Smile: A Simple Diagnostic for Selection on Observables

This paper develops a simple diagnostic for the selection on observables assumption in the case of a binary treatment variable. I show that, under common assumptions, when selection on observables does not hold, designs based on selection on observables will estimate treatment effects approaching infinity or negative infinity among observations with propensity scores close to 0 or 1. Researchers can check for violations of selection on observables either informally by looking for a "smile" shape in a binned scatterplot, or with a simple formal test. When selection on observables fails, the researcher can detect the sign of the resulting bias

Smile: A Simple Diagnostic for Selection on Observables

This paper develops a simple diagnostic for the selection on observables assumption in the case of a binary treatment variable. I show that, under common assumptions, when selection on observables does not hold, designs based on selection on observables will estimate treatment effects approaching infinity or negative infinity among observations with propensity scores close to 0 or 1. Researchers can check for violations of selection on observables either informally by looking for a "smile" shape in a binned scatterplot, or with a simple formal test. When selection on observables fails, the researcher can detect the sign of the resulting bias

Mixed state Pauli channel parameter estimation

The accuracy of any physical scheme used to estimate the parameter describing the strength of a single qubit Pauli channel can be quantified using standard techniques from quantum estimation theory. It is known that the optimal estimation scheme, with m channel invocations, uses initial states for the systems which are pure and unentangled and provides an uncertainty of O[1/m^(1/2)]. This protocol is analogous to a classical repetition and averaging scheme. We consider estimation schemes where the initial states available are not pure and compare a protocol involving quantum correlated states to independent state protocols analogous to classical repetition schemes. We show, that unlike the pure state case, the quantum correlated state protocol can yield greater estimation accuracy than any independent state protocol. We show that these gains persist even when the system states are separable and, in some cases, when quantum discord is absent after channel invocation. We describe the relevance of these protocols to nuclear magnetic resonance measurements

Observation of ultraslow translational diffusion in metallic lithium by magnetic resonance

Journal ArticleThe theory of a new magnetic-resonance technique for studying the ultra slow motion of atoms was presented in a previous paper. In this paper, we present its experimental confirmation for the case of translational diffusion in lithium metal. By this technique the mean time between atomic jumps r can be measured provided that r is less than the spin-lattice relaxation time Ti, permitting study of much slower rates of motion than previously has been possible using magnetic resonance. For lithium metal we have measured over nine orders of magnitude from r = 10- 9 sec to T = 1 sec, thereby extending by nearly five decades the results previously obtained by Holcomb and Norberg using conventional techniques. We have applied a new spin-temperature theory to the analysis of our low-temperature results in the range of its validity, TI>T>T2. By studying the variation of our relaxation time with the rf field strength Hi, we have unambiguously demonstrated the validity of the spin-temperature theory and the invalidity of perturbation theories in describing relaxation due to infrequent atomic motions in weak applied fields

Study of utraslow atomic motions by magnetic resonance

Journal ArticleMagnetic resonance has been widely used to study phenomena such as atomic diffusion and molecular reorientation. It is applicable when the mean time, r, between atomic jumps is either (a) sufficiently short to narrow the resonance line width or (b) of the correct magnitude to produce spin-lattice relaxation. Case (a) occurs when r is less than 1/Aco where Au> is the rigid lattice linewidth. Case (b) occurs when T is of the order of l/co0 , where oo0 is the Larmor frequency. Typically, case (a) is found when r < 100 /isec, case (b) when r ~ 10 ~ 8 sec. In this Letter we report a new, experimentally simple technique which enables us to study motions of a much slower rate, the criterion being roughly T < T 1 where T1 is the spin-lattice relaxation time

Low-field relaxation and the study of ultraslow atomic motions by magnetic resonance

Journal ArticleConventional resonance enables one to study motion of atoms by measurement of line width when the mean time r between jumps is less than 1/Aco, where Aa> is the rigid lattice line width, or by measurement of the spin-lattice relaxation time, Ti, when r ^ l / coo , where coo is the Larmor frequency. We describe a new technique applicable when T<TI. It is therefore applicable to the study of very slow motion. The method is analogous to measuring T\ with coo = 0. However, we are able to keep cu0 in the megacycle region by performing the experiments in the reference frame rotating at the Larmor frequency. Analysis of the technique requires solution of the problem of the effect of infrequent motion on the nuclear relaxation time when the applied static field is comparable to the local field. The relaxation time is then comparable to r, indicating that jumps are strong "collisions" for the spins. The case of strong "collisions" is not treated in the conventional treatment of Bloembergen, Purcell, and Pound. We solve the problem by use of the concept of spin temperature and the sudden approximation. Explicit formulas are given for the nuclear relaxation in the laboratory for weak static fields, and in the rotating frame for alternating fields of the order of or less than the local field. We treat both diffusional motion and molecular reorientation

Universal Behavior and the Two-component Character of Magnetically Underdoped Cuprate Superconductors

We present a detailed review of scaling behavior in the magnetically underdoped cuprate superconductors (hole dopings less than 0.20) and show that it reflects the presence of two coupled components throughout this doping regime: a non-Landau Fermi liquid and a spin liquid whose behavior maps onto the theoretical Monte Carlo calculations of the 2D Heisenberg model of localized Cu spins for most of its temperature domain. We use this mapping to extract the doping dependence of the strength, $f(x)$ of the spin liquid component and the effective interaction, J_eff(x) between the remnant localized spins that compose it; we find both decrease linearly with x as the doping level increases. We discuss the physical origin of pseudogap behavior and conclude that it is consistent with scenarios in which the both the large energy gaps found in the normal state and their subsequent superconductivity are brought about by the coupling between the Fermi liquid quasiparticles and the spin liquid excitations, and that differences in this coupling between the 1-2-3 and 2-1-4 materials can explain the measured differences in their superconducting transition temperatures and other properties.Comment: 80 pages, 43 figure

Understanding High Temperature Superconductors: Progress and Prospects

I review progress in measurements of the dynamic spin susceptibility in the normal state which yield a new phase diagram and discuss microscopic calculations which yield qualitative, and in many cases, quantitative agreement with the measured changes in the quasiparticle, transport, magnetotransport, and optical properties of the cuprate superconductors as one varies doping and temperature provided one describes the systems as nearly anti-ferromagnetic Fermi liquids in which the effective magnetic interaction between planar quasiparticles mirrors the dynamic spin susceptibility measured in NMR and INS experiments. Together with the demonstration that the NAFL pairing potential leads inexorably to a d_x2-y2,pairing state, this work provides a "proof of concept" for the NAFL description of high Tc materials. I review Eliashberg calculations of the mean-field behavior found in overdoped systems and discuss the extent to which the crossovers to pseudoscaling and pseudogap behavior found in the effective magnetic interaction and quasiparticle behavior in the optimally doped and underdoped systems may be derived microscopically. I conclude with a tentative scenario for the dependence of Tc on doping level and imperfections in different systems.Comment: 6 pages, 1 figure. To appear in a special issue of Physica C of the M2S-HTSC-V Conference held Feb. 28-Mar. 4, 1997, in Beijing, Chin

Microwaves in Quantum Computing

Quantum information processing systems rely on a broad range of microwave technologies and have spurred development of microwave devices and methods in new operating regimes. Here we review the use of microwave signals and systems in quantum computing, with specific reference to three leading quantum computing platforms: trapped atomic ion qubits, spin qubits in semiconductors, and superconducting qubits. We highlight some key results and progress in quantum computing achieved through the use of microwave systems, and discuss how quantum computing applications have pushed the frontiers of microwave technology in some areas. We also describe open microwave engineering challenges for the construction of large-scale, fault-tolerant quantum computers.Comment: Invited review article, to appear in IEEE Journal of Microwaves. 29 pages, 13 figures, $10^{6}$ to $10^{11}$ H