Today’s Plan Review 2-level system (Schordinger eq, Rabi, Bloch)

Slides:

Advertisements

Similar presentations

Advertisements

Xkcd Xkcd.com. Section 3 Recap ► Angular momentum commutators:  [J x, J y ] = iħJ z etc ► Total ang. Mom. Operator: J 2 = J x 2 + J y 2 +J z 2 ► Ladder.

Ari Borthakur, PhD Associate Director, Center for Magnetic Resonance & Optical Imaging Department of Radiology Perelman school of Medicine, University.

MR TRACKING METHODS Dr. Dan Gamliel, Dept. of Medical Physics,

Quantum trajectories for the laboratory: modeling engineered quantum systems Andrew Doherty University of Sydney.

ELEG 479 Lecture #9 Magnetic Resonance (MR) Imaging

Lecture 7. Nuclear Magnetic Resonance (NMR). NMR is a tool that enables the user to make quantitative and structural analyses on compounds in solution.

Quantum Computing with Trapped Ion Hyperfine Qubits.

David Gershoni The Physics Department, Technion-Israel Institute of Technology, Haifa, 32000, Israel and Joint Quantum Institute, NIST and University of.

Quantum Computing Lecture 19 Robert Mann. Nuclear Magnetic Resonance Quantum Computers Qubit representation: spin of an atomic nucleus Unitary evolution:

Nuclear Magnetic Resonance Spectrometry Chap 19. Absorption in CW Experiments Energy of precessing particle E = -μ z B o = -μ B o cos θ When an RF photon.

Cavity QED as a Deterministic Photon Source Gary Howell Feb. 9, 2007.

Quantum Computation Using Optical Lattices Ben Zaks Victor Acosta Physics 191 Prof. Whaley UC-Berkeley.

A few fundamentals of NMR Dieter Freude. Harry Pfeifer's NMR-Experiment 1951 in Leipzig H. Pfeifer: Über den Pendelrückkoppelempfänger (engl.: pendulum.

Carrier Wave Rabi Flopping (CWRF) Presentation by Nathan Hart Conditions for CWRF: 1.There must exist a one photon resonance with the ground state 2.The.

Resonance condition. Pulse A coil of wire placed around the X axis will provide a magnetic field along the X axis when a direct current is passed through.

PG lectures Spontaneous emission. Outline Lectures 1-2 Introduction What is it? Why does it happen? Deriving the A coefficient. Full quantum description.

3.2.2 Magnetic Field in general direction Larmor frequencies: Hamiltonian: In matrix representation 

Optically Pumping Nuclear Magnetic Spin M.R.Ross, D.Morris, P.H. Bucksbaum, T. Chupp Physics Department, University of Michigan J. Taylor, N. Gershenfeld.

Single atom lasing of a dressed flux qubit

Dressed state amplification by a superconducting qubit E. Il‘ichev, Outline Introduction: Qubit-resonator system Parametric amplification Quantum amplifier.

Quantum Devices (or, How to Build Your Own Quantum Computer)

Density Matrix Density Operator State of a system at time t:

BE 581 Intro to MRI.

T ECHNISCHE U NIVERSITÄT KAISERSLAUTERN K. Bergmann Lecture 6 Lecture course - Riga, fall 2013 Coherent light-matter interaction: Optically driven adiabatic.

Purdue University Spring 2014 Prof. Yong P. Chen Lecture 16 (3/31/2014) Slide Introduction to Quantum Optics.

3 He Polarization Tests at UIUC Danielle Chandler David Howell UIUC.

Adiabatic approximation

Ch ; Lecture 26 – Quantum description of absorption.

Purdue University Spring 2014 Prof. Yong P. Chen Lecture 6 (2/5/2014) Slide Introduction to Quantum Optics &

Beam Polarimetry Matthew Musgrave NPDGamma Collaboration Meeting Oak Ridge National Laboratory Oct. 15, 2010.

MRI Physics Dr Mohamed El Safwany, MD.. MRI Magnetic Resonance Imaging Magnetic Resonance Imaging.

1.5 Population inversion and laser operation

Pablo Barberis Blostein y Marc Bienert

Introduction to materials physics #4

Gavin W Morley Department of Physics University of Warwick Diamond Science & Technology Centre for Doctoral Training, MSc course Module 2 – Properties.

For long wavelength, compared to the size of the atom The term containing A 2 in the dipole approximation does not involve atomic operators, consequently.

Bloch spheres, Bloch vectors, and solving Schrödinger’s equation with (almost) no math Two-level time independent hamiltonians David Blasing, Quantum Mechanics.

Purdue University Spring 2016 Prof. Yong P. Chen Lecture 18 (3/24/2016) Slide Introduction to Quantum Photonics.

Shanxi University Atomic Physics Chapter 7 The interaction of atoms with radiation Atomic Physics.

Einstein’s coefficients represent a phenomenological description of the matter-radiation interaction Prescription for computing the values of the A and.

TC, U. Dorner, P. Zoller C. Williams, P. Julienne

Light Matter Interaction - Semi-classical

Departament de Física, Universitat de les Illes Balears,

Resonant magneto-optical effects in atoms

Density Matrix Density Operator State of a system at time t:

Pulse Propagation. Chapter 4.

q Magnetic Field in general direction Larmor frequencies:

Ultrafast processes in molecules

國立交通大學電子物理系專題演講 Quantum optics in 3-level superconducting artificial atoms: Controlling one-photon and two-photon transparency Abstract We experimentally.

Quantum Dots: Periodicity, spatial confinement and external fields

Biophysical Tools '04 - NMR part II

Quantum mechanics I Fall 2012

Lecture 2: Magnetic Statics

What is the origin of the nuclear magnetic dipole moment (m) and how is it oriented relative to an external magnetic field B0? 24-Nov-18.

Coupled atom-cavity system

Coherent Nonlinear Optics

Nuclear Magnetic Resonance

Basic MRI I Chapter 3 Notes.

Marco Polo, Daniel Felinto and Sandra Vianna Departamento de Física

COT 6200 Quantum Computing Fall 2010

University of California, Berkeley

“Addition” of angular momenta – Chap. 15

Chapter V Interacting Fields Lecture 2 Books Recommended:

Norm Moulton LPS 15 October, 1999

RHIC Spin Flipper M. Bai, T. Roser Collider Accelerator Department

Dynamics and decoherence of a qubit coupled to a two-level system

1H and 13C NMR Spectroscopy in Organic Chemistry

LECTURE 12 SPINS Source: D. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, 2004) R. Scherrer, Quantum Mechanics An Accessible Introduction.

Jaynes-Cummings Hamiltonian

Presentation transcript:

Lecture 11 Semi Classical 2-level system (Light-Atom interaction): Rabi & Bloch; atom, QD & NMR

Today’s Plan Review 2-level system (Schordinger eq, Rabi, Bloch) [FQ Chap 9; Blasing lecture 12] Application to NMR [FQ Appendix E] NMR/spin picture to understand 2-level system (Schordinger eq, Rabi etc) in Pauli matrices [after rotating frame transformation]

Dipole transition TDSE in c1,c2:

Weak Field Limit/Einstein Coefficients 1~ ~0 RWA

Arbitrary/Strong Field –Rabi Flop resonant TDSE with RWA (resonant Rabi osci/flop) Non-resonant Rabi oscillation (reduced amplitude) [not able to completely flop/drive to excited state] |c1|2=1-|c2|2 (non-resonant Rabi frequency)

Damped Rabi oscillation Large t behavior: (small ) Connects to weak field/Einstein ~t (small t) (resonant & moderate damping [cf.Loudon])

2-level (Rabi) on Bloch Sphere (“rotating frame”) (“pulse area”/rotation angle) 1-qubit operation “pi-pulse” “pi/2-pulse”

Experimental optical 2-level Rabi Atom (Mollow triplet)

Experimental optical 2-level Rabi Quantum Dot (artificial atom)

Experimental optical 2-level Rabi Quantum Dot (artificial atom)

(L~ )

Larmor Precession

(NMR) Rotating Frame (Rabi oscillation)

(NMR) Bloch Equation Optical analogue: optical Bloch equation

Pauli Matrices (spin-1/2) Bx By Bz Simplest way to understand 2-level TDSE (after rotating frame)

Dressed State Adiabatic passage (Landau Zener transition) Read Chap 5 in Steck book: http://atomoptics.uoregon.edu/~dsteck/teaching/quantum-optics/

Experimental optical 2-level Rabi Atom (Mollow triplet)