Hamiltonian Parameters Research Articles

An exchange coupled meso-meso linked vanadyl porphyrin dimer for quantum information processing.

We report here the synthesis of a new meso-meso (m-m) singly linked vanadyl-porphyrin dimer that crystallizes in two different pseudo-polymorphs. The single crystal continuous-wave electron paramagnetic resonance investigation evidences a small but crucial isotropic exchange interaction, J, between the two tilted, and thus distinguishable, spin centers of the order of 10-2 cm-1. The experimental and DFT studies evidence a correlation between J values and porphyrin plane tilting angle and distortion. Pulsed EPR analysis shows that the two vanadyl dimers maintain the coherence time of the monomer. With the obtained spin Hamiltonian parameters, we identify suitable transitions that could be used as computational basis states. Our results, coupled with the evaporability of porphyrin systems, establish this class of dimers as extremely promising for quantum information processing applications.

Classical and quantum metrology of the Lieb-Liniger model

We study the classical and quantum Fisher information for the Lieb-Liniger model. The Fisher information has been studied extensively when the parameter is inscribed on a quantum state by a unitary process, e.g., Mach-Zehnder or Ramsey interferometry. Here, we investigate the case that a Hamiltonian parameter to be estimated is imprinted on eigenstates of that Hamiltonian, and thus is not necessarily encoded by a unitary operator. Taking advantage of the fact that the Lieb-Liniger model is exactly solvable, the Fisher information is determined for periodic and hard-wall boundary conditions, varying number of particles, and for excited states of type-I and type-II in the Lieb-Liniger terminology. We discuss the dependence of the Fisher information on interaction strength and system size, to further evaluate the metrological aspects of the model. Particularly noteworthy is the fact that the Fisher information displays a maximum when we vary the system size, indicating that the distinguishability of the wavefunctions is largest when the Lieb-Liniger parameter is at the crossover between the Bose-Einstein condensate and Tonks-Girardeau limits. The saturability of this Fisher information by the absorption imaging method is assessed by a specific modeling of the latter.

Finite temperature quantum condensations in the space of states: general proof

We formalize and prove the extension to finite temperature of a class of quantum phase transitions, acting as condensations in the space of states, recently introduced and discussed at zero temperature (Ostilli and Presilla 2021 J. Phys. A: Math. Theor. 54 055005). In details, we find that if, for a quantum system at canonical thermal equilibrium, one can find a partition of its Hilbert space into two subspaces, and , such that, in the thermodynamic limit, and the free energies of the system restricted to these subspaces cross each other for some value of the Hamiltonian parameters, then, the system undergoes a first-order quantum phase transition driven by those parameters. The proof is based on an exact probabilistic representation of quantum dynamics at an imaginary time identified with the inverse temperature of the system. We also show that the critical surface has universal features at high and low temperatures.

Critical Current Density in d-Wave Hubbard Superconductors.

In this work, the Generalized Hubbard Model on a square lattice is applied to evaluate the electrical current density of high critical temperature d-wave superconductors with a set of Hamiltonian parameters allowing them to reach critical temperatures close to 100 K. The appropriate set of Hamiltonian parameters permits us to apply our model to real materials, finding a good quantitative fit with important macroscopic superconducting properties such as the critical superconducting temperature (Tc) and the critical current density (Jc). We propose that much as in a dispersive medium, in which the velocity of electrons can be estimated by the gradient of the dispersion relation ∇ε(k), the electron velocity is proportional to ∇E(k) in the superconducting state (where E(k)=(ε(k)-μ)2+Δ2(k) is the dispersion relation of the quasiparticles, and k is the electron wave vector). This considers the change of ε(k) with respect to the chemical potential (μ) and the formation of pairs that gives rise to an excitation energy gap Δ(k) in the electron density of states across the Fermi level. When ε(k)=μ at the Fermi surface (FS), only the term for the energy gap remains, whose magnitude reflects the strength of the pairing interaction. Under these conditions, we have found that the d-wave symmetry of the pairing interaction leads to a maximum critical current density in the vicinity of the antinodal k-space direction (π,0) of approximately 1.407236×108 A/cm2, with a much greater current density along the nodal direction (π2,π2) of 2.214702×109 A/cm2. These results allow for the establishment of a maximum limit for the critical current density that could be attained by a d-wave superconductor.

Optimal control for Hamiltonian parameter estimation in non-commuting and bipartite quantum dynamics

The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of optimal control can be used to identify time-dependent pulses applied to the system to achieve higher precision in the estimation of Hamiltonian parameters, especially in the presence of noise. Here, we extend optimally controlled estimation schemes for single qubits to non-commuting dynamics as well as two interacting qubits, demonstrating improvements in terms of maximal precision, time-stability, as well as robustness over uncontrolled protocols.

Probing quantum many-body correlations by universal ramping dynamics

Ramping a physical parameter is one of the most common experimental protocols in studying a quantum system, and ramping dynamics has been widely used in preparing a quantum state and probing physical properties. Here, we present a novel method of probing quantum many-body correlation by ramping dynamics. We ramp a Hamiltonian parameter to the same target value from different initial values and with different velocities, and we show that the first-order correction on the finite ramping velocity is universal and path-independent, revealing a novel quantum many-body correlation function of the equilibrium phases at the target values. We term this method as the non-adiabatic linear response since this is the leading order correction beyond the adiabatic limit. We demonstrate this method experimentally by studying the Bose-Hubbard model with ultracold atoms in three-dimensional optical lattices. Unlike the conventional linear response that reveals whether the quasi-particle dispersion of a quantum phase is gapped or gapless, this probe is more sensitive to whether the quasi-particle lifetime is long enough such that the quantum phase possesses a well-defined quasi-particle description. In the Bose-Hubbard model, this non-adiabatic linear response is significant in the quantum critical regime where well-defined quasi-particles are absent. And in contrast, this response is vanishingly small in both superfluid and Mott insulators which possess well-defined quasi-particles. Because our proposal uses the most common experimental protocol, we envision that our method can find broad applications in probing various quantum systems.

Microscopic Spin Hamiltonian for a Dipolar Heisenberg Magnet LiGdF4 from EPR Measurements

Low-temperature electron paramagnetic resonance measurements are performed on single crystals of LiY1 ‒xGdxF4 with low x = 0.005 and moderate x = 0.05 concentration of Gd ions. Modeling of the experimental spectra allows us to precisely determine microscopic parameters of the spin Hamiltonian of the parent LiGdF4 material, including the nearest-neighbor exchange constant. The obtained parameters are further tested by comparing a strongly anisotropic Curie–Weiss temperature obtained for LiGdF4 in our static magnetization measurements with theoretically computed values. We find a fine balance between principal magnetic interactions in LiGdF4, which results in a hidden magnetic frustration presumably leading to a delayed magnetic ordering and an enhanced magnetocaloric effect at low temperatures.

Impact of the electric field on isotropic and anisotropic spin Hamiltonian parameters.

One may obviously think that the best way to control magnetic properties relies on using a magnetic field. However, it is not convenient to focus a magnetic field on a small object, whereas it is much easier to do so with an electric field. Magnetoelectric coupling allows one to control the magnetization with the electric field and the polarization with the magnetic field and could therefore provide a solution to this problem. This paper aims at quantifying the impact of the electric field on both the isotropic magnetic exchange and the Dzyaloshinskii-Moriya interaction in the case of a binuclear system of S = 1/2 spins. This study follows previous studies that showed that very high Dzyaloshinskii-Moriya interaction, i.e., the antisymmetric exchange, can be generated when close to first order spin orbit coupling. We will, therefore, explore this regime in a model Cu(II) complex that exhibits a quasi-degeneracy of the dx2-y2 and dxy orbitals. This situation is indeed the one that allows us to obtain the largest spin orbit couplings in transition metal complexes. We will show that both the magnetic exchange and the Dzyaloshinskii-Moriya interaction are very sensitive to the electric field and that it would therefore be possible to modulate and control magnetic properties by the electric field. Finally, rationalizations of the obtained results will be proposed.

Elucidation of vibronic structure and dynamics of first eight excited electronic states of pentafluorobenzene.

Vibronic coupling in the first eight electronic excited states of Pentafluorobenzene (PFBz) is investigated in this article. In particular, the vibronic coupling between the optically bright ππ* and optically dark πσ* states of PFBz is considered. A model 8 × 8 diabatic Hamiltonian is constructed in terms of normal coordinate of vibrational modes using the standard vibronic coupling theory and symmetry selection rule. The Hamiltonian parameters are estimated with the aid of extensive ab initio quantum chemistry calculations. The topography of the first eight electronic excited states of PFBz is examined at length, and multiple multi-state conical intersections are established. The nuclear dynamics calculations on the coupled electronic surfaces are carried out from first principles by the wave packet propagation method. Theoretical results are found to be in good accord with the available experimental optical absorption spectrum of PFBz.

Theoretical investigation of the magnetic properties of ferromagnetic CrI3 monolayer

The CrI3 monolayer is the first ferromagnetic two-dimensional material experimentally discovered and the study of its properties is a hot topic. First-principles calculations and experimental measurements show that the CrI3 monolayer is a typical S=3/2 localized magnetic system. In the present work, we investigated the intrinsic magnetic properties of CrI3 monolayer based on the anisotropic Heisenberg model and using the double-time Green’s function method. The Hamiltonian parameter values of CrI3 monolayer are estimated theoretically based on the experimental Curie temperature of CrI3 monolayer and the experimental magnetic parameters of CrI3 bilayers. The spontaneous magnetization and zero-field susceptibility are calculated, and the critical behaviors of the system are analyzed. We observe that the maximum magnetic susceptibility value is sensitive to the isotropic exchange parameter and external magnetic field, but almost independent of anisotropic strengths.

EPR Analysis of Cu2+ ion Doped Potassium borodicitrate Single Crystal

In our present investigation single crystals of Potassium borodicitrate (KBDC) (for a fixed content- host lattice) with Cu2+, a guest species, as a dopant (at four 0.2, 0.5, 1 and 2 g) in weight ratio have been synthesized at room temperature by using slow evaporation method. These as-synthesized 4 crystals have been subjected to Electron Paramagnetic Resonance (EPR) studies. The EPR spectrum shows that 0.5 g dopant KBDC give a 4 equidistant hyperfine lines with the perfect symmetry confirms that the localization of Cu2+, a paramagnetic impurity, within it reveals that the maximum absorption of EPR signals happens at 0.5 g Cu2+ than any other concentrations with reference to 20° in horizontal plane than the normal and vertical recording in the same angular projection. The Spin Hamiltonian calculations are used to obtain spectroscopic field splitting factor g-tensor values, gxx = 2.0421, gyy = 2.1962, gzz = 2.2827 and hyperfine splitting factor A-tensor values Axx = 150, Ayy = 112 and Azz = 134. The K–O bond length associated with directional cosines of gzz tensor reveal that the Cu2+ is located interstitially. This optimized single crystal has furtherance been subjected to Single cystal X-ray diffraction (SXRD), Fourier transform infrared Spectrascopy (FTIR). Scanning electron microscope (SEM) Energy dispersive X-ray analysis (EDAX) and compared with pure KBDC single crystal. The XRD unit cell crystalline parameter variations reveal that there is doping effect of Cu2+ into the host lattice brings forth structural coordination of Cu2+ with KBDC. The FTIR confirms that complexation of host and guest through molecular interactions in the finger print region. The EDAX mapping shows Cu2+ presence in the crystal. HIGHLIGHTS SXRD are taken to confirm that structure of pure KBDC and Cu2+ doped KBDC are same The spin Hamiltonian parameters of KBDC-Cu2+ single crystal are calculated through EPR spectra On analyzing the spectra, it is found that the doped ion site location symmetry is identified as interstitial and experience orthorhombic local field symmetry In addition to the above studies FTIR and EDX confirms the presence of Cu2+ ion GRAPHICAL ABSTRACT

First design of a superconducting qubit for the QUB-IT experiment

Quantum sensing is a rapidly growing field of research which is already improving sensitivity in fundamental physics experiments. The ability to control quantum devices to measure physical quantities received a major boost from superconducting qubits and the improved capacity in engineering and fabricating this type of devices. The goal of the QUB-IT project is to realize an itinerant single-photon counter exploiting Quantum Non Demolition (QND) measurements and entangled qubits, in order to surpass current devices in terms of efficiency and low dark-count rates. Such a detector has direct applications in Axion dark-matter experiments (such as QUAX Alesini et al., 2021 [1]), which require the photon to travel along a transmission line before being measured. In this contribution we present the design and simulation of the first superconducting device consisting of a transmon qubit coupled to a resonator using the Qiskit-Metal software developed by IBM. Exploiting the Energy Participation Ratio (EPR) simulation we were able to extract the circuit Hamiltonian parameters, such as resonant frequencies, anharmonicity and qubit–resonator couplings.

Magnetic properties of bond-diluted nanoribbons with hexagonal and rectangular shape

An exploration of the magnetic behavior of bond-diluted mixed spin-3/2 and spin-1/2 Ising model on hexagonal and rectangular nanoribbons is considered by means of the finite cluster approximation. The effects of the bond concentration p and the crystal field D on the phase diagrams yield satisfactory results. In particular, it is found that a horizontal reentrance appears for both nanosystems; while the tricritical phenomenon may occur by the inclusion of the crystal field according to specific Hamiltonian parameters for the rectangular nanoribbon. The dependence on temperature of the total, σ- and S- sublattice magnetizations, mainly at the ground state has also emphasized the significance of the dilution in dominating the magnetic and critical characters.

Quantifying the effects of dissipation and temperature on dynamics of a superconducting qubit-cavity system

The superconducting circuits involving Josephson junction offer macroscopic quantum two-level system (qubit) which are coupled to cavity resonators and are operated via microwave signals. In this work, we study the dynamics of superconducting qubits coupled to a cavity with including dissipation in a subKelvin temperature domain. In the first step, a classical finite element method is used to simulate the cavities and basic circuit elements to model Josephson junctions. Then, the quantization of the circuit is done to obtain the full Hamiltonian of the system using energy participation ratios of the junctions. Once the parameters of Hamiltonian are obtained, the dynamics is studied via the Lindblad equation for an open quantum system using a realistic set of dissipative parameters and include temperature effects. Finally, we get frequency spectra and/or dynamics of the system with time which have quantum imprints. Such devices work at tens of milliKelvins and we search for a set of parameters which could enable to observe quantum behaviour at temperatures as high as 1 K.

Open quantum rotors: Connecting correlations and physical currents

We consider a finite one-dimensional chain of quantum rotors interacting with a set of thermal baths at different temperatures. When the interaction between the rotors is made chiral, such a system behaves as an autonomous thermal motor, converting heat currents into non-vanishing rotational ones. Such a dynamical response is strongly pronounced in the range of the Hamiltonian parameters for which the ground state of the system in the thermodynamic limit exhibits a quantum phase transition. Such working points are associated with large quantum coherence and multipartite quantum correlations within the state of the system. This suggests that the optimal operating regime of such quantum autonomous motor is one of maximal quantumness.

Analytic Linear Vibronic Coupling Method for First-Principles Spin-Dynamics Calculations in Single-Molecule Magnets.

Accurate modeling of vibronically driven magnetic relaxation from ab initio calculations is of paramount importance to the design of next-generation single-molecule magnets (SMMs). Previous theoretical studies have been relying on numerical differentiation to obtain spin-phonon couplings in the form of derivatives of spin Hamiltonian parameters. In this work, we introduce a novel approach to obtain these derivatives fully analytically by combining the linear vibronic coupling (LVC) approach with analytic complete active space self-consistent field derivatives and nonadiabatic couplings computed at the equilibrium geometry with a single electronic structure calculation. We apply our analytic approach to the computation of Orbach and Raman relaxation rates for a bis-cyclobutadienyl Dy(III) sandwich complex in the frozen-solution phase, where the solution environment is modeled by electrostatic multipole expansions, and benchmark our findings against results obtained using conventional numerical derivatives and a fully electronic description of the whole system. We demonstrate that our LVC approach exhibits high accuracy over a wide range of coupling strengths and enables significant computational savings due to its analytic, "single-shot" nature. Evidently, this offers great potential for advancing the simulation of a wide range of vibronic coupling phenomena in magnetism and spectroscopy, ultimately aiding the design of high-performance SMMs. Considering different environmental representations, we find that a point charge model shows the best agreement with the reference calculation, including the full electronic environment, but note that the main source of discrepancies observed in the magnetic relaxation rates originates from the approximate equilibrium electronic structure computed using the electrostatic environment models rather than from the couplings.

Non-Kramers iron S = 2 ions in β-Ga2O3 crystals: High-frequency low-temperature EPR study

Using high-frequency electron paramagnetic resonance (EPR), we have observed non-Kramers ions with giant fine structure splitting of the order of 100 GHz in n-type β-Ga2O3 crystals. These EPR spectra were assigned to Fe2+ ions 5D (3d 6) with S = 2. This interpretation was supported by experiments on Fermi level displacement induced by high-energy electron irradiation and photoexcitation of irradiated samples with 405-nm laser light. The values and signs of the basic parameters of the spin Hamiltonian for ions, namely Cr3+ (S = 3/2) and Fe3+ (S = 5/2), were identified, and the order of their spin levels was established.

Transient Behavior of Damage Spreading in the Two-Dimensional Blume–Capel Ferromagnet

We study the transient behavior of damage propagation in the two-dimensional spin-$1$ Blume-Capel model using Monte Carlo simulations with Metropolis dynamics. We find that, for a particular region in the second-order transition regime of the crystal field--temperature phase diagram of the model, the average Hamming distance decreases exponentially with time in the weakly damaged system. Additionally, its rate of decay appears to depend linearly on a number of Hamiltonian parameters, namely the crystal field, temperature, applied magnetic field, but also on the amount of damage. Finally, a comparative study using Metropolis and Glauber dynamics indicates a slower decay rate of the average Hamming distance for the Glauber protocol.

Analysis of the Magnetic Coupling in a Mn(II)-U(V)-Mn(II) Single Molecule Magnet.

[{Mn(TPA)I}{UO2(Mesaldien)}{Mn(TPA)I}]I formula (here TPA=tris(2-pyridylmethyl)amine and Mesaldien=N,N'-(2-aminomethyl)diethylenebis(salicylidene imine)) reported by Mazzanti and coworkers (Chatelain et al. Angew. Chem. Int. Ed. 2014, 53, 13434) is so far the best Single Molecule Magnet (SMM) in the {3d-5f} class of molecules exhibiting barrier height of magnetization reversal as high as 81.0 K. In this work, we have employed a combination of ab initio CAS and DFT methods to fully characterize this compound and to extract the relevant spin Hamiltonian parameters. We show that the signs of the magnetic coupling and of the g-factors of the monomers are interconnected. The central magnetic unit [UV O2 ]+ is described by a Kramers Doublet (KD) with negative g-factors, due to a large orbital contribution. The magnetic coupling for the {Mn(II)-U(V)} pair is modeled by an anisotropic exchange Hamiltonian: all components are ferromagnetic in terms of spin moments, the parallel component JZ twice larger as the perpendicular one J⊥ . The spin density distribution suggests that spin polarization on the U(V) center favors the ferromagnetic coupling. Further, the JZ /J⊥ ratio, which is related to the barrier height, was found to correlate to the corresponding spin contribution of the g-factors of the U(V) center. This correlation established for the first time offers a direct way to estimate this important ratio from the corresponding gS -values, which can be obtained using traditional ab initio packages and hence has a wider application to other {3d-5f} magnets. It is finally shown that the magnetization barrier height is tuned by the splitting of the [UV O2 ]+ 5 f orbitals.

Investigations on the local structure and the spin Hamiltonian parameters for Cu2+ in xCuO-(68-x)V2 O5 -32TeO2 glasses.

The defect structure, spin Hamiltonian parameters (SHPs: anisotropic factors and and the hyperfine structure constants and ), and their compositional dependence of in ( = 5, 10, 20, 30 mol%) glasses are quantitatively analyzed by using the higher-order perturbation formula of octahedral complex with tetrahedral elongation distortion. Due to the Jahn-Teller effect, the group is subjected to tetragonal elongation distortion of varying degrees. , and show nonlinear changes with the concentrations of . When = 10 mol% CuO, the degree of distortion ( ) is the smallest; when = 30 mol% CuO, the degree of distortion ( ) is the largest, which indicates that excessive distortion leads to the appearance of -axis oxygen vacancies and the coordination number of copper ions from six to four. The increasing tendency of the evaluated and reveals decreasing covalency of the whole glass system. Present theoretical studies would be useful to the explore the structural properties and optical applications of glass with different concentrations.