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PHYS 30101 Applications of quantum physics

Lecture summaries

I am posting the pdf files of my summaries of the lectures here, along with references to the corresponding sections of the textbooks, and links to any figures shown in the lectures and other relevant material. Note that papers in Nature, Science and Physical Review Letters will be accessible only from a University of Manchester computer or VPN. Lecture capture: For various technical reasons these lectures are not part of the University's lecture capture programme. However using the visualiser means that they are being "captured" in a more traditional medium: ink on paper. If anyone needs to see or copy something they missed, just ask me (as a few of you already have). Lecture 1 Topics 0 Basics of quantum mechanics PHYS 20101 summary of important concepts (pdf) Handout: Course overview (pdf) Textbook references: Rae 1.4, 2.1-2, 4 Further reading: Mandl 1; Gasiorowicz 2, 3; Phillips 3, 4, 7 Examples: Sheet 1 Lecture 2 Topics 1 Tunnelling 1.1 Time-independent Schrödinger equation 1.2 Simple barrier Summary (pdf) Textbook references: Rae 2.2, 2.6; Gasiorowicz 3.1, 4.3; Mandl 2.2 Further reading: Miller 3.2, 11.1-2 Supplementary information Nanotechnology (Wikipedia) Examples: Sheet 2, question 1 Lecture 3 Topics 1.3 General barriers Summary (pdf) Textbook references: Gasiorowicz 4.3-4; Mandl pages 36-37 Further reading: Gasiorowicz web supplements 4A, 4B; Miller 11.3-4 Supplementary information A. C. Phillips, The physics of stars (Wiley, 1994) section 4.1 Cold fusion (Wikipedia) Examples: Sheet 2, question 2 Lecture 4 Topics 1.4 Square wells 1.5 Resonant tunnelling Summary (pdf) Figures Resonant tunnelling probability Textbook references: Rae 2.5; Gasiorowicz 4.5; Mandl 2.1 (square wells) Further reading: Miller page 285 Supplementary information Finite barrier quantum well (Britney Spears' guide to semiconductor physics) Resonant tunnelling diode (Wikipedia) SiGe resonant tunnelling diodes (Semiconductor physics group, University of Cambridge) Fabry-Pérot etalon (Wikipedia) Examples: Sheet 2, question 3 Lecture 5 Topics 2 Trapped particles 2.1 Gold nanocube Summary (pdf) Textbook references: Rae 3.2 Figures Silver nanocubes, electron-microscope images and an X-ray diffraction pattern (from Y. Sun and Y. Xia, Science 298 (2002) 2176) Roman nanotechnology (The Lycurgus Cup in the British Museum) Supplementary information Medieval nanotechnology (British Museum) Colloidal gold (Wikipedia) Examples: Sheet 2, questions 4, 5 Lecture 6 Topics 2.2 Quantum dots Summary (pdf) Figures Quantum dots in solution and in cells (University of Washington) Pairs of InAs dots on a semiconductor (from G. J. Beirne et al., Phys Rev Lett 96 (2006) 137401) Circular quantum dot (from L. P. Kouwenhoven et al., Science 278 (1997) 1788) Further reading The many aspects of quantum dots (editorial) Nature Nanotechnology 5 (2010) 381 Supplementary information Manchester Chemistry/Materials research group (work on quantum dots and nanocrystals) Examples: Sheet 2, questions 4, 5 Lecture 7 Topics 2.3 Artificial atom Summary (pdf) Figures Conductance of a quantum dot as a function of the applied potentials (from L. P. Kouwenhoven et al., Science 278 (1997) 1788) Further reading L. P. Kouwenhoven et al., Science 278 (1997) 1788, Excitation spectra of circular, few-electron quantum dots Examples: Sheet 3, question 1 Lecture 8 Topics 2.4 Orthogonality 2.5 Dirac notation Summary (pdf) Textbook references: Rae 4.2-3, 6.1; Gasiorowicz 5.1-3, 6.1; Mandl 1.2, 5.1 Further reading: All you ever wanted to know about Dirac notation (but were afraid to ask) (pdf, by Judith McGovern) Boas 12.6-7, 13.3; Miller 2.7, 4 Examples: Sheet 3, question 2 Lecture 9 Topics 2.6 Perturbation theory Summary (pdf) Textbook references: Rae 7.1; Gasiorowicz 11.1; Mandl 7.1 Further reading: Miller 6.3 Examples: Sheet 3, question 3 Lecture 10 Topics 2.7 Quantum wire 2.8 Carbon nanotube Summary (pdf) Figures STM images of carbon nanotubes (from T. W. Odom et al., Nature 391 (1998) 62) Electrical conductance of a semiconducting nanotube (from J. W. G. Wilder et al., Nature 391 (1998) 59) Electrical conductances of several nanotubes (from J. W. G. Wilder et al., Nature 391 (1998) 59) Further reading Miller 8.4, 8.7-8 Gasiorowicz, 13.5-6 Density of states (Britney Spears) J. W. G. Wilder et al., Nature 391 (1998) 59, Electronic structure of atomically resolved carbon nanotubes Supplementary information Carbon nanotube (Wikipedia) Press release for the 2010 Nobel Prize in Physics, awarded to Andre Geim and Kostya Novoselov (University of Manchester) Graphene (Wikipedia) University of Manchester Condensed Matter Physics Group (with links to articles on their work on graphene) Examples: Sheet 3, question 4 Lecture 11 Topics 3 Spin and other two-state systems 3.1 Angular momentum without angles Summary (pdf) Reminder of notation for angular momenta (pdf) Textbook references: Rae 4.4, 5.1, 5.4; Gasiorowicz 7.1-2; Mandl 5.2.2, 5.8 Examples: Sheet 4, question 1 Lecture 12 Topics 3.2 Spin Summary (pdf) Textbook references: Rae 6.2-3; Gasiorowicz 10.1; Mandl 5.3 Further reading Miller 12.2-3, 12.7 Boas, 3.6-11 R. P. Feynman, The reason for antiparticles, in: R. P. Feynman and S. Weinberg, Elementary particles and the laws of physics (Cambridge, 1987) Videos: Binasuan, as performed by professional spinors Dirac's belt trick Examples: Sheet 4, questions 2, 3 Lecture 13 Topics 3.3 Magnetic moments Figures Electron g-factor Summary (pdf) Textbook references: Rae 5.3, page 132; Gasiorowicz 10.2; Mandl pages 177-178 Further reading Miller 12.1, 12.6 Examples: Sheet 4, questions 4, 5, 6 Lecture 14 Topics 3.4 Adding angular momenta Summary (pdf) Textbook references: Rae 6.6; Gasiorowicz 10.4-5; Mandl 5.4-6 Examples: Sheet 4, questions 7, 8 Lecture 15 Topics 3.5 Other two-state systems Summary (pdf) Figures Double quantum dot (from F. H. L. Koppens et al., Science 309 (2005) 1346) Figure 1 (double quantum dot), Figure 2(a) (double-dot energy eigenvalues) and Figure 4(a) (oscillations of current with pulse time) from J. Gorman D. G. Hasko and D. A. Williams, Phys. Rev. Lett. 95 (2005) 090502 Textbook references: Rae pages 263-264 Further reading Miller 14.1 Supplementary information Photon polarisation states (Wikipedia) The Delft spin Qbit project J. Gorman D. G. Hasko and D. A. Williams, Phys. Rev. Lett. 95 (2005) 090502, Charge-qubit operation of an isolated double quantum dot N. Mason, M. J. Biercuk and C. M. Marcus, Science 303 (2004) 655, Local gate control of a carbon nanotube double quantum dot Examples: Sheet 5, question 1 Lecture 16 Topics 3.6 Manipulating spins Summary (pdf) Figures Double quantum dot used to manipulate electron spin (from F. H. L. Koppens et al., Nature 442 (2006) 766) Spin resonance of an electron in a quantum dot (from F. H. L. Koppens et al., Nature 442 (2006) 766) Cycle used to control electron spin in a quantum dot (from F. H. L. Koppens et al., Nature 442 (2006) 766) Spin rotations in a quantum dot (from F. H. L. Koppens et al., Nature 442 (2006) 766) Further reading Gasiorowicz 10.3 (note difference of factor 2 in definition of B1) F. H. L. Koppens et al., Nature 442 (2006) 766, Driven coherent oscillations of a single electron spin in a quantum dot Supplementary information Electron spin resonance (Wikipedia) Press release for the 2012 Nobel Prize in Physics, awarded to Serge Haroche and David Wineland Lecture 17 Topics 4 Atoms in magnetic fields 4.1 Spin-orbit coupling Summary (pdf) Textbook references: Rae 6.5; Gasiorowicz 12.2; Mandl 7.4, 6.1.3 Examples: Sheet 5, questions 2, 3 Lecture 18 Topics 4.2 Zeeman effect Summary (pdf) Textbook references: Rae 6.5; Gasiorowicz 12.3; Mandl 7.5 Examples: Sheet 5, questions 4, 5 Lecture 18A (lecture omitted this year) Topics 4.3 Quantum dot in a magnetic field Summary (pdf) Figures Spectrum of a single electron in a nanotube (from F. Kuemmeth et al., Nature 452 (2008) 448) Further reading F. Kuemmeth et al., Nature 452 (2008) 448, Coupling of spin and orbital motion of electrons in carbon nanotubes Examples: Sheet 5, question 6 Lecture 19 Topics 5 Quantum information 5.1 Measurement 5.2 Entanglement 5.3 Identical particles Summary (pdf) Textbook references: Rae page 263, 12.2, 10.4; Gasiorowicz 13.2-4; Mandl 4.4; Miller 18.1, 18.3, 13.1-2 Further reading: Rae pages 269-270; Miller pages 425-427 Supplementary information The spin-statistics theorem (Wikipedia) R. P. Feynman, The reason for antiparticles, in: R. P. Feynman and S. Weinberg, Elementary particles and the laws of physics (Cambridge, 1987) Examples: Sheet 6, questions 1, 2 Lecture 20 Topics 5.4 Entangling electrons and photons Summary (pdf) Figures Energy levels of a quantum dot (from K. De Greve et al., Nature 491 (2012) 421) Electron-photon entanglement (from K. De Greve et al., Nature 491 (2012) 421) Further reading: K. De Greve et al., Nature 491 (2012) 421, Quantum-dot spin-photon entanglement via frequency downconversion to telecom wavelength W. B. Gao et al., Nature 491 (2012) 426, Observation of entanglement between a quantum dot spin and a single photon J. R. Schaibley et al., Phys. Rev. Lett. 110 (2013) 167401, Demonstration of quantum entanglement between a single electron spin confined to an InAs quantum dot and a photon Lecture 20A (lecture omitted this year) Topics 5.4 Hidden variables? Summary (pdf) Further reading: N. D. Mermin, Journal of Philosophy 78 (1981) 398, Quantum mysteries for anyone (JSTOR archive); also reprinted in: N. David Mermin, Boojums all the way through (Cambridge, 1990) Rae 13.2-3; Gasiorowicz 20.3; Mandl 6.3; Miller 19.1 Lecture 21 Topics 5.5 Quantum cryptography Summary (pdf) Textbook references: Rae 12.1; Miller 18.2 Further reading: Rae 12.3; Miller 18.5 Supplementary information Quantum key distribution (Wikipedia) Quantum cryptography (Wikipedia) Quantum security for bank transfer (IQOQI, Vienna) Sending entangled photons between the Canary Islands (IQOQI, Vienna) T. Jennewein et al., Physical Review Letters 84 (2000) 4729 Quantum cryptography with entangled photons K. A Patel et al., Physical Review X 2 (2012) 041010 Coexistence of high-bit-rate quantum key distribution and data on optical fiber Examples: Sheet 6, question 3 Lecture 22 Topics 5.6 Seeing without looking Further reading Elitzur-Vaidman bomb-tester (Wikipedia) A. C. Elitzur, and L. Vaidman, Found. Phys. 23 (1993) 987, Quantum mechanical interaction-free measurements P. Kwiat et al., Phys. Rev. Lett. 74 (1995) 4763, Interaction-free measurement Rae 13; Gasiorowicz 20; Miller 19 Revision Summary (pdf) Examples: Sheet 7

13th December 2013

Up: PHYS 30101