Energy Level Crossings Research Articles

Attempt to find the hidden symmetry in the asymmetric quantum Rabi model

It has been observed that the asymmetric quantum Rabi model (QRM), which does not possess any obvious symmetry, exhibits energy level crossings, which are often associated with symmetries. This observation suggests that there is in fact a symmetry in the asymmetric QRM, even though simple inspection of the model and its Hamiltonian does not reveal the nature of this symmetry. Here we present the results of numerical calculations on the energy eigenstates of the asymmetric QRM in an attempt to elucidate the nature of the symmetry. In particular, we note that the distribution of states in the Hilbert space among different symmetry classes is normally independent of system parameters and test whether this property holds for the asymmetric QRM. We find that it does not, which both helps explain why the symmetry is hidden and adds more intrigue as to what its nature might be.

Revival of Order in the Chaotic Dynamics with Position and Time Dependent Perturbed System

Studying quantum properties of a system has been quite popular in quantum mechanics. One of the most important systems that are very crucial to the framework of quantum mechanics is the system of harmonic oscillator a system whose classical evolution is known to exhibit peculiar chaotic dynamics. We are motivated to investigate the behavior of quantum properties for a system with position and time dependent perturbed. Starting with Hamiltonian, we determined the equation of motion and obtained the wave function. The energy of the whole system using the operator ordering method was found. We show that the quantum mechanical picture alludes to a chaotic dynamics as expected. This is evidenced through the appearance of energy level crossings. An additional signature to this chaotic dynamics is observed in the transition of Eigen values from real to imaginary. We also show numerically that one can give the behavior of the system is Poincare section. By so doing we confirmed that increasing and decreasing the perturbation amplitude of the system becomes chaotic.

Scenarios of local spectral property and multifunctional spin selecting for a triple quantum dot molecule: How do the bonding and antibonding orbitals contribute to the spin currents?

Molecular electronic device is considered as a promising candidate for next generation electronic component, where the basic challenge involves understanding the charge and spin transports through molecular objects. In this paper, with the help of the sophisticated numerical renormalization group technique, we study theoretically the spin selective transport in a parallel triple quantum dot molecular device pierced by a local magnetic field along z axis. Based on simplified parameters of real molecular system, we find such device acts as a multifunctional spin selector when the inter-molecule tunneling couplings are asymmetric, including two 100% polarized spin-up summits, and one 100% spin-down summit in the linear conductance. We show in detail the local density of states for the bonding and anti-boding orbitals, and attribute the spin selection to the orbital polarized Coulomb blockade effect. We demonstrate our numerical results are consistent with those estimated by the analytical techniques, including the Friedel sum rule and the energy level crossings of the isolated orbitals.

The microscopic Einstein-de Haas effect.

The Einstein-de Haas (EdH) effect, where the spin angular momentum of electrons is transferred to the mechanical angular momentum of atoms, was established experimentally in 1915. While a semiclassical explanation of the effect exists, modern electronic structure methods have not yet been applied to model the phenomenon. In this paper, we investigate its microscopic origins by means of a noncollinear tight-binding model of an O2 dimer, which includes the effects of spin-orbit coupling, coupling to an external magnetic field, and vector Stoner exchange. By varying an external magnetic field in the presence of spin-orbit coupling, a torque can be generated on the dimer, validating the presence of the EdH effect. The avoided energy level crossings and the rate of change of magnetic field determine the evolution of the spin. We also find that the torque exerted on the nuclei by the electrons in a time-varying B field is not only due to the EdH effect. The other contributions arise from field-induced changes in the electronic orbital angular momentum and from the direct action of the Faraday electric field associated with the time-varying magnetic field.

Magnetosensitivity in Dipolarly Coupled Three-Spin Systems.

The radical pair mechanism is a canonical model for the magnetosensitivity of chemical reaction processes. The key ingredient of this model is the hyperfine interaction that induces a coherent mixing of singlet and triplet electron spin states in pairs of radicals, thereby facilitating magnetic field effects (MFEs) on reaction yields through spin-selective reaction channels. We show that the hyperfine interaction is not a categorical requirement to realize the sensitivity of radical reactions to weak magnetic fields. We propose that, in systems comprising three instead of two radicals, dipolar interactions provide an alternative pathway for MFEs. By considering the role of symmetries and energy level crossings, we present a model that demonstrates a directional sensitivity to fields weaker than the geomagnetic field and remarkable spikes in the reaction yield as a function of the magnetic field intensity; these effects can moreover be tuned by the exchange interaction. Our results further the current understanding of the effects of weak magnetic fields on chemical reactions, could pave the way to a clearer understanding of the mysteries of magnetoreception and other biological MFEs and motivate the design of quantum sensors. Further still, this phenomenon will affect spin systems used in quantum information processing in the solid state and may also be applicable to spintronics.

Energy-level crossings and number-parity effects in a bosonic tunneling model

An exactly solved bosonic tunneling model is studied along a line of the coupling parameter space, which includes a quantum phase boundary line. The entire energy spectrum is computed analytically, and found to exhibit multiple energy-level crossings in a region of the coupling parameter space. Several key properties of the model are discussed, which exhibit a clear dependence on whether the particle number is even or odd. Principal among these is a number-parity effect in the quantum dynamics.

Development of in-situ trap characterisation techniques for EMCCDs

The “trap pumping” technique has seen considerable use over recent years as a means to probe the intrinsic properties of silicon defects that can impact charge transfer performance within CCD-based technologies. While the theory behind the technique is reasonably well understood, it has to date only been applied to relatively simple pixel designs where the motion of charge between pixel phases is fairly easy to predict. For some devices, the intrinsic pixel architecture is more complex and can consist of unequal phase sizes and additional implants that deform the electronic potential. Here, we present the implementation of the trap pumping technique for the CCD201-20, a 2-phase Teledyne e2v EMCCD. Clocking schemes are presented that can provide the location of silicon defects to sub-micron resolution. Experimental techniques that allow determination of trap energy levels and emission cross sections are presented. These are then implemented on an irradiated CCD201-20 to determine the energy level and emission cross section for defects thought to be the double acceptor state of the silicon divacancy (VV−−) and carbon-phosphorus (CiPs) pairs. An improvement in charge transfer performance through optimised parallel clock delay is demonstrated and found to correlate with the properties of defects found using the trap pumping technique.

Quantum thermodynamic cycle with quantum phase transition.

With the Lipkin-Meshkov-Glick (LMG) model as an illustration, we construct a thermodynamic cycle composed of two isothermal processes and two isomagnetic field processes, and we study the thermodynamic performance of this cycle accompanied by the quantum phase transition (QPT). We find that for a finite particle system working below the critical temperature, the efficiency of the cycle is capable of approaching the Carnot limit when the external magnetic field λ_{1} corresponding to one of the isomagnetic processes reaches the cross point of the ground states' energy level, which can become the critical point of the QPT in the large-N limit. Our analysis proves that the system's energy level crossings at low-temperature limits can lead to a significant improvement in the efficiency of the quantum heat engine. In the case of the thermodynamics limit (N→∞), the analytical partition function is obtained to study the efficiency of the cycle at high- and low-temperature limits. At low temperatures, when the magnetic fields of the isothermal processes are located on both sides of the critical point of the QPT, the cycle reaches maximum efficiency, and the Carnot efficiency can be achieved. This observation demonstrates that the QPT of the LMG model below critical temperature is beneficial to the thermodynamic cycle's operation.

Description of Radiation Damage in Diamond Sensors Using an Effective Defect Model

The Beam Condition Monitoring Leakage (BCML) system is a beam monitoring device in the CMS experiment at the LHC consisting of 32 poly‐crystalline (pCVD) diamond sensors. The BCML sensors, located in rings around the beam, are exposed to high particle rates originating from the colliding beams. These particles cause lattice defects, which act as traps for the ionized charge carrier leading to a reduced charge collection efficiency (CCE). The radiation induced CCE degradation was, however, much more severe than expected from low rate laboratory measurements. Measurement and simulations presented in this paper show that this discrepancy is related to the rate of incident particles. At high particle rates, the trapping rate of the ionization is strongly increased compared to the detrapping rate leading to an increased build‐up of space charge. This space charge locally reduces the internal electric field increasing the trapping rate and hence reducing the CCE even further. In order to connect these macroscopic measurements with the microscopic defects acting as traps for the ionization charge, the TCAD simulation program SILVACO was used. It allows to introduce the defects as effective donor and acceptor levels, and can calculate the electric field from Transient Current Technique (TCT) signals and CCE as a function of the effective trap properties, like density, energy level, and trapping cross section. After each irradiation step, these properties were fitted to the data on the electric field from the TCT signals and CCE. Two effective acceptor and donor levels were needed to fit the data after each step. It turned out that the energy levels and cross sections could be kept constant and the trap density was proportional to the cumulative fluence of the irradiation steps. The highly non‐linear rate dependent diamond polarization and the resulting signal loss can be simulated using this effective defect model and is in agreement with the measurement results.

Nuclear Spin Isomers: Engineering a Et4N[DyPc2] Spin Qudit

Two dysprosium isotopic isomers were synthesized: Et4 N[163 DyPc2 ] (1) with I=5/2 and Et4 N[164 DyPc2 ] (2) with I=0 (where Pc=phthalocyaninato). Both isotopologues are single-molecule magnets (SMMs); however, their relaxation times as well as their magnetic hystereses differ considerably. Quantum tunneling of the magnetization (QTM) at the energy level crossings is found for both systems via ac-susceptibility and μ-SQUID measurements. μ-SQUID studies of 1(I=5/2) reveal several nuclear-spin-driven QTM events; hence determination of the hyperfine coupling and the nuclear quadrupole splitting is possible. Compound 2(I=0) shows only strongly reduced QTM at zero magnetic field. 1(I=5/2) could be used as a multilevel nuclear spin qubit, namely qudit (d=6), for quantum information processing (QIP) schemes and provides an example of novel coordination-chemistry-discriminating nuclear spin isotopes. Our results show that the nuclear spin of the lanthanide must be included in the design principles of molecular qubits and SMMs.

Nuclear Spin Isomers: Engineering a Et4N[DyPc2] Spin Qudit

AbstractTwo dysprosium isotopic isomers were synthesized: Et4N[163DyPc2] (1) with I=5/2 and Et4N[164DyPc2] (2) with I=0 (where Pc=phthalocyaninato). Both isotopologues are single‐molecule magnets (SMMs); however, their relaxation times as well as their magnetic hystereses differ considerably. Quantum tunneling of the magnetization (QTM) at the energy level crossings is found for both systems via ac‐susceptibility and μ‐SQUID measurements. μ‐SQUID studies of 1(I=5/2) reveal several nuclear‐spin‐driven QTM events; hence determination of the hyperfine coupling and the nuclear quadrupole splitting is possible. Compound 2(I=0) shows only strongly reduced QTM at zero magnetic field. 1(I=5/2) could be used as a multilevel nuclear spin qubit, namely qudit (d=6), for quantum information processing (QIP) schemes and provides an example of novel coordination‐chemistry‐discriminating nuclear spin isotopes. Our results show that the nuclear spin of the lanthanide must be included in the design principles of molecular qubits and SMMs.

Semiclassical Trace Formula and Spectral Shift Function for Systems via a Stationary Approach

We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of $h$-pseudodifferential operators, and apply it to the study of the spectral shift function associated to a pair of selfadjoint Schrodinger operators with matrix-valued potentials. We give Weyl type semiclassical asymptotics with sharp remainder estimate for the spectral shift function, and, under the existence of a scalar escape function, a full asymptotic expansion in the strong sense for its derivative. A time-independent approach enables us to treat certain potentials with energy-level crossings.

Spectral Properties of Nonlinear Schrödinger Equation on a Ring

The stationary states of nonlinear Schr{\"o}dinger equation on a ring with a defect is numerically analyzed. Unconventional connection conditions are imposed on the point defect, and it is shown that the system displays energy level crossings and level shifts and associated quantum holonomies in the space of system parameters, just as in the corresponding linear system. In the space of nonlinearity parameter, on the other hand, the degeneracy occurs on a line, excluding the possibility of any anholonomies. In contrast to the linear case, existence of exotic phenomena such as disappearance of energy level and foam-like structure are confirmed.

Hilbert space and ground-state structure of bilayer quantum Hall systems at ν=2/λ

We analyze the Hilbert space and ground state structure of bilayer quantum Hall (BLQH) systems at fractional filling factors $\nu=2/\lambda$ ($\lambda$ odd) and we also study the large $SU(4)$ isospin-$\lambda$ limit. The model Hamiltonian is an adaptation of the $\nu=2$ case [Z.F. Ezawa {\it et al.}, Phys. Rev. {B71} (2005) 125318] to the many-body situation (arbitrary $\lambda$ flux quanta per electron). The semiclassical regime and quantum phase diagram (in terms of layer distance, Zeeeman, tunneling, etc, control parameters) is obtained by using previously introduced Grassmannian $\mathbb{G}^4_{2}=U(4)/[U(2)\times U(2)]$ coherent states as variational states. The existence of three quantum phases (spin, canted and ppin) is common to any $\lambda$, but the phase transition points depend on $\lambda$, and the instance $\lambda=1$ is recovered as a particular case. We also analyze the quantum case through a numerical diagonalization of the Hamiltonian and compare with the mean-field results, which give a good approximation in the spin and ppin phases but not in the canted phase, where we detect exactly $\lambda$ energy level crossings between the ground and first excited state for given values of the tunneling gap. An energy band structure at low and high interlayer tunneling (spin and ppin phases, respectively) also appears depending on angular momentum and layer population imbalance quantum numbers.

An Egorov Theorem for Avoided Crossings of Eigenvalue Surfaces

We study nuclear propagation through avoided crossings of electron energy levels. We construct a surface hopping semigroup, which gives an Egorov-type description of the dynamics. The underlying time-dependent Schroedinger equation has a two-by-two matrix-valued potential, whose eigenvalue surfaces have an avoided crossing. Using microlocal normal forms reminiscent of the Landau-Zener problem, we prove convergence to the true solution in the semi-classical limit.

Efficient methodology to extract interface traps parameters for TCAD simulations

In this work, a methodology to estimate ATLAS TCAD simulation parameters from experimental data is presented, with the aim of analyzing the impact of interface traps in the MOSFET threshold voltage variability of a particular technology. The method allows to calculate the parameters that define the trap behavior in TCAD simulations (trapped charge, trap energy level and capture cross section) from the parameters that can be experimentally measured (capture and emission times and single-trap threshold voltage shift). The availability of these simulation parameters will allow to study RTN and/or BTI-related variability through TCAD simulations, in reasonable computing times.

Energy levels of a quantum particle on a cylindrical surface with non-circular cross-section in electric and magnetic fields

We calculate the energy levels of a quantum particle on a cylindrical surface with non-circular cross-section in uniform electric and magnetic fields. Using separation of variables method and a change of independent variable, we show that the problem can be reduced to a one-dimensional Schrödinger equation for a periodic potential. The effects of varying the shape of the cross-section while keeping the same perimeter and the strengths of the electric and magnetic fields are investigated for elliptical, corrugated, and nearly-rectangular tubes with radial dimensions of the order of a nanometer. The geometric potential has minima at the angular positions where there is a significant amount of curvature. For the elliptical and corrugated tubes, it is shown that as the tube departs from the circular shape of cross-section the double-degeneracy between the energy levels is lifted. For the nearly-rectangular tube, it is shown that energy level crossings occur as the horizontal dimension of the tube is varied while keeping the same perimeter and radius of circular corners. The interplay between the curvature and the strength of the electric and magnetic fields determines the overall behavior of the energy levels. As the strength of the electric field increases, the overall potential gets skewed creating a potential well on the side corresponding to the more negative electric potential. The energy levels of the first few excited states approach more positive values while the ground state energy level approaches a more negative value. For large electric fields, all bound state energy levels tend to more negative values. The contribution of weak magnetic fields to the overall potential behaves in the same way as the electric field contribution but with its sign depending on the direction of the component of the momentum parallel to the cylindrical axis. Large magnetic fields lead to pairing of energy levels reminiscent of 2D Landau levels for the elliptical and nearly-rectangular tubes.

The Holstein polaron problem revisited

The Holstein Hamiltonian was proposed half a century ago; since then, decades of research have come up empty handed in the pursuit of a closed-form solution. An exact solution to the two-site Holstein model is presented in this paper. The obtained results provide a clear image of the Hamiltonian structure and allow for the investigation of the symmetry, energy level crossings and polaronic characteristics of the system. The main mathematical tool is a three-term recurrence relation between the wave function amplitudes, which was obtained using the properties of a family of orthogonal functions, namely the Poisson–Charlier polynomials. It is shown that, with the appropriate choice of basis, the eigenfunctions of the problem naturally fall into two families (parities) associated with the discrete symmetry of the Hamiltonian. The asymptotic solution to the recurrence relation is found by using the Birkhoff expansion. The asymptotic sets the truncation criterion for the wave function, which ensures the accurate calculation of the energy levels for any strength of electron–phonon interaction. The level crossing of states with different parities is discussed and the exact points of broken symmetry are found analytically. The results are used as the building blocks for studying a four-site system. The inherited symmetries lead to the formation of a sparse matrix that is convenient for numerical calculations.

The quantum needle of the avian magnetic compass

Migratory birds have a light-dependent magnetic compass, the mechanism of which is thought to involve radical pairs formed photochemically in cryptochrome proteins in the retina. Theoretical descriptions of this compass have thus far been unable to account for the high precision with which birds are able to detect the direction of the Earth's magnetic field. Here we use coherent spin dynamics simulations to explore the behavior of realistic models of cryptochrome-based radical pairs. We show that when the spin coherence persists for longer than a few microseconds, the output of the sensor contains a sharp feature, referred to as a spike. The spike arises from avoided crossings of the quantum mechanical spin energy-levels of radicals formed in cryptochromes. Such a feature could deliver a heading precision sufficient to explain the navigational behavior of migratory birds in the wild. Our results (i) afford new insights into radical pair magnetoreception, (ii) suggest ways in which the performance of the compass could have been optimized by evolution, (iii) may provide the beginnings of an explanation for the magnetic disorientation of migratory birds exposed to anthropogenic electromagnetic noise, and (iv) suggest that radical pair magnetoreception may be more of a quantum biology phenomenon than previously realized.

Degeneracies and exotic phases in an isotropic frustrated spin-1/2 chain

In the presence of an axial magnetic field, a frustrated isotropic J1–J2 model system shows many exotic phases, such as vector chiral and multipolar phases. In this paper, the phase boundaries of these exotic phases are calculated based on the order parameters, energy level crossings and magnetization jumps in the system. The order parameter of the vector chiral phase is calculated using the broken symmetry states at a finite magnetic field. The exact diagonalization and the density matrix renormalization group results are used to show that the vector chiral phase exists only in a narrow range of J2/J1 parameter space. In the quadrupolar phase, the magnetization jumps can be associated with the binding energy of two magnons localized at two different legs of the zigzag chain. The energy level crossings and degeneracies in the presence of the axial magnetic field are studied in detail using the exact diagonalization method.