Biphoton generation enhanced by nonlocal nonlinearity via Rydberg interactions.

Accelerating beams have been the subject of extensive research in the last few decades because of their self-acceleration and diffraction-free propagation over several Rayleigh lengths. Here, we investigate the propagation dynamics of a Fresnel diffraction beam using the nonlocal nonlinear Schrödinger equation (NNLSE). When a nonlocal nonlinearity is introduced into the linear Schrödinger equation without invoking an external potential, the evolution behaviors of incident Fresnel diffraction beams are modulated regularly, and certain novel phenomena are observed. We show through numerical calculations, under varying degrees of nonlocality, that nonlocality significantly affects the evolution of Fresnel diffraction beams. Further, we briefly discuss the two-dimensional case as the equivalent of the product of two one-dimensional cases. At a critical point, the Airy-like intensity profile oscillates between the first and third quadrants, and the process repeats during propagation to yield an unusual oscillation. Our results are expected to contribute to the understanding of NNLSE and nonlinear optics.

This review article focuses on biphoton sources based on the double‐ spontaneous four‐wave mixing (SFWM) process in laser‐cooled as well as room‐temperature or hot atomic ensembles. These biphoton sources have the advantage of providing stable frequencies, ultranarrow linewidths, and a tunability of the temporal biphoton width of more than one order of magnitude for high‐bandwidth applications. Therefore, the generated photons can be efficiently interfaced to, e.g., atomic quantum memories. In contrast, solid‐state biphoton sources typically require assistance by an optical cavity to operate at narrow linewidth that limits the tunability of the temporal width of the biphotons. Present state‐of‐the‐art double‐ SFWM biphoton sources can achieve one of the following results: a spectral linewidth of 50 kHz (290 kHz) or a temporal width of 13 (580 ns) with cold (hot) atoms, a detection rate of about 7 cps, and a generation rate of cps at a duty cycle of 0.4% or of cps in the steady state. The theoretical background of these biphoton sources, experimental implementations with cold and hot atoms, and progress over the years, will be illustrated.

We report the direct characterization of energy-time entanglement of narrow-band biphotons produced from spontaneous four-wave mixing in cold atoms. The Stokes and anti-Stokes two-photon temporal correlation is measured by single-photon counters with nanosecond temporal resolution, and their joint spectrum is determined by using a narrow linewidth optical cavity. The energy-time entanglement is verified by the joint frequency-time uncertainty product of 0.063±0.0044, which does not only violate the separability criterion but also satisfies the continuous variable Einstein-Podolsky-Rosen steering inequality.

We have numerically investigated the biphoton generation rate as a function of several parameters in the spontaneous four-wave mixing in cold atoms. It has been found that the biphoton generation rate can easily reach saturation with the intensity of the coupling laser increasing. The saturation intensity is mainly dependent on the dephasing rate of the ground states, unrelated to the pumping laser. It implies that though the biphoton waveform can be manipulated by the coupling laser, the generation rate of the biphoton cannot increase markedly after the saturation. The saturation effect also suggests that there is an optimal coupling laser for obtaining the largest biphoton generation rate with a sufficiently long coherence time.

We present a strategy for enhancing the quantum correlations of biphotons generated via spontaneous four-wave mixing in cold two-level atoms by employing frequency filters for the Rayleigh linear component of the spectrum.

The generation of nonclassical photon pairs with a long coherence time is key for applications that range from fundamental to quantum communication and metrology. Spontaneous four-wave mixing with electromagnetically induced transparency has been demonstrated as one of the most efficient methods; however, narrowing the bandwidth and producing photon pairs with a temporal length beyond 1 μs remains a technical challenge due to noise considerations and the need for cold atoms with a high optical depth (OD). In this work, we demonstrate the generation of narrowband photon pairs with a controllable coherence time up to 1.72 μs in a laser-cooled atomic ensemble with an OD as high as 130. At such a high OD, we find that the pump laser field spatial profile has a significant effect on the time–frequency entangled two-photon waveform. We also confirm the quantum particle nature of heralded narrowband single photons generated from this source.

This study explores the dynamics of highly dispersive optical solitons in nonlinear Schrödinger equations (NLSE) with non-local self-phase modulation (SPM) and polarization-mode dispersion (PMD). These nonlinear effects significantly influence soliton propagation and stability in advanced optical communication systems. Employing the Improved Modified Extended Tanh-Function Method (IMETFM), we derive exact soliton solutions, including bright, dark, singular, and combo solitons, under specific parametric conditions. The IMETFM effectively handles the complexity of the NLSE, incorporating higher-order dispersion terms (up to sixth-order) and non-local nonlinearities. Additionally, we perform a modulation instability (MI) analysis to examine the stability of steady-state solutions. This analysis uncovers the conditions under which instabilities emerge due to the interplay between dispersion and nonlinearity. The MI study offers critical insights into the growth of wave perturbations, thereby advancing the understanding of soliton stability dynamics. Graphical representations of the solutions illustrate their behavior, emphasizing the impact of non-local SPM, PMD, and MI on soliton dynamics. These findings offer valuable insights for optimizing high-capacity optical communication systems and fiber laser technologies, with broader implications for nonlinear wave phenomena in birefringent fibers and other nonlinear physical systems. This work advances the theoretical framework for soliton dynamics and lays a foundation for future experimental validations and practical applications in nonlinear optics.

In this first part, we study the existence and uniqueness of solutions of a general nonlinear Schrödinger system in the presence of diamagnetic field, local and nonlocal nonlinearities. This kind of systems models many important phenomena in nonlinear optics; multimodal optical fibers, optical pulse propagation, ferromagnetic film and optical pulse propagation in the birefringent fibers. They also govern the interaction of electron and nucleii through Coulombic potential and under the action of external magnetic field in quantum mechanics.

Nonlinear optical phenomena are typically local. Here we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms can be tailored. When the atoms are in an electromagnetically-induced transparency configuration, the atomic interactions are translated to long-range interactions between photons and thus to highly nonlocal optical nonlinearities. We derive and analyze the governing nonlinear propagation equation, finding a roton-like excitation spectrum for light and the emergence of order in its output intensity. These predictions open the door to studies of unexplored wave dynamics and many-body physics with highly-nonlocal interactions of optical fields in one dimension.

We address the problem of achieving a random laser with a cloud of cold atoms, in which gain and scattering are provided by the same atoms. In this system, the elastic scattering cross-section is related to the complex atomic polarizability. As a consequence, the random laser threshold is expressed as a function of this polarizability, which can be fully determined by spectroscopic measurements. We apply this idea to experimentally evaluate the threshold of a random laser based on Raman gain between non-degenerate Zeeman states and find a critical optical thickness on the order of 200, which is within reach of state-of-the-art cold-atom experiments.

We have created a dark quantum superposition state of a Rb Bose-Einstein condensate and a degenerate gas of Rb2 ground-state molecules in a specific rovibrational state using two-color photo-association. As a signature for the decoupling of this coherent atom-molecule gas from the light field, we observe a striking suppression of photo-association loss. In our experiment the maximal molecule population in the dark state is limited to about 100 Rb2 molecules due to laser induced decay. The experimental findings can be well described by a simple three mode model.

We generate narrow-band frequency-tunable entangled photon pairs from spontaneous four-wave mixing in three-level cold atoms and study their two-photon quantum interference after a beam splitter. We find that the path-exchange symmetry plays a more important role in the Hong-Ou-Mandel interference than the temporal or frequency indistinguishability, and observe coalescence interference for both degenerate and nondegenerate photons. We also observe a quantum beat in the same experimental setup using either slow or fast detectors.

In this paper, a two-Λ-type five-level system is constructed by using the Zeeman energy level of the lithium atom's hyperfine structure and interacting with two optical fields which have different polarization directions. The quantum coherence effect of the system is studied under the condition of two photon resonance. Firstly, we construct the Hamiltonian of the system under the rotation frame, and get the dark state of the system by solving the eigenvalues and eigenstates of the Hamiltonian. Then, a new coupled representation is constructed by the dark state, and the preparation of the dark state of the five-level system is further studied. Finally, the density matrix motion equations of the five-level system are established, and the numerical solution is solved by program. Through numerical simulation, we give the curve of the signal light absorption intensity with its changed detuning, and from this curve. We can see that there is a transparent window near the zero of the signal light detuning, accompanied by a normal dispersion curve. The position of the transparent window corresponds to the dark state condition for the formation of the system, that is, the system is prepared to the dark state under the two-photon resonance condition, and the atoms in the dark state do not interact with the light field, so the incident signal light appears transparent.

We propose a physical setup to realize parity-time (PT) symmetric moiré optical lattices (ML) and nonlocal optical solitons in a cold Rydberg atomic system with electromagnetically induced transparency (EIT). We also show that based on the PT symmetry lattice strength and giant nonlocal Kerr nonlinearity originated from the strong, long-range atom–atom interaction, the system supports two-dimension (2D) nonlocal solitons with very low light intensity. By using numerical simulation method, we uncover the formation, properties, and dynamics of higher-order solitons and vortical ones. Our study opens a route for developing non-Hermitian nonlinear optics, especially for realizing and controlling high-dimensional weak-light optical solitons through adjustable PT-symmetric moiré lattice parameters and giant nonlocal optical nonlinearity.

We introduce a one-dimensional phenomenological model of a nonlocal medium featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, we find families of solitons of two types, even-parity (fundamental) and dipole-mode (odd-parity) ones. Stability of the solitons is explored by means of computation of eigenvalues associated with modes of small perturbations, and tested in direct simulations. We find that the stability of the fundamental solitons strictly follows the Vakhitov-Kolokolov criterion, whereas the dipole solitons can be destabilized through a Hamiltonian-Hopf bifurcation. The solitons of both types may be stable in the nonlocal model with only quintic self-attractive nonlinearity, in contrast with the instability of all solitons in the local version of the quintic model.