Two-level System Research Articles

Unveiling the Impact of Degeneracy in an Isolated Two-Level System: An Undergraduate Problem

The study of isolated two-level systems (e.g. paramagnetic salt) is an integral part of every statistical mechanics coursework at undergraduate level. However, the thermodynamical properties of such a system are usually explained with very brief introduction to the degeneracy associated with the levels. Therefore, in this study, we revisited the macroscopic properties such as entropy, temperature and specific heat of a degenerate two-level system (both symmetric and asymmetric cases). We believe that this simple and analytic calculation may give very useful insight to undergraduate students.

Approximate analytic solution of the dissipative semiclassical Rabi model under parametric multi-tone modulations

Abstract We present an analytic method for obtaining the dynamics of the dissipative time-modulated
semiclassical Rabi model, which describes a two-level system (qubit) with time-dependent parameters, 
coupled to a single-mode bosonic field via the dipole-interaction and to
a thermal reservoir. We consider the simultaneous harmonic
modulations of the qubit transition frequency and the qubit-field coupling strength,
with arbitrary frequencies, and obtain closed analytic expressions for the
density operator under the coarse-graining approximation. Our
approximate results are in excellent ageement with exact numerical data, and
illustrate how the qubit state can be controlled in the dispersive regime by properly
adjusting the system parameters.

Modeling of fluence-dependent hole-burned spectra and hole-growth kinetics using multiple two-level system model.

Numerical formalism is presented that perfectly describes resonant low-temperature hole-burned spectra (including zero-phonon holes, ZPHs) and spectral hole-growth dynamics of Al-phthalocyanine tetrasulphonate embedded in hyperquenched glassy water films over more than seven orders of fluence magnitude (0.4 µJ/cm2-5.9 J/cm2). Frequency changes during spectral hole-burning (HB) are traditionally explained with the help of a single extrinsic two-level-system (TLSext) associated with impurity molecules. The new multiple two-level system (n-TLSext) models and data analysis presented in this work show that each chromophore in an amorphous medium can couple with multiple independent TLSext, which maintain perfect photo-memory, allowing a full return of the photoproduct to the initial ("preburn") state. Modeling reveals that the experimentally observed narrow photoproduct peak at higher energies, in close vicinity of the zero-phonon hole (ZPH), reflects a dynamical feature of the HB process populating so-called "terminal" states (states that do not interact with laser excitation). Within the n-TLSext model, each chromophore possesses multiple possibilities to create a photoproduct when in interaction with the burning laser, i.e., chromophores can interact with burning laser-light multiple times until reaching the terminal states. Due to phonon-assisted absorption, terminal states are typically at higher energies than the ZPH, in agreement with the hole burned spectra reported for many molecules embedded in various amorphous solids. However, many HB systems reveal both blue- (high-energy) and red-shifted (low-energy) antiholes (i.e., photoproducts). We suggest that future modeling of resonant holes in various proteins using our n-TLSext model will provide more insight on the complexity of the protein energy landscape.

Suppression of quantum dissipation: a cooperative effect of quantum squeezing and quantum measurement

The ability to isolate a quantum system from its environment is of fundamental interest and importance in optical quantum science and technology. Here we propose an experimentally feasible scheme for beating environment-induced dissipation in an open two-level system coupled to a parametrically driven cavity. The mechanism relies on a novel, to the best of our knowledge, cooperation between light–matter coupling enhancement and frequent measurements. We demonstrate that, in the presence of the cooperation, the system dynamics can be completely dominated by the effective system–cavity interaction, and the dissipative effects from the system–environment coupling can be surprisingly ignored. This work provides a generic method of dissipation suppression in a variety of quantum mechanical platforms, including natural atoms and superconducting circuits.

Quantization rule for transition suppression in dynamic two-level system

Abstract The transmission probability in a generic two-quasi-state system is addressed. An approximate expression for the transmission probability between the two quasi-states is derived for the case where the energy gap between the two states varies. Unlike the Landau-Zener formula, the temporal change can have a generic form and can vanish several times. In particular, when the energy gap vanishes twice, an analytical quantization rule for the suppression of transmission between two quasi-states is derived.

Quantum optimal control of the driven dissipative two-level system

Quantum optimal control of the driven dissipative two-level system

Legal regulation of education in Ukraine. Part 6: Features of admission to higher education in Ukraine

This article examines the legal issues of regulating the access of citizens of Ukraine to higher education of the third educational and scientific degree (doctor of philosophy) in the paradigm of international acts, the Constitution of Ukraine, the Laws of Ukraine, and Resolutions of the Cabinet of Ministers of Ukraine in the field of education. This is related to the existence of certain legal conflicts in the education sector, which arose as a result of the ambiguity and imperfection of the legislation of Ukraine on education, which the Ministry of Education and Science of Ukraine uses to illegally restrict the access of citizens of Ukraine to higher education of the third educational and scientific degree. Taking into account the requirements of the Constitution of Ukraine, the Universal Declaration of Human Rights of the United Nations, and the Convention for the Protection of Human Rights and Fundamental Freedoms, the article presents the results of a study of the peculiarities of the application of the provisions of the relevant legislative acts in the field of education (with all changes and additions introduced as of September 1, 2024), namely the Law of Ukraine “On Education” (dated September 5, 2017, under No. 2145-VIII), the Law of Ukraine “On Higher Education” (dated July 1, 2014, under No. 1556- VII) and the “Procedure for Training Candidates for Higher Education Degrees of Doctor of Philosophy and Doctor of Sciences in institutions of higher education (scientific institutions)”, approved by Resolution No. 261 of the Cabinet of Ministers of Ukraine (dated March 23, 2016). At the same time, the research is mainly focused on the peculiarities of applying the above­mentioned legislative acts to determine the differences in the conditions of access to free and paid education and the established legitimacy and feasibility of certain elements of such conditions. Principally this concerns the introduction by the State of Ukraine of unified professional exams and other tests (with the use of external independent evaluation) as a condition for access to the next stage of tests, namely, entrance exams and other tests for admission to study introduced by higher education institutions of Ukraine. That is, the legality of establishing a two-level system of competitions and entrance tests for those who wish to obtain a higher education of the third educational and scientific degree (doctor of philosophy) on a paid basis (i.e., at their own expense or the expense of non-state grants and scholarships) is being considered. The article is the sixth one within the cycle of studies in which the peculiarities of access of Ukrainian citizens to higher education in martial law conditions are addressed.

Role of chirping in pulsed single-photon spectroscopy

We investigate the precision of estimating the interaction strength between a two-level system (TLS) and a single-photon pulse when the latter is subject to chirping. We consider linear, quadratic, and sinusoidal temporal phases applied to Gaussian and exponential temporal profiles. At the asymptotic time, when the TLS has fully decayed to its ground state, the fundamental precision depends solely on the magnitude of its spectral amplitude. For quadratically phase-modulated Gaussian pulses, this is entirely determined by the spectral bandwidth. We provide expressions for evaluating the fundamental precision for general temporal profiles and phase modulations. Finally, we show that experimentally feasible mode-resolved measurements are optimal, or close to it, for chirped, pulsed single-photon spectroscopy. Published by the American Physical Society 2024

Path-filtering in path-integral simulations of open quantum systems using GFlowNets.

An important class of methods for modeling dynamics in open quantum systems is based on the well-known influence functional (IF) approach to solving path-integral equations of motion. Within this paradigm, path-filtering schemes based on the removal of IF elements that fall below a certain threshold aim to reduce the effort needed to calculate and store the influence functional, making very challenging simulations possible. A filtering protocol of this type is considered acceptable as long as the simulation remains mathematically stable. This, however, does not guarantee that the approximated dynamics preserve the physics of the simulated process. In this paper, we explore the possibility of training Generative Flow Networks (GFlowNets) to produce filtering protocols while optimizing for mathematical stability and for physical accuracy. Trained using the trajectory balance objective, the model produces sets of paths to be added to a truncated initial set; it is rewarded if the combined set of paths gives rise to solutions in which the trace of the density matrix is conserved, the populations remain real, and the dynamics approach the exact reference. Using a simple two-level system coupled to a dissipative reservoir, we perform proof-of-concept simulations and demonstrate the elegant and surprising filtering solutions proposed by the GFlowNet.

Исследование многоуровневых моделей управления вагонопотоками в адрес припортовых станций с применением теории дифференциальных уравнений

Purpose: To consider the issue of sustainability of multi-level control systems for car flows to port railway stations in the conditions of intellectualization of transportation management processes. To assess the influence of three-level and two-level control systems for the operational work of port roads on the quality of planning the supply of trains to port stations under various modes of operational operation of railways. Determine the conditions for the stability of the car flow control system by constructing and studying the corresponding hard and soft mathematical models described by autonomous systems of ordinary linear differential equations. Methods: In this study, the methods of the theory of stability of solutions of differential equations, as well as the theory of control and dynamical systems are used. A phase space is used in a visual representation, a qualitative and quantitative analysis of the behavior of phase trajectories in it is performed, corresponding to undisturbed and perturbed solutions of systems of differential equations describing the constructed models of control systems. Results: A comparison of the characteristics of multistage car traffic control systems is given. A study of the stability of multilevel models of car traffic management in the context of the intellectualization of management functions is proposed. In the environment of the analytical computing system, the conditions of asymptotic stability in time of a two-level wagon traffic control system are found and studied. Practical importance: The results obtained by computational experiment make it possible to assess the stability of the functioning of port-side transport and technological systems in the context of changes in the organization of production and the intellectualization of transportation management processes. Computer mathematics systems make it possible to implement the heuristic component of research and obtain theoretically sound and visual solutions to problems of optimizing cargo and wagon traffic control modes.

The impact of quantum correlations on parameter estimation in a spin reservoir

We study the impact of quantum correlations existing within the system-environment thermal equilibrium state while estimating the parameters of the spin reservoir. By employing various physical situations of interest, we present results for the reservoir temperature and its coupling strength with the central two-level system. The central system (probe) interacts with the bunch of randomly oriented spin systems and attains a thermal equilibrium state. We consider a projective measurement which prepares the probe’s initial state, and then the global system (probe and reservoir) evolves unitarily. The reduced density operator encapsulates the information about the spin reservoir which can be extracted by doing measurements on the probe. The precision of such measurement is quantified by quantum Fisher information. We repeat this process if the probe-reservoir initial state is not correlated (product state). We compare the estimation results for both with and without the outturn of initial correlations. In the temperature estimation case, our results are promising as one can significantly improve the accuracy of the estimates by including the effect of initial correlations. A similar trend prevails in the case of coupling strength estimation especially at low temperatures.

Non-linear charged dS spacetime and its thermodynamics and Schottky Anomaly

Abstract In this paper, firstly, the conditions and existence region for the coexistence of the black hole and cosmological horizons in Non-linear charged dS (NLC-dS) spacetime are discussed, subsequently, the thermodynamic quantities for which the boundary conditions are satisfied in spacetime in the coexistence region of the two horizons are discussed, and the effective thermodynamic quantities in the NLC-dS spacetime in the coexistence region with two horizons are presented. Based on these, the heat capacity in the coexistence region with two horizons is addressed, the behavior of the heat capacity in the NLC-dS spacetime in the aforementioned region is found to exhibit the characteristics of Schottky specific heat. In order to investigate the intrinsic reason of the heat capacity in spacetime, regarding the two horizons in the NLC-dS spacetime as two distinct energy levels, consequently, the microscopic particles at different horizons exhibit disparate energies. Using the heat capacity relationship between the two-energy level in an ordinary thermodynamic system, the heat capacity in dS spacetime is discussed, it is observed that the behavior of the heat capacity is analogous to that of the two-energy levels in an ordinary thermodynamic system. The number of microscopic particles in the two-level system is approximated by comparing the maximum value of the heat capacity of the system with the maximum value obtained by treating the two horizons in the NLC-dS spacetime as a two-energy-level system of two distinct energies. This conclusion reflects the quantum properties of the coexistence region with two horizons in the NLC-dS spacetime. It provides a new avenue for further study of the thermodynamic properties of black holes and the quantum properties of de Sitter spacetime.

TLS noise reduction in microwave kinetic inductance detectors using a parallel plate capacitor with a three-layer dielectric

<p>Over the past two decades, microwave kinetic inductance detectors (MKIDs) have gained exceptional importance in millimeter and sub-millimeter astronomy. MKIDs consist of thin strip resonators capable of detecting changes in the surface impedance of superconductor strips, which result from variations in resonance circuit properties. The principal noise in MKIDs comprises excess frequency noise and two-level system noise. In this paper, we propose a technique to mitigate the effect of two-level system (TLS) noise in MKIDs using a parallel plate capacitor with three layers of high ε dielectrics. To achieve this, we employ three layers of Al<sub>2</sub>O<sub>3</sub>, HfO<sub>2</sub>, and TiO<sub>2</sub> with equal thickness between the capacitor plates. The experimental results demonstrate a nearly 30% reduction in TLS power spectral density.<strong></strong></p>

Квазиоптимальный закон управления для лагранжевых систем с дефицитом управляющих воздействий

Mechanical systems with a deficit of control influences are essentially nonlinear dynamic systems of high order, which are characterized by the presence of significant dynamic interaction between the elements. Therefore, the task of control synthesis should be considered in the initial nonlinear formulation, since the use of linear synthesis methods can lead to a loss of stability or significantly worsen the quality of the control process. When solving the problem of synthesis with a deficit of control influences, it is advisable to analyze such a mechanical system as a non-stationary one and use the principle of decomposition in conjunction with the maximum condition of generalized power, which makes it possible to find the structure of a universal two-level control system. The resulting quasi-optimal control provides an increase in the stability area and the quality of the transient process in terms of a quadratic criterion in comparison with known linear algorithms.

Mechatronic technological system based on CNC and intelligent mechatronic mechanism

A mechatronic technological system (MTS) has been developed. It consisting of a CNC metal-cutting machine tool and a mechatronic spindle, made on the basis of an intelligent mechatronic mechanism (IMM). The main elements of the technological system – the CNC and IMM devices – are parts of a single hierarchical, two-level control system, representing, respectively, the upper and lower control levels in this system. The upper control level – the CNC device – ensures stabilization of the kinematic parameters of machining (displacement, speed, acceleration) and their software change in accordance with the CNC control program. The lower control level – the IMM device – ensures stabilization of the power parameters of mechanical machining (cutting axial force and torque) and their software change in accordance with the technological requirements for the surface quality and the physical-and-mechanical state of the surface layer of the machined parts. At both control levels (the upper and lower ones), closed automatic control systems “by deviation” of the adjustable kinematic (upper control level) and power (lower control level) parameters of mechanical machining are functioning. Moreover, the automatic control system of the lower control level of the hierarchy in relation to a similar automatic control system of the upper control level, implements the method of automatic control “by disturbance”. This, in addition to directly ensuring surface finish and surface integrity, allows improving the quality of stabilization of kinematic cutting parameters at the upper control level. Experimental studies of MTS were carried out when machining parts from various materials (steel, polymer composite materials, superhard crystals and stones, other difficult-to-machine materials).

Modeling the processes of transendothelial transport of LDL and macrophage migration

Atherosclerosis is a multifactorial process involving various pathological mechanisms: inflammation, lipoprotein modification, cholesterol accumulation, endothelial dysfunction, oxidative stress and formation of atherosclerotic plaque. The main participants in the development of this disease are endothelial cells, leukocytes and smooth muscle cells of intima. The adult endothelium contains heterogeneous cells, including typical endothelial cells (TEC) and giant multinucleated EC variants (MVEC). The process of passing molecules is called transendothelial transport (TET). The purpose of this work is to model the processes of TET of low-density lipoproteins (LDL) and monocyte migration using various EC variants. In the study, a human EC line (EA.hy926) was used. Multicore variants of EC (MVEC) were obtained by treating EC with a 50% solution of polyethylene glycol 6000. To study LDL transcytosis and monocyte migration, tablets with inserts (0.4 or 3.0 micron pore diameter, respectively) forming a two-level system were used. The LDL transmission rate was assessed by measuring the amount of cholesterol in the upper and lower chambers every 2, 5 and 24 hours. A modified Folch method was used to measure the amount of cholesterol. The cholesterol content was adjusted according to the total protein level in the well, measured by the Lowry method. The migration of macrophages was estimated by direct counting of cells. The content of internalized cholesterol in the MVEC was statistically significantly higher than in the EC. The rate of LDL transport did not differ. The rate of passage of the endothelial barrier formed by MVEC by macrophages was higher at points 2 and 5 hours. After 24 hours the number of migrated cells did not differ. The rate of transendothelial transport for typical and multinucleated variants of EC did not statistically differ. Although the presence of MBEC does not affect the transport of lipoproteins into the subendothelial layer, the fact that multinucleated cells accumulate lipid droplets more actively than typical ECS may indicate an important role in the pathogenesis of atherosclerosis. The rate of macrophage migration after 2 and 5 hours was higher for MVEC than for TEC, whereas immature macrophages did not migrate through the endothelial barrier for 24 hours.

Two-Tier Modular Anharmonic Small Matrix Path Integral with Composite Spin-Boson Baths.

The anharmonic small matrix path integral (anh-SMatPI) algorithm is adapted to composite environments, where each anharmonic bath unit couples to the system and to its own harmonic bath. The propagation matrices are obtained from numerical evaluation of the composite influence functional, which is based on separate iterative path integral calculations for each bath module. The numerically exact nature of the algorithm is demonstrated on a two-level system (TLS) coupled to dissipative TLS baths of one, two, and 50 units.

Kinetics in the Two-Level System with Strong Time-De-pendent Coupling of Its States to the Phonon Bath: Spin-Boson Description

Using the methods of nonequilibrium statistical mechanics, the master equation for the density matrix of an open dissipative quantum system is obtained under conditions, when the coupling between the electronic states of the system and the nuclear displacements in it is controlled by the alternating field. A time-dependent polaron transformation is proposed, which made it possible to solve kinetic equations using an expansion in a parameter characterizing transitions between “phonon-dressed” electronic states of the system. As an example, a mechanism is shown that can control the kinetics in a two-level system by applying a periodic force field to electron-phonon coupling.

Essential vs Removable Bath Anharmonicity: Path Integral Results with Model Electronic-Vibrational Baths.

Fully quantum mechanical real-time path integral calculations on a two-level system (TLS) interacting with a simple or composite anharmonic bath are presented. The bath consists of a few or many units, each comprising two or three electronic states coupled to secondary harmonic vibrational baths. The primitive harmonic bath approximation leads to qualitatively wrong system dynamics at high temperatures, while the effective harmonic bath mapping becomes exact in the macroscopic bath limit. Significant deviations are observed when the number of bath units is small, including skewing and blue shifts in the population oscillations and enhanced or suppressed coherence. These effects reflect the essential anharmonic character of the bath and cannot be captured by harmonic bath treatments.

Two-level system loss: Significant not only at millikelvin

Tow-level system (TLS) loss in amorphous dielectric materials has been intensively studied at millikelvin temperatures due to its impact on superconducting qubit devices and incoherent detectors. However, the significance of TLS loss in superconducting transmission lines at liquid helium temperatures remains unclear. This study investigates TLS loss in amorphous SiO2 at liquid helium temperatures (about 4 K) within a frequency range of 130–170 GHz, using niobium microstrip and coplanar waveguide resonators. Our results demonstrate notable power and temperature dependence of dielectric loss, with the dielectric loss and quasiparticle loss exchanging dominance at around 4 K. These findings are consistent with TLS models and provide crucial insight for the design of superconducting devices operating at liquid helium temperatures.