Quantum States of Neutrons in Magnetic Thin Films

We have studied experimentally and theoretically the interaction of polarized neutrons with magnetic thin films and magnetic multilayers. In particular, we have analyzed the behavior of the critical edges for total external reflection in both cases. For a single film we have observed experimentally and theoretically a simple behavior: the critical edges remain fixed and the intensity varies according to the angle between the polarization axis and the magnetization vector inside the film. For the multilayer case we find that the critical edges for spin up and spin down polarized neutrons move towards each other as a function of the angle between the magnetization vectors in adjacent ferromagnetic films. Although the results for multilayers and single thick layers appear to be different, in fact the same spinor method explains both results. An interpretation of the critical edges behavior for the multilyers as a superposition of ferromagnetic and antifferomagnetic states is given.Comment: 6 pages, 5 figure

Two-stage Kondo effect in a four-electron artificial atom

An artificial atom with four electrons is driven through a singlet-triplet transition by varying the confining potential. In the triplet, a Kondo peak with a narrow dip at drain-source voltage V_ds=0 is observed. The low energy scale V_ds* characterizing the dip is consistent with predictions for the two-stage Kondo effect. The phenomenon is studied as a function of temperature T and magnetic field B, parallel to the two-dimensional electron gas. The low energy scales T* and B* are extracted from the behavior of the zero-bias conductance and are compared to the low energy scale V_ds* obtained from the differential conductance. Good agreement is found between kT* and |g|muB*, but eV_ds* is larger, perhaps because of nonequilibrium effects.Comment: 7 pages, 7 figures. Added labels on Fig. 3f and one referenc

Generalized Toffoli gates using qudit catalysis

We present quantum networks for a n-qubit controlled gate C^{n-1}(U) which use a higher dimensional (qudit) ancilla as a catalyser. In its simplest form the network has only n two-particle gates (qubit-qudit) -- this is the minimum number of two-body interactions needed to couple all n+1 subsystems (n qubits plus one ancilla). This class of controlled gates includes the generalised Toffoli gate C^{n-1}(X) on n qubits, which plays an important role in several quantum algorithms and error correction. A particular example implementing this model is given by the dispersive limit of a generalised Jaynes-Cummings Hamiltonian of an effective spin-s interacting with a cavity mode.Comment: 5 pages, 3 fig

Spin-Dependent Tunneling of Single Electrons into an Empty Quantum Dot

Using real-time charge sensing and gate pulsing techniques we measure the ratio of the rates for tunneling into the excited and ground spin states of a single-electron AlGaAs/GaAs quantum dot in a parallel magnetic field. We find that the ratio decreases with increasing magnetic field until tunneling into the excited spin state is completely suppressed. However, we find that by adjusting the voltages on the surface gates to change the orbital configuration of the dot we can restore tunneling into the excited spin state and that the ratio reaches a maximum when the dot is symmetric.Comment: 4 pages, 3 figure

Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-$N$ space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as $_2F_1$ Gau\ss{} hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using $q$-product and series representations implied by Jacobi's $\vartheta_i$ functions and Dedekind's $\eta$-function. The corresponding representations can be traced back to polynomials out of Lambert--Eisenstein series, having representations also as elliptic polylogarithms, a $q$-factorial $1/\eta^k(\tau)$, logarithms and polylogarithms of $q$ and their $q$-integrals. Due to the specific form of the physical variable $x(q)$ for different processes, different representations do usually appear. Numerical results are also presented.Comment: 68 pages LATEX, 10 Figure

Electrical control of spin relaxation in a quantum dot

We demonstrate electrical control of the spin relaxation time T_1 between Zeeman split spin states of a single electron in a lateral quantum dot. We find that relaxation is mediated by the spin-orbit interaction, and by manipulating the orbital states of the dot using gate voltages we vary the relaxation rate W= (T_1)^-1 by over an order of magnitude. The dependence of W on orbital confinement agrees with theoretical predictions and from these data we extract the spin-orbit length. We also measure the dependence of W on magnetic field and demonstrate that spin-orbit mediated coupling to phonons is the dominant relaxation mechanism down to 1T, where T_1 exceeds 1s.Comment: 4 pages, 3 figure

Quantum control in foundational experiments

We describe a new class of experiments designed to probe the foundations of quantum mechanics. Using quantum controlling devices, we show how to attain a freedom in temporal ordering of the control and detection of various phenomena. We consider wave-particle duality in the context of quantum-controlled and the entanglement-assisted delayed-choice experiments. Then we discuss a quantum-controlled CHSH experiment and measurement of photon's transversal position and momentum in a single set-up.Comment: Contribution to the Proceedings of the workshop Horizons of Quantum Physics, Taipei, 14-18.10.2012. Published version: two new authors, modified and streamlined presentation, new section on quantum control in complementary position/momentum measurement