, and the quarter-wave voltage was identical to that of a conventional LN EO Q-switch. Additionally, the possible influences caused by the small angular variation between the wave normal and optic axis were found to be negligible. To the best of our knowledge, this is the first time that a LN crystal has been (xztw)-1.2°/1.2°-cut and used successfully in a pulse-on cavity without using a QWP or analyzer. The performance of the novel Q-switched laser and its temperature dependence were verified to be almost identical to those of a conventional pulse-on LN EO Q-switched laser, which strongly demonstrates the practicability of our novel Q-switch. This novel Q-switch design enables a more compact, lossless and stable laser cavity, which is of great concern for engineering applications.

Photon echoes for a system of large negative spin and few photons

Persistent photon echoes (revivals) are seen for a large number (N) of two-level molecules (TLMs) prepared initially in the all-down state interacting in a lossless cavity with a photon distribution with a small mean photon number. This case has not been addressed previously revealing characteristic times proportional to the square root of N. Unexpectedly, this behavior is independent of the initial photon distribution (including thermal) and long after the initial echoes die out, they re-emerge completely. Entropy, disentanglement and the Q function are considered with complete disentanglement only occurring at the revival times. Comparison is made to established results.

Ultrawideband Flush-Mounted Antenna

A wideband compact antenna that can be flush mounted on a platform for high-power broadside transmitting applications is introduced. The proposed design comprises a transvers electromagnetic (TEM) horn embedded in a shaped rectangular cavity. The detrimental interaction with the lossless cavity is mitigated by properly integrating the TEM horn inside the cavity. This approach allows the antenna to radiate as an aperture antenna at low frequencies while maintaining good radiation features from the TEM horn at higher frequencies. Elliptically shaped ridges are also added inside the cavity to improve gain and the quality of radiation patterns at the high-frequency end. The proposed antenna has electrical size of ∼0.28 $\lambda $ × 0.54 $\lambda $ × 0.3 $\lambda $ (length × width × depth) at the turn-on frequency and has VSWR 5 dBi, and good radiation patterns with low cross polarization from 2 to 7 GHz.

Switchable 10 nm-spaced dual-wavelength SLM fiber laser with sub-kHz linewidth and high OSNR using a novel multiple-ring configuration

A switchable dual-wavelength (10 nm spacing) single-longitudinal-mode (SLM) erbium-doped fiber laser (EDFL) that uses a multiple-ring configuration was demonstrated experimentally. A novel theoretically lossless triple-ring passive secondary cavity composed of three optical couplers was utilized to select the SLM from the dense main cavity longitudinal modes for the first time. Using two superimposed fiber Bragg gratings as one compact mode-restricting element and introducing the nonlinear polarization rotation effect to alleviate the strong mode competition for the fiber laser, a highly stable dual-wavelength mode-hop-free SLM operation with sub-kHz linewidths and optical signal to noise ratios (OSNRs) of >69 dB was achieved for both lasing wavelengths. By adjusting the polarization controllers, the dual-wavelength operation could be easily switched to single-wavelength lasing with a linewidth of <1 kHz and an OSNR of >72 dB. The proposed EDFL may find many important applications, such as the generation of very pure terahertz waves.

Nonlinear Jaynes–Cummings model for two interacting two-level atoms

In this work we examine a nonlinear version of the Jaynes–Cummings model for two identical two-level atoms allowing for Ising-like and dipole–dipole interplays between them. The model is said to be nonlinear in the sense that it can incorporate both a general intensity-dependent interaction between the atomic system and the cavity field and/or the presence of a nonlinear medium inside the cavity. As an example, we consider a particular type of atom-field coupling based upon the so-called Buck–Sukumar model and a lossless Kerr-like cavity. We describe the possible effects of such features on the evolution of some quantities of current interest, such as atomic excitation, purity, concurrence, the entropy of the field and the evolution of the latter in phase space.