Two-level System Research Articles

Exceptional Points and Exponential Sensitivity for Periodically Driven Lindblad Equations

In this contribution to the memorial issue of Göran Lindblad, we investigate the periodically driven Lindblad equation for a two-level system. We analyze the system using both adiabatic diagonalization and numerical simulations of the time-evolution, as well as Floquet theory. Adiabatic diagonalization reveals the presence of exceptional points in the system, which depend on the system parameters. We show how the presence of these exceptional points affects the system evolution, leading to a rapid dephasing at these points and a staircase-like loss of coherence. This phenomenon can be experimentally observed by measuring, for example, the population inversion. We also observe that the presence of exceptional points seems to be related to which underlying Lie algebra the system supports. In the Floquet analysis, we map the time-dependent Liouvillian to a non-Hermitian Floquet Hamiltonian and analyze its spectrum. For weak decay rates, we find a Wannier-Stark ladder spectrum accompanied by corresponding Stark-localized eigenstates. For larger decay rates, the ladders begin to dissolve, and new, less localized states emerge. Additionally, their eigenvalues are exponentially sensitive to perturbations, similar to the skin effect found in certain non-Hermitian Hamiltonians.

ФОРМИРОВАНИЕ ТУРИСТСКОРЕКРЕАЦИОННОГО КЛАСТЕРА В РЕГИОНЕ: ЦЕЛЕСООБРАЗНОСТЬ И ПРОГНОЗ

The article assesses the feasibility of establishing a regional economic cluster. The assessment is tested for the tourism industry. It is based on a two-level classification system of Russian regions and simulation modeling. The classification made it possible to single out typological groups of regions with different industry orientations and to identify groups of different industry development levels. Simulation modeling required studying a number of indicators of the tourism industry and identifying patterns and processes occurring in it in a formalized form. Using built models, the results of the tourism industry between 2018–2027 were predicted. Along with that, the investments were provided for the establishment and development of a tourist and recreational cluster.

Dynamical phase and quantum heat at fractional frequencies

We demonstrate a genuine quantum feature of heat: the power emitted by a qubit (quantum two-level system) into a reservoir under continuous driving shows peaks as a function of frequency $f$. These resonant features appear due to the accumulation of the dynamical phase during the driving. The position of the $n$th maximum is given by $f=f_{\rm M}/n$, where $f_{\rm M}$ is the mean frequency of the qubit in the cycle, and their positions are independent of the form of the drive and the number of heat baths attached, and even the presence or absence of spectral filtering. We show that the waveform of the drive determines the intensity of the peaks, differently for odd and even resonances. This quantum heat is expected to play a crucial role in the performance of driven thermal devices such as quantum heat engines and refrigerators. We also show that by optimizing the cycle protocol, we recover the favorable classical limit in fast driven systems without the use of counter-diabatic drive protocols and we demonstrate an entropy preserving non-unitary process. We propose that this non-trivial quantum heat can be detected by observing the steady-state power absorbed by a resistor acting as a bolometer attached to a driven superconducting qubit.

Double layer steganography technique using DNA sequences and images.

Information security has become increasingly challenging as a result of massive advancements in information and communication technologies. Due to the necessity of exchanging private information and the open nature of the network, there is an increased risk of various types of attacks. Consequently, data security is an essential component of data communication. One of the most effective methods used to achieve secrecy is steganography. This method hides data within a cover object without raising suspicion. The level of security is improved when two steganography methods are combined. This approach is known as multilevel steganography, which hides sensitive data in two cover objects in order to provide a two-level security system. Accordingly, we developed a technique that focuses on protecting secrecy while also being robust to attacks. The new technique uses a multi-layer steganography mechanism by using DNA sequences and images as carriers for sensitive data. The technique intends to hide secret messages in the DNA using the substation algorithm, and then the fake DNA is embedded in an image utilizing the discrete cosine transform (DCT) method. Eventually, the stego image is sent to the intended recipient. Different types of images with different sizes and lengths of messages and DNA sequences were used during the experiments. The results show that the proposed mechanism is resistant to histogram and chi-square attacks. The maximum mean value observed was 0.05, which means the histograms of the original and stego images are nearly identical, and the stego image does not raise any suspicion regarding the existence of secret information. In addition, the imperceptibility ratios were good, as the highest PSNR and MSE values were 0.078 and 72.2, respectively. Finally, the PNG and BMP images show excellent results. On the other hand, the JPG images failed to meet the expected ratio of imperceptibility and security.

Analytic approach to the Landau–Zener problem in bounded parameter space

Three analytic solutions to the Schrödinger equation for the time-dependent Landau–Zener (LZ) Hamiltonian are presented. They correspond to specific finite-time driving paths in a bounded parameter space of a two-level system. Two of these paths go through the avoided crossing of levels, either with a constant speed or with variable speed that decreases in the region of reduced energy gap, the third path bypasses the crossing such that the energy gap remains constant. The solutions yield exact time dependencies of the excitation probability for the system evolving from the ground state of the initial Hamiltonian. The LZ formula emerges as an approximation valid within a certain interval of driving times for the constant-speed driving through the avoided crossing. For long driving times, all solutions converge to the prediction of the adiabatic perturbation theory. The excitation probability vanishes at some discrete time instants.

Analytically Solvable Model for Qubit-Mediated Energy Transfer between Quantum Batteries.

The coherent energy transfer between two identical two-level systems is investigated. Here, the first quantum system plays the role of a charger, while the second can be seen as a quantum battery. Firstly, a direct energy transfer between the two objects is considered and then compared to a transfer mediated by an additional intermediate two-level system. In this latter case, it is possible to distinguish between a two-step process, where the energy is firstly transferred from the charger to the mediator and only after from the mediator to the battery, and a single-step in which the two transfers occurs simultaneously. The differences between these configurations are discussed in the framework of an analytically solvable model completing what recently discussed in literature.

An Alternative to the Born Rule: Spectral Quantization

We show that there is a hidden freedom in quantum many-body theory associated with overcompleteness of the time evolution through the single-particle subspace of a many-body system. To fix the freedom, an additional constraint is necessary. We argue that the appropriate constraint on the time evolution through the subspace is to quantize the propagation of entangled pairs of particles, represented by the single-particle spectral function, instead of individual particles. This solution method creates a surface that indicates the multiplicity of every solution to the inverse problem defined by matching the freedom to the constraint. Upon measurement, the system collapses nonlocally onto a single quantized solution. In addition to a combinatoric multiplicity, each solution acquires a multiplicity due to its stability when subject to a small variation in the microscopic degrees of freedom. Numerical calculations for a two-level system show that our theory improves upon standard theory in the description of non-quasiparticle spectral features. Our reinterpretation of quantum many-body theory is not based on the Born rule and offers a more faithful representation of experiments than current theory by modeling individual, quantized events with an explicit collapse model.

Squeezing Properties of Degenerate High-Order Hyper-Raman Lines Emitted by Two-Level System

Squeezing Properties of Degenerate High-Order Hyper-Raman Lines Emitted by Two-Level System

Exploiting Molecular Symmetry to Quantitatively Map the Excited-State Landscape of Iron-Sulfur Clusters.

Cuboidal [Fe4S4] clusters are ubiquitous cofactors in biological redox chemistry. In the [Fe4S4]1+ state, pairwise spin coupling gives rise to six arrangements of the Fe valences ("valence isomers") among the four Fe centers. Because of the magnetic complexity of these systems, it has been challenging to understand how a protein's active site dictates both the arrangement of the valences in the ground state as well as the population of excited-state valence isomers. Here, we show that the ground-state valence isomer landscape can be simplified from a six-level system in an asymmetric protein environment to a two-level system by studying the problem in synthetic [Fe4S4]1+ clusters with solution C3v symmetry. This simplification allows for the energy differences between valence isomers to be quantified (in some cases with a resolution of <0.1 kcal/mol) by simultaneously fitting the VT NMR and solution magnetic moment data. Using this fitting protocol, we map the excited-state landscape for a range of clusters of the form [(SIMes)3Fe4S4-X/L]n, (SIMes = 1,3-dimesityl-imidazol-4,5-dihydro-2-ylidene; n = 0 for anionic, X-type ligands and n = +1 for neutral, L-type ligands) and find that a single ligand substitution can alter the relative ground-state energies of valence isomers by at least 103 cm-1. On this basis, we suggest that one result of "non-canonical" amino acid ligation in Fe-S proteins is the redistribution of the valence electrons in the manifold of thermally populated excited states.

Some Properties of Fractal Tsallis Entropy

We introduce fractal Tsallis entropy and show that it satisfies Shannon–Khinchin axioms. Analogously to Tsallis divergence (or Tsallis relative entropy, according to some authors), fractal Tsallis divergence is defined and some properties of it are studied. Within this framework, Lesche stability is verified and an example concerning the microcanonical ensemble is given. We generalize the LMC complexity measure (LMC is Lopez-Ruiz, Mancini and Calbert), apply it to a two-level system and define the statistical complexity by using the Euclidean and Wootters’ distance measures in order to analyze it for two-level systems.

Quantum Otto cycle under strong coupling.

Quantum heat engines are often discussed under the weak-coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption cannot be justified on the quantum scale. In this study, a quantum Otto cycle model that can be generally applied without the weak-coupling assumption is proposed. We replace the thermalization process in the weak-coupling model with a process comprising thermalization and decoupling. The efficiency of the proposed model is analytically calculated and indicates that, when the contribution of the interaction terms is neglected in the weak-interaction limit, it reduces to that of the earlier model. The sufficient condition for the efficiency of the proposed model not to surpass that of the weak-coupling model is that the decoupling processes of our model have a positive cost. Moreover, the relation between the interaction strength and the efficiency of the proposed model is numerically examined by using a simple two-level system. Furthermore, we show that our model's efficiency can surpass that of the weak-coupling model under particular cases. From analyzing the majorization relation, we also find a design method of the optimal interaction Hamiltonians, which are expected to provide the maximum efficiency of the proposed model. Under these interaction Hamiltonians, the numerical experiment shows that the proposed model achieves higher efficiency than that of its weak-coupling counterpart.

Multiple-photon bundle emission in the n-photon Jaynes-Cummings model.

We study the multiple-photon bundle emission in the n-photon Jaynes-Cummings model composed of a two-level system coupled to a single-mode optical field via the n-photon exciting process. Here, the two-level system is strongly driven by a near-resonant monochromatic field, and hence the system can work in the Mollow regime, in which a super-Rabi oscillation between the zero-photon state and the n-photon state can take place under proper resonant conditions. We calculate the photon number populations and the standard equal-time high-order correlation functions, and find that the multiple-photon bundle emission can occur in this system. The multiple-photon bundle emission is also confirmed by investigating the quantum trajectories of the state populations and both the standard and generalized time-delay second-order correlation functions for multiple-photon bundle. Our work paves the way towards the study of multiple-photon quantum coherent devices, with potential application in quantum information sciences and technologies.

Cavity transmission in a QD-cavity system using Cluster Expansion: Beyond the mean-field approach

We theoretically study the temporal evolution of the mean number of photons in a strongly coupled cavity quantum dot system driven by a symmetric laser pulse using the Cluster Expansion method. The quantum dot is modeled as a two-level system that interacts with a single mode of the quantized electromagnetic field according to the Jaynes–Cummings model. We compare our results with those obtained through the Master Equation method and find that second-order Cluster Expansion is sufficient to reproduce the transmission spectrum without losing the fundamental physical processes and with a relatively low computational cost.

Leggett–Garg inequality in Markovian quantum dynamics: role of temporal sequencing of coupling to bath

We study Leggett–Garg inequalities (LGIs) for a two level system (TLS) undergoing Markovian dynamics described by unital maps. We first find the analytic expression of LG parameter K 3 (simplest variant of LGIs) in terms of the parameters of two distinct unital maps representing time evolution for intervals: t 1 to t 2 and t 2 to t 3. We then show that the maximum violation of LGI for all possible unital maps can never exceed well known Lüders bound of over the full parameter space. We further show that if the map for the time interval t 1 to t 2 is non-unitary unital then irrespective of the choice of the map for interval t 2 to t 3 we can never reach Lüders bound. On the other hand, if the measurement operator eigenstates remain pure upon evolution from t 1 to t 2, then depending on the degree of decoherence induced by the unital map for the interval t 2 to t 3 we may or may not obtain Lüders bound. Specifically, we find that if the unital map for interval t 2 to t 3 leads to the shrinking of the Bloch vector beyond half of its unit length, then achieving the bound is not possible. Hence our findings not only establish a threshold for decoherence which will allow for , but also demonstrate the importance of temporal sequencing of the exposure of a TLS to Markovian baths in obtaining Lüders bound.

Geometric phases of mixed quantum states: A comparative study of interferometric and Uhlmann phases

Two geometric phases of mixed quantum states, known as the interferometric phase and Uhlmann phase, are generalizations of the Berry phase of pure states. After reviewing the two geometric phases and examining their parallel-transport conditions, we specify a class of cyclic processes that are compatible with both conditions and therefore accumulate both phases through their definitions, respectively. Those processes then facilitate a fair comparison between the two phases. We present exact solutions of two-level and three-level systems to contrast the two phases. While the interferometric phase exhibits finite-temperature transitions only in the three-level system but not the two-level system, the Uhlmann phase shows finite-temperature transitions in both cases. Thus, using the two geometric phases as finite-temperature topological indicators demonstrates the rich physics of topology of mixed states.

Two-photon correlations in detuned resonance fluorescence

We discuss two-photon correlations from the side peaks that are formed when a two-level system emitter is driven coherently, with a detuning between the driving source and the emitter (quasi-resonance fluorescence). We do so in the context of the theories of frequency-resolved photon correlations and homodyning, showing that their combination leads to a neat picture compatible with perturbative two-photon scattering that was popular in the early days of quantum electrodynamics. This should help to control, enhance and open new regimes of multiphoton emission. We also highlight a way to evidence the quantum coherent nature of the process from photoluminescence only, through the observation of a collapse of the symmetry of the lineshape accompanied by a surge of its intensity of emission. We discuss several of our results in the light of recent experimental works.

Thermometry of strongly correlated fermionic quantum systems using impurity probes

We study quantum-impurity models as a platform for quantum thermometry. A single quantum spin-$\frac{1}{2}$ impurity is coupled to an explicit, structured, fermionic thermal sample system, which we refer to as the environment or bath. We critically assess the thermometric capabilities of the impurity as a probe, when its coupling to the environment is of Ising or Kondo exchange type. In the Ising case, we find sensitivity equivalent to that of an idealized two-level system, with peak thermometric performance obtained at a temperature that scales linearly in the applied control field, independent of the coupling strength and environment spectral features. By contrast, a richer thermometric response can be realized for Kondo impurities, since strong probe-environment entanglement can then develop. At low temperatures, we uncover a regime with a universal thermometric response that is independent of microscopic details, controlled only by the low-energy spectral features of the environment. The many-body entanglement that develops in this regime means that low-temperature thermometry with a weakly applied control field is inherently less sensitive, while optimal sensitivity is recovered by suppressing the entanglement with stronger fields.

Historical and urban-planing development оf the Pryvokzalnii district of Chernivtsi

Historical and urban-planing development оf the Pryvokzalnii district of Chernivtsi

Pulse overlap artifacts and double quantum coherence spectroscopy.

The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used.

Controllable sidebands of resonance fluorescence of a two-level system driven by bichromatic field

Strong polychromatic driving reshapes characteristics of the resonance fluorescence spectrum of a two-level system. Employing bichromatic driving feild with a low beat-frequency smaller than the emission rate of the system we demonstrate the exotic features of the fluorescence spectrum calculated by the numerical Floquet-Liouville approach and analytical method. It is found that fluorescence spectrum possesses two broadened sidebands in the place of the Rabi sidebands under certain conditions. Moreover, the heights and widths of the sidebands can be controlled by tuning the driving parameters. The properties of the spectrum is determined by the transitions between the Floquet states in a rotating frame. The broadened sidebands result from the quasi-continuous quasienergy spectrum which happens with steering the beat frequency lower. The present study provides insights into the Floquet engineering of the fluorescence spectral features with polychromatic excitation fields.