Abstract We investigate a hybrid quantum system consisting of two coupled optical cavities, each containing an ensemble of coherently pumped artificial or real two-level atoms. The system is modelled within the dressed-state formalism, accounting for coherent driving and dissipative interactions with independent electromagnetic reservoirs. Focusing on the regime where the Rabi frequency greatly exceeds the collective spontaneous emission and cavity decay rates, respectively, we derive the equations of motion characterizing the system and analyse its steady-state behaviours. Special attention is given to the scenario in which only one cavity contains a pumped multi-atom ensemble, and as a consequence, coherent excitation transfer to the second cavity occurs via cavity–cavity coupling. In this case, the mean photon number in the second cavity mode scales proportional to the squared number of atoms, i.e., N2 from the first cavity. The proposed model offers insight into light–matter interaction in composite systems and suggests viable mechanisms for engineering collective interactions and non-local excitation transport in quantum optical platforms.
Abstract We investigate a hybrid quantum system consisting of two coupled optical cavities, each containing an ensemble of coherently pumped artificial or real two-level atoms. The system is modelled within the dressed-state formalism, accounting for coherent driving and dissipative interactions with independent electromagnetic reservoirs. Focusing on the regime where the Rabi frequency greatly exceeds the collective spontaneous emission and cavity decay rates, respectively, we derive the equations of motion characterizing the system and analyse its steady-state behaviours. Special attention is given to the scenario in which only one cavity contains a pumped multi-atom ensemble, and as a consequence, coherent excitation transfer to the second cavity occurs via cavity–cavity coupling. In this case, the mean photon number in the second cavity mode scales proportional to the squared number of atoms, i.e., N2 from the first cavity. The proposed model offers insight into light–matter interaction in composite systems and suggests viable mechanisms for engineering collective interactions and non-local excitation transport in quantum optical platforms.
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.
We present a study of the quantum statistical properties of light emitted by two coherently driven atoms coupled to a single-mode cavity, an ideal setup to precisely investigate various aspects of collective behavior over a wide range of couplings to cavity and external drive. At high pumping and coupling, we predict the possibility of steady-state hyperradiance accompanied by (super-)bunching for an out of phase radiation. The mean photon number can be up to 2 orders of magnitude higher than in the single atom case. The highest nonclassicality in the sense of the smallest Mandel Q parameter is found when spontaneous emission, cavity decay, coherent pumping, and atom-cavity coupling are comparable. A quantum version of the negative binomial distribution with parameters directly related to Q characterizes the photon distribution in the cavity and its quantum features.
We propose a possibility to study the quantum light excitation of atomic systems. To confine our study, we limit the configuration to two and four level emitters as target systems. Source and target are coupled via unidirectional waveguide. We numerically implement the cascaded formalism and use the source-target approach. Herein, we focus on continuous excitation scenarios where the source system is excited by continuous incoherent or coherent pumping. We demonstrate that, to a certain extent, one can control the target system's photon statistics via the source system pumping mechanism. Additionally, different coupling regimes in both cavities can change the output of the target system. In addition, we show that via tuning the cavity’s parameters one can produce an exotic type of quasi-probability distributions, a flat Fock state distributions. We also discuss the different obtained photon statistics for different coupling regimes. The used quantum light source, driven by spontaneous emission, can be categorized as a single photon source or two photon source. Therefore, the thesis is divided also according to these types of quantum light sources into two parts: In the first part of the thesis, after review of the theoretical methods, which are applied in the thesis , we specifically study coupled cavities. The first cavity, pumped incoherently, performs effectively as a single photon source. We consider system-bath interaction in the coupling waveguide, i.e boson-boson interaction, for the photon occurring in the system .We demonstrate that even for a simple scenario , where thermal bath modes couple to the system, the photon statistics of the source is not completely mapped to the target system. This suggest that the environment for such a coupled systems influence the photon statistics of the source while transferring it into the target system. In the case of direct coupling of emitters to the waveguide the influence of the environment, as a dissipator, on the photon statistics can be seen in photon number distribution. Additionally, higher order correlation functions for the target system deviate drastically from the source system and show a mixture of quantum coherent and incoherent dynamics. For the case of indirect coupling of emitters to the waveguide, when the modes of two cavities are coupled, the mediating environment also influences the photon statistics of the target system. This phenomenon manifests itself in the second-order correlation function of the source and target, wherein, while the source behaves in the anti-bunched regime, the target system shows highly bunched pattern. In the second part of thesis, we study the production of two photons in nonlinear optics. As an example, we propose an optical setup where we can produce entangled pairs of photons through the dynamical Casimir effect(DCE). By applying the laser on a superconducting surface of a metal dielectric we induce a surface plasmon polariton (SPP). SPP give rise to the enhancement of DCE such as the efficiency of two photon production exceed the common nonlinear optical processes for instance parametric down conversion. We show that the resonant enhancement of the emission of two photons happens when the excitation wavelength coincides with the amplitude of the laser light. Another even more efficient source for the two photon emission is a biexciton excitation of a quantum dot. We provide a formalism for a cascaded biexciton which can be used to show how the source biexciton, pumped coherently or incoherently, influences the target biexciton through a unidirectional waveguide, modeled as a thermal bath.
We examine the dynamics of evolution for an ensemble of three-level Λ atoms localized in a coupled cavity. In this scheme, when many atoms interact with one of the cavities, we observe Rabi oscillations between an atom and the other cavity. We show strong coupling between the ensemble and cavity is not necessary. The effective coupling can be improved by increasing the number of atoms. When the amplitude of the classical field is not equal to the photon hopping rate, for zero detunings, we achieve resonance and observe oscillations. The excited state of the atoms in one cavity may be eliminated hence suppressing atomic spontaneous emissions with an increase in the number of atoms. The optimal process range of hopping rate and classical field amplitude are found to optimize performance for a given parametric condition.
We propose a cavity quantum electrodynamic system consisting of a five-level atom coupled to a single mode of the cavity electromagnetic field. The study is focused on the regime of strong coupling between the cavity and atom. Pump laser fields and cavity fields connect the split energy levels of the atom. Instead of the well-known two-level Dicke model obtained by adiabatic elimination of the high-energy levels, we consider the pump lasers' detunings to the atomic transitions to be very small such that we can examine the influence of the higher-energy states. We have studied the effect of an external coherent drive and incoherent pumping on these higher-energy levels and observed the enhancement of intracavity photon numbers due to quantum coherence effects. The amplification of intracavity photons is achieved even without a population inversion. However, the effect of the coherent and incoherent drive is negligible for very large detunings when the higher-energy states are adiabatically eliminated. At zero and small detunings, the system reaches the steady state at an earlier instant of time for higher incoherent pumping. We find an almost agreeable steady-state behavior of the system's exact full quantum dynamics model and its semiclassical approximation. Our model tries to accurately simulate the open system by considering the cavity decay, spontaneous decay, and dephasing of the system.
We investigate a cavity mode that interacts with a three-level atom in an open cavity that is coupled to a vacuum reservoir and is driven by coherent light. In our analysis, the interaction of the three-level atom with the external vacuum reservoir is taken into account and the noise operators of the vacuum reservoir are placed in normal order. While the spontaneous emission rate fluctuates as [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], the cavity damping constant and stimulated emission decay constant, both set to 0.8, govern the system dynamics. Both the plus and negative components of the cavity light display quadrature squeezing. For coherent driving strengths [Formula: see text] and [Formula: see text] at [Formula: see text], and [Formula: see text] at [Formula: see text], the plus quadrature exhibits [Formula: see text] squeezing below the vacuum level, indicating that increasing the coherent drive can compensate for the decoherence introduced by spontaneous emission. Moreover, for [Formula: see text], the minus quadrature achieves [Formula: see text] squeezing. At high driving strengths, the squeezing in both quadratures becomes independent of spontaneous emission. In the absence of spontaneous emission, the mean photon number increases, and the photon number distribution shows a higher probability for even photon numbers than for odd ones, with the overall distribution decreasing as the photon number increases.