INTRODUCTION TO NMR and NMR QIP

Size: px
Start display at page:

Download "INTRODUCTION TO NMR and NMR QIP"

Transcription

1 Books (NMR): Spin dynamics: basics of nuclear magneac resonance, M. H. LeviF, Wiley, 200. The principles of nuclear magneasm, A. Abragam, Oxford, 96. Principles of magneac resonance, C. P. Slichter, Springer, 990. Reviews (): NMR techniques for quantum control and computa>on, LMK Vandersypen and I. Chuang, Reviews of Modern Physics (2004) vol. 76 (4) pp Quantum informa>on processing using nuclear and electron magne>c resonance: review and prospects, et al., arxiv: NMR Based Quantum Informa>on Processing: Achievements and Prospects, D. G. Cory et al., arxiv:quant- ph/

2 Spin- /2 nucleus NMR freq (at 0 T) abundance H 426 MHz 99.9% 3 C 07.% 5 N % 9 F 40 00% 28 Si % 3 P 75 00% Nuclei with an odd (even) number of nucleons possess half- integer (integer) spin Nuclei with an even number of protons and neutrons are spinless

3 H NMR Hamiltonian: 2 coupled spins in liquid- state NMR (e.g. 3 C- labelled Chloroform) ( =) H 0 = ( 2 ω σ z + ω 2 σ 2z + πj 2 σ z σ ) 2z 3 C Chloroform molecule, CHCl 3 Larmor frequency (rad/s): External magneac field (T): Coupling strength (Hz): J kl ω k = γ k B B Chemical shielding: For the same isotope, γ j = γ ( 0 δ ) j for nucleus at the j th chemical site. Ability to address different nuclei as qubits

4 Larmor precession H 0 = ω σ z 2 U(t) = e iω tσ z 2 = Take ψ = + 2 U(t) ψ = e iω t 2 + e +iω t e +iωt =e iω t i = +

5 H Eigenstates of the Hamiltonian H 0 = ( 2 ω σ z + ω 2 σ 2z + πj 2 σ z σ ) 2z : H state 2: 3 C eigenvalue ( 2 ω + ω + πj 2 2) 2 ω + ω 2 πj 2 ( 2 ω ω πj 2 2) ( ) ( 2 ω ω + πj 2 2) ω = 2π 426MHz ω 2 = 2π 07MHz J 2 200Hz B =0T ( 2 ω + ω 2) ( 2 ω + ω 2 ) ( 2 ω ω 2) ( 2 ω ω 2 ) + π 2 J 2 π 2 J 2 π 2 J 2 + π 2 J 2 3 C Chloroform molecule, CHCl 3

6 NMR transifons (spectrum) ( 2 ω + ω 2) + π 2 J ( 2 ω + ω 2) ( 2 ω ω 2) π 2 J 2 π 2 J 2 2πJ 2πJ ( 2 ω ω 2) + π 2 J 2 ω ω 2 frequency These are magneac dipole transiaons, and are thus driven by an oscillaang (RF) magneac field Need transverse spin operators σ x,σ y ( )

7 RF Hamiltonian: H rf (t) = Ω(t) 2 θ(t) = ω rf t + φ [ σ x cos(θ(t)) + σ y sin(θ(t)) ] RF amplitude RF frequency B x cos(ω rf t) Re B + e iω rf t ( )

8 RotaFng reference frame transformafon * R(t) = e iω rf tσ z 2 e iω 2rf tσ 2z 2 ψ R = R(t) ψ lab id ψ lab dt = H lab ψ lab id ψ R dt = H R ψ R H lab = H 0 + H rf (t) * H R = 2 ω ω rf *This is for the case of two isotopes doubly- rotaang frame [( )σ z + ( ω 2 ω 2rf )σ 2z + πj 2 σ z σ 2z ] + [ 2 Ω (t) ( σ x cos(φ ) + σ y sin(φ ))] + [ 2 Ω (t) σ cos(φ 2 ( ) + σ sin(φ ) 2x 2 2y 2 )]

9 RotaFng frame = We had Larmor precession in Lab frame: U(t) ψ = e iω t 2 + e +iωt 2 But in the rotaang frame (on resonance): + i R(t) U(t) + U(t) ψ R = U(t)R(t) ψ = + 2 =

10 Resonant pulses as Bloch sphere rotafons Consider a one- spin system on resonance: ω = ω rf H R = [( 2 ω ω rf )σ z + Ω (t)( σ x cos(φ ) + σ y sin(φ ))] In NMR, we can control both RF phase ( φ) and amplitude ( Ω) in Ame, so we can perform arbitrary single spin rotaaons U(t) = e iω t ( σ x cos(φ )+σ y sin(φ ) ) / 2 R y (π /2) φ = π /2 Ωt = π /2 R x (π /2) φ = π Ωt = π /2 - Y X ( 0 + ) 2 Y - Y X Y ( 0 + i ) 2

11 Example of two- qubit control: the CNOT gate H(t) = ( 2 ω σ z + ω 2 σ 2z + πjσ z σ 2z ) + H rf (t) Zeeman coupling RF pulses (control)

12 q q R z (90) R y (90) R y ( 90) R x (90) U = e iπ 2 I 2 σ y 2 t = π /2J Ame U 2 = e i π 2 σ z σ 2z / 2 U 3 = e iπ 2 σ z 2 I 2 U 4 = e +iπ 2 I σ 2y 2 U CNOT = U 5 U 4 U 3 U 2 U = 0 0 I 2 + σ 2x U 5 = e iπ 2 I σ 2x 2

13 The thermal state A general mixed state: ρ = k a k ψ k ψ k Thermal equilibrium (Boltzmann distribuaon): ρ th = e H 0 kt Tr e H 0 ( kt ) In the high temperature limit ( ) H 0 << kt ρ th 2 I H 0 I kt 2 4kT ω σ z + ω 2 σ 2z ( ) (two- spin case) ω kt ~ 0 5 at room temperature in NMR

14 The thermal state ρ th 2 I H 0 I kt 2 4kT ω σ z + ω 2 σ 2z ( ) The idenaty term cannot be changed by pulses or observed So we define a deviaaon density matrix: ρ dev = H 0 kt ω σ z + ω 2 σ 2z (the J coupling term is ~0-6 Ames smaller than Zeeman energy) σ z indicates a populaaon difference between spin- up and spin- down states

15 Pseudopure states To iniaalize an NMR quantum info. processor, we want a pure state or at least one that behaves like a pure state: ρ pp = I 2 α ψ ψ Example: making a H 3 C pseudopure state ρ dev 4σ z + σ 2z =

16 Example: making a H 3 C pseudopure state Apply three permutaaon circuits and sum results: ρ dev ρ dev = I ρ dev ʹ ρ dev 00 00

17 Measurement in NMR Bulk magneazaaon of j th isotope: B // ˆ z M z j = µ j ( n j n ) j 90 degree ( readout ) pulse rotates magneazaaon to x- y plane: Z M z Ensemble of idenacal, non- interacang processor molecules - Y X M x Y

18 Measurement in NMR In the lab frame, magneazaaon precesses in the x- y plane, at the Larmor frequency Z - Y X M x Y the oscillaang magneac flux induces an emf in the solenoid coil via Faraday s law.

19 Measurement in NMR This corresponds to an expectaaon value measurement, with observables: M x = Tr ρ σ kx M y = Tr ρ σ ky k k We call these observables transverse magneazaaon

20 Measurement in NMR Example: - qubit tomography of an arbitrary state ρ dev Expt. ρ dev M x, M y P x,p y Expt. 2 ρ dev R y (π /2) M x P z Unfortunately, the # of expts grows exponenaally with # qubits for any implementaaon!

21 Measurement in NMR : FT spectrum V 0 M x (0) NMR transi>ons Voltage T 2 V 0 /e Fourier transform Δω ~ T 2 Time amp M x (0) Frequency free- inducaon signal ( ) M x (t) = Tr e ih 0 t ρ(0)e +ih 0 t σ x

22 RelaxaFon and decoherence General Kraus operator sum: ρ A k ρa k + k k A k + A k = I Z RelaxaAon Dephasing Spin operators σ x,σ y σ z X Y Example: pure dephasing A = e iφσ z ρ dφ e iφσ z ρe+iφσ z f (φ,t,t 2 ) Lorentzian with Ame- dependent FWHM ( ) a be t /T 2 b * e t /T 2 Dephasing on the Bloch sphere a

23 Pure dephasing Or in another form: Z Λ(ρ) = ( p) ψ ψ + pσ z ψ ψ σ z With Kraus operators: A 0 = pi Y A = pσ z p = e t /T 2 2 Dephasing on the Bloch sphere

24 RelaxaFon A 0 = p 0 0 η A = p 0 η 0 0 A 2 = η 0 p 0 A 3 = p 0 0 η 0 see e.g. Nielsen & Chuang ( Λ(ρ) = a a 0)e t /T + a 0 be t / 2T b * e t / 2T ( a 0 a)e t /T + ( a ) 0 For pure relaxaaon, T 2 = 2T In liq. state NMR, typically T 2 ~ s T ~ 5-20 s

25 NMR Spectrometer

26 The Deutsch- Jozsa algorithm on two qubits H 0 R y 90 R z 90 3 C 0 R x R y R y 90 τ = π 2J ( U 0,U 0 ) R x ±90

27 constant: f 00 balanced: f 0 balanced: f 0 constant: f Jones and Mosca, 998

28 State- of- the- art 2- qubit molecule: histadine Pseudopure state demonstrated (Negrevergne et al, PRL 96, 7050 (2006))

29 Benchmarking control ~0.005 average gate error for 3- qubit control; ~0-4 for single qubit C. A. Ryan, M. Laforest and R. Laflamme, Randomized benchmarking of single and mulaqubit control in liquid- state NMR quantum informaaon processing, New J. Phys (2009)

30 Control in solid- state NMR 4 itera>ons of heat- bath algorithmic cooling C. A. Ryan,, O. Moussa, and R. Laflamme, PRL 00, 4050 (2008)

31 Books (NMR): Spin dynamics: basics of nuclear magneac resonance, M. H. LeviF, Wiley, 200. The principles of nuclear magneasm, A. Abragam, Oxford, 96. Principles of magneac resonance, C. P. Slichter, Springer, 990. Reviews (): NMR techniques for quantum control and computa>on, LMK Vandersypen and I. Chuang, Reviews of Modern Physics (2004) vol. 76 (4) pp Quantum informa>on processing using nuclear and electron magne>c resonance: review and prospects, et al., arxiv: NMR Based Quantum Informa>on Processing: Achievements and Prospects, D. G. Cory et al., arxiv:quant- ph/

INTRODUCTION TO NMR and NMR QIP

INTRODUCTION TO NMR and NMR QIP Books (NMR): Spin dynamics: basics of nuclear magnetic resonance, M. H. Levitt, Wiley, 2001. The principles of nuclear magnetism, A. Abragam, Oxford, 1961. Principles of magnetic resonance, C. P. Slichter,

More information

The Deutsch-Josza Algorithm in NMR

The Deutsch-Josza Algorithm in NMR December 20, 2010 Matteo Biondi, Thomas Hasler Introduction Algorithm presented in 1992 by Deutsch and Josza First implementation in 1998 on NMR system: - Jones, JA; Mosca M; et al. of a quantum algorithm

More information

Measuring Spin-Lattice Relaxation Time

Measuring Spin-Lattice Relaxation Time WJP, PHY381 (2009) Wabash Journal of Physics v4.0, p.1 Measuring Spin-Lattice Relaxation Time L.W. Lupinski, R. Paudel, and M.J. Madsen Department of Physics, Wabash College, Crawfordsville, IN 47933 (Dated:

More information

NMR, the vector model and the relaxation

NMR, the vector model and the relaxation NMR, the vector model and the relaxation Reading/Books: One and two dimensional NMR spectroscopy, VCH, Friebolin Spin Dynamics, Basics of NMR, Wiley, Levitt Molecular Quantum Mechanics, Oxford Univ. Press,

More information

Introduction to NMR Quantum Information Processing

Introduction to NMR Quantum Information Processing Introduction to NMR Quantum Information Processing arxiv:quant-ph/00717v1 30 Jul 00 Contents R. Laflamme, E. Knill, D. G. Cory, E. M. Fortunato, T. Havel, C. Miquel, R. Martinez, C. Negrevergne, G. Ortiz,

More information

The NMR Inverse Imaging Problem

The NMR Inverse Imaging Problem The NMR Inverse Imaging Problem Nuclear Magnetic Resonance Protons and Neutrons have intrinsic angular momentum Atoms with an odd number of proton and/or odd number of neutrons have a net magnetic moment=>

More information

Spectral Broadening Mechanisms

Spectral Broadening Mechanisms Spectral Broadening Mechanisms Lorentzian broadening (Homogeneous) Gaussian broadening (Inhomogeneous, Inertial) Doppler broadening (special case for gas phase) The Fourier Transform NC State University

More information

Chemistry 431. Lecture 23

Chemistry 431. Lecture 23 Chemistry 431 Lecture 23 Introduction The Larmor Frequency The Bloch Equations Measuring T 1 : Inversion Recovery Measuring T 2 : the Spin Echo NC State University NMR spectroscopy The Nuclear Magnetic

More information

Classical behavior of magnetic dipole vector. P. J. Grandinetti

Classical behavior of magnetic dipole vector. P. J. Grandinetti Classical behavior of magnetic dipole vector Z μ Y X Z μ Y X Quantum behavior of magnetic dipole vector Random sample of spin 1/2 nuclei measure μ z μ z = + γ h/2 group μ z = γ h/2 group Quantum behavior

More information

Factoring 15 with NMR spectroscopy. Josefine Enkner, Felix Helmrich

Factoring 15 with NMR spectroscopy. Josefine Enkner, Felix Helmrich Factoring 15 with NMR spectroscopy Josefine Enkner, Felix Helmrich Josefine Enkner, Felix Helmrich April 23, 2018 1 Introduction: What awaits you in this talk Recap Shor s Algorithm NMR Magnetic Nuclear

More information

Biochemistry 530 NMR Theory and Practice

Biochemistry 530 NMR Theory and Practice Biochemistry 530 NMR Theory and Practice Gabriele Varani Department of Biochemistry and Department of Chemistry University of Washington Lecturer: Gabriele Varani Biochemistry and Chemistry Room J479 and

More information

MR Fundamentals. 26 October Mitglied der Helmholtz-Gemeinschaft

MR Fundamentals. 26 October Mitglied der Helmholtz-Gemeinschaft MR Fundamentals 26 October 2010 Mitglied der Helmholtz-Gemeinschaft Mitglied der Helmholtz-Gemeinschaft Nuclear Spin Nuclear Spin Nuclear magnetic resonance is observed in atoms with odd number of protons

More information

Magnetic Resonance in Quantum Information

Magnetic Resonance in Quantum Information Magnetic Resonance in Quantum Information Christian Degen Spin Physics and Imaging group Laboratory for Solid State Physics www.spin.ethz.ch Content Features of (nuclear) magnetic resonance Brief History

More information

Experimental Realization of Shor s Quantum Factoring Algorithm

Experimental Realization of Shor s Quantum Factoring Algorithm Experimental Realization of Shor s Quantum Factoring Algorithm M. Steffen1,2,3, L.M.K. Vandersypen1,2, G. Breyta1, C.S. Yannoni1, M. Sherwood1, I.L.Chuang1,3 1 IBM Almaden Research Center, San Jose, CA

More information

Spin Relaxation and NOEs BCMB/CHEM 8190

Spin Relaxation and NOEs BCMB/CHEM 8190 Spin Relaxation and NOEs BCMB/CHEM 8190 T 1, T 2 (reminder), NOE T 1 is the time constant for longitudinal relaxation - the process of re-establishing the Boltzmann distribution of the energy level populations

More information

Spectral Broadening Mechanisms. Broadening mechanisms. Lineshape functions. Spectral lifetime broadening

Spectral Broadening Mechanisms. Broadening mechanisms. Lineshape functions. Spectral lifetime broadening Spectral Broadening echanisms Lorentzian broadening (Homogeneous) Gaussian broadening (Inhomogeneous, Inertial) Doppler broadening (special case for gas phase) The Fourier Transform NC State University

More information

Quantum Information Processing with Liquid-State NMR

Quantum Information Processing with Liquid-State NMR Quantum Information Processing with Liquid-State NMR Pranjal Vachaspati, Sabrina Pasterski MIT Department of Physics (Dated: May 8, 23) We demonstrate the use of a Bruker Avance 2 NMR Spectrometer for

More information

Classical Description of NMR Parameters: The Bloch Equations

Classical Description of NMR Parameters: The Bloch Equations Classical Description of NMR Parameters: The Bloch Equations Pascale Legault Département de Biochimie Université de Montréal 1 Outline 1) Classical Behavior of Magnetic Nuclei: The Bloch Equation 2) Precession

More information

PHYSICAL REVIEW A, 66,

PHYSICAL REVIEW A, 66, PHYSICAL REVIEW A, 66, 022313 2002 Quantum-information processing by nuclear magnetic resonance: Experimental implementation of half-adder and subtractor operations using an oriented spin-7õ2 system K.

More information

Quantum Computing with NMR: Deutsch-Josza and Grover Algorithms

Quantum Computing with NMR: Deutsch-Josza and Grover Algorithms Quantum Computing with NMR: Deutsch-Josza and Grover Algorithms Charles S. Epstein and Ariana J. Mann MIT Department of Physics (Dated: March 4, ) A Bruker Avance NMR Spectrometer was used to perform simple

More information

Lecture #6 NMR in Hilbert Space

Lecture #6 NMR in Hilbert Space Lecture #6 NMR in Hilbert Space Topics Review of spin operators Single spin in a magnetic field: longitudinal and transverse magnetiation Ensemble of spins in a magnetic field RF excitation Handouts and

More information

Nuclear Magnetic Resonance Spectroscopy

Nuclear Magnetic Resonance Spectroscopy Nuclear Magnetic Resonance Spectroscopy Ecole Polytechnique Département de Chimie CHI 551 Dr. Grégory Nocton Bureau 01 30 11 A Tel: 44 02 Ecole polytechnique / CNRS Laboratoire de Chimie Moléculaire E-mail:

More information

Classical Description of NMR Parameters: The Bloch Equations

Classical Description of NMR Parameters: The Bloch Equations Classical Description of NMR Parameters: The Bloch Equations Pascale Legault Département de Biochimie Université de Montréal 1 Outline 1) Classical Behavior of Magnetic Nuclei: The Bloch Equation 2) Precession

More information

Nuclear Magnetic Resonance Imaging

Nuclear Magnetic Resonance Imaging Nuclear Magnetic Resonance Imaging Simon Lacoste-Julien Electromagnetic Theory Project 198-562B Department of Physics McGill University April 21 2003 Abstract This paper gives an elementary introduction

More information

Electron spins in nonmagnetic semiconductors

Electron spins in nonmagnetic semiconductors Electron spins in nonmagnetic semiconductors Yuichiro K. Kato Institute of Engineering Innovation, The University of Tokyo Physics of non-interacting spins Optical spin injection and detection Spin manipulation

More information

NMR Quantum Computation

NMR Quantum Computation NMR Quantum Computation C/CS/Phs 191: Quantum Information Science and Technolog 11/13/2003 Thaddeus Ladd Department of Applied Phsics Stanford Universit tladd@stanford.edu Solution NMR Quantum Computation

More information

Spin Dynamics Basics of Nuclear Magnetic Resonance. Malcolm H. Levitt

Spin Dynamics Basics of Nuclear Magnetic Resonance. Malcolm H. Levitt Spin Dynamics Basics of Nuclear Magnetic Resonance Second edition Malcolm H. Levitt The University of Southampton, UK John Wiley &. Sons, Ltd Preface xxi Preface to the First Edition xxiii Introduction

More information

Topics. The concept of spin Precession of magnetic spin Relaxation Bloch Equation. Bioengineering 280A Principles of Biomedical Imaging

Topics. The concept of spin Precession of magnetic spin Relaxation Bloch Equation. Bioengineering 280A Principles of Biomedical Imaging Bioengineering 280A Principles of Biomedical Imaging Fall Quarter 2006 MRI Lecture 1 Topics The concept of spin Precession of magnetic spin Relaxation Bloch Equation 1 Spin Intrinsic angular momentum of

More information

The Nuclear Emphasis

The Nuclear Emphasis The Nuclear Emphasis Atoms are composed of electrons and nuclei we ll focus almost exclusively on the physical properties of the nucleus and the chemicoelectronic attributes of its environment. The nucleus

More information

13C. Los Alamos Science Number

13C. Los Alamos Science Number CI CI 13C 13C 1 CI H 6 Los Alamos Science Number 7 00 and Quantum Information Processing Raymond Laflamme, Emanuel Knill, David G. Cory, Evan M. Fortunato, Timothy F. Havel, Cesar Miquel, Rudy Martinez,

More information

COPYRIGHTED MATERIAL. Production of Net Magnetization. Chapter 1

COPYRIGHTED MATERIAL. Production of Net Magnetization. Chapter 1 Chapter 1 Production of Net Magnetization Magnetic resonance (MR) is a measurement technique used to examine atoms and molecules. It is based on the interaction between an applied magnetic field and a

More information

Biophysical Chemistry: NMR Spectroscopy

Biophysical Chemistry: NMR Spectroscopy Spin Dynamics & Vrije Universiteit Brussel 25th November 2011 Outline 1 Pulse/Fourier Transform NMR Thermal Equilibrium Effect of RF Pulses The Fourier Transform 2 Symmetric Exchange Between Two Sites

More information

Magnetic Resonance Imaging. Pål Erik Goa Associate Professor in Medical Imaging Dept. of Physics

Magnetic Resonance Imaging. Pål Erik Goa Associate Professor in Medical Imaging Dept. of Physics Magnetic Resonance Imaging Pål Erik Goa Associate Professor in Medical Imaging Dept. of Physics pal.e.goa@ntnu.no 1 Why MRI? X-ray/CT: Great for bone structures and high spatial resolution Not so great

More information

MRI Physics I: Spins, Excitation, Relaxation

MRI Physics I: Spins, Excitation, Relaxation MRI Physics I: Spins, Excitation, Relaxation Douglas C. Noll Biomedical Engineering University of Michigan Michigan Functional MRI Laboratory Outline Introduction to Nuclear Magnetic Resonance Imaging

More information

Nuclear spin maser with a novel masing mechanism and its application to the search for an atomic EDM in 129 Xe

Nuclear spin maser with a novel masing mechanism and its application to the search for an atomic EDM in 129 Xe Nuclear spin maser with a novel masing mechanism and its application to the search for an atomic EDM in 129 Xe A. Yoshimi RIKEN K. Asahi, S. Emori, M. Tsukui, RIKEN, Tokyo Institute of Technology Nuclear

More information

Experimental Quantum Computing: A technology overview

Experimental Quantum Computing: A technology overview Experimental Quantum Computing: A technology overview Dr. Suzanne Gildert Condensed Matter Physics Research (Quantum Devices Group) University of Birmingham, UK 15/02/10 Models of quantum computation Implementations

More information

Joint Project between Japan and Korea M. Jeong, M. Song, S. Lee (KAIST, Korea) +KBSI T. Ueno, M. Matsubara (Kyoto University, Japan)+Fukui Univ.

Joint Project between Japan and Korea M. Jeong, M. Song, S. Lee (KAIST, Korea) +KBSI T. Ueno, M. Matsubara (Kyoto University, Japan)+Fukui Univ. Joint Project between Japan and Korea M. Jeong, M. Song, S. Lee (KAIST, Korea) +KBSI T. Ueno, M. Matsubara (Kyoto University, Japan)+Fukui Univ. +Vasiliev(Turku) 31 P NMR at low temperatures ( down to

More information

10.4 Continuous Wave NMR Instrumentation

10.4 Continuous Wave NMR Instrumentation 10.4 Continuous Wave NMR Instrumentation coherent detection bulk magnetization the rotating frame, and effective magnetic field generating a rotating frame, and precession in the laboratory frame spin-lattice

More information

Observations of Quantum Dynamics by Solution-State NMR Spectroscopy

Observations of Quantum Dynamics by Solution-State NMR Spectroscopy arxiv:quant-ph/9905061v1 0 May 1999 Observations of Quantum Dynamics by Solution-State NMR Spectroscopy Marco Pravia, Evan Fortunato, Yaakov Weinstein, Mark D. Price, Grum Teklemariam, Richard J. Nelson,

More information

Magnetic Resonance in Quantum

Magnetic Resonance in Quantum Magnetic Resonance in Quantum Information Christian Degen Spin Physics and Imaging group Laboratory for Solid State Physics www.spin.ethz.ch Content Features of (nuclear) magnetic resonance Brief History

More information

Biomedical Imaging Magnetic Resonance Imaging

Biomedical Imaging Magnetic Resonance Imaging Biomedical Imaging Magnetic Resonance Imaging Charles A. DiMarzio & Eric Kercher EECE 4649 Northeastern University May 2018 Background and History Measurement of Nuclear Spins Widely used in physics/chemistry

More information

V27: RF Spectroscopy

V27: RF Spectroscopy Martin-Luther-Universität Halle-Wittenberg FB Physik Advanced Lab Course V27: RF Spectroscopy ) Electron spin resonance (ESR) Investigate the resonance behaviour of two coupled LC circuits (an active rf

More information

Nuclear Magnetic Resonance Imaging

Nuclear Magnetic Resonance Imaging Nuclear Magnetic Resonance Imaging Jeffrey A. Fessler EECS Department The University of Michigan NSS-MIC: Fundamentals of Medical Imaging Oct. 20, 2003 NMR-0 Background Basic physics 4 magnetic fields

More information

A Hands on Introduction to NMR Lecture #1 Nuclear Spin and Magnetic Resonance

A Hands on Introduction to NMR Lecture #1 Nuclear Spin and Magnetic Resonance A Hands on Introduction to NMR 22.920 Lecture #1 Nuclear Spin and Magnetic Resonance Introduction - The aim of this short course is to present a physical picture of the basic principles of Nuclear Magnetic

More information

Introduction of Key Concepts of Nuclear Magnetic Resonance

Introduction of Key Concepts of Nuclear Magnetic Resonance I have not yet lost that sense of wonder, and delight, that this delicate motion should reside in all ordinary things around us, revealing itself only to those who looks for it. E. M. Purcell, Nobel Lecture.

More information

Fundamental MRI Principles Module 2 N. Nuclear Magnetic Resonance. X-ray. MRI Hydrogen Protons. Page 1. Electrons

Fundamental MRI Principles Module 2 N. Nuclear Magnetic Resonance. X-ray. MRI Hydrogen Protons. Page 1. Electrons Fundamental MRI Principles Module 2 N S 1 Nuclear Magnetic Resonance There are three main subatomic particles: protons positively charged neutrons no significant charge electrons negatively charged Protons

More information

Control of Spin Systems

Control of Spin Systems Control of Spin Systems The Nuclear Spin Sensor Many Atomic Nuclei have intrinsic angular momentum called spin. The spin gives the nucleus a magnetic moment (like a small bar magnet). Magnetic moments

More information

NMR: Formalism & Techniques

NMR: Formalism & Techniques NMR: Formalism & Techniques Vesna Mitrović, Brown University Boulder Summer School, 2008 Why NMR? - Local microscopic & bulk probe - Can be performed on relatively small samples (~1 mg +) & no contacts

More information

Biophysical Chemistry: NMR Spectroscopy

Biophysical Chemistry: NMR Spectroscopy Relaxation & Multidimensional Spectrocopy Vrije Universiteit Brussel 9th December 2011 Outline 1 Relaxation 2 Principles 3 Outline 1 Relaxation 2 Principles 3 Establishment of Thermal Equilibrium As previously

More information

NMR Spectroscopy: A Quantum Phenomena

NMR Spectroscopy: A Quantum Phenomena NMR Spectroscopy: A Quantum Phenomena Pascale Legault Département de Biochimie Université de Montréal Outline 1) Energy Diagrams and Vector Diagrams 2) Simple 1D Spectra 3) Beyond Simple 1D Spectra 4)

More information

arxiv:quant-ph/ v1 13 Oct 2004

arxiv:quant-ph/ v1 13 Oct 2004 Liquid state NMR simulations of quantum many-body problems C. Negrevergne, 1, R. Somma, 2, 3 G. Ortiz, 2 E. Knill, 4 and R. Laflamme 1 1 Institute for Quantum Computing, University of Waterloo, Waterloo,

More information

Topics. Spin. The concept of spin Precession of magnetic spin Relaxation Bloch Equation

Topics. Spin. The concept of spin Precession of magnetic spin Relaxation Bloch Equation Bioengineering 280A Principles of Biomedical Imaging Fall Quarter 2005 MRI Lecture 1 Topics The concept of spin Precession of magnetic spin Relaation Bloch Equation Spin Intrinsic angular momentum of elementary

More information

DNP in Quantum Computing Eisuke Abe Spintronics Research Center, Keio University

DNP in Quantum Computing Eisuke Abe Spintronics Research Center, Keio University DNP in Quantum Computing Eisuke Abe Spintronics Research Center, Keio University 207.08.25 Future of Hyper-Polarized Nuclear Spins @IPR, Osaka DNP in quantum computing Molecule Pseudo-pure state Algorithmic

More information

T 1, T 2, NOE (reminder)

T 1, T 2, NOE (reminder) T 1, T 2, NOE (reminder) T 1 is the time constant for longitudinal relaxation - the process of re-establishing the Boltzmann distribution of the energy level populations of the system following perturbation

More information

The Basics of Magnetic Resonance Imaging

The Basics of Magnetic Resonance Imaging The Basics of Magnetic Resonance Imaging Nathalie JUST, PhD nathalie.just@epfl.ch CIBM-AIT, EPFL Course 2013-2014-Chemistry 1 Course 2013-2014-Chemistry 2 MRI: Many different contrasts Proton density T1

More information

arxiv:quant-ph/ v2 28 Aug 2006

arxiv:quant-ph/ v2 28 Aug 2006 Numerical simulation of Quantum Teleportation in a chain of three nuclear spins system taking into account second neighbor iteration G.V. López and L. Lara Departamento de Física, Universidad de Guadalajara

More information

We have seen that the total magnetic moment or magnetization, M, of a sample of nuclear spins is the sum of the nuclear moments and is given by:

We have seen that the total magnetic moment or magnetization, M, of a sample of nuclear spins is the sum of the nuclear moments and is given by: Bloch Equations We have seen that the total magnetic moment or magnetization, M, of a sample of nuclear spins is the sum of the nuclear moments and is given by: M = [] µ i i In terms of the total spin

More information

3 Chemical exchange and the McConnell Equations

3 Chemical exchange and the McConnell Equations 3 Chemical exchange and the McConnell Equations NMR is a technique which is well suited to study dynamic processes, such as the rates of chemical reactions. The time window which can be investigated in

More information

Spin-Boson Model. A simple Open Quantum System. M. Miller F. Tschirsich. Quantum Mechanics on Macroscopic Scales Theory of Condensed Matter July 2012

Spin-Boson Model. A simple Open Quantum System. M. Miller F. Tschirsich. Quantum Mechanics on Macroscopic Scales Theory of Condensed Matter July 2012 Spin-Boson Model A simple Open Quantum System M. Miller F. Tschirsich Quantum Mechanics on Macroscopic Scales Theory of Condensed Matter July 2012 Outline 1 Bloch-Equations 2 Classical Dissipations 3 Spin-Boson

More information

An introduction to Solid State NMR and its Interactions

An introduction to Solid State NMR and its Interactions An introduction to Solid State NMR and its Interactions From tensor to NMR spectra CECAM Tutorial September 9 Calculation of Solid-State NMR Parameters Using the GIPAW Method Thibault Charpentier - CEA

More information

NMR of CeCoIn5. AJ LaPanta 8/15/2016

NMR of CeCoIn5. AJ LaPanta 8/15/2016 NMR of CeCoIn5 AJ LaPanta 8/15/2016 In Co-NMR measurements on CeCoIn5, we see an increasing peak width below 50K. We interpret this as the growth of antiferromagnetic regions surrounding Cadmium dopants

More information

Basic principles COPYRIGHTED MATERIAL. Introduction. Introduction 1 Precession and precessional

Basic principles COPYRIGHTED MATERIAL. Introduction. Introduction 1 Precession and precessional 1 Basic principles Introduction 1 Precession and precessional Atomic structure 2 (Larmor) frequency 10 Motion in the atom 2 Precessional phase 13 MR-active nuclei 4 Resonance 13 The hydrogen nucleus 5

More information

Chem 325 NMR Intro. The Electromagnetic Spectrum. Physical properties, chemical properties, formulas Shedding real light on molecular structure:

Chem 325 NMR Intro. The Electromagnetic Spectrum. Physical properties, chemical properties, formulas Shedding real light on molecular structure: Physical properties, chemical properties, formulas Shedding real light on molecular structure: Wavelength Frequency ν Wavelength λ Frequency ν Velocity c = 2.998 10 8 m s -1 The Electromagnetic Spectrum

More information

Quantum Mechanics FKA081/FIM400 Final Exam 28 October 2015

Quantum Mechanics FKA081/FIM400 Final Exam 28 October 2015 Quantum Mechanics FKA081/FIM400 Final Exam 28 October 2015 Next review time for the exam: December 2nd between 14:00-16:00 in my room. (This info is also available on the course homepage.) Examinator:

More information

2.0 Basic Elements of a Quantum Information Processor. 2.1 Classical information processing The carrier of information

2.0 Basic Elements of a Quantum Information Processor. 2.1 Classical information processing The carrier of information QSIT09.L03 Page 1 2.0 Basic Elements of a Quantum Information Processor 2.1 Classical information processing 2.1.1 The carrier of information - binary representation of information as bits (Binary digits).

More information

The quantum state tomography on an NMR system

The quantum state tomography on an NMR system Physics Letters A 305 (2002 349 353 www.elsevier.com/locate/pla The quantum state tomography on an NMR system Jae-Seung Lee Department of Physics, Korea Advanced Institute of Science and Technology, 373-1

More information

Introduction to MRI. Spin & Magnetic Moments. Relaxation (T1, T2) Spin Echoes. 2DFT Imaging. K-space & Spatial Resolution.

Introduction to MRI. Spin & Magnetic Moments. Relaxation (T1, T2) Spin Echoes. 2DFT Imaging. K-space & Spatial Resolution. Introduction to MRI Spin & Magnetic Moments Relaxation (T1, T2) Spin Echoes 2DFT Imaging Selective excitation, phase & frequency encoding K-space & Spatial Resolution Contrast (T1, T2) Acknowledgement:

More information

Chapter 7. Nuclear Magnetic Resonance Spectroscopy

Chapter 7. Nuclear Magnetic Resonance Spectroscopy Chapter 7 Nuclear Magnetic Resonance Spectroscopy I. Introduction 1924, W. Pauli proposed that certain atomic nuclei have spin and magnetic moment and exposure to magnetic field would lead to energy level

More information

Physical Background Of Nuclear Magnetic Resonance Spectroscopy

Physical Background Of Nuclear Magnetic Resonance Spectroscopy Physical Background Of Nuclear Magnetic Resonance Spectroscopy Michael McClellan Spring 2009 Department of Physics and Physical Oceanography University of North Carolina Wilmington What is Spectroscopy?

More information

Relaxation. Ravinder Reddy

Relaxation. Ravinder Reddy Relaxation Ravinder Reddy Relaxation What is nuclear spin relaxation? What causes it? Effect on spectral line width Field dependence Mechanisms Thermal equilibrium ~10-6 spins leads to NMR signal! T1 Spin-lattice

More information

Introduction to NMR! Ravinder Reddy!

Introduction to NMR! Ravinder Reddy! Introduction to NMR! Ravinder Reddy! Brief History of NMR! First detection of NMR! MSNMR! FT NMR! 2D NMR! 2D-NMR and protein structure! Development of MRI! Outline! Concept of SPIN! Spin angular momentum!

More information

The Theory of Nuclear Magnetic Resonance Behind Magnetic Resonance Imaging. Catherine Wasko Physics 304 Physics of the Human Body May 3, 2005

The Theory of Nuclear Magnetic Resonance Behind Magnetic Resonance Imaging. Catherine Wasko Physics 304 Physics of the Human Body May 3, 2005 The Theory of Nuclear Magnetic Resonance Behind Magnetic Resonance Imaging Catherine Wasko Physics 304 Physics of the Human Body May 3, 2005 Magnetic resonance imaging (MRI) is a tool utilized in the medical

More information

PARAMAGNETIC MATERIALS AND PRACTICAL ALGORITHMIC COOLING FOR NMR QUANTUM COMPUTING

PARAMAGNETIC MATERIALS AND PRACTICAL ALGORITHMIC COOLING FOR NMR QUANTUM COMPUTING st Reading International Journal of Quantum Information Vol., No. (2) c World Scientific Publishing Company PARAMAGNETIC MATERIALS AND PRACTICAL ALGORITHMIC COOLING FOR NMR QUANTUM COMPUTING JOSÉ M. FERNANDEZ

More information

e 2m p c I, (22.1) = g N β p I(I +1), (22.2) = erg/gauss. (22.3)

e 2m p c I, (22.1) = g N β p I(I +1), (22.2) = erg/gauss. (22.3) Chemistry 26 Molecular Spectra & Molecular Structure Week # 7 Nuclear Magnetic Resonance Spectroscopy Along with infrared spectroscopy, nuclear magnetic resonance (NMR) is the most important method available

More information

Principles of Magnetic Resonance Imaging

Principles of Magnetic Resonance Imaging Principles of Magnetic Resonance Imaging Hi Klaus Scheffler, PhD Radiological Physics University of 1 Biomedical Magnetic Resonance: 1 Introduction Magnetic Resonance Imaging Contents: Hi 1 Introduction

More information

VIII. NUCLEAR MAGNETIC RESONANCE (NMR) SPECTROSCOPY

VIII. NUCLEAR MAGNETIC RESONANCE (NMR) SPECTROSCOPY 1 VIII. NUCLEAR MAGNETIC RESONANCE (NMR) SPECTROSCOPY Molecules are extremely small entities; thus, their direct detection and direct investigation is still almost impossible. For the detection and detailed

More information

Quantum Computing with Para-hydrogen

Quantum Computing with Para-hydrogen Quantum Computing with Para-hydrogen Muhammad Sabieh Anwar sabieh@lums.edu.pk International Conference on Quantum Information, Institute of Physics, Bhubaneswar, March 12, 28 Joint work with: J.A. Jones

More information

Superoperators for NMR Quantum Information Processing. Osama Usman June 15, 2012

Superoperators for NMR Quantum Information Processing. Osama Usman June 15, 2012 Superoperators for NMR Quantum Information Processing Osama Usman June 15, 2012 Outline 1 Prerequisites 2 Relaxation and spin Echo 3 Spherical Tensor Operators 4 Superoperators 5 My research work 6 References.

More information

10.3 NMR Fundamentals

10.3 NMR Fundamentals 10.3 NMR Fundamentals nuclear spin calculations and examples NMR properties of selected nuclei the nuclear magnetic moment and precession around a magnetic field the spin quantum number and the NMR transition

More information

Control of quantum two-level systems

Control of quantum two-level systems Control of quantum two-level sstems R. Gross, A. Mar & F. Deppe, Walther-Meißner-Institut (00-03) 0.3 Control of quantum two-level sstems.. General concept AS-Chap. 0 - How to control a qubit? Does the

More information

NANOSCALE SCIENCE & TECHNOLOGY

NANOSCALE SCIENCE & TECHNOLOGY . NANOSCALE SCIENCE & TECHNOLOGY V Two-Level Quantum Systems (Qubits) Lecture notes 5 5. Qubit description Quantum bit (qubit) is an elementary unit of a quantum computer. Similar to classical computers,

More information

NMR Dynamics and Relaxation

NMR Dynamics and Relaxation NMR Dynamics and Relaxation Günter Hempel MLU Halle, Institut für Physik, FG Festkörper-NMR 1 Introduction: Relaxation Two basic magnetic relaxation processes: Longitudinal relaxation: T 1 Relaxation Return

More information

Physical fundamentals of magnetic resonance imaging

Physical fundamentals of magnetic resonance imaging Physical fundamentals of magnetic resonance imaging Stepan Sereda University of Bonn 1 / 26 Why? Figure 1 : Full body MRI scan (Source: [4]) 2 / 26 Overview Spin angular momentum Rotating frame and interaction

More information

Quantum Optics and Quantum Informatics FKA173

Quantum Optics and Quantum Informatics FKA173 Quantum Optics and Quantum Informatics FKA173 Date and time: Tuesday, 7 October 015, 08:30-1:30. Examiners: Jonas Bylander (070-53 44 39) and Thilo Bauch (0733-66 13 79). Visits around 09:30 and 11:30.

More information

INTRIQ. Coherent Manipulation of single nuclear spin

INTRIQ. Coherent Manipulation of single nuclear spin INTRIQ Coherent Manipulation of single nuclear spin Clément Godfrin Eva Dupont Ferrier Michel Pioro-Ladrière K. Ferhat (Inst. Néel) R. Ballou (Inst. Néel) M. Ruben (KIT) W. Wernsdorfer (KIT) F. Balestro

More information

Lecture 5: Bloch equation and detection of magnetic resonance

Lecture 5: Bloch equation and detection of magnetic resonance Lecture 5: Bloch equation and detection of magnetic resonance Lecture aims to eplain:. Bloch equations, transverse spin relaation time and *. Detection of agnetic Resonance: Free Induction Deca Bloch equations

More information

Experimental Methods for Quantum Control in Nuclear Spin Systems

Experimental Methods for Quantum Control in Nuclear Spin Systems Tim Havel and David Cory Dept. of Nuclear Engineering Massachusetts Institute of Technology Experimental Methods for Quantum Control in Nuclear Spin Systems Together with: Jonathan Baugh, Hyang Joon Cho,

More information

Short Course in Quantum Information Lecture 8 Physical Implementations

Short Course in Quantum Information Lecture 8 Physical Implementations Short Course in Quantum Information Lecture 8 Physical Implementations Course Info All materials downloadable @ website http://info.phys.unm.edu/~deutschgroup/deutschclasses.html Syllabus Lecture : Intro

More information

Biophysical Chemistry: NMR Spectroscopy

Biophysical Chemistry: NMR Spectroscopy Nuclear Magnetism Vrije Universiteit Brussel 21st October 2011 Outline 1 Overview and Context 2 3 Outline 1 Overview and Context 2 3 Context Proteins (and other biological macromolecules) Functional characterisation

More information

The Physical Basis of Nuclear Magnetic Resonance Part I ESMRMB. Jürgen R. Reichenbach

The Physical Basis of Nuclear Magnetic Resonance Part I ESMRMB. Jürgen R. Reichenbach The Physical Basis of Nuclear agnetic Resonance Part I Jürgen R. Reichenbach odule 1 October 17, 216 Outline of odule Introduction Spin and magnetic moment Spin precession, Larmor frequency agnetic properties

More information

arxiv:quant-ph/ v1 1 Oct 1999

arxiv:quant-ph/ v1 1 Oct 1999 NMR quantum computation with indirectly coupled gates arxiv:quant-ph/9910006v1 1 Oct 1999 David Collins, 1 K. W. Kim, 1, W. C. Holton, 1 H. Sierzputowska-Gracz, 2 and E. O. Stejskal 3 1 Department of Electrical

More information

Fundamental MRI Principles Module Two

Fundamental MRI Principles Module Two Fundamental MRI Principles Module Two 1 Nuclear Magnetic Resonance There are three main subatomic particles: protons neutrons electrons positively charged no significant charge negatively charged Protons

More information

Computational speed-up with a single qudit

Computational speed-up with a single qudit Computational speed-up with a single qudit Z. Gedik, 1 I. A. Silva, 2 B. Çakmak, 1 G. Karpat, 3 E. L. G. Vidoto, 2 D. O. Soares-Pinto, 2 E. R. deazevedo, 2 and F. F. Fanchini 3 1 Faculty of Engineering

More information

ν 1H γ 1H ν 13C = γ 1H 2π B 0 and ν 13C = γ 13C 2π B 0,therefore = π γ 13C =150.9 MHz = MHz 500 MHz ν 1H, 11.

ν 1H γ 1H ν 13C = γ 1H 2π B 0 and ν 13C = γ 13C 2π B 0,therefore = π γ 13C =150.9 MHz = MHz 500 MHz ν 1H, 11. Problem Set #1, CEM/BCMB 4190/6190/8189 1). Which of the following statements are rue, False, or Possibly rue, for the hypothetical element X? he ground state spin is I0 for 5 4 b. he ground state spin

More information

NUCLEAR MAGNETIC RESONANCE QUANTUM COMPUTATION

NUCLEAR MAGNETIC RESONANCE QUANTUM COMPUTATION COURSE 1 NUCLEAR MAGNETIC RESONANCE QUANTUM COMPUTATION J. A. JONES Centre for Quantum Computation, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK PHOTO: height 7.5cm, width 11cm Contents 1 Nuclear

More information

Quantum computation and quantum information

Quantum computation and quantum information Quantum computation and quantum information Chapter 7 - Physical Realizations - Part 2 First: sign up for the lab! do hand-ins and project! Ch. 7 Physical Realizations Deviate from the book 2 lectures,

More information

10.5 Circuit quantum electrodynamics

10.5 Circuit quantum electrodynamics AS-Chap. 10-1 10.5 Circuit quantum electrodynamics AS-Chap. 10-2 Analogy to quantum optics Superconducting quantum circuits (SQC) Nonlinear circuits Qubits, multilevel systems Linear circuits Waveguides,

More information

Spin. Nuclear Spin Rules

Spin. Nuclear Spin Rules Spin Bioengineering 280A Principles of Biomedical Imaging Fall Quarter 2012 MRI Lecture 1 Intrinsic angular momentum of elementary particles -- electrons, protons, neutrons. Spin is quantized. Key concept

More information

Experimental Realization of Brüschweiler s exponentially fast search algorithm in a 3-qubit homo-nuclear system

Experimental Realization of Brüschweiler s exponentially fast search algorithm in a 3-qubit homo-nuclear system Experimental Realization of Brüschweiler s exponentially fast search algorithm in a 3-qubit homo-nuclear system Li Xiao 1,2,G.L.Long 1,2,3,4, Hai-Yang Yan 1,2, Yang Sun 5,1,2 1 Department of Physics, Tsinghua

More information

K-space. Spin-Warp Pulse Sequence. At each point in time, the received signal is the Fourier transform of the object s(t) = M( k x

K-space. Spin-Warp Pulse Sequence. At each point in time, the received signal is the Fourier transform of the object s(t) = M( k x Bioengineering 280A Principles of Biomedical Imaging Fall Quarter 2015 MRI Lecture 4 k (t) = γ 2π k y (t) = γ 2π K-space At each point in time, the received signal is the Fourier transform of the object

More information