Maxwell-Bloch Equations Research Articles

A comparative study of electromagnetically induced transparency (EIT) in Λ-, V-, and Ξ-type systems using Laguerre–Gaussian (LG) laser beams

In this paper, a theoretical investigation of electromagnetically induced transparency (EIT) using Laguerre–Gaussian (LG) beams has been carried out for the three canonical atom-laser coupled systems (e.g. [Formula: see text]-, V-, and [Formula: see text]-type) in [Formula: see text]Rb atom. The required optical Bloch equations (OBEs) are derived for each system. The OBEs are analytically solved in steady-state condition under the weak probe field approximation. We have used the iterative perturbative technique to obtain the probe coherence term. The probe response w.r.t. probe detuning for different orders of the orbital angular momentum (OAM) number of both the pump and probe LG beams has been studied. We have also studied the effect of the OAM number on probe response in both Doppler-free and Doppler-broadened mediums. It has been observed that the EIT signal is squeezed for nonzero OAM number of the pump beam with arbitrary OAM number of the probe beam. It is found that for higher-order OAM number, the EIT signal is further squeezed. The modification of the EIT signal is attributed because of the spatial-dependent Rabi frequency. Our study demonstrates that the dynamic of the probe field inside an atomic medium may be controlled by tuning the OAM number of the LG beam.

Spatially structured optical effects in semiconductor quantum dots via biexciton coherence

In this paper, we study the spatially structured optical effects that occur when weak laser lights interact with coherently prepared semiconductor quantum dots (SQDs). Initially, the SQD is prepared in a coherent superposition of the lower exciton states. By utilizing two weak optical vortex fields that couple to a biexciton state, we observe spatially dependent effects of the absorption of probe fields. Using the well-established Maxwell–Bloch equations, we analyze the generation of composite optical vortex beams within this system. Our investigation revolves around the formation of different types of spatially dependent beams, exploring their properties and characteristics. Additionally, the transfer of optical vortices through the parametric generation process is examined, for the case where only one vortex beam is present at the beginning of the medium. This study provides insights into the spatially structured optical phenomena in coherently prepared SQDs and contributes to the understanding of light–matter interactions in such systems.

Modelling of the multitransition periodic flaring in G9.62+0.20E

ABSTRACT We present detailed modelling of periodic flaring events in the 6.7 GHz and 12.2 GHz methanol lines as well as the OH 1665 MHz and 1667 MHz transitions observed in the G9.62+0.20E star-forming region. Our analysis is performed within the framework of the one-dimensional Maxwell–Bloch equations, which intrinsically cover the complementary quasi-steady state maser and transient superradiance regimes. We find that the variations in flaring time-scales measured for the different species/transitions, and sometimes even for a single spectral line, are manifestations of and are best modelled with Dicke’s superradiance, which naturally accounts for a modulation in the duration of flares through corresponding changes in the inversion pump. In particular, it can explain the peculiar behaviour observed for some features, such as the previously published result for the OH 1667 MHz transition at vlsr = +1.7 km s−1 as well as the methanol 6.7 GHz line at vlsr = −1.8 km s−1, through a partial quenching of the population inversion during flaring events.

Maxwell–Bloch equations without spectral broadening: the long-time asymptotics of an input pulse in a long two-level laser amplifier

We study the problem of propagation of an input electromagnetic pulse through a long two-level laser amplifier under trivial initial conditions. In this paper, we consider an unstable model described by the Maxwell–Bloch equations without spectral broadening. Previously, this model was studied by Manakov in (1982 Zh. Eksp. Teor. Fiz. 83 68–75) and together with Novokshenov in (1986 Teor. Mat. Fiz. 69 40–54). We consider this model in a more natural formulation as an initial-boundary (mixed) problem using a modern version of the inverse scattering transform method in the form of a suitable Riemann–Hilbert (RH) problem. The RH problem arises as a result of applying the Fokas–Its method of simultaneous analysis of the corresponding spectral problems for the Ablowitz–Kaup–Newell–Segur equations. This approach makes it possible to obtain rigorous asymptotic results at large times, which differ significantly from the previous ones. Differences take place both near the light cone and in the tail region, where a new type of solitons is found against an oscillating background. These solitons are physically relevant, their velocities are smaller than the speed of light. The number of such solitons can be either finite or infinite (in the latter case, the set of zeros has a condensation point at infinity). Such solitons cannot be reflectionless, they are generated by zeros of the reflection coefficient of the input pulse (and not by poles of the transmission coefficient). Thus our approach shows the presence of a new phenomenon in soliton theory, namely, the boundary condition (input pulse) of a mixed problem under trivial initial conditions can generate solitons due to the zeros of the reflection coefficient, while the poles of the transmission coefficient do not contribute to the asymptotics of the solution.

The rogue wave type solutions from multiple solitons interactions in the rotating reduced Maxwell–Bloch equations

Rogue waves are usually considered as the large amplitude waves that come from nowhere and disappear without trace. The formation of rogue waves are generally related to the degradation of breather solutions. In some special cases, a special form of the interactions between two solitons can be explained by the breather solutions. The types of soliton collisions are very rich, such as weak interactions, strong interactions, and solitons decay: rogue waves (the large amplitude waves that come from nowhere and disappear without trace), and partial-rogue waves (the large amplitude waves that come from nowhere but leave with a trace). Different from the rogue waves and partial-rogue waves, we mainly study the rogue wave type solutions (the large amplitude waves that come and leave with a trace) from the degeneracy in soliton solutions caused by the interactions of solitons synchronization and resonance in the Rotating reduced Maxwell–Bloch equations, which originated from circularly polarized light propagation on two isotropic electronic field components from optical system. These results systematically illustrate the formation of rogue wave type solutions in terms of boundary conditions, spectral parameters and the number of soliton interactions.

Optical Spectra of Plasmon–Exciton Core–Shell Nanoparticles: A Heuristic Quantum Approach

Light–matter coupling in plasmonic nanocavities has been widely studied in the past years. Yet, for core–shell particles, popular electromagnetic models that use the classical Lorentz oscillator to describe the shell predict extinction spectra with three maxima, if the plasmon and the shell absorption are in resonance. In contrast, experiments exhibit only two peaks, as also expected from simple quantum models of hybrid states. In order to reconcile the convenient and widely used classical electromagnetic description with experimental data, we connect it to the quantum world by conceiving a heuristic quantum model. Our model is based on the permittivity of a two-level system in a classical electric field derived from the optical Bloch equations. The light–matter coupling is included via the collective vacuum Rabi frequency Ω0. Using our model, we obtain excellent agreement with a series of experimental extinction spectra of particles with various coupling strengths due to a systematic size variation. The suppression of the third maximum, which mainly stems from the absorption in the shell, can be interpreted as a vacuum induced power broadening, which may occur in lossy (plasmonic) cavities below the strong-coupling regime.

Self-consistent simulations of intracavity terahertz comb difference frequency generation by mid-infrared quantum cascade lasers

Portable terahertz (THz) frequency comb sources are highly desired for applications in rotational molecular spectroscopy and sensing. To date, direct THz quantum cascade laser (QCL) frequency comb generation is not achievable at room temperature. However, THz comb generation based on intracavity difference frequency generation (DFG) in mid-infrared (mid-IR) QCLs is a promising alternative. Here, we present a numerical study of THz DFG-QCL comb formation in mid-IR QCLs based on a self-consistent multi-domain simulation approach. The dynamical simulations are performed using our open-source software tool mbsolve, which provides a flexible and efficient codebase for solving the generalized full-wave Maxwell–Bloch equations. Here, DFG in the active region of a dual-wavelength mid-IR QCL is considered for the generation of THz radiation. The mixing process and, thus, THz generation require a high second-order intersubband nonlinear susceptibility in the QCL active region and can be obtained by targeted quantum engineering. The associated nonlinear effects are included in the Hamiltonian of our Maxwell–Bloch simulation approach. All necessary input parameters for the description of the quantum system are determined self-consistently using our in-house ensemble Monte Carlo software tool for stationary carrier transport simulations. Notably, such simulations require a full-wave Maxwell–Bloch solver that does not employ the common rotating wave approximation, as a broadband optical field extending from the THz to the mid-IR region is investigated. Our modeling approach and the obtained simulation results for two THz DFG-QCL comb setups are validated against experimental data, showing reasonable agreement. Furthermore, we obtain a locked frequency modulated comb state for mid-IR and THz regimes.

Integrability of the vector nonlinear Schrödinger–Maxwell–Bloch equation and the Cauchy matrix approach

Integrability of the vector nonlinear Schrödinger–Maxwell–Bloch equation and the Cauchy matrix approach

Novel entropic dynamics of donor–acceptor quantum dot system

We explore various aspects of the entropy of the donor–acceptor QD system (GaAs – (Ga, Al)As) under the effect of terahertz excitation and magnetic field. We solve the optical Bloch equations of the system in presence of the total dephasing rate. The analysis illustrate the presence of the sudden death and sudden birth of entropy. It is shown that these phenomena can be controlled using system parameters and likewise determining the influence of the magnetic field on the donor–acceptor system. By selectively choosing the system’s parameters, it is possible to control the dynamics of entropy.

Coherent control of the orbital occupation driving the insulator-to-metal Mott transition in V2O3

Managing light-matter interactions on timescales faster than the loss of electronic coherence is key for achieving full quantum control of the final products in solid-solid transformations. In this Letter, we demonstrate coherent optical control of the orbital occupation that determines the insulator-to-metal transition in the prototypical Mott insulator ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$. Selective excitation of a specific interband transition with two phase-locked light pulses manipulates the occupation of the correlated bands in a way that depends on the coherent evolution of the photoinduced superposition of states. A comparison between experimental results and numerical solutions of the optical Bloch equations provides an electronic coherence time on the order of 5 fs. Temperature-dependent experiments suggest that the electronic coherence time is enhanced in the vicinity of the insulator-to-metal transition critical temperature, thus highlighting the role of fluctuations in determining the electronic coherence. These results open different routes to selectively switch the functionalities of quantum materials and coherently control solid-solid electronic transformations.

Sensitivity extension of atom-based amplitude-modulation microwave electrometry via high Rydberg states

The Rydberg atom-based microwave electric field sensor has high sensitivity for weak RF-field detection. Selection of Rydberg states with larger electric dipole moment is beneficial to enhance the sensitivity, and we choose Rydberg states with its principal quantum number up to n ∼ 80. We study the probe laser transmission response to a microwave field for these chosen high Rydberg states at room temperature. It agrees well with theoretical simulation based on an optical Bloch equation with considered microwave-atom interaction and Doppler broadening effect. In our experiment, the microwave sensing sensitivity based on 85 Rb transition | 78 S 1 / 2 ⟩ → | 78 P 3 / 2 ⟩ arrives at 5.102(49) nV cm − 1 Hz − 1 / 2 at 1 kHz.

Bright-dark soliton solutions and their elastic interaction analysis for a reduced integrable spin Hirota–Maxwell–Bloch equation

Under consideration is a reduced integrable spin Hirota–Maxwell–Bloch (rsHMB) equation, which may have potential applications in describing femtosecond pulse propagation through an erbium doped fiber. With the aid of symbolic computation, we establish the N-fold Darboux transformation (DT) of rsHMB equation based on its known 2 × 2 matrix spectral problem. As an application of the resulting DT, we can get bright-dark soliton and breather solutions of rsHMB equation. Through graphical and asymptotic analysis, the soliton elastic collisions are shown and discussed graphically, and some important soliton physical features including wave velocity, amplitude and energy are analyzed. The consequences and properties presented in this paper may be helpful to comprehend the transmission of optical soliton in erbium doped fiber.

Light-induced dynamic microcavities created in a resonant medium by collision of non-harmonic rectangular 1-fs light pulses

Recently, interest in extremely short unipolar electromagnetic pulses with non-harmonic shape (e.g. rectangular or triangular) is rising. Such pulses do not contain a carrier frequency and have an ultra-wide spectrum. Compared to conventional harmonic multicycle pulses, they are faster and more efficient in controlling the properties of quantum systems, which allows, in the future, for faster data transmission and processing. With coherent interaction of extremely short light pulses with a medium, formation and ultrafast control of population difference gratings and polarization structures are possible when the pulses both overlap and do not overlap in the medium. In this work, based on the numerical solution of Maxwell–Bloch equations, we demonstrate possible creation of a dynamic “microcavity” as a burst of population difference, arising from the collision of rectangular unipolar 1-femtosecond pulses of self-induced transparency in a two-level resonant medium. Potential to control the microcavities parameters (changing the depth, turning it on, erasing it, etc.) is demonstrated.

Optical Bloch modeling of magnetic dipole transitions in a four-state system and its application in ion trapping: tutorial

This tutorial covers the derivation of the optical Bloch equations for a four-state atomic system interacting with an electromagnetic field via magnetic dipole transitions. The derivation of the equations is discussed at length and from first principles such that any student or graduate with a basic quantum mechanics background could follow. The tutorial shows numerical simulations of the model under different conditions, rounding off the understanding of the dependencies of the model. Finally, the functionality of the model is shown by fitting the model to experimental data of ytterbium-171 ions undergoing Rabi oscillations.

Exclusive Effect in Rydberg Atom-Based Multi-Band Microwave Communication

We have demonstrated a Rydberg atom-based two-band communication with the optically excited Rydberg state coupled to another pair of Rydberg states by two microwave fields, respectively. The initial Rydberg state is excited by a three-color electromagnetically-induced absorption in rubidium vapor cell via cascading transitions, with all of them located in infrared bands: a 780 nm laser servers as a probe to monitor the optical transmittancy via transition 5S1/2→5P3/2, 776 nm and 1260 nm lasers are used to couple the states 5P3/2 and 5D5/2 and states 5D5/2 and 44F7/2. Experimentally, we show that two channel communications carried on the two microwave transitions influence each other irreconcilably, so that they cannot work at their most sensitive microwave-optical conversion points simultaneously. For a remarkable communication quality for both channels, the two microwave fields both have to make concessions to reach a common microwave-optical gain. The optimized balance for the two microwave intensities locates at EMW1=6.5 mV/cm and EMW2=5.5 mV/cm in our case. This mutual exclusive influence is theoretically well-explained by an optical Bloch equation considering all optical and microwave field interactions with atoms.

Transient fluorescence with a single trapped ion

In this paper, we present a method to measure transient fluorescent dynamics with single trapped ions in a Paul trap. We use 40Ca+ ions that exhibit a Λ-type three-level system and measure the characteristic optical pumping times between the ground S1/2 and the meta-stable D3/2 levels. We prepare one of these states and then pump it to the opposite via the excited P1/2 state. By measuring the scattered photons of the ion, we retrieve transient curves of the atomic fluorescence. These curves provide fundamental information about the atomic system, such as branching fractions and excited-state lifetimes, as well as experimental parameters like the efficiency of the detection system and the saturation parameter of one of the transitions. Finally, we study the time-dependent fluorescence as a function of optical power and detuning of the lasers and find a very good agreement with simulating the dynamics via a three-level open quantum system through a set of optical Bloch equations. Being able to record time-dependent fluorescence is of particular interest as it contains information about the temperature, cooling, and heating dynamics of the ion.

Influence of Free Motion of Atoms on Atomic Density-Dependent Effects in Nonlinear Laser Spectroscopy of Resonant Gas Media

We develop a nonlinear theory of propagation of a monochromatic light wave in a gas of two-level atoms under the condition of inhomogeneous Doppler lineshape broadening, while considering a self-consistent solution of the Maxwell–Bloch equations in the mean-field approximation using a single atom density matrix formalism. Our approach shows a significant deformation of the Doppler resonant lineshape (shift, asymmetry), which depends on the atomic density. These effects are a consequence of only the free motion of atoms in a gas and is not associated with interatomic interaction. In particular, the frequency shift of the field-linear contribution to the transmission signal is more than an order of magnitude greater than the shift due to the interatomic dipole–dipole interaction, and the first nonlinear correction has an even stronger deformation, which exceeds the effect of the interatomic interaction by three orders of magnitude. The found effects caused by the free motion of atoms require a significant revision of the existing picture of spectroscopic effects, which depend on the atomic density in a gas.

Evolution on spatial patterns of structured laser beams: from spontaneous organization to multiple transformations

Spatial patterns are a significant characteristic of lasers. The knowledge of spatial patterns of structured laser beams is rapidly expanding, along with the progress of studies on laser physics and technology. Particularly in the last decades, owing to the in-depth attention on structured light with multiple degrees of freedom, the research on spatial and spatiotemporal structures of laser beams has been promptly developed. Such beams have hatched various breakthroughs in many fields, including imaging, microscopy, metrology, communication, optical trapping, and quantum information processing. Here, we would like to provide an overview of the extensive research on several areas relevant to spatial patterns of structured laser beams, from spontaneous organization to multiple transformations. These include the early theory of beam pattern formation based on the Maxwell–Bloch equations, the recent eigenmodes superposition theory based on the time-averaged Helmholtz equations, the beam patterns extension of ultrafast lasers to the spatiotemporal beam structures, and the structural transformations in the nonlinear frequency conversion process of structured beams.

Searching for alignment-to-orientation conversion in the ground state of atomic Cs with circularly polarized laser probe

In this study we explored the possibilities for observing the angular momentum alignment-to-orientation conversion (AOC) in the ground state of various alkali metals: K, Rb, Cs. For theoretical analysis we used a model that is based on the Optical Bloch equations for the density matrix. In our model we took into account the interaction of the laser light with all hyperfine levels, which are mixed as the magnetic field increases. The radiation’s coherence properties were also included. Finally, the results were averaged over the Doppler profile. Additionally we simulated signals where the ground- or the excited-state coherent processes were numerically switched off in order to determine the origins of the features of the obtained signals. We also performed experiments on Cs atoms with two laser beams: a linearly polarized Cs D 1 pump and circularly polarized Cs D 2 probe. We used the pump beam to create angular momentum alignment in the ground state and observed the transmission signal of the probe beam as we changed the magnetic field. A detailed analysis of the experimentally obtained transmission signal from a single circularly polarized probe laser component is provided. Finally, prospects for observing AOC experimentally are discussed, as well as experiments were even a weak AOC signal could lead to systematic errors.

Scheme for the excitation of thorium-229 nuclei based on electronic bridge excitation

Thorium-229 possesses the lowest first nuclear excited state, with an energy of approximately 8 eV. The extremely narrow linewidth of the first nuclear excited state, with an uncertainty of 53 THz, prevents direct laser excitation and realization of the nuclear clock. We present a proposal using the Coulomb crystal of a linear chain formed by ^{229}Th^{3+} ions, where the nuclei of ^{229}Th^{3+} ions in the ion trap are excited by the electronic bridge (EB) process. The 7P_{1/2} state of the thorium-229 nuclear ground state is chosen for EB excitation. Using the two-level optical Bloch equation under experimental conditions, we calculate that 2 out of 36 prepared thorium ions in the Coulomb crystal can be excited to the first nuclear excited state, and it takes approximately 2 h to scan over an uncertainty of 0.22 eV. Taking advantage of the transition enhancement of EB and the long stability of the Coulomb crystal, the energy uncertainty of the first excited state can be limited to the order of 1 GHz.