Multiwave Mixing Research Articles

Quantum thermalization via multiwave mixing

We discuss thermalization in a multimode quantum cavity under unitary evolution. According to general principles, an isolated system with quadratic couplings does not exhibit thermalization. However, we find that nonlinearities, here three-wave perturbation, typical for instance in superconducting Josephson systems, may lead to thermalization into a Bose-Einstein distribution of occupations of the modes. The temperature of this state is dictated by energy conservation in this closed system, and the thermal distribution is robust against weak disturbances. We discuss how our findings open up new avenues to experimentally probe fundamental assumptions of statistical physics in solid-state systems. Published by the American Physical Society 2024

Coherent control of spatially structured multi-wave mixing induced optical properties in atomic medium

Coherent control of spatially structured multi-wave mixing induced optical properties in atomic medium

Inelastic two-wave mixing induced high-efficiency transfer of optical vortices

A scheme for high-efficiency transfer of optical vortices is proposed by an inelastic two-wave mixing (ITWM) process in an inverted-Y four-level atomic medium, which is originally prepared in a coherent superposition of two ground states. The orbital angular momentum (OAM) information in the incident vortex probe field can be transferred to the generated signal field through the ITWM process. Choosing reasonable experimentally realizable parameters, we find that the presence of the off-resonance control field can greatly improve the conversion efficiency of optical vortices, rather than in the absence of a control field. This is caused by the broken of the destructive interference between two one-photon excitation pathways. Furthermore, we also extend our model to an inelastic multi-wave mixing process and demonstrate that the transfer efficiency between multiple optical vortices strongly depends on the superposition of the ground states. Finally, we explore the composite vortex beam generated by collinear superposition of the incident vortex probe and signal fields. It is obvious that the intensity and phase profiles of the composite vortex can be effectively controlled via adjusting the intensity of the control field. Potential applications of our scheme may exist in OAM-based optical communications and optical information processing.

All-optical flip-flop by carbon/metal nanostructures in a multi-wave mixing

This work presents a design of a flip-flop controlled by the nonlinear optical response exhibited by a dynamic distribution of nanostructures in a liquid. Silver decorated carbon nanotubes suspended in ethanol were employed. The flip-flop proposed corresponds to a probabilistic NAND latch. The nonlinear nanofluids were studied by two-wave mixing experiments with nanosecond pulses at 532 nm wavelength. The behavior of the system is based on the Brownian motion with influence over the nonlinear transmittance of the nanostructures associated with a probabilistic optical bit. The optical response of the latch system output states was defined by the irradiance dependent on nonlinear optical absorption of the nanofluid. Specifically, the optical logical outputs depend on the state present at the optical inputs and the previous optical output states regulated by the feedback of the system. The nonlinear optical evolution of the effects in the nanofluids was explored as probabilistic phenomena governed by a concentration gradient of nanoparticles. The evaluation of the stability of a nanofluid defines the variables in the probabilistic system proposed. This work highlights the potential of nanohybrid materials for processing probabilistic functions, switching quantum effects, and for developing optical sensors.

Intrinsic symmetry of nonlocal nonlinear optical susceptibility tensor in degenerate multi-wave mixing

Using energy and momentum conservation laws, we obtained the intrinsic symmetry relations for the nonlocal nonlinear optical susceptibility tensor in lossless nth order nonlinear medium of arbitrary symmetry class for the case when less than n + 1 electromagnetic waves with different frequencies interact. Particular attention is devoted to the relations of the components of this tensor, which cannot be obtained as limiting case from the symmetry relations for the nonlocal nonlinear susceptibility tensor describing interaction of exactly n + 1 waves with different frequencies. The examples of these symmetry relations for degenerate second- and third-order processes often considered are given.

Extraordinary Five-Wave Mixing in a Zinc Oxide Microwire on a Au Film.

Coherent multiwave mixing is in demand for optical frequency conversion, imaging, quantum information science, etc., but has rarely been demonstrated in solid-state systems. Here, we observed three- and five-wave mixing (5WM) in a c-axis growth zinc oxide microwire on a Au film with picosecond pulses in the near-infrared region. An output 5WM of 4.7 × 10-7 μW, only 2-3 orders smaller than the three-wave mixing, is achieved when the excitation power is as low as 1.5 mW and the peak power density as weak as ∼107 W/cm2. The excitation power dependence of 5WM agrees well with the perturbation limit under the low intensity but exhibits a strong deviation at a high pumping power. This extraordinary behavior is attributed to the cooperative resonant enhancement effect when pumping in the near-infrared range. Our study offers a potential solid-state platform for on-chip multiwave mixing and quantum nonlinear optics, such as generating many-photon entangled states or the construction of photon-photon quantum logic gates.

Multichannel nonreciprocal amplifications using cesium vapor

Multichannel synchronous amplifications are an inevitable key problem in quantum communication process, which can broaden the bandwidth of transmitted signals and establish correlation among different optical channels. Here we study a nonreciprocal system with four concurrent amplification channels using hot cesium atoms, both theoretically and experimentally. For the forward probe field, the double--electromagnetically induced transparency structure is formed and the phase-matching condition of the multiwave mixing process is satisfied, which are both destroyed when the probe field is reversed. In addition, the four-channel nonreciprocal amplifications are formed in the Zeeman sublevels of the system with special selection of light field polarization, which will also dramatically enhance the signal-to-noise ratio by suppressing the spontaneous emission noise of the system. In our experiment, the quadruple nonreciprocal amplifications are achieved with the maximum forward gain reaching 30 dB and the reverse suppression reaching--23 dB. The gain adjustability allows the construction of a gain-loss balanced system, providing a scheme for an atomic system to engineer a parity-time-symmetric (or -antisymmetric) structure.

Thermalization of the Ablowitz-Ladik lattice in the presence of non-integrable perturbations.

We investigate the statistical mechanics of the photonic Ablowitz-Ladik lattice, the integrable version of the discrete nonlinear Schrödinger equation. In this regard, we demonstrate that in the presence of perturbations, the complex response of this system can be accurately captured within the framework of optical thermodynamics. Along these lines, we shed light on the true relevance of chaos in the thermalization of the Ablowitz-Ladik system. Our results indicate that when linear and nonlinear perturbations are incorporated, this weakly nonlinear lattice will thermalize into a proper Rayleigh-Jeans distribution with a well-defined temperature and chemical potential, in spite of the fact that the underlying nonlinearity is non-local and hence does not have a multi-wave mixing representation. This result illustrates that in the supermode basis, a non-local and non-Hermitian nonlinearity can in fact properly thermalize this periodic array in the presence of two quasi-conserved quantities.

Analysis of Combination Frequencies Arising from the Ionization of Gases by Multicolor Femtosecond Pulses

Ionization-induced multiwave mixing is attracting much interest nowadays due to the possibility of generating short pulses of secondary radiation over a very wide spectral range, from terahertz to far ultraviolet. This paper presents an analytical method for calculating the amplitudes of arbitrary spectral components of free electron currents arising under the action of multicolor ionizing laser pulses. We show that this method can be used to obtain the dependences of characteristics of a frequency-tunable third harmonic of the intense component of a three-color pulse obtained in an optical parametric generator. The obtained results are in good agreement with quantum mechanical calculations.

Analysis of the Spontaneous Emission Limited Linewidth of an Integrated III–V/SiN Laser

AbstractThis article describes a calculation of the spontaneous emission limited linewidth of a semiconductor laser consisting of hybrid or heterogeneously integrated, silicon and III–V intracavity components. Central to the approach are a) description of the multi‐element laser cavity in terms of composite laser/free‐space eigenmodes, b) use of multimode laser theory to treat mode competition and multiwave mixing, and c) incorporation of quantum‐optical contributions to account for spontaneous emission effects. Application of the model is illustrated for the case of linewidth narrowing in an InAs quantum‐dot laser coupled to a high‐ SiN cavity.

Field-resolved high-order sub-cycle nonlinearities in a terahertz semiconductor laser

The exploitation of ultrafast electron dynamics in quantum cascade lasers (QCLs) holds enormous potential for intense, compact mode-locked terahertz (THz) sources, squeezed THz light, frequency mixers, and comb-based metrology systems. Yet the important sub-cycle dynamics have been notoriously difficult to access in operational THz QCLs. Here, we employ high-field THz pulses to perform the first ultrafast two-dimensional spectroscopy of a free-running THz QCL. Strong incoherent and coherent nonlinearities up to eight-wave mixing are detected below and above the laser threshold. These data not only reveal extremely short gain recovery times of 2 ps at the laser threshold, they also reflect the nonlinear polarization dynamics of the QCL laser transition for the first time, where we quantify the corresponding dephasing times between 0.9 and 1.5 ps with increasing bias currents. A density-matrix approach reproducing the emergence of all nonlinearities and their ultrafast evolution, simultaneously, allows us to map the coherently induced trajectory of the Bloch vector. The observed high-order multi-wave mixing nonlinearities benefit from resonant enhancement in the absence of absorption losses and bear potential for a number of future applications, ranging from efficient intracavity frequency conversion, mode proliferation to passive mode locking.

Tailored Subcycle Nonlinearities of Ultrastrong Light-Matter Coupling.

We explore the nonlinear response of tailor-cut light-matter hybrid states in a novel regime, where both the Rabi frequency induced by a coherent driving field and the vacuum Rabi frequency set by a cavity field are comparable to the carrier frequency of light. In this previously unexplored strong-field limit of ultrastrong coupling, subcycle pump-probe and multiwave mixing nonlinearities between different polariton states violate the normal-mode approximation while ultrastrong coupling remains intact, as confirmed by our mean-field model. We expect such custom-cut nonlinearities of hybridized elementary excitations to facilitate nonclassical light sources, quantum phase transitions, or cavity chemistry with virtual photons.

Multi-wave mixing in the high harmonic regime: monitoring electronic dynamics.

It has been demonstrated that electronic coherences across many eV can be detected in pump-probe experiments involving high harmonic sources. An additional degree of control over the phase matching can be employed by investigating a more general class of multi-wave mixing. Non-collinear multi-wave mixing of high harmonics with energy (q1ω1 + q2ω2) can be selectively detected along the direction of (q1k1 + q2k2). Simulations based on a recently developed semi-perturbative approach show that only the specific harmonic signals with q1ω1 close to the energy difference between ground state and excited states are observable when the two input pulses are well separated in time. The coherent dynamics between different states can be selectively tracked by detecting the time-delay dependent signals with different q1k1, which can overcome the potential spectral congestion in real experiments. Additionally, such non-collinear geometry can be used to separate the dephasing induced decay and collision induced recovery behaviors of pump-probe high harmonic signal typically observed in the time-resolved high harmonic pump-probe signals.

Spatial and frequency multimode in the dressing parametric amplified multiwave mixing process

The quantum multimode of correlated fields is essential for future quantum-correlated imaging. Here we investigate multimode properties theoretically and experimentally for the parametric amplified multiwave mixing process. The multimode behavior of the signals in our system stems from spatial phase mismatching caused by frequency resonant linewidth. In the spatial domain, we observe the emission rings with an uneven distribution of photon intensity in the parametric amplified four-wave mixing process, suggesting different spatial modes. The symmetrical distribution of spatial spots indicates the spatial correlation between the Stokes and anti-Stokes signals. While in the frequency domain, the multimode character is reflected as multiple peaks splitting in the signals’ spectrum. A novelty in our experiment, the number of multimodes both in the spatial and frequency domains can be controlled by dressing lasers by modifying the nonlinear susceptibility. Finally, we extend the multimode properties to the multiwave mixing process. The results can be applied in quantum imaging.

Multi-wave mixing using a single vector optical field

The traditional multiwave mixing setups are always complicated because multiple laser beams are involved, and they are required to be aligned into certain spatial configurations to get the phase-matching condition satisfied. Here, we report on a multiwave mixing method using a single vector optical field. The spatially separated phase-matching beams are obtained after the vector light passes through a polarizer. Filtering out part(s) of them and focusing the remaining ones into the Rb vapor cell, we detected degenerate four-wave mixing, degenerate six-wave mixing, and coexisting degenerate four-wave mixing signals under different circumstances. As the beams participating in the multiwave mixing processes originate from the same phase plane of the vector laser beam, their relative positions are fixed for the setup so that this method has the potential to resist for turbulence compared with the traditional methods. Besides, the entire system is simple and easy to align because the complicated optical setup is avoided. This work provides a convenient tool for multiwave mixing generation and has great potential in spectroscopy, light squeezing, nonlinear optics, and so on.

Mutual Enhancement of Brunel Harmonics

A mechanism of a significant increase in the yield of Brunel harmonics, which are the lowest odd harmonics generated in a plasma in the process of tunnel ionization of atoms and molecules by an intense laser pulse, has been proposed and analyzed. This mechanism is based on the mutual enhancement of harmonics at the parametric interaction with the field at the fundamental frequency caused by the degenerate ionization-induced multiwave mixing. The results of analytical and numerical calculations show that this can increase the intensities of the generated harmonics by several orders of magnitude.

Reduction of Quantum Phase Fluctuations in Multi-Wave Mixing Via Measured Phase Operators

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Parametric amplification of Rydberg six- and eight-wave mixing processes

We study the parametric amplification of electromagnetically induced transparency-assisted Rydberg six- and eight-wave mixing signals through a cascaded nonlinear optical process in a hot rubidium atomic ensemble both theoretically and experimentally. The shift of the resonant frequency (induced by the Rydberg–Rydberg interaction) of parametrically amplified six-wave mixing signal is observed. Moreover, the interplays between the dressing effects and Rydberg–Rydberg interactions in parametrically amplified multiwave mixing signals are investigated. The linear amplification of Rydberg multiwave mixing processes with multichannel nature acts against the suppression caused by Rydberg–Rydberg interaction and dressing effect.

Fibre multi-wave mixing combs reveal the broken symmetry of Fermi–Pasta–Ulam recurrence

In optical fibres, weak modulations can grow at the expense of a strong pump to form a triangular comb of sideband pairs, until the process is reversed. Repeated cycles of such conversion and back-conversion constitute a manifestation of the universal nonlinear phenomenon known as Fermi–Pasta–Ulam recurrence. However, it remains a major challenge to observe the coexistence of different types of recurrences owing to the spontaneous symmetry-breaking nature of such a phenomenon. Here, we implement a novel non-destructive technique that allows the evolution in amplitude and phase of frequency modes to be reconstructed via post-processing of the fibre backscattered light. We clearly observe how control of the input modulation seed results in different recursive behaviours emerging from the phase-space structure dictated by the spontaneously broken symmetry. The proposed technique is an important tool to characterize other mixing processes and new regimes of rogue-wave formation and wave turbulence in fibre optics.

Novel Rydberg eight-wave mixing process controlled in the nonlinear phase of a circularly polarized field.

Eight-wave mixing (EWM) is a seven-order nonlinear process that can reflect nonclassical features within multiple optical fields, thus imparting certain advantages. In this study, we directly observed the EWM spectrum and spatial images that show Rydberg atoms under a circularly polarized probe field in a five-level coherently prepared atomic system. Such circular polarization dressing fields can obtain high-contrast Rydberg EWM overcome the difficulties of several multi-wave mixing (MWM) signals always coexist, and the multi-parameter controlling Rydberg EWM mechanism is established by changing the power and detuning and polarization of the dressing fields. These controllable high-order MWM processes present a contrast ratio of 96% and a narrow linewidth of <30 MHz compared with low-order mixing processes under identical conditions (e.g., six-wave mixing). The corresponding MWM spatial images are presented, and they can partly reflect the underlying nonlinear phase variation, whereas the given theory can predict the experimental results.