Optics InfoBase is the Optical Society's online library for flagship journals, partnered and copublished journals, and recent proceedings from OSA conferences.

Non-Hermitian optical systems with parity-time ($PT$) symmetry have recently revealed many intriguing prospects that outperform conservative structures. The previous works are mostly rooted in complex arrangements with controlled gain-loss interplay. Here, we demonstrate anti-$PT$ symmetry inherent in the nonlinear optical interaction based upon forward optical four-wave mixing in a laser-cooled atomic ensemble with negligible linear gain and loss. We observe that the pair of frequency modes undergo a nontrivial anti-$PT$ phase transition between coherent power oscillation and optical parametric amplification in presence of a large phase mismatch.

Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some phase-transition threshold. This stems from the existence of a parameter in the Hamiltonian governing characteristics features of eigenvalues and eigenfunctions. Varying this parameter causes real eigenvalues to coalesce and become complex conjugate pairs, signaling the occurrence of a nontrivial phase transition and the breakdown of PT symmetry. Such an appealing discovery has aroused extensive theoretical interest in extending canonical quantum theory by including non-Hermitian but PT-symmetric operators in the last two decades. Despite much fundamental theoretical success in the development of PT-symmetric quantum mechanics, an experimental observation of pseudo-Hermiticity remains elusive as these systems with complex potential seem absent in Nature. But nevertheless, the notion of PT symmetry has survived in many other branches of physics including optics, photonics, AMO physics, acoustics, electronic circuits, and material science over the past ten years, where a judicious balance of gain and loss constitutes ingeniously a PT-symmetric system. Here, although we concentrate upon reviewing recent progress on PT symmetry in optical microcavity systems, we also wish to present some new results that may help to accelerate the research in the area. These compound photonic structures with gain and loss provide a powerful platform for testing various theoretical proposals on PT symmetry, and initiate new possibilities for shaping optical beams and pulses beyond conservative structures. Throughout this article there is an effort to clearly present the physical aspects of PT-symmetry in optical microcavity systems, but mathematical formulations are reduced to the indispensable ones. Readers who prefer strict mathematical treatments should resort to the extensive list of references. Despite the rapid progress on the subject, new ideas and applications of PT symmetry using optical microcavities are still expected in the future.

Non-Hermitian (NH) extension of quantum-mechanical Hamiltonians represents one of the most significant advancements in physics. During the past two decades, numerous captivating NH phenomena have been revealed and demonstrated, but all of which can appear in both quantum and classical systems. This leads to the fundamental question: what NH signature presents a radical departure from classical physics? The solution of this problem is indispensable for exploring genuine NH quantum mechanics, but remains experimentally untouched so far. Here, we resolve this basic issue by unveiling distinct exceptional entanglement phenomena, exemplified by an entanglement transition, occurring at the exceptional point of NH interacting quantum systems. We illustrate and demonstrate such purely quantum-mechanical NH effects with a naturally dissipative light-matter system, engineered in a circuit quantum electrodynamics architecture. Our results lay the foundation for studies of genuinely quantum-mechanical NH physics, signified by exceptional-point-enabled entanglement behaviors.

Entangled multiphoton sources are essential for both fundamental tests of quantum foundations and building blocks of contemporary optical quantum technologies. While efforts over the past three decades have focused on creating multiphoton entanglement through multiplexing existing biphoton sources with linear optics and postselections, our work presents a groundbreaking approach. We observe genuine continuous-mode time-energy-entangled W-class triphotons with an unprecedented production rate directly generated through spontaneous six-wave mixing (SSWM) in a four-level triple-Λ atomic vapor cell. Using electromagnetically induced transparency and coherence control, our SSWM scheme allows versatile narrowband triphoton generation with advantageous properties, including long temporal coherence and controllable waveforms. This advancement is ideal for applications like long-distance quantum communications and information processing, bridging single photons and neutral atoms. Most importantly, our work establishes a reliable and efficient genuine triphoton source, facilitating accessible research on multiphoton entanglement.

We have theoretically analyzed nonclassical paired photons generated spontaneously from a four-level inverted-Y atomic system. We discuss the feasibility of biphoton generation due to different pumping arrangements. Two types of correlated photon pair emissions have been carefully examined: dressed cascade and dressed double-$\Lambda$ emissions. In the dressed cascade two-photon emission, the coincidence counting rate may exhibit a damped Rabi oscillation, in contrast with a simple exponential decay feature in the literatures. In the dressed double-$\Lambda$ configuration, we show that not only is the temporal correlation of entangled Stokes–anti-Stokes photons in agreement with discussions presented by Wen et al. [Phys. Rev. A 76, 013825 (2007)], but also the oscillation period may be manipulated by altering either the control Rabi frequency or the dressing Rabi frequency or both. All the observed damped Rabi oscillations in the two-photon coincidences result from the destructive interference among the possible four-wave mixing processes occurring in the atom-field interaction system. This feature of the two-photon amplitude is governed by the convolution between the phase matching and third-order nonlinear susceptibility. The methodology adopted here can be applied to other atomic-level configurations and provides a useful tool to study the spectroscopy of the system. The generated narrow-band photon pairs may have potential applications in long-distance quantum communication and quantum information processing.