Quantum Optical Model Research Articles

Effect of Mth coherent state on the interaction between two two-level atoms and two-mode quantized field

The objective of this work is to measure the influence of the Mth coherent state on the optics model of two atoms interacting with two-mode quantized field. Also, two atoms interacting together is included in this optics model. The time-dependent wave function is computed analytically. The two-mode quantized field is in the Mth coherent state while the two atoms have two levels. The influence of the Mth coherent state on the quantum model is measured via studying the atomic inversion, von Neumann entropy, variance squeezing, correlation function and Husimi function. The influence of each mode of the quantized field separately and both modes together are discussed. The statistical measures indicate that the nonclassical quantized features increase in the presence of the Mth coherent state, and it features a controlling mechanism. This study opens up a wide range of a large number of serious applications for the quantum optics models.

Understanding the Quantum Rabi Ring Using Analogies to Quantum Magnetism.

We map a quantum Rabi ring, consisting of N cavities arranged in a ring geometry, into an effective magnetic model containing the XY exchange and the Dzyaloshinskii-Moriya (DM) interactions. The analog of the latter is induced by an artificial magnetic field, which modulates photon hopping between nearest-neighbor cavities with a phase. This mapping facilitates the description and understanding of the different phases in the quantum optical model through simple arguments of competing magnetic interactions. For the square geometry (N=4) the rich phase diagram exhibits three superradiant phases denoted as ferro-superradiant, antiferro-superradiant, and chiral superradiant. In particular, the DM interaction is responsible for the chiral phase in which the energetically degenerate configurations of the order parameters are similar to the in-plane magnetizations of skyrmions with different helicities. The antiferro-superradiant phase is suppressed in the triangle geometry (N=3) as geometric frustration contributes to stabilize the chiral phase even for small values of the DM interaction. The chiral phases for odd and even N show a different scaling behavior close to the phase transition. The equivalent behavior on both systems opens the possibility of simulating chiral magnetism in a few-body quantum optical platform, as well as understanding one system using the insights gained from the other.

On Faithful Matrix Representations of q-Deformed Models in Quantum Optics

Consider the q -deformed Lie algebra, t q : K ^ 1 , K ^ 2 q = 1 − q K ^ 1 K ^ 2 , K ^ 3 , K ^ 1 q = s K ^ 3 , K ^ 1 , K ^ 4 q = s K ^ 4 , K ^ 3 , K ^ 2 q = t K ^ 3 , K ^ 2 , K ^ 4 q = t K ^ 4 , and K ^ 4 , K ^ 3 q = r K ^ 1 , where r , s , t ∈ ℝ − 0 , subject to the physical properties: K ^ 1 and K ^ 2 are real diagonal operators, and K ^ 3 = K ^ 4 † , ( † is for Hermitian conjugation). The q -deformed Lie algebra, t q is introduced as a generalized model of the Tavis–Cummings model (Tavis and Cummings 1968, Bashir and Sebawe Abdalla 1995), namely, K ^ 1 , K ^ 2 = 0 , K ^ 1 , K ^ 3 = − 2 K ^ 3 , K ^ 1 , K ^ 4 = 2 K ^ 4 , K ^ 2 , K ^ 3 = K ^ 3 , K ^ 2 , K ^ 4 = K ^ 4 , and K ^ 4 , K ^ 3 = K ^ 1 , which is subject to the physical properties K ^ 1 and K ^ 2 are real diagonal operators, and K ^ 3 = K ^ 4 † . Faithful matrix representations of the least degree of t q are discussed, and conditions are given to guarantee the existence of the faithful representations.

Quantum analog of the Kolmogorov-Arnold-Moser theorem in the anisotropic Dicke model and its possible implications in the hybrid Sachdev-Ye-Kitaev models

The classical Kolmogorov-Arnold-Moser (KAM) theorem provides the underlying mechanism for the stability of the solar system under some small chaotic perturbations. Despite many previous efforts, any quantum version of the KAM theorem remains elusive. In this work, we provide a quantum KAM theorem in the context of the anisotropic Dicke model, which is the most important quantum optics model. It describes a single mode of photons coupled to $N$ qubits with both a rotating wave (RW) term and a counter-RW (CRW) term. As the ratio of the CRW over the RW term increases from zero to one, the systems evolves from quantum integrable to quantum chaotic. We establish a quantum KAM theorem to characterize such an evolution quantitatively by both large-$N$ expansion and random matrix theory and find agreement from the two complementary approaches. Connections and differences between the Dicke models and Sachdev-Ye-Kitaev (SYK) or hybrid SYK models are examined. A possible quantum KAM theorem in terms of other quantum chaos criteria such as the quantum Lyapunov exponent is also discussed.

Entanglement and atomic inversion for two two-level atoms interacting with an intensity-dependent quantized field

Our aim is to present an analytical solution for the quantum optics model that has two two-level atoms interacting together and interacting with an intensity-dependent quantized field. The quantized field is initially in binomial state and based on the Lamb–Dicke parameter and associated Laguerre polynomials. While two atoms are symmetric and initially in superposition state. Besides, the quantum entanglement between the quantum system components under the effect of the parameters of detuning, coupling, binomial, Lamb–Dicke and the initial state of the model is discussed. Several phenomena have been clearly observed and analyzed, such as entanglement sudden death (ESD) followed by entanglement sudden birth (ESB) in the concurrence and the negativity curves, and long-lived quantum coherence in the von Neumann entropy curve. In addition, the presence of revivals and collapses in the atomic population inversion curves has been figured out. Our analysis aims to help the scientists to determine the critical values required of quantum system parameters to control entanglement dynamics.

Theoretical analysis of a polarized two-photon Michelson interferometer with broadband chaotic light

Two-photon interference of broadband chaotic light in a Michelson interferometer is theoretically and numerically studied with a two-photon-absorption detector when polarizations are taken into account. Under the frame of quantum optics, the theoretical analysis is based on two-photon interference and Feynman path integral theory. A two-photon coherence matrix is introduced to calculate the second-order interference pattern. Our research shows that polarization is another dimension, as well as time and space, to tune the second-order interference pattern in the two-photon interference process. Polarizations can act as switches to manipulate the interference process and may open the door to some new experimental schemes. The quantum optical vector model is also helpful to understand the physics of second-order interference when the light source is quantum.

Generalization of the Tavis-Cummings model for multi-level anharmonic systems: Insights on the second excitation manifold.

Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light-matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis-Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N2 × N2 Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.

Experimental Realization of the Rabi-Hubbard Model with Trapped Ions

Quantum simulation provides important tools in studying strongly correlated many-body systems with controllable parameters. As a hybrid of two fundamental models in quantum optics and in condensed matter physics, the Rabi-Hubbard model demonstrates rich physics through the competition between local spin-boson interactions and long-range boson hopping. Here, we report an experimental realization of the Rabi-Hubbard model using up to 16 trapped ions and present a controlled study of its equilibrium properties and quantum dynamics. We observe the ground-state quantum phase transition by slowly quenching the coupling strength, and measure the quantum dynamical evolution in various parameter regimes. With the magnetization and the spin-spin correlation as probes, we verify the prediction of the model Hamiltonian by comparing theoretical results in small system sizes with experimental observations. For larger-size systems of 16 ions and 16 phonon modes, the effective Hilbert space dimension exceeds 2^{57}, whose dynamics is intractable for classical supercomputers.

Exciton–polarons in two-dimensional semiconductors and the Tavis–Cummings model

The elementary optical excitations of a two-dimensional electron or hole system have been identified as exciton-Fermi-polarons. Nevertheless, the connection between the bound state of an exciton and an electron, termed trion, and exciton–polarons is subject of ongoing debate. Here, we use an analogy to the Tavis–Cummings model of quantum optics to show that an exciton–polaron can be understood as a hybrid quasiparticle—a coherent superposition of a bare exciton in an unperturbed Fermi sea and a bright collective excitation of many trions. The analogy is valid to the extent that the Chevy Ansatz provides a good description of dynamical screening of excitons and provided the Fermi energy is much smaller than the trion binding energy. We anticipate our results to bring new insight that could help to explain the striking differences between absorption and emission spectra of two-dimensional semiconductors.

Chaos in a deformed Dicke model

The critical behavior in an important class of excited state quantum phase transitions is signaled by the presence of a new constant of motion only at one side of the critical energy. We study the impact of this phenomenon in the development of chaos in a modified version of the paradigmatic Dicke model of quantum optics, in which a perturbation is added that breaks the parity symmetry. Two asymmetric energy wells appear in the semiclassical limit of the model, whose consequences are studied both in the classical and in the quantum cases. Classically, Poincaré sections reveal that the degree of chaos not only depends on the energy of the initial condition chosen, but also on the particular energy well structure of the model. In the quantum case, Peres lattices of physical observables show that the appearance of chaos critically depends on the quantum conserved number provided by this constant of motion. The conservation law defined by this constant is shown to allow for the coexistence between chaos and regularity at the same energy. We further analyze the onset of chaos in relation with an additional conserved quantity that the model can exhibit.

Beyond the Rabi model: Light interactions with polar atomic systems in a cavity

The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single-cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering an atom without permanent dipole moments, whose excitation energy is quasiresonant with the cavity photon energy, and by neglecting the nonresonant (counter-rotating) terms. In this case, after including the decay of either the atom or the cavity mode to a continuum, one can derive the well-known phenomenology of quasiresonant transitions, including the fluorescence triplets. In this work we consider the most general Rabi model, incorporating the effects of permanent atomic electric dipole moments. Based on a perturbative analysis, we compare the intensities of emission lines induced by rotating terms, counter-rotating terms, and parity-symmetry-breaking terms in order to identify the parameter regimes in which these different contributions play a significant role. The analysis reveals that the emission strength related to the existence of permanent dipoles may surpass the one due to the counter-rotating interaction terms but is usually much weaker than the emission due to the main, resonant coupling. This ratio can be modified in systems with a reduced dimensionality or by engineering the energy spectral density of the continuum.

Connecting Fano interference and the Jaynes-Cummings model in cavity magnonics

We show that Fano interference can be realized in a macroscopic microwave cavity coupled to a spin ensemble at room temperature. Via a formalism developed from the linearized Jaynes-Cummings model of cavity electromagnonics, we show that generalized Fano interference emerges from the photon–magnon interaction at low cooperativity. In this regime, the reflectivity approximates the scattering cross-section derived from the Fano-Anderson model. Although asymmetric lineshapes in this system are often associated with the Fano formalism, we show that whilst Fano interference is actually present, an exact Fano form cannot be achieved from the linear Jaynes-Cummings model. In the Fano model an additional contribution arises, which is attributed to decoherence in other systems, and in this case is due to the resonant nature of the photonic mode. The formalism is experimentally verified and accounts for the asymmetric lineshapes arising from the interaction between magnon and photon channels. As the magnon–photon coupling strength is increased, these channels merge into hybridized magnon–photon modes and the generalized Fano interference picture breaks down. Our results are universally applicable to systems underlying the linearized Jaynes-Cummings Hamiltonian at low cooperativity and connect the microscopic parameters of the quantum optical model to generalized Fano lineshapes.

Describing High-Order Harmonic Generation Using Quantum Optical Models

Optical generation of high-order harmonics is a prototypical example of nonlinear light–matter interactions in the high-field regime. Quantum optical effects have recently been demonstrated to have a significant influence on this phenomenon. These findings underline the importance of understanding the dynamics of the quantized electromagnetic field during high-order harmonic generation. In the following, we discuss the challenges that are related to the theoretical description of this process and summarize the results that were obtained using the high-field, multimode generalization of well-known quantum optical models that are based on the concept of the two-level atom.

Magnetically induced optical transparency in a plasmon-exciton system

Plasmonic structures such as metal nanoparticles (MNPs) provide a promising way to explore and control light in a solid-state environment. Here, we study a hybrid system composed of a localized surface plasmon mode of a MNP interacting with a semiconductor quantum dot (QD) subject to a Faraday magnetic field. The MNP-QD system is driven by an externally applied probe laser field and then its scattering photons are detected in the far field. To this end, employing a full quantum optical model, we theoretically calculate and demonstrate the scattering spectrum of the system via a combination of analytical and numerical techniques with realistic parameters. It is found that the applied magnetic field can be utilized to efficiently regulate and control the scattering line shapes. In particular, a class of optical transparency is induced in the scattering spectrum of the plasmon-excition (plexcitonic) system that we refer to as magnetically induced plexcitonic transparency. At the same time, a sharp double-Fano resonance profile is generated in the presence of the magnetic field. The predicted features of the spectra have potential applications in designing sensitive on-chip devices.

On the [formula omitted]-deformed Dirac oscillator in [formula omitted]-dimensional space–time

We point out invalid results concerning a q-deformed Dirac oscillator in two dimensions (2D DO) studied by some authors. We propose another deformed variant of this model and obtain its exact energy eigenvalues and their associated eigenstates. We find in particular that the deformation breaks the infinite degeneracy of the energy spectrum, thereby changing drastically the dynamics of the oscillator. The behavior of the system in the presence of a constant transverse magnetic field is investigated in detail. The parallelism with Jaynes–Cummings (JC) and Anti-Jaynes–Cummings (AJC) models of quantum optics, and the zitterbewegung (ZB) phenomenon are also discussed.

Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion

Quantum phase transitions (QPTs) are usually associated with many-body systems in the thermodynamic limit when their ground states show abrupt changes at zero temperature with variation of a parameter in the Hamiltonian. Recently it has been realized that a QPT can also occur in a system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report an experimental demonstration of a QPT in the QRM using a 171Yb+ ion in a Paul trap. We measure the spin-up state population and the average phonon number of the ion as two order parameters and observe clear evidence of the phase transition via adiabatic tuning of the coupling between the ion and its spatial motion. An experimental probe of the phase transition in a fundamental quantum optics model without imposing the thermodynamic limit opens up a window for controlled study of QPTs and quantum critical phenomena.

Polaritonic Chemistry: Collective Strong Coupling Implies Strong Local Modification of Chemical Properties.

A fundamental question in the field of polaritonic chemistry is whether collective coupling implies local modifications of chemical properties scaling with the ensemble size. Here we demonstrate from first-principles that an impurity present in a collectively coupled chemical ensemble features such locally scaling modifications. In particular, we find the formation of a novel dark state for a nitrogen dimer chain of variable size, whose local chemical properties are altered considerably at the impurity due to its embedding in the collectively coupled environment. Our simulations unify theoretical predictions from quantum optical models (e.g., collective dark states and bright polaritonic branches) with the single molecule quantum chemical perspective, which relies on the (quantized) redistribution of charges leading to a local hybridization of light and matter. Moreover, our findings suggest that recently developed ab initio methods for strong light-matter coupling are suitable to access these local polaritonic effects and provide a detailed understanding of photon-modified chemistry.

Green's-function formalism for resonant interaction of x rays with nuclei in structured media

The resonant interaction between x-ray photons and nuclei is one of the most exciting subjects of the burgeoning field of x-ray quantum optics. A resourceful platform used so far are thin-film x-ray cavities with embedded layers or M\"ossbauer nuclei such as $^{57}\mathrm{Fe}$. A new quantum optical model based on the classical electromagnetic Green's function is developed to investigate theoretically the nuclear response inside the x-ray cavity. The model is versatile and provides an intuitive picture about the influence of the cavity structure on the resulting spectra. We test its predictive powers with the help of the semiclassical coherent scattering formalism simulations and discuss our results for increasing complexity of layer structures.

Dicke model.

The Dicke model is a fundamental model of quantum optics, which describes the interaction between light and matter. In the Dicke model, the light component is described as a single quantum mode, while the matter is described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model shows a mean-field phase transition to a superradiant phase. This transition belongs to the Ising universality class and was realized experimentally in cavity quantum electrodynamics experiments. Although the superradiant transition bears some analogy with the lasing instability, these two transitions belong to different universality classes.

Dissipation-induced bistability in the two-photon Dicke model

The Dicke model is a paradigmatic quantum-optical model describing the interaction of a collection of two-level systems with a single bosonic mode. Effective implementations of this model made it possible to observe the emergence of superradiance, i.e., cooperative phenomena arising from the collective nature of light-matter interactions. Via reservoir engineering and analogue quantum simulation techniques, current experimental platforms allow us not only to implement the Dicke model but also to design more exotic interactions, such as the two-photon Dicke model. In the Hamiltonian case, this model presents an interesting phase diagram characterized by two quantum criticalities: a superradiant phase transition and a spectral collapse, that is, the coalescence of discrete energy levels into a continuous band. Here, we investigate the effects of both qubit and photon dissipation on the phase transition and on the instability induced by the spectral collapse. Using a mean-field decoupling approximation, we analytically obtain the steady-state expectation values of the observables signaling a symmetry breaking, identifying a first-order phase transition from the normal to the superradiant phase. Our stability analysis unveils a very rich phase diagram, which features stable, bistable, and unstable phases depending on the dissipation rate.