Gain saturation is ubiquitous but has not been fully explored in the newly developed field of non-Hermitian optics. On the other hand, the nonclassical properties of light are highly relevant to the gain saturation that influences the quantum noise accompanying light amplification. In this paper, we systematically examine the gain saturation effects in a non-Hermitian system of coupled gain-loss waveguides. We explain the impact of gain saturation on a quantum light field dynamically evolving in the coupled system. In contrast to the ideal situation without gain saturation, one can achieve a quasisteady state under the gain saturation. Moreover, gain saturation reduces the influence of amplification noise and thereby better preserves such quantum features as entanglement. We illustrate the effects of gain saturation by examining the time evolution of the Wigner function, entanglement of the light fields, and the cross-correlation function between the two output modes. Significant differences exist between unsaturated and saturated situations, especially for low photon numbers.
Gain saturation is ubiquitous but has not been fully explored in the newly developed field of non-Hermitian optics. On the other hand, the nonclassical properties of light are highly relevant to the gain saturation that influences the quantum noise accompanying light amplification. In this paper, we systematically examine the gain saturation effects in a non-Hermitian system of coupled gain-loss waveguides. We explain the impact of gain saturation on a quantum light field dynamically evolving in the coupled system. In contrast to the ideal situation without gain saturation, one can achieve a quasisteady state under the gain saturation. Moreover, gain saturation reduces the influence of amplification noise and thereby better preserves such quantum features as entanglement. We illustrate the effects of gain saturation by examining the time evolution of the Wigner function, entanglement of the light fields, and the cross-correlation function between the two output modes. Significant differences exist between unsaturated and saturated situations, especially for low photon numbers.
We examine the gain saturation effect in non-Hermitian systems of coupled gain–loss waveguides and whispering-gallery-mode microresonators, through which a continuous-variable (CV) entanglement of light fields is generated. Here, we consider squeezed vacuum inputs for coupled waveguide setup and coherent drive for coupled microresonators, and study the influence from the saturation of the used optical gain. Unlike the ideal situation without gain saturation, it is possible to generate stabilized entanglement measured by logarithmic negativity under gain saturation. Both types of setups realize steady CV entanglement, provided that the gain saturation is sufficiently quick. Particularly, with the coupled microresonators which are pumped by coherent drive, the created CV entanglement is actually out of the gain noise with a squeezing characteristic, under the condition of fast saturation of the initial optical gain.
It is generally difficult to study the dynamical properties of a quantum system with both inherent quantum noises and nonperturbative nonlinearity. Due to the possibly drastic intensity increase of an input coherent light in gain-loss waveguide couplers with parity-time (PT) symmetry, the Kerr effect from a nonlinearity added into the system can be greatly enhanced and is expected to create macroscopic entangled states of the output light fields with huge photon numbers. Meanwhile, quantum noises also coexist with the amplification and dissipation of the light fields. Under the interplay between the quantum noises and nonlinearity, the quantum dynamical behaviors of the systems become rather complicated. However, the important quantum noise effects have been mostly neglected in previous studies about nonlinear PT-symmetric systems. Here we present a solution to this nonperturbative quantum nonlinear problem, showing the real-time evolution of the system observables. The enhanced Kerr nonlinearity is found to give rise to a previously unknown decoherence effect that is irrelevant to the quantum noises and imposes a limit on the emergence of macroscopic nonclassicality. In contrast to what happens in linear systems, the quantum noises exert significant impact on the system dynamics and can create nonclassical light field states in conjunction with the enhanced Kerr nonlinearity. This study on the noise involved in quantum nonlinear dynamics of coupled gain-loss waveguides can help to better understand the quantum noise effects in many nonlinear systems.
We use a non-Lindbladian master equation of the Scully-Lamb laser model for the analysis of light propagation in a parity-time symmetric photonic system composed of coupled active and passive whispering-gallery microresonators. Performing the semiclassical approximation, we obtain a set of two nonlinear coupled differential equations describing the time evolution of intracavity fields. These coupled equations are able to explain the experimentally observed light nonreciprocity [Peng et al., Nat. Phys. 10, 394 (2014); Chang et al., Nat. Photon. 8, 524 (2014)]. We show that this effect arises from the interplay between gain saturation in the active microcavity, intercavity coupling, and losses in the cavities. Additionally, using this approach, we study the effect of the gain saturation on exceptional points, i.e., exotic degeneracies in non-Hermitian systems. Namely, we demonstrate that the inclusion of gain saturation leads to a modification of the exceptional points in the presence of intense intracavity fields. The Scully-Lamb master equation for systems of coupled optical structures, as proposed and applied here, constitutes a promising tool for the study of quantum optical effects in coupled systems with losses, gain, and gain saturation.
Loss was typically considered a nemesis to optics, which should always be avoided or compensated. On the other hand, gain would be a valuable asset, allowing for mitigating losses and increasing the signal power. However, research has blurred those boundaries, demonstrating that their role can not be simply categorized this way. For instance, loss gives access to nonlinear eects in linear devices, and linear gain introduce additional noise to a quantum system. Undeniably, their role in quantum optics can not be ignored, and this is the path this Ph.D. dissertation follows. First, a general method to compute the input-output relations in any lossy linear N-port device is presented. The method, based on the singular value decomposition (SVD), allows for the analysis of quantum interference in the device and, at the same time, provides an intuitive picture of its classical operation principle. The method's applicability is demonstrated by using dierent reciprocal and nonreciprocal devices. In particular, using this SVD-based procedure to analyze quantum interference in a Wilkinson power divider (WPD) reveals interesting physics in the device. It is theoretically demonstrated that WPDs grant access to coherent perfect absorption (CPA) quantum state transformations in CPA networks with a smaller footprint and a reduced number of elements, which might contribute to reducing the size and complexity of optical networks. Additionally, numerical simulations suggest that WPDs can be designed in a pure silicon-on-insulator platform by taking advantage of radiative losses. Balanced gain-loss optical systems are also investigated. In particular, a method that identies the photonic quantum eigenmodes of the spatial evolution in coupled gain-loss waveguides is proposed, indicating that the associated statistics could be measured using standard detection techniques. Therefore, the noise generation in dierent coupled waveguides is studied, emphasizing its relation with the linear or nonlinear nature of the gain/loss mechanism. The existence of phase transition points in the eigenvalue/eigenvector structure, the possibility of gain and loss mechanisms of different nature to compensate for each other, and the nontrivial properties of the system's uctuations are some of the outcomes of the presented study, thus contributing to a better understanding of non-Hermitian quantum systems. Last but not least, relevant results on scattering theory are presented. The generalized optical theorem is used to derive upper bounds on the cross-polarized backscattering cross-section of systems integrated with a ground plane. Moreover, viable strategies to design these backscatterers based on highly-directive scattering systems are identified.
Optical parametric amplification is a process that leads to the generation of quantum states of light. In the limit of low single-pass gain, this process is often referred to as parametric down conversion, and produces entangled two-photon states. Such states have played a key role in recent studies of quantum optical effects such as quantum teleportation. As the gain of the parametric amplification process is increased, the generated light field still possesses strong quantum correlations, but not of the sort associated with two-photon states. Here we present an analysis of the output state of a parametric amplifier as a function of the single-pass gain, and we find certain signatures of quantum light (such as the vanishing of the coincidence rate in a Hong-Ou-Mandel interferometer) disappear in the high-gain limit, whereas others (such as the existence of two-photon interference fringes) remain. Consequently, the intense light field generated by a high-gain parametric amplifier can be utilized in such applications of quantum optics.
Non-Hermitian quantum mechanics has emerged as a powerful framework for describing open quantum systems, particularly in optical platforms where engineered gain and loss can lead to exotic phenomena. This paper theoretically investigates the synthesis of non-Hermitian quantum light within driven photonic crystals. We propose a methodology that leverages the unique dispersion engineering capabilities of photonic crystals, coupled with controlled introduction of gain and loss elements and strong classical driving fields. Our approach aims to generate novel quantum light states characterized by non-Hermitian properties, such as modified photon statistics, entanglement, and the manifestation of exceptional points in quantum correlations. The paper outlines the theoretical foundations, reviews relevant prior work in non-Hermitian optics and quantum light generation in photonic structures, and details a specific methodology involving coupled resonator systems and nonlinear optical processes. We predict that such driven non-Hermitian photonic crystals can offer unprecedented control over quantum light properties, enabling the generation of squeezed states with enhanced sensitivity, robust entangled photon pairs, and potentially new regimes for quantum metrology and information processing. The discussion addresses the implications of these findings for fundamental quantum optics and their potential experimental realizations, highlighting the challenges and promising avenues for future research.