Here we investigate the Bloch oscillations (BOs) in a photonic spectral lattice created with four-wave mixing Bragg scattering (FWM-BS). By injecting a signal and two pumps with different frequencies into a silicon nitride waveguide, a spectral lattice can be created for the generated idlers through successive FWM-BS. The phase-mismatch during FWM-BS acts as an effective force that induces BOs in the spectral lattice. Both the oscillation period and amplitude are determined by the magnitude of the effective force. With cascaded FWM-BS processes, the spectrum of idlers experiences a directional shift as the phase differences of pumps are modulated. Additionally, introducing long-range couplings in the spectral lattice will change the trajectory of BOs within each period. The pattern of BOs for a single frequency input can also be tailored. This Letter provides a new platform to realize BOs in the frequency dimension and paves a promising way for broadband frequency control with all-optical schemes.
Here we investigate the Bloch oscillations (BOs) in a photonic spectral lattice created with four-wave mixing Bragg scattering (FWM-BS). By injecting a signal and two pumps with different frequencies into a silicon nitride waveguide, a spectral lattice can be created for the generated idlers through successive FWM-BS. The phase-mismatch during FWM-BS acts as an effective force that induces BOs in the spectral lattice. Both the oscillation period and amplitude are determined by the magnitude of the effective force. With cascaded FWM-BS processes, the spectrum of idlers experiences a directional shift as the phase differences of pumps are modulated. Additionally, introducing long-range couplings in the spectral lattice will change the trajectory of BOs within each period. The pattern of BOs for a single frequency input can also be tailored. This Letter provides a new platform to realize BOs in the frequency dimension and paves a promising way for broadband frequency control with all-optical schemes.
The possibility to perform broad wavelength generation and conversion is of great interest in classical and quantum optics. With the introduction of integrated nonlinear silicon photonics, these tasks have been made even more viable thanks to the combination of the high nonlinear refractive index of silicon with the high confinement provided by the photonic waveguides. Exploiting this platform, several solutions for wavelength conversion have been investigated, for both optical processing [1] and applications in the Mid Infrared (MIR) [2]. The possibility to perform broad and controllable wavelength generation can be exploited also for creating integrated sources of quantum states of light based on single photons [3] or correlated photon pairs [4]. Both the generation and conversion can be accomplished by means of Four Wave Mixing (FWM). FWM is a nonlinear optical process in which two pump photons at frequency are converted into signal and idler photons at frequencies and ω/ respectively (with ωI/ωS). In the particular case of wavelength conversion, FWM is stimulated by a seed wave at the same wavelength of the signal (idler) that will be converted to the wavelength of the idler (signal). FWM has to satisfy the energy conservation, according to which the relation ωP+ ωP= ωS+ ωIholds, and its efficiency is ruled by the phase matching condition. This latter condition is related to the phase mismatch among the waves involved in the FWM process, that is evaluated as Δk = kp+ kp−kS−kI, where kP, kS, kIare the wavevectors for the pump, the signal and the idler, respectively. When Δk = 0, the phase matching condition is fulfilled and the efficiency of FWM is maximized. What is important for wavelength generation and conversion is the spectral position of the phase matching condition, which determines the wavelength at which the maximum efficiency of the conversion or generation process is achieved. Because of this, techniques for the control of the phase matching condition have been developed, focusing on the possibility to tailor the Group Velocity Dispersion (GVD) through a proper engineering of the waveguide geometry [5]. While these techniques consider only the first order waveguide mode, here we propose to exploit the higher order modes propagating inside a multimode waveguide. The dispersion of the higher order modes can be used to tune the spectral position of the phase matching condition for the FWM process, achieving controllable and large spectral translation in both Stimulated Four Wave Mixing (sFWM) and Spontaneous Four Wave Mixing (SFWM).
In this work, we propose and theoretically analyze a new scheme for generation of counterpropagating photon pairs in photonic crystal waveguides through the process of spontaneous four-wave mixing. Using the fundamental properties of periodic Bloch modes in a standard photonic crystal waveguide, we demonstrate how modal phase-matching can be reached between forward-propagating pump modes and counterpropagating signal and idler modes, for generation of degenerate and non-degenerate photon pairs. We then show how this scheme can be used for generation of photon pairs that are nearly uncorrelated in the spectral degree of freedom. Such a source will be highly interesting as a heralded source of single photons, especially as the spectrally separable signal and idler photons are also spatially separated directly at the source. We conduct our investigation based on a design in silicon, yet our design concept is general and can in principle be applied to any nanostructured material platform.
Bloch oscillations (BOs) are oscillations of electrons under external constant forces in a lattice, revealing the wavelike behavior of electrons. BOs lead to the localization of the wave packet that is called Wannier-Stark localization (WSL), resulting in the inhibition of conductivity. We simulate BOs experimentally in a one-dimensional superconducting circuit with nine qubits. The nine qubits form a one-dimensional lattice and an electron is mapped to a photon. We experimentally realize the coherent control of BOs by applying a well-controlled driving force with a frequency close to BOs. We observe the competition between localization and delocalization of the wave pocket by changing the drive parameters. Our study demonstrates the visualized wave behavior of electrons and proves a way to modulate electron transport in a perfect lattice. Published by the American Physical Society 2024
In this work, we report the modeling and the experimental demonstration of intermodal spontaneous as well as stimulated four-wave mixing (FWM) in silicon waveguides.In intermodal FWM, the phase-matching condition is achieved by exploiting the different dispersion profiles of the optical modes in a multimode waveguide.Since both the energy and the wave vectors have to be conserved in the FWM process, this leads to a wide tunability of the generated photon wavelength, allowing us to achieve a large spectral conversion.We measured several waveguides that differ by their widths and demonstrate large signal generation spanning from the pump wavelength (1550 nm) down to 1202 nm.A suited setup evidences that the different waves propagated indeed on different order modes, which supports the modeling.Despite observing a reduced efficiency with respect to intramodal FWM due to the decreased modal overlap, we were able to show a maximum spectral distance between the signal and idler of 979.6 nm with a 1550 nm pump.Our measurements suggest the intermodal FWM is a viable means for large wavelength conversion and heralded photon sources.
Atomic interaction leads to dephasing and damping of Bloch oscillations (BOs) in optical lattices, which limits observation and applications of BOs. How to obtain persistent BOs is particularly important. Here, the nonlinear Bloch dynamics of the Bose–Einstein condensate with two-body and three-body interactions in deep optical lattices is studied. The damping rate induced by interactions is obtained. The damping induced by two-body interaction plays a dominant role, while the damping induced by three-body interaction is weak. However, when the two-body and three-body interactions satisfy a threshold, long-lived coherent BOs are observed. Furthermore, the Bloch dynamics with periodical modulation of linear force is studied. The frequencies of linear force corresponding to resonance and pseudoresonance are obtained, and rich dynamical phenomena, i.e., stable and strong BOs, drifting and dispersion of wave packet, are predicted. The controllable Bloch dynamics is provided with the periodic modulation of the linear force.
Nonlinear degenerate four wave mixing and cross phase modulation are established approaches for all optical frequency manipulation in a silicon chip. These approaches require exact group velocity and/or phase velocity matching of pump, signal, and idler. On the other hand, several experimental demonstrations were presented recently, where frequency of light was changed by a free carrier front propagating in a silicon waveguide. This Doppler-like effect is less known, but has important advantages for frequency manipulation on chip. It requires no phase velocity matching and is not dependent on the shape and duration of the pump pulse. It also allows packet switching and can operate in a pump power independent regime. Here, we shortly review the work on front induced indirect transitions in silicon slow light waveguides. We consider three possible interaction regimes: transmission through the front, reflection from the front, and moving with the front called surfing. We derive analytical equations for the front with a linearly rising edge, which provide a unified description of the frequency shift in all three regimes. Finally, we compare the front induced dynamic frequency conversion to the frequency shifting based on nonlinear effects like cross-phase modulation and four wave mixing.