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Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction…
We have measured a quantum ratchet effect for vortices moving in a quasi-one-dimensional Josephson junction array. In this solid-state device the shape of the vortex potential energy, and consequently the band structure, can be accurately…
At total filling factor $\nu_T=1$, interlayer phase coherence in quantum Hall bilayers can result in a tunneling anomaly resembling the Josephson effect in the presence of strong fluctuations. The most robust experimental signature of this…
Quantum corrals are two dimensional structures built atom by atom on an atomically clean metallic surface using a scanning tunneling microscope. These two dimensional structures ``corral'' electrons in the surface states of noble metals…
Recently we have discussed a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so…
An experiment to test for relativistic frame dragging effects with quantum interferometry is proposed. The idea that the classical trajectories of the interferometer surround a spherical mass source whose angular momentum is perpendicular…
I review recent novel experimental and theoretical advances in the physics of quantum Hall effect bilayers. Of particular interest is a broken symmetry state which optimizes correlations by putting the electrons into a coherent…
This paper summarizes the final results of the electron counting capacitance standard experiment at the Physikalisch-Technische Bundesanstalt (PTB) achieved since the publication of a preliminary result in 2012. All systematic uncertainty…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
The quantum Hall effect is one of the most extensively studied topological effects in solid state physics. The transitions between different quantum Hall states exhibit critical phenomena described by universal critical exponents. Numerous…
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
Quantum effects, such as entanglement, Einstein-Podolsky-Rosen steering, and Bell correlations, can enhance metrological sensitivity beyond the standard quantum limit. These correlations are typically generated through interactions between…
We discuss and review the basic physics that leads to superfluidity/superconductivity in certain quantum Hall states, in particular the so-called double-layered (mmm) state. In the K-matrix description of the quantum correlation in quantum…
Advances in quantum mechanics have long underpinned metrology by enabling practical realizations of units through quantum effects. With the 2019 SI revision, traceability is anchored in defined fundamental constants, reinforcing the…
Low-capacitance Josephson junction systems as well as coupled quantum dots, in a parameter range where single charges can be controlled, provide physical realizations of quantum bits, discussed in connection with quantum computing. The…
Recently\cite{BQG}, it was shown that quantum effects of matter could be identified with the conformal degree of freedom of the space-time metric. Accordingly, one can introduce quantum effects either by making a scale transformation (i.e.…
Quantum effects in metrology can in principle enhance measurement precision from the so-called standard quantum limit to the Heisenberg Limit. Further advancements in quantum metrology largely rely on innovative metrology protocols that can…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
We present a review on quantum metrology and sensing, from its foundations to current applications. Highlights of the review include consideration of both frequentist and Bayesian approaches to parameter estimation; single as well as…
Using the path-integral formalism, we show that photons possess a nontrivial quantum metric in momentum space. We derive the semiclassical action and equations of motion by taking into account the quantum metric. In media with a spatially…