The first demonstration of electron spin detection in solid state materials came with the advent of electron spin resonance in the 1940's. Electron spin resonance (ESR) is an ensemble measurement, sensitive to the minute magnetic moment of an electron spin only when integrated over 10^9 or more electrons. Over the past 5 years, a variety of experimental techniques have been developed that push the detection limit down to the single electron level. These efforts have been motivated in part by aspirations of quantum information processing, and in part by a more fundamental interest in spin decoherence mechanisms and interactions with the spin degree of freedom in a solid state material. This series of seminars will present an overview of these developments, their motivations, and an outlook for the future.

Trapped ions are a promising experimental platform for preparing large amounts of quantum entanglement, eventually on a scale large enough for quantum computing applications. The laser and ion-trap technologies which have been developed so far offer the opportunity to apply them to more specialized and potentially less demanding applications in the short term. One of these applications involves using trapped ions and tailored laser-induced forces between them to perform quantum simulations of designer Hamiltonians on the scale of tens of ions. Laser-addressed arrays of ions are naturally adept at simulating networks of interacting spins, which can exhibit quantum magnetism analogous to familiar condensed matter models. The ultimate goal would be to reveal quantum fluctuations, correlations, and dynamics in a quantum magnet, all at the level of single atoms; measurements in the short term on small numbers of ions will provide a specific experiment framework with which to address several questions, including what the technical and fundamental limitations are to ion-trap simulation.

A quantum computer aspires to perform computations that a "classical" computer can only perform very poorly, requiring exponentially large memory or processing time. Tasks like factoring (Shor), database searching (Grover) and efficiently simulating many-body quantum systems, are examples of problems where quantum algorithms are known and are faster than the best (known) classical ones. However, realizing quantum information processing in the lab is extremely difficult. It requires two almost mutually exclusive conditions -- weak coupling to the environment for low decoherence, along with strong coupling to the user for precise control and measurement. In this lecture I will introduce the concept of quantum information processing, before focusing on its implementation -- the requirements, the obstacles and the (possible) solutions.

Anyons are particles with exchange phase other than that of fermions (pi) or bosons (2pi). This intriguing property is only possible intwo spatial dimensions. A simple physical picture, due to Wilczek, of such a particle is a composite of charge and magnetic flux. Anyons were proposed to exist as the excitations of Laughlin's strongly- interacting fractional quantum Hall states and were recently claimed to have been observed experimentally. The search for other condensed- matter systems exhibiting these exotic particles is ongoing. In this talk I will review the relevant concepts and describe our recent theoretical proposal for a system whose excitations are anyons that, remarkably, can be built by filling a set of single-particle states of essentially noninteracting electrons. The system consists of an artificially structured type-II superconducting film adjacent to a 2D electron gas (2DEG) in the integer quantum Hall regime with unit filling fraction. A vacancy in an otherwise periodic vortex lattice in the superconductor creates a bound state in the 2DEG with total charge -e/2. The composite of this fractionally charged hole and the missing flux due to the vacancy is an almost literal realization of Wilczek's picture of an anyon with exchange phase pi/4. In collaboration with Marcel Franz, Conan Weeks, and Gili Rosenberg Reference: cond-mat/0703001 and references therein.

1. Some basic ideas and techniques in quantum magnetism
2. Quantum Spin glasses and spin liquids
3. Large-scale quantum phenomena in spin systems

The recent development of phase-sensitive techniques has finally settled the decade - long d-wave versus s-wave debate in favor of an order parameter with d _{x²- y²} symmetry in various cuprate superconductors. We will briefly review the experiments using the half-flux-quantum effect as a definitive signature for d-wave pairing symmetry. In particular, a series of recent tricrystal experiments will be presented to demonstrate that the d-wave pair state in this class of superconductors is robust against time reversal symmetry breaking, and a wide-range of temperature and doping variations. We will discuss the consequences of establishing the d-wave pair state for the nature of the superconducting ground state and its low energy excitations in high temperature superconductors. Also will be addressed is the question of whether unconventional (d-wave) superconductivity (pairing mechanism, isotope effect, nm-scale charge inhomogeneity- - ) can be understood in terms of conventional wisdom, the Fermi-liquid based BCS theory.

Presence of multifunctional coupling in a material offers new set of physics and enables to design novel devices. This has prompted us to investigate the growth and properties of well-ordered La₂CoMnO₆ films on SrTiO₃. The B-site ordering is achieved by growing the films at relatively high temperatures (~ 800 ^oC) and O₂ pressures (~ 600 mTorr). We present the structural and magnetic properties of these films. Despite their single ferromagnetic transition around 240 K, we demonstrate that they possess a bi-domain structure with distinct magnetic characteristics. Films exhibit a maximum 5.8 µ_B/f.u. saturation magnetization and magnetic easy axis parallel to SrTiO₃ (110). Further films display a non-linear magnetodielectric effect at low temperature. The origin of the bi-domain structure and magnetodielectric effect is briefly discussed.
Supported by NSERC, FQRNT, CIAR and CFI.

Radiation properties of superconducting terahertz antennas are related to relaxation mechanisms of electronic excitations. Past studies focused mainly on modifying their configurations to improve performance. Looking for the influence of the structural properties of these films on radiation, we compare the characteristics of YBa₂Cu₃O_7-d antennas made on LaAlO₃ and MgO substrates. In order to get only the intrinsic YBCO properties with no geometrical dependence, we have explored several geometries. Our results clearly show that their emission spectrum is plagued with resonant signatures arising from the geometry. This study allows us to find the key parameters that govern terahertz radiation processes in high temperature superconductors.

Traditionally, band insulators which obey time reversal symmetry have only received limited attention. Recently it has been realized that due to spin-orbit coupling, novel spin transport phenomena such as the spin Hall effect can occur in these systems. Certain insulators can have localized gapless states at the edge, analogous to quantum Hall systems. An analog of the Hall conductance for these systems is the "Z₂ invariant." I describe a new approach to the Z₂ characterization of two dimensional band insulators which clarifies the connection with robust edge states. I also present a new characterization of three dimensional band insulators and other systems with time reversal symmetry. Systems which might realize the exotic phases of this characterization and the connection with chiral lattice gauge theory will also be discussed.

The role of frustration in the Hubbard model is studied on the square lattice with nearest and next-nearest neighbour hoppings t and t' using the Variational cluster approximation[1]. We find two phases with long-range magnetic order: the usual antiferromagnet (AF1) phase, stable at small values of t'/t, and the AF2 phase with the ordering wave-vector (0,pi), stable at large frustrations. These are separated by a phase with no magnetic order. We also find the d-wave superconductivity for small values of U<5t and a broad range of frustrations. The Mott-Hubbard transition is discussed in this context. Our findings may be applied to a variety of experimental systems with in-plane magnetic frustrations, including the cobaltates. The results are compared with the classical phase diagram obtained from the large-U expansion and from the J1-J2 frustrated Heisenberg model. [1] M. Potthoff, M. Aichhorn, C. Dahnken, Phys. Rev. Lett. 91, 206402 (2003).

Impurity doping is one of the most effective means of tuning the properties of materials. We have discovered a possible way for orbital hierarchy inversion, valence control, and magneto-crystalline anisotropy rotation in complex oxides, by embedding ‘localized’ impurity orbitals in a ‘delocalized’ host matrix. Here we present a comprehensive analysis of experimental and theoretical results on Sr3(Ru1-xMnx)2O7 by a combination of x-ray absorption spectroscopy (XAS), density functional theory (LSDA) and cluster multiplet calculations. We find that Mn impurities do not exhibit the same 4+ valence of Ru, but behave as Mn3+ acceptors; furthermore, the extra electron occupies in-plane eg orbitals instead of the out-of-plane 3z2 - r2 orbital predicted by crystal field theory, a counterintuitive result which might be termed as “ inverse Jahn-Teller effect”. This behavior has profound implications for the spin and orbital ordering of the system as a whole, with a magnetocrystalline anisotropy that gradually goes from out-of-plane to in-plane as the Mn doping level is increased. Overall, the behavior is intriguingly similar to that of Mn doped GaAs and may be relevant to the physics of dilute magnetic semiconductors. This may also indicate new pathways toward the design of novel orbital and magnetic materials, e.g. dilute 3d impurities in 4d or even 5d hosts.

After 20 years of research, the high-temperature copper oxide superconductors still remain of fundamental interest. One question arising as one goes from the overdoped regime, where a large well defined Fermi surface is exhibited, to the underdoped regime, characterized by the pseudogap phase, concerns the manner nature uses to bridge those two regimes.
One way to deal with this issue, is to explore the ground state of the pseudogap phase. We hence performed resistivity measurement on ultrahigh quality YBa₂Cu₃O_6.5 Ortho II ordered samples, under high magnetic field as a method to reveal the ground state of underdoped cuprates. We observed quantum oscillations, the most direct and robust bulk probe of a Fermi surface. The low frequency of those oscillations indicates that the electronic ground state is made of small pocket(s), as opposed to the large Fermi surface observed in the overdoped regime. We shall interpret this result in the context of band structure calculations, and also in the light of different theories predicting small Fermi pockets in the underdoped regime.

Several recent experiments have demonstrated that superconducting circuits are ideal systems for the study of quantum mechanical effects on large scale and promising candidates for quantum computation. It was recently proposed [1] and experimentally demonstrated [2,3] that superconducting circuits fabricated inside a high quality on-chip transmission line resonator can be used to study solid-state analogs of quantum optics and, in particular, to reach the strong-coupling regime of cavity quantum electrodynamics (CQED). Moreover, in the dispersive regime, were the qubit transition frequency is well detuned from the resonator frequency, the resonator can be used as a tool to readout the quantum state of the superconducting qubit in a quantum non-demolition way. In this poster, we study important non-linear effects and how they affect the measurement process. In particular, we find that in the presence of pure dephasing of the qubit, the resonator can act as a heat bath on the qubit, thereby possibly ruining its quantum non-demolition properties. [1] A. Blais, R.-S. Huang, A. Walraff, S. M. Girvin and R. J. Schoelkopf, Phys. Rev. A 69, 062320 (2004). [2] A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin and R. J. Schoelkopf, Nature 431, 162 (2004). [3] D. I. Schuster, A. A. Houck, J. A. Schreier, A. Wallraff, J. M. Gambetta, A. Blais, L. Frunzio, B. Johnson, M. H. Devoret, S. M. Girvin and R. J. Schoelkopf. Nature, 445, 515 (2007).

We have performed x-ray scattering measurements on single crystals of the doped spin-Peierls compound Ti{1-x}Sc{x}OCl (x = 0, 0.01, 0.03). These measurements reveal that the introduction of non-magnetic impurities, even at the level of 1%, has a profound effect on the unconventional spin-Peierls behavior of the system. Sc-doping results in the suppression of commensurate fluctuations in both the pseudogap and incommensurate spin-Peierls phases of TiOCl, and completely prevents the formation of a long-range ordered spin-Peierls state. We have observed broad incommensurate scattering in the doped compound, which arises at Tc2 ~ 93 K and persists down to ~ 7 K with no evidence of a lock-in transition. The width of this incommensurate scattering is largely independent of temperature, and suggests correlation lengths on the order of ~ 12 A below Tc2. The wave-vector of the incommensurate modulation, (delta, 0.5, 0), decreases between Tc2 and Tc1 ~ 63 K, but remains constant at ~ (0.055, 0.5, 0) below Tc1. While the concentration of non-magnetic impurities does not appear to affect the width or the wave-vector of the incommensurate scattering, increased Sc-doping does result in a significant decrease in the observed scattering intensity.

At the magic 1/8 doping, superconductivity in La_2-xBa_xCuO₄ is strongly suppressed. However, ARPES measurements above T_c show that there is still a gap in the single particle excitation spectrum with d-wave symmetry and point-like nodes. Here we present low temperature thermal conductivity measurements in the superconducting and the field induced normal state which are compatible with this scenario. We also discuss the recent observations of 2D superconducting fluctuations in this compound.

Motivated by recent experiments on Na₄Ir₃O₈ [Takagi,unpublished], we study the classical antiferromagnet on a frustrated three-dimensional lattice obtained by selectively removing one of four sites in each tetrahedron of the pyrochlore lattice. This "hyper-kagome" lattice consists of corner-sharing triangles. We present the results of large-N mean field theory and Monte Carlo computations on O(N) classical spin models. We find the classical ground states to be highly degenerate. Nonetheless, at low temperatures, nematic order emerges via "order by disorder" in the Heisenberg model ($N$=3), representing the dominance of coplanar spin configurations. Above this transition, the spin-spin correlations show a dipolar form which can be understood to arise from a generalized "Gauss' law" constraint. Implications for ongoing experiments are discussed.

We report superconducting properties of Sr₂RuO₄-Sr₃Ru₂O₇ eutectic crystals, consisting of the spin-triplet superconductor Sr₂RuO₄ with the monolayer stacking of RuO₂ planes and the metamagnetic normal metal Sr₃Ru₂O₇ with the bilayer stacking. Sr₃Ru₂O₇ has not been reported to become superconducting until now, but our AC susceptibility measurements reveal two superconducting transitions reproducibly occurring in the Sr₃Ru₂O₇ region of the eutectic crystals. The shielding fraction of the superconductivity reaches essentially 100% at low AC fields. However, it is easily suppressed by AC fields larger than 0.1 mT. Moreover, no anomaly is observed in the specific heat. These facts suggest that the superconductivity observed in the Sr₃Ru₂O₇ region does not come from bulk superconductors. Among other possibilities, we discuss a model with monolayers of RuO₂ planes contained as stacking faults to explain these experimental results.

Layered oxides continue to provide interesting superconducting states. In addition to the square lattice in the layered cuprates and ruthenates, a triangular lattice of cobalt and oxygen in Na_x(H₃O)_zCoO₂?yH₂O yields unconventional superconductivity. We report here physical properties of another layered oxide having a triangular lattice, PdCoO₂. Its delafossite structure is closely related to that of NaCoO₂, a mother compound of Na_x(H₃O)_zCoO₂?yH₂O, but with a different layer stacking. It also contains a triangular lattice of Pd. Using single crystals, we identified two prominent phonon modes at 520 cm^-1 and 712 cm^-1 in the Raman spectra, and absorption from 600 to 1200 cm^-1 in the infrared spectra. We clarified that these high frequency phonon modes account for the unusual temperature dependence of the specific heat, which reaches only 65% of the classical Dulong and Petit’s value even at 250 K. These optic phonons also account for the deviation from the T-linear behavior of the resistivity expected for typical electron-acoustic phonon scattering. Despite the influence of these high-frequency phonon modes, no sign of superconductivity was detected down to 15 mK.

We study the effects of time-independent nonequilibrium drive on an open 2D electron gas system coupled to 2D longitudinal acoustic phonons using the Keldysh path integral method. The layer electron-phonon system is defined at the two-dimensional interface between a pair of three-dimensional Fermi liquid leads, which act both as a particle pump and an infinite bath. The nonequilibrium steady state is achieved in the layer by assuming the leads to be thermally equilibrated at two different chemical potentials. This subjects the layer to an out-of-plane voltage and drives a steady-state charge current perpendicular to the system. We compute the effects of small voltages on the in-plane electron-phonon scattering rate and the electron effective mass at zero temperature. We also find that the obtained nonequilibrium modification to the acoustic phonon velocity and the Thomas-Fermi screening length reveal the possibility of tuning these quantities with the external voltage.

Pr_1-xCa_xMnO₃ (PCMO) has been extensively investigated due to its wide composition range of charge ordering (CO). In order to see the effect of epitaxial strain on the electronic structure, we have performed an in-situ photoemission study of PCMO thin films grown on LaAlO₃ (001) substrates. From the core-level photoemission study, we found that the chemical potential shift was not suppressed unlike bulk PCMO. In the valence-band spectra, we found no spectral weight at the Fermi level (E_F) or doping-induced spectral weight transfer toward E_F also unlike bulk PCMO. These results are a spectroscopic evidence for the absence of the same type of CO in thin films.