# Applied Physics (APh) Courses (2021-22)

APh/Ph 112 ab.
Noise and Stochastic Resonance.
9 units (3-0-6):
second, third terms.
Prerequisites: Ph 12 abc, ACM 95/100 ab and Ph 106 abc, equivalent background, or instructor's permission.
The presence of noise in experimental systems is often regarded as a nuisance since it diminishes the signal to noise ratio thereby obfuscating weak signals or patterns. From a theoretical perspective, noise is also problematic since its influence cannot be elicited from deterministic equations but requires stochastic-based modeling which incorporates various types of noise and correlation functions. In general, extraction of embedded information requires that a threshold be overcome in order to outweigh concealment by noise. However, even below threshold, it has been demonstrated in numerous systems that external forcing coupled with noise can actually boost very weak signatures beyond threshold by a phenomenon known as stochastic resonance. Although it was originally demonstrated in nonlinear systems, more recent studies have revealed this phenomenon can occur in linear systems subject, for example, to color-based noise. Techniques for optimizing stochastic resonance are now revolutionizing modeling and measurement theory in many fields ranging from nonlinear optics and electrical systems to condensed matter physics, neurophysiology, hydrodynamics, climate research and even finance. This course will be conducted in survey and seminar style and is expected to appeal to theorists and experimentalists alike. Review of the current literature will be complimented by background readings and lectures on statistical physics and stochastic processes as needed.
Instructor: Troian.

APh/Ph 115.
Physics of Momentum Transport in Hydrodynamic Systems.
9 units (3-0-6):
second term.
Prerequisites: ACM 95 or equivalent.
Contemporary research in many areas of physics requires some knowledge of the principles governing hydrodynamic phenomena such as nonlinear wave propagation, symmetry breaking in pattern forming systems, phase transitions in fluids, Langevin dynamics, micro- and optofluidic control, and biological transport at low Reynolds number. This course offers students of pure and applied physics a self-contained treatment of the fundamentals of momentum transport in hydrodynamic systems. Mathematical techniques will include formalized dimensional analysis and rescaling, asymptotic analysis to identify dominant force balances, similitude, self-similarity and perturbation analysis for examining unidirectional and Stokes flow, pulsatile flows, capillary phenomena, spreading films, oscillatory flows, and linearly unstable flows leading to pattern formation. Students must have working knowledge of vector calculus, ODEs, PDEs, complex variables and basic tensor analysis. Advanced solution methods will be taught in class as needed. Not offered 2021-2022.
Instructor: Troian.

APh/Ph/Ae 116.
Physics of Thermal and Mass Transport in Hydrodynamic Systems.
9 units (3-0-6):
third term.
Prerequisites: ACM 95 or equivalent and APh/Ph 115 or equivalent.
Contemporary research in many areas of physics requires some knowledge of how momentum transport in fluids couples to diffusive phenomena driven by thermal or concentration gradients. This course will first examine processes driven purely by diffusion and progress toward description of systems governed by steady and unsteady convection-diffusion and reaction-diffusion. Topics will include Fickian dynamics, thermal transfer in Peltier devices, Lifshitz-Slyozov growth during phase separation, thermocouple measurements of oscillatory fields, reaction-diffusion phenomena in biophysical systems, buoyancy driven flows, and boundary layer formation. Students must have working knowledge of vector calculus, ODEs, PDEs, complex variables and basic tensor analysis. Advanced solution methods such as singular perturbation, Sturm-Liouville and Green's function analysis will be taught in class as needed. Not offered 2021-2022.
Instructor: Troian.

Ph/APh/EE/BE 118 ab.
Physics of Measurement.
9 units (3-0-6):
second, third terms.
Prerequisites: Ph 127, APh 105, or equivalent, or permission from instructor.
This course explores the fundamental underpinnings of experimental measurements from the perspectives of coupling, responsivity, noise, backaction, and information. Its overarching goal is to enable students to develop intuition about, and to critically evaluate, a diversity of real measurement systems - and to provide a framework for estimating the ultimate and practical limits to information that can be extracted from them. Topics will include physical signal transduction and responsivity, fundamental noise processes, modulation, frequency conversion, synchronous detection, signal-sampling techniques, digitization, signal transforms, spectral analyses, and correlation methods. The first term will cover the essential fundamental underpinnings, while topics in second term will focus their application to high frequency, microwave, and fast time-domain measurements where distributed approaches become imperative. The second term (in alternate years) may focus on topics that include either measurements at the quantum limit, biosensing and biological interfaces, of functional brain imaging. Not offered 2021-22.
Instructor: Roukes.

Ph/APh 137 abc.
Atoms and Photons.
9 units (3-0-6):
first, second terms.
Prerequisites: Ph 125 ab or equivalent, or instructor's permission.
This course will provide an introduction to the interaction of atomic systems with photons. The main emphasis is on laying the foundation for understanding current research that utilizes cold atoms and molecules as well as quantized light fields. First term: resonance phenomena, atomic/molecular structure, and the semi-classical interaction of atoms/molecules with static and oscillating electromagnetic fields. Techniques such as laser cooling/trapping, coherent manipulation and control of atomic systems. Second term: quantization of light fields, quantized light matter interaction, open system dynamics, entanglement, master equations, quantum jump formalism. Applications to cavity QED, optical lattices, and Rydberg arrays. Third term [not offered 2021-2022]: Topics in contemporary research. Possible areas include introduction to ultracold atoms, atomic clocks, searches for fundamental symmetry violations, synthetic quantum matter, and solid state quantum optics platforms. The emphasis will be on reading primary and contemporary literature to understand ongoing experiments.
Instructors: Hutzler, Endres.

APh/Ph 138 ab.
Quantum Hardware and Techniques.
9 units (3-0-6):
third term, a and b offered in alternating years.
Prerequisites: Ph 125abc or Ph 127ab or Ph137ab or instructor's permission.
This class covers multiple quantum technology platforms and related theoretical techniques, and will provide students with broad knowledge in quantum science and engineering. It will be split into three-week modules covering: applications of near-term quantum computers, superconducting qubits, trapped atoms and ions, topological quantum matter, solid state quantum bits, tensor-product states.
Instructors: Faraon, Minnich.

Ph/APh 223 ab.
Advanced Condensed-Matter Physics.
9 units (3-0-6):
second, third terms.
Prerequisites: Ph 135 or equivalent, or instructor's permission.
Advanced topics in condensed-matter physics, with emphasis on the effects of interactions, symmetry, and topology in many-body systems. Ph/APh 223a covers second quantization, Hartree-Fock theory of the electron gas, Mott insulators and quantum magnetism, spin liquids, bosonization, and the integer and fractional quantum Hall effect. Ph/APh 223b will continue with BCS theory of superconductivity, Ginzburg-Landau theory, elements of unconventional and topological superconductors, theory of superfluidity, Bose-Hubbard model and bosonic Mott insulators, and some aspects of quantum systems with randomness.
Instructor: Alicea.

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The online version of the Caltech Catalog is provided as a convenience; however, the printed version is the only authoritative source of information about course offerings, option requirements, graduation requirements, and other important topics.