Research
Quantum criticality and Superconductivity
A 3D phase diagram from PRL 115, 247002, showing the superconducting and ferroelectric phases as a function of carrier doping, isotope replacement and temperature.
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Superconductivity and Quantum phase transitions are two examples of extraordinary phenomena that truly require both Quantum Mechanics, and many body physics, in order to be explained. Exploring the possible connections between them can teach us a lot on the fundamental physics of many body systems. Naturally, this can also have many practical implications.
The behavior of Tc around a QCP which is tunable by isotope substitution, from
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The relation of the two phenomena can be viewed from many angles, but my interest is in finding microscopic model describing an concrete physical relationship. The path is to consider some modes that are related to the quantum phase transition and consider their coupling to electrons.
An example of this can be the phonons that are related to a ferroelectric phase transition. Once the microscopic interaction is specified, it is possible, in principle, to calculate macroscopic observable, such as order parameters and critical temperatures. Using these results one can study how the characteristic of superconductivity and the quantum phase transition affect each other.
Weak measurements
The weak value of an operator.
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The technique of Weak Measurements is the standard measuring procedure with two modifications: it is performed on pre- and post-selected quantum systems and the coupling strength to the measuring device is weakened. The outcomes of Weak Measurements are Weak Values and they are very different for the eigenvalues of the measured operators, or from any possible expectation values. My interest in Weak Measurement is twofold:
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Practical benefits. Harnessing the peculiar theoretical results, regarding Weak Values, in order to achieve useful improvements. The context is typically measurements precision. The simplicity of the formalism tougher with the counter intuitive results can assist in optimizing experimental setups or engineering new ones.
- Fundamental concepts. Experiments that are utilizing Weak Measurements, or displaying Weak Values in other ways, can highlight the extraordinary nature of quantum mechanics. Analyzing these experiments and their results can improve our understanding of quantum mechanics and might result in an expansion of theory.
