Ladder-type System Research Articles

Synthesis of Regular Ladder-Type Fluorenylidene-Xanthene Oligomers via Nucleophilic Aromatic Substitution Reaction.

Fluorenylidene-xanthene and related polycyclic systems are typical examples of bistricyclic aromatic enes (BAEs); however, polycyclic systems of fluorenylidene-xanthene are relatively scarce. Here we synthesized a series of novel ladder-type polycyclic systems containing fluorenylidene-xanthene units, differing from the classic Barton's two-fold extrusion reaction. In the new synthetic scheme, the very popular Suzuki reaction was first used to couple the corresponding precursors, then a catalyst-free nucleophilic aromatic substitution reaction between Ar-F and Ar-OH groups in the backbone afforded ladder-type O-heteroarenes. Moreover, the new synthetic strategy is also suitable for the synthesis of other heterocyclic and polycyclic aromatic hydrocarbons. Some of these products showed reversible mechanochromism properties.

Tethered Helical Ladder-Type Aromatic Lactams.

Tethered nonplanar aromatics (TNAs) make up an important class of nonplanar aromatic compounds showing unique features. However, the knowledge on the synthesis, structures, and properties of TNAs remains insufficient. In this work, a new type of TNAs, the tethered aromatic lactams, is synthesized via Pd-catalyzed consecutive intramolecular direct arylations. These molecules possess a helical ladder-type conjugated system of up to 13 fused rings. The overall yields ranged from 3.4 to 4.3%. The largest of the tethered aromatic lactams, 6L-Bu-C14, demonstrates a guest-adaptive hosting capability of TNAs for the first time. When binding fullerene guests, the cavity of 6L-Bu-C14 became more circular to better accommodate spherical fullerene molecules. The host-guest interaction is thoroughly studied by X-ray crystallography, theoretical calculations, fluorescence titration, and nuclear magnetic resonance (NMR) titration experiments. 6L-Bu-C14 shows stronger binding with C70 than with C60 due to the better convex-concave π-π interaction. P and M enantiomers of all tethered aromatic lactams show distinct and persistent chiroptical properties and demonstrate the potential of chiral TNAs as circularly polarized luminescence (CPL) emitters.

Azimuthal modulation of light propagation through 1DPCs via efficient nonlinear frequency mixing

The present study aims to investigate the transmitted and reflected light beams from a one-dimensional defect photonic crystal (1DPC) composed of a three-level ladder-type quantum system. The lower leg of the ladder scheme is driven by a weaker probe beam, while the upper leg is driven by a stronger control beam. Unlike natural atoms, this type of model with broken symmetry permits the generation of a sum-frequency signal beam between the majority of higher and lower quantum states, resulting in the formation of a cyclic closed-loop arrangement for the interaction between light and matter. The Laguerre Gaussian (LG) field with strong coupling and a weak probe light interact with the quantum system. A new weak signal light is produced as a result of the system’s symmetric breakdown, and the medium becomes azimuthal dependent. We investigate the spatial dependence of the transmitted and reflected light from a defect 1DPC by using azimuthal modulation of the LG light. Additionally, we will discuss how the absorption spectrum’s spatial modulation varies with winding numbers. We discover that in certain regions, the gain can be realized without population inversion under certain specified parametric parameters.

Influence of phase diffusion on atomic grating in a three-level ladder-type system in lower-level microwave-driven scheme

In this paper, we consider a scheme for electromagnetically induced grating (EIG) in a three-level ladder-type system. A microwave field of finite bandwidth making a standing-wave pattern is applied on lower levels. In addition, we have also introduced an indirect pump in our system. A weak probe field is then applied to study the effects of phase diffusion associated with the microwave control field on EIG. It is found that phase diffusion associated with the strong microwave control field strongly affect the diffraction. We have incorporated the effect of different system parameters such as the strength of the microwave field, indirect pumping mechanism, interaction length, and detuning in the weak probe field. Interestingly, the stronger microwave control field retrieves the loss in diffraction intensity caused by the phase diffusion. Our results show that the introduction of detuning in the optical probe field results in the enhancement of the phase grating effect. Furthermore, our results show that an optimized indirect pump field can slightly improve the first-order diffraction intensities both in the absence and presence of phase diffusion.

Effect of neighboring transitions on the transformation between electromagnetically induced transparency and two-photon absorption

We report the effect of neighboring transitions on the transformation between electromagnetically induced transparency (EIT) and two-photon absorption (TPA) in an open multi-level ladder type system of 87Rb atom, the EIT peak exhibits split and asymmetric line feature owing to a neighboring transition line with a stronger relative hyperfine transition strength factor. By comparing the signals of the 5S1/2−5P3/2−5D3/2,5/2 transitions when increasing the power of the coupling laser, it can be found that avoiding neighboring effects due to Doppler broadening in a real atom, a lower decay rate of the excited state and a higher hyperfine transition strength ratio between the coupling and probe lasers are the crucial factors that enhance the transformation efficiency between TPA and EIT and the resolution of the switched spectra. Detailed theoretical calculations, considering the crucial factors, are consistent with the experimental results.

Electromagnetically induced transparency, narrow absorption and transient response in a three-photon excitation process

The probe absorption characteristic of a four-level ladder-type system, in presence of two strong coherent radiation fields, is investigated analytically by following the density operator method. The parameters of 85Rb 5S1/2→5P3/2→5D5/2→63P3/2 transition are used in the simulation. In addition to the control field acting between the first excited state and the second excited state, if a switching field is applied to couple the second excited state to a Rydberg state, two-photon electromagnetically induced transparency (EIT) is converted into double EIT (DEIT) window having a strong central absorption peak. In a thermal vapor, the double EIT window is transformed into three transparency windows depending on the values of the control and switching Rabi frequencies. These multiple transparency windows vanish for certain combinations of the Rabi frequencies of the control and switching fields and the probe absorption is enhanced. It is also demonstrated how a very narrow optical band stop filter can be conceptualized by using three-photon excitation scheme. The transient optical response of the medium under three-photon transition is also investigated under both Doppler free and Doppler broadened conditions.

Theoretical study of coherent optical phenomena in a three lasers driven four-level ladder-type system involving a Rydberg state

A comparative theoretical study of two-photon electromagnetically induced transparency (EIT), absorption (EIA) and three-photon electromagnetically induced transparency (TPEIT), absorption (TPEIA) and their associated dispersion and group index profiles are presented by using a four-level ladder-type system of both stationary and moving 85Rb Rydberg atoms. We have observed EIT, EIA and their respective positive and negative dispersive slopes under two-photon conditions, while the TPEIT, TPEIA signals and the respective multiple positive and negative dispersive slopes at around zero detuning of the probe field are observed under the three-photon conditions. It is found that the control and manipulation of the coherent optical responses under three-photon conditions are much richer than the two-photon conditions. The group index profiles related to the dispersion of the medium have been studied under both two- and three-photon conditions to compare and explain the optical switching between the subluminal and superluminal modes of propagation for both stationary and moving atomic medium. The influence of the ‘pump’ Rabi frequency on the group index has also been investigated to illustrate the action of optical switching. Finally, the existence of the four-wave mixing (FWM) process due to the action of three optical fields in the EIT medium is also discussed.

Transition frequency measurement of highly excited Rydberg states of 87Rb for a wide range of principal quantum numbers

We report our measurements of the absolute transition frequencies of 5P3/2, F = 3 to nS and nD Rydberg states of 87Rb with high principal quantum numbers in a wide range of values (n = 45-124). The measurements were performed using Rydberg Electromagnetically Induced Transparency (EIT) in ladder-type three-level systems. We measure the transition frequencies with an accuracy of ≤ 2 MHz. We determine the values of the Rydberg-Ritz parameter for 87Rb from our experimental measurements of the transition frequencies. Our measurements of the absolute transition frequencies of the highly excited Rydberg states would be useful for diverse applications in quantum information processing, quantum simulation and quantum sensing with Rydberg atoms.

Dynamical propagation and all-optical switching in a ladder-type three-level system under the influence of spontaneously generated coherence

We investigate the dynamical of pulse propagation and all-optical switching via a spontaneously generated coherence (SGC) in a three-level ladder-type atomic medium driven by a coupling field under the presence of incoherent pumping. Results show that the SGC causes modulations at the leading edge of the pulse envelope shape. These modulations increase with the together growth of SGC and distance. Furthermore, it is shown that the continuous-wave input probe field is switched ON or OFF by periodically modulating the coupling field. The spontaneously generated coherence has a strong effect on switching efficiency and switching pulse shape. The proposed scheme may have applications in the design of optical switching and optical gain devices in optical telecommunications.

Tailoring solid-state single-photon sources with stimulated emissions.

The coherent interaction of electromagnetic fields with solid-state two-level systems can yield deterministic quantum light sources for photonic quantum technologies. To date, the performance of semiconductor single-photon sources based on three-level systems is limited mainly due to a lack of high photon indistinguishability. Here we tailor the cavity-enhanced spontaneous emission from a ladder-type three-level system in a single epitaxial quantum dot through stimulated emission. After populating the biexciton (XX) of the quantum dot through two-photon resonant excitation, we use another laser pulse to selectively depopulate the XX state into an exciton (X) state with a predefined polarization. The stimulated XX-X emission modifies the X decay dynamics and improves the characteristics of a polarized single-photon source, such as a source brightness of 0.030(2), a single-photon purity of 0.998(1) and an indistinguishability of 0.926(4). Our method can be readily applied to existing quantum dot single-photon sources and expands the capabilities of three-level systems for advanced quantum photonic functionalities.

Distinction of electromagnetically induced transparency and Autler-Towners splitting in a Rydberg-involved ladder-type cold atom system.

Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are two similar quantum coherent phenomena but have different mechanisms and applications. Akaike information criteria (AIC), an objective method to discriminate EIT and ATS from an experimental viewpoint, has been employed in a variety of systems. Here we use AIC method to quantitively discriminate a series of spectra of cold atoms in a Rydberg-involved upper-driving ladder-type. The derived weights of EIT and ATS reflect that our spectra change from EIT-ATS intermediate region to ATS-dominated region along Rabi frequency of coupling field increases. We find that there are two factors affecting EIT-ATS weights in a Rydberg-involved three-level system: dephasing rate, induced by the interactions among Rydberg atoms, makes the EIT-ATS crossover move to the direction of low Rabi frequency of coupling field and the experimental noise makes the difference between EIT and ATS weights reduce at elsewhere. Our investigation could provide a meaningful reference for the observations and applications of Rydberg-involved quantum coherent spectroscopy.

Measuring the Hyperfine Splitting and Deriving the Hyperfine Interaction Constants of the Cesium 5p67d 2D5/2 Excited State

The measurement of the cesium (Cs) 5p67d2D5/2 excited state’s hyperfine splitting intervals and hyperfine interaction constants was experimentally investigated using a ladder-type (852 nm + 698 nm) three-level Cs system (5p66s2S1/2–5p66p2P3/2–5p67d2D5/2) with a room-temperature Cs atomic vapor cell. By scanning the 698 nm coupling laser’s frequency, the Doppler-free high-resolution electromagnetically-induced transparency (EIT)-assisted double-resonance optical pumping (DROP) spectra were demonstrated via transmission enhancement of the locked 852 nm probe laser. The EIT-assisted DROP spectra were employed to study the hyperfine splitting intervals for the Cs 5p67d2D5/2 excited state with a room-temperature Cs atomic vapor cell, and the radio-frequency modulation sideband of a waveguide-type electro-optic phase modulator (EOPM) was introduced for frequency calibration to improve the accuracy of frequency interval measurement. The existence of EIT makes the DROP spectral linewidth much narrower, and it is very helpful to significantly improve the spectroscopic resolution. Benefiting from the higher signal-to-noise ratio (SNR) and much better resolution of the EIT-assisted DROP spectra, the hyperfine splitting intervals between the hyperfine folds of (F” = 6), (F” = 5), and (F” = 4) of the Cs 5p67d2D5/2 state (HFS6″–5″ = −10.60(17) MHz and HFS5″–4″ = −8.54(15) MHz) were measured and, therefore, the magnetic dipole hyperfine interaction constant (A = −1.70(03) MHz) and the electrical quadrupole hyperfine interaction constant (B = −0.77(58) MHz) were derived for the Cs 5p67d2D5/2 state. These constants constitute an important reference value for an improvement of the precise measurement and determination of basic physical constants.

Inverted-ladder-type optical excitation of potassium Rydberg states with hot and cold ensembles

We present experimental results on the sub-Doppler Rydberg spectroscopy of potassium in a hot cell and cold atoms, performed with two counter-propagating laser beams of 405 nm and 980 nm in the inverted ladder-type system (4S1/2-5P3/2-nS1/2 and nD3/2;5/2). Such an inverted ladder-type scheme is predicted to be without sub-Doppler electromagnetically induced transparency (EIT) feature in a thermal ensemble under the weak-probe approximation. Instead, we utilized a strong probe field and successfully observed a transparency window with a width narrower than 50~MHz. Our all-order numerical simulation is in satisfactory agreement with the experimental results. This narrow linewidth allows us to measure the energy levels of the Rydberg levels from $n$=20-70 with improved accuracy. The deduced ionization energy agrees with the previous measurements. Furthermore, the two-photon Rydberg excitation scheme was applied to the cold ensembles to study the ground-state atoms population decrease in the MOT for various Rydberg states. Our experimental observations suggested two distinct regimes of the trap losses under different probe detuning conditions. While the far off-resonance case (\delta p>>0) can be described by the picture of dressed atom, the on-resonance case (\delta p~0) reveals more interesting results. The higher Rydberg states suffer larger trap loss. Besides, even with similar level energies, the excitation to nD states result in faster escape of the ground-state atom from trap than nearby nS states.

Effects of finite bandwidth on atomic grating in a three level ladder type system

In this paper, we study the atomic grating produced by a three-level ladder type system which interacts with a strong standing microwave drive field of finite bandwidth. The upper levels of the atoms are coupled by the drive field while the probe field is applied on the lower two levels. We find that in the presence of phase fluctuations associated with the microwave drive field, the diffraction intensities are significantly affected. Our results show that if the probe and microwave drive are on resonance with their respective atomic transitions, then the diffraction intensities can be improved by properly adjusting the strength of the drive field. However, if the probe field is detuned from the resonance, then the diffraction intensities can be improved by appropriately selecting the strength of the drive field, probe detuning and interaction length of the medium. Interestingly, our results also show that the effects of phase grating can also be enhanced by a pertinent choice of various parameters even in the presence of phase diffusion. This results in the suppression of the zeroth order intensity while the first order intensity is increased.

Temporal dynamics of zero-delay second order correlation function and spectral entanglement of two photons emitted from ladder-type atomic three-level systems.

We theoretically investigate temporal dynamics of the second order cross correlation function at zero delay time (G12(2)(t)) and spectral entanglement of two photons emitted from an atomic three-level cascade. In Heisenberg's picture, a closed set of quantum kinetic equations of motion for G12(2)(t) is derived within density matrix formalism with cluster expansion rule. G12(2)(t) shows qualitatively distinctive features depending on the spectral entanglement of two photons. Although incoherent photon pairs generated from spontaneous radiation of the excited electron are not entangled, their correlation and anti-correlation properties can be found in G12(2)(t) depending on the radiative decay rates. In the coherent excitation regime where the light emitter is located in a high Q-cavity, and its atomic polarizations are predominantly initialized, spectral entanglement between two coherent photons is established. We show that G12(2)(t) is well fitted by the entanglement criterion by Duan-Giedke-Cirac-Zoller and explain the close relationship between them by means of the optically forbidden transition in the three-level cascade.

Effect of Doppler broadening on giant self-Kerr nonlinearity in a five-level ladder-type system

In this paper, we propose an analytical model to study the effect of Doppler broadening on self-Kerr nonlinearity in a five-level ladder-type atomic system. First- and third-order susceptibilities and the self-Kerr nonlinear coefficient are found as the function of temperature and parameters of laser fields. The analytical model is applied to hot $^{85}{\rm Rb}$85Rb and $^{87}{\rm Rb}$87Rb atoms, and it is shown that under the electromagnetically induced transparency (EIT) effect, the self-Kerr nonlinear coefficient is enhanced around three transparent spectral regions. When the temperature of atomic vapor increases (i.e., Doppler width increases), the depth and width of the EIT windows decrease accordingly, and therefore the amplitude of the Kerr nonlinear coefficient decreases significantly. In addition, because the frequency gaps between hyperfine levels of upper excited state ${{5\rm D}_{5/2}}$5D5/2 of $^{85}{\rm Rb}$85Rb atoms are much smaller than those of $^{87}{\rm Rb}$87Rb atoms, the EIT windows as well as the nonlinear dispersion curves for $^{85}{\rm Rb}$85Rb atoms are closer than those for $^{87}{\rm Rb}$87Rb atoms as the Doppler effect presents. The analytical results agree well with the experimental observation when reducing to a three-level atomic system. The analytical model can be used to easily fit the experimental observations of self-Kerr nonlinearity in a five-level atomic system under different temperature conditions and apply to a variety of applications relating to all-optical-switching techniques.

Transient amplification without population inversion in a two-field-driven ladder-type three-level system

In this paper, the transient absorption and particle population in a two-field-driven ladder-type three energy level atomic system is simulated numerically with the density matrix equations which describe the interaction of photon and material. It is found that under the radiation of strong coupling and weak probe fields, the probe absorption shows the character of damped oscillation from the time of laser being switched on to the steady state, which presents phenomenon of full transparency. There exists negative absorption during the variation process. But most of the population is on the ground state energy level all the time. This indicates that amplification without population inversion appears during the course of transparency formation. The driving of the coupling field will produce a time-dependent coherent term. Analyzing the variation of both of the population distribution and coherent term with time, it is found that transient amplification without inversion originates from the quantum interference which is related with coupling field. Thus amplification without inversion can be obtained by controlling the intensity of laser fields and the time for laser interaction.

Unique magnetism in a graphene ladder-type Ising system under an applied transverse field

The phase diagrams and magnetization curves of a graphene ladder-type Ising system under an applied transverse field are investigated by using the effective-field theory with correlations. They have exhibited many characteristic phenomena, such as the reentrant phenomena exhibiting the three transition temperatures. In particular, the thermal variations of transverse magnetizations have exhibited some characteristic features not found in other transverse Ising models.

Reentrant Phenomena in an Antiferromagnetic Ising Nanoparticle and a Ladder-Type Ising System under an Applied Transverse Field

The phase diagrams and magnetization curves of antiferromagnetic nanoparticle and ladder-type system are investigated by using the effective-field theory with correlations. They have exhibited some characteristic features, such as the reentrant phenomena, when a finite transverse field h is applied and even when h = 0.0.

Integer and fractional electromagnetically induced Talbot effects in a ladder-type coherent atomic system.

Both integer and fractional electromagnetically induced Talbot effects are experimentally investigated in a coherent rubidium 5S1/2 - 5P3/2 - 5D5/2 ladder-type system. By launching a probe laser into a periodically modulated lattice constructed by two crossed coupling fields with a small angle inside the rubidium vapor, a high-resolution diffraction pattern is obtained. The diffraction pattern is reproduced completely at detection positions of an integer multiple of twice the Talbot lengths. Meanwhile, the fractional Talbot effect, presented as complicated subimages at special positions, is also clearly observed. Furthermore, the theoretical simulations are conducted and agree well with the experimental results. These results pave the way for studying the control of light dynamics based on the periodically modulated medium.