Nondegenerate Levels Research Articles

Study of thermodynamic properties of N particles in one-dimensional harmonic oscillator potential

We have calculated the partition function and hence the energy and the specific heat of a two-particle system in n numbers of finite nondegenerate energy levels of equal spacing distributed according to classical and quantum statistics. We have then extended our study for N identical particles placed in 1D harmonic oscillator potential. It is observed that the specific heat of bosons and fermions are exactly the same in this potential at any temperature, and at high temperature the results are similar to that for the classical particles. The partition function of a system of two particles placed in 2D harmonic oscillator potential has also been determined as comparison.

Non-Abelian effects in dissipative photonic topological lattices

Topology is central to phenomena that arise in a variety of fields, ranging from quantum field theory to quantum information science to condensed matter physics. Recently, the study of topology has been extended to open systems, leading to a plethora of intriguing effects such as topological lasing, exceptional surfaces, as well as non-Hermitian bulk-boundary correspondence. Here, we show that Bloch eigenstates associated with lattices with dissipatively coupled elements exhibit geometric properties that cannot be described via scalar Berry phases, in sharp contrast to conservative Hamiltonians with non-degenerate energy levels. This unusual behavior can be attributed to the significant population exchanges among the corresponding dissipation bands of such lattices. Using a one-dimensional example, we show both theoretically and experimentally that such population exchanges can manifest themselves via matrix-valued operators in the corresponding Bloch dynamics. In two-dimensional lattices, such matrix-valued operators can form non-commuting pairs and lead to non-Abelian dynamics, as confirmed by our numerical simulations. Our results point to new ways in which the combined effect of topology and engineered dissipation can lead to non-Abelian topological phenomena.

Subregular W-algebras of type A

Subregular W-algebras are an interesting and increasingly important class of quantum hamiltonian reductions of affine vertex algebras. Here, we show that the [Formula: see text] subregular W-algebra can be realized in terms of the [Formula: see text] regular W-algebra and the half lattice vertex algebra [Formula: see text]. This generalizes the realizations found for [Formula: see text] and [Formula: see text] in [D. Adamović, Realizations of simple affine vertex algebras and their modules: The cases [Formula: see text] and [Formula: see text], Comm. Math. Phys. 366 (2019) 1025–1067, arXiv:1711.11342 [math.QA]; D. Adamović, K. Kawasetsu and D. Ridout, A realization of the Bershadsky–Polyakov algebras and their relaxed modules, Lett. Math. Phys., 111 (2021) 1–30, arXiv:2007.00396 [math.QA]] and can be interpreted as an inverse quantum hamiltonian reduction in the sense of Adamović. We use this realization to explore the representation theory of [Formula: see text] subregular W-algebras. Much of the structure encountered for [Formula: see text] and [Formula: see text] is also present for [Formula: see text]. Particularly, the simple [Formula: see text] subregular W-algebra at nondegenerate admissible levels can be realized purely in terms of the [Formula: see text] minimal model vertex algebra and [Formula: see text].

Dynamics and uncertainty for maximally entangled bipartite system constrained on a helicoid

The classical and quantum dynamics of particles constrained on a right helicoid is discussed via Dirac approach. We show how the uncertainty in measurement for observables of maximally entangled system is affected by the total number of constrained particles sigma , external magnetic field vec {mathcal {B}}; as well as by geometric parameters like the pitchrho and the radial position of particles. In doing so we also highlight numeric bounds on the external field strengths to tune both intraparticle and bipartite entanglement and we remark that the bipartite entanglement is more robust to changes in the fields than the intraparticle entanglement, in this framework. We also highlight specific parameter regimes which lead the uncertainty (in measurement) to achieve respective parameter independence and, for a particular subset of commutation relations, the system remains confined in the quantum regime even in the limit sigma rightarrow infty . It is observed that the uncertainties are strongly influenced by the geometric parameters e.g., rho , and the strength of bipartite as well as intraparticle entanglement might be controllable through rho . The energy equation for this setup is obtained and the additional terms are discussed which arise due to quantum correlations, orbit–orbit interaction and the normal Zeeman effect, which leads to the splitting of the energy level into 11 non-degenerate levels. Finally we comment that, a linkage of this phenomenology with Aharonov–Bohm like effect might be possible by strictly confining vec {mathcal {B}} along the central axis of the helicoid.

Magneto-optic Kerr effect in Gd20Co80 alloy

The magneto-optical Kerr effect in Gd20Co80 alloy and cobalt thin films has been studied in a broad spectral range applying spectral ellipsometry experimental technique. The results of the experiments showed the complex nature of the complex Kerr angle dispersion curves. A quantum mechanical formalism for degenerate and non-degenerate Landau levels for quasi-free electrons in ferromagnetic material has been developed in order to analyze the experimental data. The equivalence of relations for off-diagonal dielectric tensor elements for non-degenerate Landau levels to the classical case of the motion of quasi-free electrons along circular trajectories in a magnetic field has been theoretically shown. The degenerate Landau levels in this approach are the result of motion of electrons in small confined volumes near rare-earth alloy atoms. Rotation of light polarization occurs in this case due to transitions between subbands having different magnetic quantum numbers. This theoretical approach allowed us to interpret in detail shapes and sign of the complex Kerr angle dispersion curves, which actually include the contributions of optical transitions between degenerate and non-degenerate energy levels. The complex Kerr angle sign is determined by the magnetization magnetic field direction for non-degenerate Landau levels and the Hund rule for degenerate Landau levels.

Driving quantum systems with periodic conditional measurements

We investigate the effect of conditional null measurements on a quantum system and find a rich variety of behaviors. Specifically, quantum dynamics with a time independent $H$ in a finite dimensional Hilbert space are considered with repeated strong null measurements of a specified state. We discuss four generic behaviors that emerge in these monitored systems. The first arises in systems without symmetry, along with their associated degeneracies in the energy spectrum, and hence in the absence of dark states as well. In this case, a unique final state can be found which is determined by the largest eigenvalue of the survival operator, the non-unitary operator encoding both the unitary evolution between measurements and the measurement itself. For a three-level system, this is similar to the well known shelving effect. Secondly, for systems with built-in symmetry and correspondingly a degenerate energy spectrum, the null measurements dynamically select the degenerate energy levels, while the non-degenerate levels are effectively wiped out. Thirdly, in the absence of dark states, and for specific choices of parameters, two or more eigenvalues of the survival operator match in magnitude, and this leads to an oscillatory behavior controlled by the measurement rate and not solely by the energy levels. Finally, when the control parameters are tuned, such that the eigenvalues of the survival operator all coalesce to zero, one has exceptional points that corresponds to situations that violate the null measurement condition, making the conditional measurement process impossible.

Thermodynamics of Precision in Markovian Open Quantum Dynamics.

The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this Letter, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.

Heat rectification through single and coupled quantum dots

We study heat rectification through quantum dots in the Coulomb blockade regime using a master equation approach. We consider both cases of two-terminal and four-terminal devices. In the two-terminal configuration, we analyze the case of a single quantum dot with either a doubly-degenerate level or two non-degenerate levels. In the sequential tunneling regime we analyze the behaviour of heat currents and rectification as functions of the position of the energy levels and of the temperature bias. In particular, we derive an upper bound for rectification in the closed-circuit setup with the doubly-degenerate level. We also prove the absence of a bound for the case of two non-degenerate levels and identify the ideal system parameters to achieve nearly perfect rectification. The second part of the paper deals with the effect of second-order cotunneling contributions, including both elastic and inelastic processes. In all cases we find that there exists ranges of values of parameters (such as the levels’ position) where rectification is enhanced by cotunneling. In particular, in the doubly-degenerate level case we find that cotunneling corrections can enhance rectification when they reduce the magnitude of the heat currents. For the four-terminal configuration, we analyze the non-local situation of two Coulomb-coupled quantum dots, each connected to two terminals: the temperature bias is applied to the two terminals connected to one quantum dot, while the heat currents of interest are the ones flowing in the other quantum dot. Remarkably, in this situation we find that non-local rectification can be perfect as a consequence of the fact that the heat currents vanish for properly tuned parameters.

Spin-Dependent Polaron Dynamics in Organic Ferromagnets.

The spin-dependent polaron dynamics in organic ferromagnets under driven electric fields are investigated by using the extended Su-Schrieffer-Heeger (SSH) model coupled with a nonadiabatic dynamics method. It is found that the spin-down polaron with the same spin orientation as the radicals drifts faster than the spin-up one under the same driven electric field. In an applicable range of driven electric fields, the velocity of the spin-down polaron is about 3.4 times that of the spin-up one. The dynamical property of the polaron with each spin (up or down) is asymmetric upon the reversal of the driven electric fields. The diverse dynamical properties of polarons with specific spins can be attributed to the spin nondegenerate polaron energy levels, the dipole moment generated by the asymmetrical polaron charge distributions and the strong electron-lattice coupling in organic ferromagnets. Our findings are expected to be useful for improving organic ferromagnet based spintronic devices.

Nonreciprocal transition between two nondegenerate energy levels

Stimulated emission and absorption are two fundamental processes of light–matter interaction, and the coefficients of the two processes should be equal. However, we will describe a generic method to realize the significant difference between the stimulated emission and absorption coefficients of two nondegenerate energy levels, which we refer to as a nonreciprocal transition. As a simple implementation, a cyclic three-level atom system, comprising two nondegenerate energy levels and one auxiliary energy level, is employed to show a nonreciprocal transition via a combination of synthetic magnetism and reservoir engineering. Moreover, a single-photon nonreciprocal transporter is proposed using two one-dimensional semi-infinite coupled-resonator waveguides connected by an atom with nonreciprocal transition effect. Our work opens up a route to design atom-mediated nonreciprocal devices in a wide range of physical systems.

Learning the best nanoscale heat engines through evolving network topology

The quest to identify the best heat engine has been at the center of science and technology. Considerable studies have so far revealed the potentials of nanoscale thermal machines to yield an enhanced thermodynamic efficiency in noninteracting regimes. However, the full benefit of many-body interactions is yet to be investigated; identifying the optimal interaction is a hard problem due to combinatorial explosion of the search space, which makes brute-force searches infeasible. We tackle this problem with developing a framework for reinforcement learning of network topology in interacting thermal systems. We find that the maximum possible values of the figure of merit and the power factor can be significantly enhanced by electron-electron interactions under nondegenerate single-electron levels with which, in the absence of interactions, the thermoelectric performance is quite low in general. This allows for an alternative strategy to design the best heat engines by optimizing interactions instead of single-electron levels. The versatility of the developed framework allows one to identify full potential of a broad range of nanoscale systems in terms of multiple objectives.

Organic Multiferroic Magnetoelastic Complexes.

The design of crystal structures aids the discovery of interesting physical phenomena in organic crystals. In this work, the optimization of the coronene-tetracyanoquinodimethane (TCNQ) structure generates non-degenerate energy levels of spin-up and spin-down electrons after charge transfer, producing spontaneous spin polarization, leading to pronounced ferromagnetism. The deformed crystal lattice can significantly affect the saturation magnetization of organic ferromagnets to present a remarkable magnetoelastic coupling. Furthermore, the magnetic-field-induced lattice shrinkage of the ferromagnetic crystals supports a spin-lattice-interaction-dependent magnetoelastic coupling. This concept of organic magnetoelastic coupling will pave the way for the rapid mechanical control of spin polarization in organic multiferroic magnetoelastic materials.

A continuous 1 052 nm and 1 061 nm dual-wavelength Nd:YAG laser

Exploiting a specially designed Fabry-Perot filter as output coupler, a continuous 1 052 nm and 1 061 nm dual-wavelength laser is realized. The threshold, slope efficiency and maximum power of the 1 052 nm and 1 061 nm dual-wavelength laser are 2.55 W, 17.5% and 571 mW, respectively. The competition and coexistent relationships between 1 052 nm, 1 061 nm and 1 064 nm are analyzed. Involved non-degenerate Stark energy level structures are used to classify dual-wavelength lasers. According to this method, dual-wavelength lasers can be classified as different upper and lower non-degenerate Stark energy levels, the same upper but different lower Stark energy levels, different upper but the same lower Stark energy levels. Representative Nd:YAG dual-wavelength lasers are classified according to this criterion. It is found that the realization of front two type lasers is easy and that of third type lasers is challenging. This method can be used as a level of difficulty reference for the realization of dual-wavelength lasers.

Exact T = 0 eigenstates of the isovector pairing Hamiltonian

We derive the exact T = 0 seniority-zero eigenstates of the isovector pairing Hamiltonian for an even number of protons and neutrons. Nucleons are supposed to be distributed over a set of non-degenerate levels and to interact through a pairing force with constant strength. We show that these eigenstates (and among them, in particular, the ground state) are linear superpositions of products of T = 1 collective pairs arranged into T = 0 quartets. This grouping of protons and neutrons first into T = 1 collective pairs and then into T = 0 quartets represents the distinctive feature of these eigenstates. This work highlights, for the first time on the grounds of the analytic expression of its eigenstates, the key role played by the isovector pairing force in the phenomenon of nuclear quarteting.

AN APPLICATION OF THE DEMOCRATIC MAPPING IN REALISTIC SYSTEMS

The democratic mapping is used for the calculation of low lying states of nuclei in the sd and fp shells. In addition to demonstrating the applicability of the method in realistic cases where many non-degenerate levels are present, the method allows for the ranking of the various bosons according to their importance as building blocks of low lying states. It is proven that the s and d bosons are the most important building blocks, followed by the d' and g bosons. Thus one of the basic assumptions of the Interacting Boson Model (IBM) is proven to be correct. Very good agreement between the boson calculation and the shell model results is obtained for A = 20 nuclei when 12 bosons are taken into account, while an even larger number of bosons is required to reproduce the low-lying states of the A = 44 nuclei. In order to obtain equally good results with a smaller number of bosons one needs to introduce effective boson hamiltonians which correspond to truncated fermion spaces.

Orbital angular momentum transfer via spontaneously generated coherence

We study the orbital angular momentum (OAM) transfer from a weak Laguerre–Gaussian (LG) field to a weak plane wave in two closed-loop three-level V-type atomic systems. In the first scheme, the atomic system has two non-degenerate upper levels where the corresponding transition is excited by a microwave plane wave. It is analytically shown that the microwave field induces an OAM transfer from an LG field to a generated third field. It is demonstrated that the efficiency of the OAM transfer decreases when the thermal velocity distribution of atoms is considered. In the second scheme, we consider a three-level V-type atomic system with two near-degenerate excited states and study the effect of the quantum interference due to the spontaneous emission on the OAM transfer. It is found that spontaneously generated coherence (SGC) induces the OAM transfer from the LG field to the weak planar field, and the OAM transfer does not occur in the absence of the SGC. The suggested models offer a rather simple method for the OAM transfer that can be used in quantum information processing and data storage.

Exotic impurity-induced states in single-layer h -BN: The role of sublattice structure and intervalley interactions

By using a combination of density functional theory, tight-binding, and effective mass calculations, we explore the electronic properties of donor and acceptor states of substitutional impurities in single-layer $h$-BN. We find that the impurity level structure inside the electronic gap is quite exotic, as it strongly depends on the sublattice position of the impurity and its behavior as a donor or an acceptor. For instance, when an acceptor atom replaces a nitrogen atom, the intervalley interaction induced by the impurity potential is found to be strong and the resulting level structure consists only of nondegenerate levels with strong valley and spin splitting. On the other hand, when an acceptor replaces a boron atom, the intervalley interaction is much weaker and near-valley-degenerate levels are found. Donor impurities behave in a similar fashion. The differences between these two types of level structures can be traced to the peculiar sublattice-resolved electronic structure of pristine $h$-BN, in which the valence and conduction wave functions at the $K$ and ${K}^{\ensuremath{'}}$ points are composed only of nitrogen and boron ${p}_{z}$ orbitals, respectively, and to the dependence of the intervalley interaction on them. We predict that this impurity level structure must also be present in other two-dimensional semiconductors and insulators with similar sublattice-resolved electronic states, such as other hexagonal III-V binary compounds and, consequently, offer the possibility of engineering the optical properties of these materials for potential applications in future devices.

Graphane with carbon dimer defects: Robust in-gap states and a scalable two-dimensional platform for quantum computation

We study the energy level structures of the defective graphane lattice, where a carbon dimer defect is created by removing the hydrogen atoms on two nearest-neighbor carbon sites. Robust defect states emerge inside the bulk insulating gap of graphane. While for the stoichiometric half-filled system there are two doubly degenerate defect levels, there are four nondegenerate and spin-polarized in-gap defect levels in the system with one electron less than half filling. A universal set of quantum gates can be realized in the defective graphane lattice, by triggering resonant transitions among the defect states via optical pulses and \emph{ac} magnetic fields. The sizable energy separation between the occupied and the empty in-gap states enables precise control at room temperature. The spatial locality of the in-gap states implies a qubit network of extremely high areal density. Based on these results, we propose that graphane as a unique platform could be used to construct the future all-purpose quantum computers.

Spatially dependent atom-photon entanglement

The atom-photon entanglement using the Laguerre-Gaussian (LG) beams is studied in the closed-loop three-level V-type quantum systems. We consider two schemes with near-degenerate and non-degenerate upper levels: in the first, the effect of the quantum interference due to the spontaneous emission is taken into account and in the second, a microwave plane wave is applied to the upper levels transition. It is shown that the atom-photon entanglement in both schemes depends on the intensity profile as well as the orbital angular momentum (OAM) of the applied fields so that the various spatially dependent entanglement patterns can be generated by Laguerre-Gaussian beams with different OAMs. However, due to the zero intensity,no entanglement appears in the center of the optical vortex beams. As a result, the entanglement between dressed atom and its spontaneous emissions in different points of the atomic vapor cell can be controlled by the OAM of the applied fields. Moreover, our numerical results show that the number of the local maximum degree of entanglement (DEM) peaks depends on the OAM of the applied fields. The degrees of freedom for OAM play a crucial role in spatially dependent atom-photon entanglement in such a way that it may possess broad applications in high-dimensional quantum information processing and data storage.

Photon–photon correlations with a V-type three-level system interacting with two quantized field modes

We carry out a model study on the interaction of a $V$-type three-level emitter with two quantized cavity modes which are weakly driven by two classical fields. The emitter may be an atom or a molecule with nondegenerate upper levels in general. The lifetimes of the two upper levels are assumed to be much longer than the lifetime of the cavity photons. We calculate the two-time second order coherence function, namely Hanbury Brown-Twiss function $g^{(2)}(\tau)$ where $\tau$ is the time delay between the two modes. We analyze the photon-photon correlations between the two cavity modes in terms of $g^{(2)}(\tau)$. The variation of $g^{(2)}(\tau)$ as a function of $\tau$ exhibits collapse and revival type oscillations as well as quantum beats for relatively short $\tau$ while in the limit $\tau \rightarrow \infty$, $g^{(2)}(\tau) \simeq 1$. We further show that the two cavity field modes are entangled when $g^{(2)}(0) > 2$. We develop a dressed state picture with single photon in each mode to explain the results and use the negativity of the partial transpose of the reduced field density matrix to show the entanglement between field modes. The model presented in this paper may be useful for generating entangled photon pairs, and also manipulating photon-photon correlations with a cavity QED set up.