Introduction to Quantum Dynamics and Control

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1 EE 290O. Advanced Topics in Control: Introduction to Quantum Dynamics and Control Instructor: Alireza Shabani Contact : shabani@berkeley.edu Office: Gilman, Room 19 Cory 278 Office Hours: Wednesdays 3-4 pm All announcements will be posted on bspace. 1

2 Quantum Technology: Physical theories, a historical chart Birth of Quantum Mechanics Quantum Mechanics versus classical mechanics First Quantum Revolution Second Quantum Revolution Control Theory: Classical Classical Control Theory Modern Classical Control Theory Quantum Control Theory 2

3 Quantum Technology: Physical theories, a historical chart Birth of Quantum Mechanics Quantum Mechanics versus classical mechanics First Quantum Revolution Second Quantum Revolution Control Theory: Classical Classical Control Theory Modern Classical Control Theory Quantum Control Theory 3

4 Physical theories, a historical/intuitive chart Object Speed slower faster Object Size smaller larger Newtonian Mechanics Quantum Mechanics Electromagnetic Relativity Theory Quantum Field Theory,... 4

5

6 Quantum Technology: Physical theories, a historical chart Birth of Quantum Mechanics Quantum Mechanics versus classical mechanics First Quantum Revolution Second Quantum Revolution Control Theory: Classical Classical Control Theory Modern Classical Control Theory Quantum Control Theory 6

7 Birth of Quantum Mechanics Classical physics (existing theories of the 19th century) failed to explain a number of experiments: Black-body radiation and ultra-violate catastrophe (Gustav Kirchhoff, 1877): Thermodynamics predict infinite radiation power. Planck solved the problem in 1901 by introducing the concept of discrete energy elements: energy quanta. Non-classical feature: Light behaves like a particle rather than a wave. 7

8 Birth of Quantum Mechanics Photoelectric Effect (Heinrich Hertz 1887): Classical Maxwell wave theory of light: The more intense the incident light the greater the energy with which the electrons should be ejected from the metal. Non-classical feature: Light behaves like a particle rather than a wave. 8

9 Birth of Quantum Mechanics Electron Diffraction (Thomson and Davisson-Germer 1927) Wave diffraction phenomenon Non-classical feature: Electrons behave like a wave rather than a particle. 9

10 Quantum Technology: Physical theories, a historical chart Birth of Quantum Mechanics Quantum Mechanics versus classical mechanics First Quantum Revolution Second Quantum Revolution Control Theory: Classical Classical Control Theory Modern Classical Control Theory Quantum Control Theory 10

11 Quantum Mechanics Quantum mechanics provides a mathematical description of the dual particle-like and wave-like nature behavior and interactions of matter and energy. In principle quantum mechanics applies to any object of any size. However the quantum effects (wave-particle behavior) is most noticeable for very small objects. Largest manmade quantum object: A piezoelectric resonator cooled down to 0.1 K, A. D. O Connell et al., Nature 464, 697 (2010). 11

12 Relationship between classical mechanics and quantum mechanics All physics you learned in high school and college as mechanics and electromagnetic laws are just approximations to quantum mechanics. Classical mechanics is just an approximation to quantum mechanics. It provides good description of phenomena if the object under studied is not well isolated from its environment. 1 nm 1 μm 1 mm 1 m Quantum Quantum- Classical Classical 12

13 Quantum Technology: Physical theories, a historical chart Birth of Quantum Mechanics Quantum Mechanics versus classical mechanics First Quantum Revolution Second Quantum Revolution Control Theory: Classical Classical Control Theory Modern Classical Control Theory Quantum Control Theory 13

14 First Quantum Revolution 20th Century: Formulation of quantum mechanics and technological revolution. Wave nature of electrons Particle nature of light Atoms and molecules structure Photovoltaic LASER Semiconductors physics Solar cells, CD, photocopy machines, surgeries... Integrated circuits 14

15 Quantum Technology: Physical theories, a historical chart Birth of Quantum Mechanics Quantum Mechanics versus classical mechanics First Quantum Revolution Second Quantum Revolution Control Theory: Classical Classical Control Theory Modern Classical Control Theory Quantum Control Theory

16 Second Quantum Revolution In the 20th century quantum mechanics revealed the secrets of the nature at atomic scales. Then we used this knowledge do design some classical machines either novel or with significantly higher efficiency in compare to their old ancestors. In the 21st century, we are going to make quantum machines, complex systems governed by the laws of quantum physics. - Miniaturization is the dominant trend in modern technology. The electronic, optical and mechanical devices are reaching to the length scales that need design based on quantum principles. - The principles of quantum mechanics offer the promise of exceptional performance over what classical physics has offered to us. J.P.Dowling and G.J.Milburn, Phil. Trans. R. Soc. A 361, 3655 (2003). G.J.Milburn, Schrödinger's machines:the quantum technology reshaping everyday life, W.H. Freeman & Co., Jun 30, (1997). 16

17 Quantum Technologies Quantum photonics Quantum optics Quantum sensor Quantum lithography and microscopy Quantum teleportation Spintronics Coherent quantum electronics Molecular coherent quantum electronics Solid-state quantum computers Coherent matter technology Atom optics Atom lasers Quantum electromechanical systems Single-spin magnetic resonance force microscopy Quantum information technology: Quantum algorithms Quantum cryptography Quantum coding Quantum circuit design Quantum Computer 17

18 Transistors reach quantum regime The evolution of transistor gate length (minimum feature size) and the density of transistors in microprocessors over time. 2 Gate MOSFET AIST, Japan M. Ferain etc, Nature 479, 310 (2011). 18

19 Few-electron single-crystal silicon quantum dot transistor Quantum tunneling M. Fuechsle etc, Nature Nano. 5, 502 (2010). 19

20 Quantum Technology Tools Quantum Metrology: High precision measurement of quantum systems. Quantum Control: Classical control theory is complete to guide a quantum machine. Quantum Communication: Quantum-based protocols more powerful than their classical counterparts in order to inter-connect components of a quantum complex. Quantum Computation: Quantum mechanics enables exponentially more efficient algorithms than can be implemented on a classical computer. Building a quantum computer is the ultimate goal of quantum technology. 20

21 Quantum Technology: Physical theories, a historical chart Birth of Quantum Mechanics Quantum Mechanics versus classical mechanics First Quantum Revolution Second Quantum Revolution Control Theory: Classical Classical Control Theory Modern Classical Control Theory Quantum Control Theory

22 Control Theory of Quantum Systems Design of a machine becomes complete when it is accompanied with the knowledge of how to control it for the purpose it is built for. 22

23 Everyday Feedback Control system Cold Water Hot Water: 23

24 Control Theory Open loop control: Input Controller (Actuator) Input System (Plant) Output Closed-loop (feedback) control: Input- Reference Controller (Actuator) Input System (Plant) Output Measurement (Monitor) 24

25 Control Theory Input- Reference Controller (Actuator) Input System (Plant) Output Measurement (Monitor) 25

26 Quantum Technology: Physical theories, a historical chart Birth of Quantum Mechanics Quantum Mechanics versus classical mechanics First Quantum Revolution Second Quantum Revolution Control Theory: Classical Classical Control Theory Modern Classical Control Theory Quantum Control Theory

27 Classical Classical Control Theory Classical classical control theory is based on frequency domain analysis of the system and controller. A linear system P is controlled by a linear controller C while being monitored by the a linear sensor F. A laplace domain characterization and analysis of all components: 27

28 Modern Classical Control Theory Modern classical control theory utilizes the time domain state-space representation. The state of the system P is parameterized by a number of variables X = {x i } t.... X = f (X, u) t Y t = g (X, u) 28

29 Quantum Control Theory Classical approach: Open loop (coherent control) Measurement-based feedback control (real-time) Quantum approach: Coherent feedback control (not-covered in this course) 29

30 Open-Loop Control Quantum control theory is base on the modern classical theory. Open loop quantum problems are among the bilinear control problems: X t = AX + uf X Population control: dp dt =(r birth r death )P 30

31 Feedback Control Closed loop quantum control is totally different from its classical counterpart for two reasons: 1- Quantum states cannot be copied. 2- In contrast to classical realm, a quantum system cannot measured without destroying the system state. A feedback quantum control problems turns into a stochastic control problem. X t = AX + uf X + G(X)ξ Better control necessitates deeper understanding of natural laws, so quantum control can help us to better understand quantum physics. 31

32 Next Session: Linear Algebra for Quantum Mechanics or Linear algebra with Dirac Notations 32

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