Stopping molecular rotation using coherent ultra-low-energy magnetic manipulations.

Rotational motion lies at the heart of intermolecular, molecule-surface chemistry and cold molecule science, motivating the development of methods to excite and de-excite rotations. Existing schemes involve perturbing the molecules with photons or electrons which supply or remove energy comparable to the rotational level spacing. Here, we study the possibility of de-exciting the molecular rotation of a D2 molecule, from a J=2 to the non-rotating J=0 state, without using an energy-matched perturbation. We show that a magnetic field which splits the rotational projection states by only pico eV, can change the probability that a molecule-surface collision will stop a molecule from rotating and lose rotational energy which is 9 orders larger than that of the magnetic manipulation. Calculations confirm the origin of the control scheme, but also underestimate rotational flips (Δm_J≠0), highlighting the importance of the results as a sensitive benchmark for further developing theoretical models of molecule-surface interactions.

Spin-dependent transport through helical Aharonov-Bohm interferometer

We discuss spin-dependent transport via tunneling Aharonov-Bohm interferometer formed by helical edge states tunnel-coupled to helical leads. We focus on the experimentally relevant high-temperature case as compared to the level spacing and obtain the full 4×4 matrix of transmission coefficients in the presence of magnetic impurities. We show that spin conserving and spin-flip transmission coefficients of the setup can be effectively tuned by the magnetic flux. These features are attractive due to possible applications for spintronics, magnetic field detection, and quantum computing.

Weak integrability breaking and level spacing distribution

Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent crossover between integrable and chaotic level spacing statistics {which marks the onset of quantum chaotic behaviour, is markedly different for weak vs. strong breaking of integrability. In particular}, for the gapless case we find that the crossover coupling as a function of the volume LL scales with a 1/L^{2}1/L2 law for weak breaking as opposed to the 1/L^{3}1/L3 law previously found for the strong case.

Logical construction of the ionization energy theory and the origin of physical categories

Logical proofs and definitions are developed to establish (1) that the energy-level spacings,for each chemical element (from the periodic table of chemical elements) can be converted to the ionization energies, (2) both and the ionization energies are unique, and (3) the averaged ionization energy of any quantum matter is proportional to the averaged ionization energy of its constituent chemical elements, if and only if 6= 0 and is not an irrelevant constant. Physical atoms are then constructed to define the physical sets such that these sets are members of a specific physical class where each class belongs to a specific physical category, P. However, there is not a single structure-preserving functor from one energy-level spacing physical category, P to another P′. Therefore, the existence of many P implies the existence of different categories of physical systems and quantum matter.

Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics

Clifford circuits are insufficient for universal quantum computation or creating tt-designs with t\ge 4t≥4. While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum of a time evolved random product state is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T (\pi/8)(π/8) gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution.

Coherent spin transport through helical edge states of topological insulator

We study coherent spin transport through helical edge states of topological insulator tunnel-coupled to metallic leads. We demonstrate that unpolarized incoming electron beam acquires finite polarization after transmission through such a setup provided that edges contain at least one magnetic impurity. The finite polarization appears even in the fully classical regime and is therefore robust to dephasing. There is also a quantum magnetic field-tunable contribution to the polarization, which shows sharp identical Aharonov-Bohm resonances as a function of magnetic flux—with the period hc/2e—and survives at relatively high temperature. We demonstrate that this tunneling interferometer can be described in terms of ensemble of flux-tunable qubits giving equal contributions to conductance and spin polarization. The number of active qubits participating in the charge and spin transport is given by the ratio of the temperature and the level spacing. The interferometer can effectively operate at high temperature and can be used for quantum calculations. In particular, the ensemble of qubits can be described by a single Hadamard operator. The obtained results open wide avenue for applications in the area of quantum computing.

A Brief Introduction to Stationary Quantum Chaos in Generic Systems

We review the basic aspects of quantum chaos (wave chaos) in mixed-type Hamiltonian systems with divided phase space, where regular regions containing the invariant tori coexist with the chaotic regions. The quantum evolution of classically chaotic bound systems does not possess the sensitive dependence on initial conditions, and thus no chaotic behaviour occurs, as the motion is always almost periodic. However, the study of the stationary solutions of the Schrödinger equation in the quantum phase space (Wigner functions or Husimi functions) reveals precise analogy of the structure of the classical phase portrait. In classically integrable regions the spectral (energy) statistics is Poissonian, while in the ergodic chaotic regions the random matrix theory applies. If we have the mixed-type classical phase space, in the semiclassical limit (short wavelength approximation) the spectrum is composed of Poissonian level sequence supported by the regular part of the phase space, and chaotic sequences supported by classically chaotic regions, being statistically independent of each other, as described by the Berry-Robnik distribution. In quantum systems with discrete energy spectrum the Heisenberg time tH = πℏ/ΔE, where ΔE is the mean level spacing (inverse energy level density), is an important time scale. The classical transport time scale tT (transport time) in relation to the Heisenberg time scale tH (their ratio is the parameter α = tH / tT ) determines the degree of localization of the chaotic eigenstates, whose measure A is based on the information entropy. We show that A is linearly related to the normalized inverse participation ratio. We study the structure of quantum localized chaotic eigenstates (their Wigner and Husimi functions) and the distribution of localization measure A. The latter one is well described by the beta distribution, if there are no sticky regions in the classical phase space. Otherwise, they have a complex nonuniversal structure. We show that the localized chaotic states display the fractional power-law repulsion between the nearest energy levels in the sense that the probability density (level spacing distribution) to find successive levels on a distance S goes like ∝ S β for small S , where 0 ≤ β ≤ 1, and β = 1 corresponds to completely extended states, and β = 0 to the maximally localized states. β goes from 0 to 1 when α goes from 0 to ∞, β is a function of <A>, as demonstrated in the quantum kicked rotator, the stadium billiard, and a mixed-type billiard.