Four-wave Mixing Spectra Research Articles

Pump-probe response and four-wave mixing in quantum dot exciton-biexciton – metal nanoparticle hybrid

We investigate theoretically the pump-probe response and the four-wave mixing spectrum in a hybrid system composed of a semiconductor quantum dot coupled to a spherical metal nanoparticle including both ground to exciton and exciton-biexciton transitions. We use a density matrix methodology for the calculation of the absorption/gain, dispersion and four-wave mixing spectra and examine their spectral characteristics, for different interparticle distances and under different pump field detuning conditions with respect to the one-photon and the two-photon resonance transitions. We also analyze the form of the spectra using a metastate theory, a description based on the coupling between the excitonic and the plasmonic transitions, while the dressed-state picture is applied in order to predict the positions at which the spectral resonances arise on the spectra.

Controllable Fano-type optical response and four-wave mixing via magnetoelastic coupling in an opto-magnomechanical system

We analytically investigate the Fano-type optical response and the four-wave mixing (FWM) process by exploiting the magnetoelasticity of a ferromagnetic material. The deformation of the ferromagnetic material plays the role of mechanical displacement, which is simultaneously coupled to both optical and magnon modes. We report that the magnetostrictively induced displacement leads to realization of Fano profiles in the output field and is effectively well-tuned through adjusting the system parameters, such as effective magnomechanical coupling, magnon detuning, and cavity detuning. It is found that the magnetoelastic interaction also gives rise to the FWM phenomenon. The number of the FWM signals mainly depends upon the effective magnomechanical coupling and the magnon detuning. Moreover, the FWM spectrum exhibits suppressive behavior upon increasing (decreasing) the magnon (cavity) decay rate. The present scheme will open new perspectives in highly sensitive detection and quantum information processing.

Four-wave mixing properties in bilayer graphene nanosystem

Graphene thin films are often used to manufacture various optoelectronic nanodevices owing to their advantages such as light weight, small size, high quality factor, and good conductivity. So far, there have been few studies of the four-wave mixing characteristics in a bilayer graphene nanosystem, especially theoretical research. In this work, we study theoretically the four-wave mixing properties in a bilayer graphene nanosystem. Firstly, the analytical formula of the four-wave mixing signal is derived by quantum mechanical method, which is divided into three steps. 1) Total Hamiltonian of the system is written in the rotating wave approximation. 2) By using the Heisenberg equation of motion and the commutation relations between different operators, the corresponding density matrix equations are obtained. 3) To solve these density matrix equations, we make an ansatz and obtain the analytical formula of the four-wave mixing signal. Secondly, we explore the dependence of the four-wave mixing signal on the phonon-exciton coupling strength, pumping intensity and the detuning between the exciton and the pump field. The calculated results show that the lineshape of four-wave mixing spectrum can be switched among two-peaked, three-peaked, four-peaked, five-peaked and six-peaked by adjusting the phonon-exciton coupling strength, the pumping intensity, and the detuning between the exciton and the pump field. In a weak phonon-exciton coupling regime (i.e. phonon-exciton coupling strength <i>g</i> < dephasing rate of exciton <i>Γ</i><sub>2</sub>), the intensity of the left peak and right peak of four-wave mixing signal first increase and then decrease with the increase of the pumping intensity <inline-formula><tex-math id="M1">\begin{document}$ {\varOmega }_{{\text{pu}}}^{\text{2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M1.png"/></alternatives></inline-formula>. In the intermediate and strong phonon-exciton coupling regime (i.e. <i>g</i> = <i>Γ</i><sub>2</sub> and <i>g</i> > <i>Γ</i><sub>2</sub>), the four-wave mixing spectrum exhibits a two-peaked structure. The maximum values of these two peaks increase as <inline-formula><tex-math id="M2">\begin{document}$ {\varOmega }_{{\text{pu}}}^{\text{2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M2.png"/></alternatives></inline-formula> increases, and their spacing is equal to 2<i>g</i>. Especially, for a given pumping intensity <inline-formula><tex-math id="M3">\begin{document}$ {\varOmega }_{{\text{pu}}}^{\text{2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M3.png"/></alternatives></inline-formula> (= 10 THz<sup>2</sup>), the maximum value of the peak for <i>g</i> = 4 THz becomes 0.4% of that for <i>g</i> = 1 THz, indicating that the phonon-exciton coupling inhibits the enhancement of the four-wave mixing signal to a certain extent. Our findings can not only offer an efficient way to measure the phonon-exciton coupling strength in the bilayer graphene system, but also help one to further explore the underlying physical mechanism in such a nanosystem.

Pulley Couplers for Broadband Microcomb Generation in Si3N4 Ring Resonators

Microresonator solitons enable high repetition-rate optical frequency combs. Their spectral span scales inversely with the strength of the resonator’s anomalous group velocity dispersion. In a thick (800 nm) silicon nitride platform, wide resonator waveguides (>2 µm) with weak anomalous dispersion are especially promising for the generation of broadband spectra. As wider waveguides have a weaker evanescent field, the coupling strength to their bus waveguide is reduced. To address this challenge, alternative coupler designs, such as pulley couplers are required. Here, we investigate pulley couplers for wide waveguide specifically targeted at broadband soliton generation. We observe significant improvement of the coupling ideality compared to conventional coupler geometries and broadband four-wave mixing spectra are observed in 2.8 µm wide microresonators.

Ultra-strong optical four-wave mixing signal induced by strong exciton-phonon and exciton-plasmon couplings.

We propose a scheme to generate ultra-strong four-wave mixing (FWM) signal based on a suspended monolayer graphene nanoribbon nanomechanical resonator (NR) coupled to an Au nanoparticle (NP). It is shown that, the FWM spectrum can switch among two-peaked, three-peaked, four-peaked or five-peaked via the modulation of exciton-phonon and exciton-plasmon couplings. This is mainly attributed to the vibrational properties of NR related to the exciton-phonon coupling, and the energy-level splitting of the localized exciton correlated to three classes of resonances consisting of three-photon resonance, Rayleigh Resonance, and AC-Stark atomic resonance. Especially, in a dual-strong coupling regime, the gains for these peaks can be as high as nine orders of magnitude (∼ 109) around the lower bistable threshold due to a combined effect of two couplings. Our findings not only offer an efficient way to measure the vibrational frequency of NR and the exciton-phonon coupling strength but also provide a possibility to fabricate high-performance optoelectronic nanodevices.

Four-wave mixing in a ladder configuration of warm 87Rb atoms: a theoretical study.

We present a theoretical study of the four-wave mixing (FWM) spectra of 5S1/2 - 5P3/2 - 5D5/2 ladder-type transitions of 87Rb atoms. The density matrix equations are solved by considering all the magnetic sublevels to calculate the FWM signals in the atomic vapor cell. These results are subsequently compared with the experimental results. We observe that the FWM signal propagating exactly opposite to the driving field is measured experimentally. Additionally, we demonstrate the effects of optical depth, laser linewidths, and the coupling field power on the FWM spectra. Finally, the origin of the dispersive-like FWM signal is investigated by intentionally varying the intrinsic atomic properties.

Controllable four-wave mixing response in a dual-cavity hybrid optomechanical system* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11504258, 61775043, and 11805140) and the Natural Science Foundation of Shanxi Province, China (Grant Nos. 201801D221021 and 201801D221031).

We systematically investigate the four-wave mixing (FWM) spectrum in a dual-cavity hybrid optomechanical system, which is made up of one optical cavity with an ensemble of two-level atoms and another with a mechanical oscillator. In this work, we propose that the hybrid dual-cavity optomechanical system can be employed as a highly sensitive mass sensor due to the fact that the FWM spectrum generated in this system has a narrow spectral width and the intensity of the FWM can be easily tuned by controlling the coupling strength (cavity–cavity, atom–cavity). More fascinatingly, the dual-cavity hybrid optomechanical system can also be used as an all-optical switch in view of the easy on/off control of FWM signals by adjusting the atom-pump detuning to be positive or negative. The proposed schemes have great potential applications in quantum information processing and highly sensitive detection.

Dynamics of free electron wave packets with coherent extreme ultraviolet four-wave mixing fields

We discuss the generation of cascaded extreme ultraviolet four-wave mixing fields with a single-gas-cell configuration and use them to study the dynamics of free electron wave packets of the noble gases. The temporal evolution of atomic dipoles in the vicinity of one-electron excitation Rydberg states 3s3p6np of argon and 4s4p6n′p of krypton is reflected in the intensity profiles of the four-wave mixing spectra. Different interference pathways for these dipole-allowed transitions are revealed in the time-delay-dependent phase shift of the four-wave mixing fields. The results of this study may be promising for studies of more complex systems.

Four‐Wave Mixing Response via Hybrid Coulomb‐Coupled Cavity Optomechanics

AbstractThe generation and manipulation of the four‐wave mixing (FWM) phenomenon is reported in a hybrid electrostatically Coulomb‐coupled optomechanical system as a result of light–matter interaction. The cavity is driven by a strong coherent pump and a weak probe field simultaneously in the presence of nanomechanical resonators (NMRs), and the output field can produce a new frequency component called the FWM frequency. In a hybrid Coulomb‐coupled cavity scheme, the existence of optomechanical coupling due to radiation pressure gives rise to the FWM phenomenon, which is shown both analytically and numerically. A controllable enhancement of the FWM intensity is found by tuning the pump field strength and its spectrum disappears upon switching the strength off. A significant enhancement in the FWM spectrum with two peaks is also predicted due to the Coulomb coupling strength existing between two electrostatically coupled NMR1 and NMR2. A suppressive behavior of the FWM signal is also observed upon increasing the cavity decay rate and a substantial modulation in the signal by changing the probe‐pump field detuning. Finally, the FWM spectrum is very sensitive to both the effective resonance frequencies and effective masses of the NMRs.

Four-wave mixing dynamics of a strongly coupled quantum-dot–microcavity system driven by up to 20 photons

The Jaynes-Cummings (JC) model represents one of the simplest ways in which single qubits can interact with single photon modes, leading to profound quantum phenomena like superpositions of light and matter states. One system, that can be described with the JC model, is a single quantum dot embedded in a micropillar cavity. In this joint experimental and theoretical study we investigate such a system using four-wave mixing (FWM) micro-spectroscopy. Special emphasis is laid on the dependence of the FWM signals on the number of photons injected into the microcavity. By comparing simulation and experiment, which are in excellent agreement with each other, we infer that up to ~20 photons take part in the observed FWM dynamics. Thus we verify the validity of the JC model for the system under consideration in this non-trivial regime. We find that the inevitable coupling between the quantum dot exciton and longitudinal acoustic phonons of the host lattice influences the real time FWM dynamics and has to be taken into account for a sufficient description of the quantum dot-microcavity system. Performing additional simulations in an idealized dissipation-less regime, we observe that the FWM signal exhibits quasi-periodic dynamics, analog to the collapse and revival phenomenon of the JC model. In these simulations we also see that the FWM spectrum has a triplet structure, if a large number of photons is injected into the cavity.

Acoustic phonon sideband dynamics during polaron formation in a single quantum dot.

When an electron-hole pair is optically excited in a semiconductor quantum dot, the host crystal lattice adapts to the presence of the generated charge distribution. Therefore, the coupled exciton-phonon system has to establish a new equilibrium, which is reached in the form of a quasiparticle called a polaron. Especially, when the exciton is abruptly generated on a timescale faster than the typical lattice dynamics, the lattice cannot follow adiabatically. Consequently, rich dynamics on the picosecond timescale of the coupled system is expected. In this study, we combine simulations and measurements of the ultrafast, coherent, nonlinear optical response, obtained by four-wave mixing (FWM) spectroscopy, to resolve the formation of this polaron. By detecting and investigating the phonon sidebands in the FWM spectra for varying pulse delays and different temperatures, we have access to the influence of phonon emission and absorption processes, which finally result in the emission of an acoustic wave packet.

Nonlinear optical effect and nonlinear optical mass sensor based on graphene optomechanical system

Graphene, atomically thin two-dimensional (2D) nanomaterial consisting of a single layer of carbon atoms, has received tremendous attention in the past few decades. Graphene may be considered as an excellent nanomaterial for fabricating nanomechanical resonator systems to investigate the quantum behavior of the motion of micromechanical resonators because of its unique properties of low mass density, high frequency, high quality-factor, and intrinsically small size. Additionally, graphene optomechanics based on a bilayer graphene resonator coupled to a microwave on-chip cavity, where light and micromechanical motion interact via the radiation pressure, has been demonstrtated experimentally recently. In this work, we demonstrate theoretically the nonlinear optical effect including optical bistability and four-wave mixing under the regimes woth different parameters and detunings in a graphene resonator-microwave cavity system. When the graphene optomechanics is driven by one strong pump laser beam, we find that the optical bistability can be controlled by tuning the power and the frequency of the pump beam. The four-wave mixing (FWM) phenomenon is also investigated and we find that sharp peaks in the FWM spectrum exactly are located at the resonant frequency of graphene resonator. Therefore, a straight nonlinear optical means for determining the resonant frequency of the graphene resonator is presented. Setting the cavity field resonating with pump field, and then scanning the probe frequency across the cavity frequency, one can easily and exactly obtain the resonant frequency of the resonator from the FWM spectrum. We further theoretically propose a mass sensor based on the graphene optomechanical system. The mass of external nanoparticles deposited onto the graphene resonator can be measured conveniently by tracking the shift of resonant frequency due to mass changing in the FWM spectrum. Compared with optomechanical mass sensors in linear regime, the nonlinear optical mass sensor may be immune to the detection noise. The system may have potential applications in communication networks for frequency conversion and provide a new platform for high sensitive sensing devices.

Optomechanically induced transparency and nonlinear responses based on graphene optomechanics system

Due to its unique properties of low mass density, high frequency, high quality-factor and intrinsically small size, graphene has received significant attention and is considered as an ideal material for fabricating nanomechanical systems. In this work, we demonstrate theoretically the coherent optical propagation under different detuning regimes in the graphene resonator-microwave cavity system. In the red detuning, optomechanically induced transparency induced the slow light effect is investigated and the maximum group delay can reach 0.4 ms. In the blue detuning, advancing microwave signal can reach 0.12 ms, and the parametric amplification process can behave as an optical transistor to amplify a weak microwave field via manipulating the pump field. Further, we research the nonlinear effects of four-wave mixing (FWM), and the FWM intensity can be efficiently controlled and modulated by the pump power, such as FWM spectrum can present the phenomenon of normal mode splitting with controlling the pump power. A straightforward optical means for determining the frequency of the resonator by the FWM spectrum is also presented. The graphene optomechanics may indicate applications in quantum information processing.

Rabi oscillations of a quantum dot exciton coupled to acoustic phonons: coherence and population readout

While the advanced coherent control of qubits is now routinely carried out in low frequency (GHz) systems like single spins, it is far more challenging to achieve for two-level systems in the optical domain. This is because the latter evolve typically in the THz range, calling for tools of ultrafast, coherent, nonlinear optics. Using four-wave mixing micro-spectroscopy, we here measure the optically driven dynamics of a single exciton quantum state confined in a semiconductor quantum dot. In a combined experimental and theoretical approach, we reveal the intrinsic Rabi oscillation dynamics by monitoring both central exciton quantities, i.e., its occupation and the microscopic coherence, as resolved by the four-wave mixing technique. In the frequency domain this oscillation generates the Autler-Townes splitting of the light-exciton dressed states, directly seen in the four-wave mixing spectra. We further demonstrate that the coupling to acoustic phonons strongly influences the FWM dynamics on the picosecond timescale, because it leads to transitions between the dressed states.

Stimulated emission from ladder-type two-photon coherent atomic ensemble.

We investigated the stimulated emission from a ladder-type two-photon coherent atomic ensemble, for the 5S1/2 - 5P3/2 - 5D5/2 transition of 87Rb atoms. Under the ladder-type two-photon resonance condition obtained using pump and coupling lasers, we observed broad four-wave mixing (FWM) light stimulated from two-photon coherence induced by the seed laser coupled between the ground state of 5S1/2 and the first excited state of 5P3/2. A dip in the FWM spectrum was obtained for three-photon resonance due to V-type two-photon coherence using the pump and seed lasers. From the FWM spectra obtained for varying frequency detuning and seed-laser power, we determined that the seed laser acts as a stimulator for FWM generation, but also acts as a disturber of FWM due to V-type two-photon coherence.

Experimental study of the third-order nonlinearity of atomic and molecular gases using 10-μm laser pulses

We present measurements of the third-order optical nonlinearity of Kr, Xe, ${\mathrm{N}}_{2}, {\mathrm{O}}_{2}$, and air at a wavelength near 10 \textmu{}m by using four-wave mixing of $\ensuremath{\sim}15\ensuremath{-}\mathrm{GW}/\mathrm{c}{\mathrm{m}}^{2}$, 200-ps (full width at half maximum) $\mathrm{C}{\mathrm{O}}_{2}$ laser pulses. Measurements in molecular gases resulted in an asymmetric four-wave mixing spectrum indicating that the nonlinear response is strongly affected by the delayed, rotational contribution to the effective nonlinear refractive index. Within the uncertainty of our measurements, we have found that the long-wavelength nonlinear refractive indices of these gases are consistent with measurements performed in the near IR.

Four-wave mixing in an asymmetric double quantum dot molecule

The four-wave mixing (FWM) effect of a weak probe field, in an asymmetric semiconductor double quantum dot (QD) structure driven by a strong pump field is theoretically studied. Similarly to the case of examining several other nonlinear optical processes, the nonlinear differential equations of the density matrix elements are used, under the rotating wave approximation. By suitably tuning the intensity and the frequency of the pump field as well as by changing the value of the applied bias voltage, a procedure used to properly adjust the electron tunneling coupling, we control the FWM in the same way as several other nonlinear optical processes of the system. While in the weak electron tunneling regime, the impact of the pump field intensity on the FWM is proven to be of crucial importance, for even higher rates of the electron tunneling it is evident that the intensity of the pump field has only a slight impact on the form of the FWM spectrum. The number of the spectral peaks, depends on the relation between specific parameters of the system.

Pump–probe and Four-wave Mixing Spectra Arising from Recoil-induced Resonance in an Operating Cesium Magneto-Optical Trap

We present experimental observation of recoil-induced resonance (RIR) in an operating cesium magneto-optical trap (MOT) by both pump–probe absorption and four-wave mixing spectra simultaneously. We investigate the dependence of amplitudes of these two spectra on pump beam intensity and frequency. The measurement results agree well with the recoil-induced theory with modifications of Raman transition effect and atomic number. The systematical study on RIR spectra is meaningful for the diagnostic measurement of cold atoms in an operating MOT.

Influence of the frequency detuning on the four-wave mixing efficiency in three-level system coupled by standing-wave

In a Λ-type three-level atomic system coupled by an off-resonant standing-wave, the reflected four-wave mixing (FWM) spectrum is studied. It shows that the maximum reflection efficiency occurs when both of the coupling and probe fields are tuned off resonances from the atomic transitions. The essence of enhanced reflection is that the nonlinear efficiency of the FWM based on coherent atoms is improved due to the significant reduction of phase mismatch. The theoretical analysis shows good agreement with the experimental results. Furthermore, the influence of the atomic number density on the coupling frequency detuning of the optimum reflection efficiency and the linewidth are also investigated.

Bistable four-wave mixing response in a semiconductor quantum dot coupled to a photonic crystal nanocavity.

We perform a theoretical study of the bistable four-wave mixing (FWM) response in a coupled system comprised of a semiconductor quantum dot (SQD) and a photonic crystal (PC) nanocavity in which the SQD is embedded. It is shown that the shape of the FWM spectrum can switch among single-peaked, double-peaked, triple-peaked, and four-peaked arising from the vacuum Rabi splitting and the exciton-nanocavity coupling. Especially, we map out bistability phase diagrams within a parameter subspace of the system, and find that it is easy to turn on or off the bistable FWM response by only adjusting the excitation frequency or the pumping intensity. Our results offer a feasible means for measuring the SQD-PC nanocavity coupling strength and open a new avenue to design optical switches and memories.