Constant Detuning Research Articles

Modeling and experimental characterization of two-wave mixing in Yb-doped fiber amplifiers.

Two-wave mixing between forward- and backward-propagating signal light has recently been observed in frequency-modulated single-frequency fiber laser systems. The phenomenon is a potential limiting factor for power scaling of such frequency-tunable lasers. In this contribution, we derive a perturbative coupled-mode theory for two signals that counter-propagate in an Yb-doped fiber with a constant frequency detuning. We apply the theory to analyze experimental results dedicated to extracting the central material parameter that relates the Yb inversion to a (real) refractive-index change. The perturbative theory is derived to all orders, and argued to be convergent. The experimental results and our analysis support previous estimates of the ratio between changes in the gain coefficient and the refractive index.

Molecular formations and spectra due to electron correlations in three-electron hybrid double-well qubits

We show that systematic full configuration-interaction (FCI) calculations enable prediction of the energy spectra and the intrinsic spatial and spin structures of the many-body wave functions as a function of the detuning parameter for the case of three-electron hybrid qubits based on GaAs asymmetric double quantum dots. Specifically, in comparison with the case of weak interactions and treating the entire three-electron double-dot hybrid qubit as an integral unit, it is shown that the predicted spectroscopic patterns, originating from strong electron correlations, manifest the formation of Wigner molecules (WMs). Signatures of WM formation include: (1) a strong suppression of the energy gaps relative to the non-interacting-electrons modeling, and (2) the appearance of a pair of avoided crossings arising between states associated with two-electron occupancies in the left and right wells. The Wigner molecule is a physical entity associated with electron localization within each well and it cannot be captured by the previously employed independent-particle or two-site-Hubbard theoretical modeling of the hybrid qubits. The emergence of strong WMs is investigated in depth through the concerted use of FCI-adapted diagnostic tools like charge and spin densities, as well as conditional probability distributions. Furthermore, the energy spectrum as a function of the strength of the Coulomb repulsion (at constant detuning) is calculated in order to complement the thorough analysis of the factors contributing to WM emergence. We report remarkable agreement with recent experimental measurements. The present FCI methodology for multi-well quantum dots can be straightforwardly extended to treat valleytronic two-band Si/SiGe hybrid qubits, where the central role of the WMs was confirmed recently.

Experimental Observation of Interorbital Coupling.

Interorbital coupling refers to the possibility of exciting orbital states by otherwise orthogonal noninteracting modes, a forbidden process in photonic lattices due to intrinsic propagation constant detuning. In this Letter, using a femtosecond (fs) laser writing technique, we experimentally demonstrate that fundamental and excited orbital states can couple each other when located at different spatial positions. We perform a full characterization of an asymmetric double-well-like potential and implement a scan method to effectively map the dynamics along the propagation coordinate. Our fundamental observation also constitutes a direct solution for a spatial mode converter device, which could be located in any position inside a photonic glass chip. By taking advantage of the phase structure of higher-order photonic modes and the effective negative coupling generated, we propose a trimer configuration as a phase beam splitter, which could be of great relevance for multiplexing and interference-based photonic concatenated operations.

Gain Scheduled Multivariable control of a Continuous Stirred Tank Reactor

Most chemical reactors, representing Multi-Input Multi-Output (MIMO) systems, are highly nonlinear and require complex control than single-input single-output (SISO) systems. In the present work, the system is linearized around different operating points. As linear design strategies are intended to work in linear regions, they are employed to evaluate local controller parameters. Decentralized controllers using constant detuning factor and decoupling controllers using static decouplers are designed. A gain scheduler is developed to deal with changes in operating conditions. The performances are evaluated by simulating the nonlinear equations of the system. Decentralized controllers cannot mitigate the interactions due to its structure possessing single loop. It is exhibited that the decoupling controllers offer better control for tracking of desired set point and rejection of load disturbances than those of decentralized controllers. The superiority of the suggested controller has been portrayed by performing simulation study on a Continuous Stirred Tank Reactor (CSTR).

Controlling light tunneling by adiabatic passage in two modulated nonlinear waveguides

We theoretically investigate light propagation in two coupled nonlinear waveguides with a certain static propagation constant detuning between two waveguides and with the linear refractive index modulated along the propagation direction. By slowly varying the amplitude of modulation, we steer the light to the desired output waveguide when equal amounts of lights are launched into each waveguide. We reveal that depending on the sign of the static propagation constant mismatch (detuning) between two waveguides, the launched light can be completely switched to either of waveguides. Additionally, we numerically examine the performances of light switching for general inputs and modulation amplitudes, and show that the localization of output light is robust against small to moderate variations in the final modulation amplitude, phase difference and intensity distribution of input field between two waveguides. More importantly, according to the principle of the proposed scheme, we are capable of steering the output light to the targeted waveguide at extremely low input power. In theory, our findings can be explained qualitatively by means of adiabatic navigation of the so-called nonlinear Floquet states.

Single-pass high-gain tapered free-electron laser with transverse diffraction in the postsaturation regime

It has been well known that the resonant interaction of an ultrarelativistic electron beam and the radiation field in the single-pass high-gain free electron laser (FEL) amplifier leads to the optical gain guiding. The transverse Laplacian term of the slowly varying wave equation in the linear regime can be approximated as a constant detuning parameter, i.e., |∇⊥2|∼kR/zR where kR is the resonant wave number and zR is the Rayleigh range of the laser. In the post-saturation regime, the radiation power begins to oscillate about an equilibrium for the untapered case while continues to grow by undulator tapering. Moreover, in this regime the gain guiding decreases and the simple constant detune is no longer valid. In this paper we study the single-pass high-gain FEL performance in the post-saturation regime with inclusion of diffraction effect and undulator tapering. Our analysis relies upon two constants of motion, one from the energy conservation and the other from the adiabatic invariant of the action variable. By constructing a two-dimensional axisymmetric wave equation and the coupled one-dimensional electron dynamical equations, the performance of a tapered FEL in the postsaturation regime can be analyzed, including the fundamental mode profile, the power efficiency and the scaled energy spread. We begin the analytical investigation with two different axisymmetric electron beam profiles, the uniform and bounded parabolic ones. It is found that the tapered FEL power efficiency can be smaller but close to the taper ratio provided the resonant phase remains constant and the beam-wave is properly matched. Such a tapered efficiency is nearly independent of transverse electron beam size before significant electron detrapping occurs. This is essentially different from the untapered case, where the power extraction efficiency is around the essential FEL gain bandwidth (or ρ, the Pierce or FEL parameter) and depends on the beam size. It is also found that the power enhancement due to undulator tapering is attributed more by the field increase outside the transverse electron beam than that inside the transverse electron beam. Several scaling properties on the taper ratio and the transverse electron beam size are also discussed in this paper.3 MoreReceived 29 January 2018DOI:https://doi.org/10.1103/PhysRevAccelBeams.21.060702Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsSynchrotron radiation & free-electron lasersAccelerators & Beams

Mollow spectrum influenced by collisional fluctuations described by a stochastic model of collisions

In this paper, we consider the influence of collisional fluctuations on optical phenomena. The fluctuations are taken into account by a simple shift of the constant detuning, involved in a set of optical Bloch equations by collision frequency noise in which this noise is modelled by a two-step random telegraph signal. Following that, the stochastic Bloch equations can be solved analytically in an exact way. As an example, we consider in detail the Mollow spectrum of resonance fluorescence for the case of an arbitrary detuning of the laser frequency, where velocity of the emitters simply has a deterministic value or is distributed with the Maxwell–Boltzmann density in which volume of the buffer gas is arbitrary.

Laser cooling of electron – ion plasma in the case of optimal scanning of the laser frequency

Laser cooling of ions of electron – ion plasma is studied under the action of spontaneous radiation pressure forces. It is shown that the use of a constant detuning of the laser frequency from the quantum transition frequency in ions significantly limits the conditions under which the ions are cooled. To extend the range of initial temperatures of possible cooling of ions and to increase the cooling efficiency we suggest scanning the laser frequency detuning so that the cooling rate remained maximal in the process of changing the temperature of ions. In the case of an optimal detuning, we have found an asymptotic expression for the cooling rate and identified intervals of electron concentrations and temperatures, where cooling of ions is possible.

Interaction of a Λ-type three-level atom with a single-mode field without rotating wave approximation: perturbation theory approach

In this article, by using the perturbation theory, we analytically solve the eigenvalue problem for the Hamiltonian describing the interaction of a Λ-type three-level atom with a single-mode radiation field without the rotating wave approximation (RWA). For this purpose, the atom–field interaction Hamiltonian, which contains the counter-rotating terms (CRTs), is transformed to an analytically solvable Hamiltonian by applying three successive unitary transformations. According to our calculations, the contribution of CRTs within the transformed Hamiltonian is in fact replaced by transforming the ‘constant detuning’ with the ‘intensity-dependent detuning’ in the first order, and the ‘constant atom–field coupling’ with the intensity-dependent coupling in the second order of the perturbation parameters. Then, by solving the eigenvalue problem for the transformed Hamiltonian, the eigenvector of the considered atom–field Hamiltonian is obtained analytically. Finally, after achieving the state vector of the atom–field system at an arbitrary time, a few nonclassical properties of the system state are investigated numerically. Meanwhile, we compare our results with the presence of RWA, from which the role of CRTs will be established.

Thirty five classes of solutions of the quantum time-dependent two-state problem in terms of the general Heun functions

We derive 35 five-parametric classes of the quantum time-dependent two-state models solvable in terms of the general Heun functions. Each of the classes is defined by a pair of generating functions the first of which is referred to as the amplitude- and the second one as the detuning-modulation function. The classes suggest numerous families of specific field configurations with different physical properties generated by appropriate choices of the transformation of the independent variable, real or complex. There are many families of models with constant detuning or constant amplitude, numerous classes of chirped pulses of controllable amplitude and/or detuning, families of models with double or multiple (periodic) crossings, periodic amplitude modulation field configurations, etc. The detuning modulation function is the same for all the derived classes. This function involves four arbitrary parameters, that is, two more than the previously known hypergeometric classes. These parameters in general are complex and should be chosen so that the resultant detuning is real for the applied (arbitrary) complex-valued transformation of the independent variable. The generalization of the detuning modulation function to the four-parametric case is the most notable extension since many useful properties of the two-state models described by the Heun equation are due to namely the additional parameters involved in this function. Many of the derived amplitude modulation functions present different generalizations of the known hypergeometric models. In several cases the generalization is achieved by multiplying the amplitude modulation function of the corresponding prototype hypergeometric class by an extra factor including an additional parameter. Finally, many classes suggest amplitude modulation functions having forms not discussed before. We present several families of constant-detuning field configurations generated by a real transformation of the independent variable. The members of these families are symmetric or asymmetric two-peak finite-area pulses with controllable distance between the peaks and controllable amplitude of each of the peaks. We show that the edge shapes, the distance between the peaks as well as the amplitude of the peaks are controlled almost independently, by different parameters. We identify the parameters controlling each of the mentioned features and discuss other basic properties of pulse shapes. We show that the pulse edges may become step-wise functions and determine the positions of the limiting vertical-wall edges. We show that the pulse width is controlled by only two of the involved parameters. For some values of these parameters the pulse width diverges and for some other values the pulses become infinitely narrow. We show that the effect of the two mentioned parameters is almost similar, that is, both parameters are able to independently produce pulses of almost the same shape and width. We determine the conditions for generation of pulses of almost indistinguishable shape and width, and present several such examples. Finally, we present a constant-amplitude periodic level-crossing model and several families of constant-detuning field configurations generated by complex transformations of the independent variable.

Fifteen classes of solutions of the quantum two-state problem in terms of the confluent Heun function

We derive 15 classes of time-dependent two-state models solvable in terms of the confluent Heun functions. These classes extend over all the known families of three- and two-parametric models solvable in terms of the hypergeometric and the confluent hypergeometric functions to more general four-parametric classes involving three-parametric detuning modulation functions. In the case of constant detuning, the field configurations describe excitations of two-state quantum systems by symmetric or asymmetric pulses of controllable width and edge-steepness. The classes that provide constant detuning pulses of finite area are identified and the factors controlling the corresponding pulse shapes are discussed. The positions and the heights of the peaks are mostly defined by two of the three parameters of the detuning modulation function, while the pulse width is mainly controlled by the third one, the constant term. The classes suggest numerous symmetric and asymmetric chirped pulses and a variety of models with two crossings of the frequency resonance. We discuss the excitation of a two-level atom by a pulse of Lorentzian shape with a detuning providing one or two crossings of the resonance. We derive closed form solutions for particular curves in the 3D space of the involved parameters which compose the complete return spectrum of the considered two-state quantum system.

Rogue waves in Lugiato-Lefever equation with variable coefficients

Abstract In this paper, we theoretically investigate the generation of optical rogue waves from a Lugiato-Lefever equation with variable coefficients by using the nonlinear Schrödinger equation-based constructive method. Exact explicit rogue-wave solutions of the Lugiato-Lefever equation with constant dispersion, detuning and dissipation are derived and presented. The bright rogue wave, intermediate rogue wave and the dark rogue wave are obtained by changing the value of one parameter in the exact explicit solutions corresponding to the external pump power of a continuous-wave laser.

Robust Rydberg-interaction gates with adiabatic passage

We show that with adiabatic passage, one can reliably drive two-photon optical transitions between the ground states and interacting Rydberg states in a pair of atoms. For finite Rydberg-interaction strengths an adiabatic pathway towards the doubly Rydberg excited state is identified when a constant detuning is applied with respect to an intermediate optically excited level. The Rydberg interaction among the excited atoms provides a phase that may be used to implement quantum gate operations on atomic ground-state qubits.

A stochastic model of the influence of buffer gas collisions on Mollow spectra

In this paper we consider the influence of collisional fluctuations on the Mollow spectra of resonance fluorescence (RF). The fluctuations are taken into account by a simple shift of the constant detuning, involved in a set of optical Bloch equations by collision frequency noise which is modelled by a two-step random telegraph signal (RTS). We consider in detail the Mollow spectra for RF in the case of an arbitrary detuning of the laser frequency, where the emitter is a member of a statistical ensemble in thermodynamic equilibrium with the buffer gas at temperature $T$ which is treated as a colored environment, and velocity $v$ is distributed with the Maxwell-Boltzmann density.

Calculations of operating schemes for a passive harmonic cavity in HLS- II

A passive higher harmonic cavity (HHC) will be used in the Hefei Light Source II Project (HLS- II) to lengthen the bunch and consequently increase the beam lifetime dominated by Touschek scattering. The effects of constant voltage and constant detuning have been calculated and compared over the operating current from 0.4 to 0.2 A on the bunch lengthening for the passive normal conducting harmonic cavity system in HLS- II. The results show that the bunch shape has less change and the lifetime improvement factors are not less than 2.7 over the beam currents for the constant voltage case. The constant voltage operating scheme may be applied to our machine.

PI tuning of five-phase drives with third harmonic injection

The tuning of PI gains for a five-phase induction motor with indirect field oriented control and third harmonic injection is analyzed. Third harmonic injection allows to increase the output torque density. A study of the local linearized system shows that rotor time constant detuning and drive load play a crucial role in transient behavior. Also, it is shown that the PI tuning has to be obtained as a balance between conflicting interests. Some measures of the transient performance are presented and used to derive guidelines for setting the PI controller. The proposed guidelines involve a numerical procedure applicable to any drive with third harmonic injection, with either constant or variable ratio to the fundamental component. The results are illustrated by a set of simulation experiments.

Preparing a laser cooled plasma for stopping highly charged ions

We present a new cooling scheme for the preparation of highly charged ions for future in-trap precision experiments. A plasma of laser cooled 24Mg+ ions trapped in a 3D harmonic confinement potential is used as a stopping medium for the highly charged ions. We focus on the dynamic evolution of the plasma, determining suitable cooling conditions for fast recooling of the 24Mg+ ions. The results of a realistic parallel simulation of the complete stopping process presented here indicate that a small, constant detuning of the laser frequency is sufficient for subsequent recooling of the plasma, thus maintaining the stability of the plasma.

Fluorescence spectrum of a two-level atom driven by a multiple modulated field

We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving field is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mollow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving field. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we show that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied.

Landau-Zener model: Effects of finite coupling duration.

We present the generalization of the Landau-Zener model for a constant coupling of a finite duration. The exact evolution matrix is expressed in terms of sums of by-products of parabolic cylinder functions estimated at the turn-on time and at the turn-off time of the coupling. Various approximations in terms of simpler functions are derived and applied to several physically distinct cases. They allow us to study the dependence of the transition probability on the interaction parameters: coupling strength, coupling duration, and detuning slope. Furthermore, the analytic approximations reveal the effects of the finite coupling duration as well as those caused by adding a constant detuning shift, absence of a level crossing, turn-on time or turn-off time near the crossing (``half crossing''), turn-on time and turn-off time near the crossing (``nonsubstantial crossing''). The results are used to obtain analytic approximations to the time evolution in the original Landau-Zener model. Furthermore, following related studies on other models, we define the Landau-Zener class of models that, along with the finite Landau-Zener model presented in this work, contains an infinite number of members that give the same transition probability. Comparison of this class to the Allen-Eberly class shows that the two classes contain members with the same coupling but different detuning chirps as well as members with the same chirp but different couplings. The former case reveals chirp effects while the latter demonstrates shape effects. \textcopyright{} 1996 The American Physical Society.

Coherent excitation by asymmetric pulses

It is shown that any pulse with a time-asymmetric envelope and a constant non-zero detuning excites a two-level quantum system with a probability of nearly one-half provided the pulse is very asymmetric, adiabatic in the slowly rising part of its envelope, sudden in the steep part and the peak Rabi frequency is much greater than the detuning. Three particular cases are considered analytically: the asymmetric hyperbolic-secant, the Bambini-Berman and the exponential pulse, which illustrate the general conclusions. The results are applied to a special three-level 'vee' system whose two transitions are driven by two asymmetric laser pulses of the same Rabi frequencies and the same detunings. Analysis shows that if such a system is prepared initially in its ground state, effective population depletion of this state can be achieved, the results being quite insensitive to variations in the Rabi frequency and the detuning.