Central Library

Normal view MARC view ISBD view

Quantum optics and quantum computation : an introduction / Dipankar Bhattacharyya and Jyotirmoy Guha.

By: Bhattacharyya, Dipankar (Professor of physics) [author.].
Contributor(s): Guha, Jyotirmoy [author.] | Institute of Physics (Great Britain) [publisher.].
Material type: materialTypeLabelBookSeries: IOP (Series)Release 22: ; IOP series in advances in optics, photonics and optoelectronics: ; IOP ebooks2022 collection: Publisher: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2022]Description: 1 online resource (various pagings) : illustrations.Content type: text Media type: electronic Carrier type: online resourceISBN: 9780750327152; 9780750327145.Subject(s): Quantum optics | Quantum computing | Optical physics | Optics and photonicsAdditional physical formats: Print version:: No titleDDC classification: 535.2 Online resources: Click here to access online Also available in print.
Contents:
1. Bra ket algebra of Dirac -- 1.1. The bra and ket notation of Dirac -- 1.2. Hermitian conjugation -- 1.3. Definition of inner product (also called overlap) -- 1.4. Definition of outer product -- 1.5. Eigenvalue equation -- 1.6. Linear vector space -- 1.7. Linear independence -- 1.8. Linear dependence -- 1.9. Span (expansion of an arbitrary ket)/expansion postulate -- 1.10. Ket space, bra space, dual space -- 1.11. Physical significance of inner product <m|n> -- 1.12. Norm and the process of normalization -- 1.13. Ortho-normalization (orthogonal + normalized) -- 1.14. Orthonormal basis (orthogonal + normalized + linearly independent + span) -- 1.15. Expansion postulate -- 1.16. Projection operator -- 1.17. Normal matrix -- 1.18. Spectral theorem -- 1.19. Elements of a matrix in Bra Ket notation -- 1.20. Hermitian matrix operator -- 1.21. Unitary matrix -- 1.22. Diagonalization of a matrix--change of basis -- 1.23. Triangle laws (inequality and equality) -- 1.24. Cauchy-Schwarz laws (inequality and equality) -- 1.25. Commutator bracket -- 1.26. Trace -- 1.27. Pauli spin matrices -- 1.28. Orthogonal matrix operator -- 1.29. Standard method of ortho-normalization Graham-Schmidt ortho-normalization procedure -- 1.30. Definition of average value -- 1.31. Some definitions -- 1.32. Kroneckar product (symbol [Kronecker product]) or direct product or tensor product -- 1.33. Further reading -- 1.34. Problems
2. Postulates of quantum mechanics -- 2.1. First postulate : observables are replaced by operators -- 2.2. Second postulate : state vector and wave function -- 2.3. Third postulate : process of measurement -- 2.4. Fourth postulate : Time evolution of a state -- 2.5. Solution of the Schr�odinger equation -- 2.6. Unitary operator keeps the length of state vector constant -- 2.7. Heisenberg's uncertainty principle or principle of indeterminism -- 2.8. Further reading -- 2.9. Problems
3. Introduction to quantum computing -- 3.1. Introduction -- 3.2. Some basic ideas about classical and quantum computing -- 3.3. Definition of certain terms relating to quantum computing -- 3.4. Journey towards quantum computing -- 3.5. Need for quantum computers -- 3.6. Landauer's principle -- 3.7. Quantum computing -- 3.8. Bits 0 and 1 -- 3.9. A bit of Boolean algebra -- 3.10. Gate -- 3.11. Computational complexity -- 3.12. Further reading -- 3.13. Problems
4. Quantum bits -- 4.1. Qubits and comparison with classical bits -- 4.2. Qubit model applied to the Stern-Gerlach experiment -- 4.3. Qubit model applied to polarized photon (computational and Hadamard basis introduced) -- 4.4. Bloch sphere representation of a qubit -- 4.5. Multiple qubits -- 4.6. Explicit representation of the basis states -- 4.7. Bell state or EPR pair (or state) -- 4.8. Global phase and relative phase -- 4.9. Measurement depends on choice of basis -- 4.10. Further reading -- 4.11. Problems
5. Quantum circuits -- 5.1. Quantum gate and quantum circuit -- 5.2. Single-qubit gates -- 5.3. Quantum NOT gate or Pauli �X gate (�[sigma]x) -- 5.4. �Z gate or Pauli �Z gate (�[sigma]z) -- 5.5. Pauli �Y gate or �[sigma]y -- 5.6. Phase shift gates (�P gate, �S gate, �T gate) -- 5.7. Hadamard gate �H, Hadamard basis |+>, | - > -- 5.8. Unitary matrix as length preserving matrix -- 5.9. Rotation gates �RX([theta]), �RY([theta]), �RZ([theta]) -- 5.10. Multi-qubit gates -- 5.11. Controlled-NOT gate or CNOT gate -- 5.12. Preparing Bell states -- 5.13. Swap gate -- 5.14. Controlled U gates -- 5.15. Toffoli quantum gate or CCNOT gate (controlled controlled NOT gate) -- 5.16. Controlled SWAP gate or CS gate or Fredkin gate -- 5.17. Deutsch gate -- 5.18. Implementing classical computation by quantum gates -- 5.19. Plan of a quantum circuit -- 5.20. Quantum half adder circuit -- 5.21. Quantum full adder circuit -- 5.22. Oracle (black box) in quantum computer -- 5.23. Hadamard transformation on each of n qubits leads to a linear superposition of 2n states -- 5.24. Process of measurement -- 5.25. Quantum coin flipping -- 5.26. Further reading -- 5.27. Problems
6. Teleportation and super dense coding -- 6.1. Quantum no-cloning theorem -- 6.2. Teleportation -- 6.3. Super dense coding (or dense coding) (of Bennett and Wiesner) -- 6.4. Further reading -- 6.5. Problems
7. Pure and mixed state -- 7.1. Pure state -- 7.2. Mixed state -- 7.3. Density operator (introduced by Von Neumann) -- 7.4. Density operator for a pure state -- 7.5. Average -- 7.6. Density operator of a mixed state (or an ensemble) -- 7.7. Quantum mechanics of an ensemble -- 7.8. Density matrix for a two-level spin system (Stern-Gerlach experiment) -- 7.9. Single-qubit density operator in terms of Pauli matrices -- 7.10. Some illustration of density matrix for pure and mixed states -- 7.11. Partially mixed, completely mixed, maximally mixed states -- 7.12. Time evolution of density matrix : Liouville-Von Neumann equation -- 7.13. Partial trace and the reduced density matrix -- 7.14. Measurement theory of mixed states -- 7.15. Positive operator valued measure (POVM) -- 7.16. Further reading -- 7.17. Problems
8. Quantum algorithms -- 8.1. Quantum parallelism -- 8.2. Reversibility -- 8.3. XOR is addition modulo 2 -- 8.4. Quantum arithmetic and function evaluations -- 8.5. Deutsch algorithm -- 8.6. Deutsch-Jozsa (DJ) algorithm -- 8.7. Bernstein-Vazirani algorithm -- 8.8. Simon algorithm -- 8.9. Grover's search algorithm -- 8.10. Discrete integral transform -- 8.11. Quantum Fourier transform -- 8.12. Finding period using QFT -- 8.13. Implementation of QFT -- 8.14. Some definitions and GCD evaluation -- 8.15. Inverse modulo -- 8.16. Shor's algorithm -- 8.17. Further reading -- 8.18. Problems
9. Quantum error correction -- 9.1. Error in classical computing -- 9.2. Errors in quantum computing/communication -- 9.3. The phase flip -- 9.4. Qubit transmission from Alice to Bob -- 9.5. Converting a phase flip error to qubit flip error -- 9.6. Shor's nine-qubit error code -- 9.7. Further reading -- 9.8. Problems
10. Quantum information -- 10.1. Classical information theory -- 10.2. Decision tree -- 10.3. Measure of information : Shannon's entropy -- 10.4. Statistical entropy and Shannon's information entropy -- 10.5. Communication system -- 10.6. Shannon's noiseless coding theorem -- 10.7. Prefix code, binary tree -- 10.8. Quantum information theory, Von Neumann entropy -- 10.9. Further reading -- 10.10. Problems
11. EPR paradox and Bell inequalities -- 11.1. EPR paradox -- 11.2. David Bohm's version of EPR paradox (1951) -- 11.3. Bell's (Gedanken) experiment : EPR and Bell's inequalities -- 11.4. Clauser, Horne, Shimony and Holt's inequality -- 11.5. Further reading -- 11.6. Problems
12. Cryptography--the art of coding -- 12.1. A bit of history of cryptography -- 12.2. Essential elements of cryptography -- 12.3. One-time pad -- 12.4. RSA cryptosystem -- 12.5. Fermat's little theorem -- 12.6. Euler theorem -- 12.7. Chinese remainder theorem -- 12.8. RSA algorithm -- 12.9. Quantum cryptography -- 12.10. Protocol of quantum cryptography -- 12.11. Further reading -- 12.12. Problems
13. Experimental aspects of quantum computing -- 13.1. Basic principle of nuclear magnetic resonance quantum computing -- 13.2. Further reading
14. Light-matter interactions -- 14.1. Interaction Hamiltonian -- 14.2. Rabi oscillations -- 14.3. Weak field case -- 14.4. Strong field case : Rabi oscillations -- 14.5. Damping phenomena -- 14.6. The density matrix -- 14.7. Pure and mixed states -- 14.8. Equation of motion of the density operator -- 14.9. Inclusion of decay phenomena -- 14.10. Vector model of density matrix equations of motion -- 14.11. Power broadening and saturation of the spectrum -- 14.12. Spectral line broadening mechanism -- 14.13. Natural broadening -- 14.14. Collision or pressure broadening -- 14.15. Inhomogeneous broadening or Doppler broadening -- 14.16. Further reading -- 14.17. Problems
15. Laser spectroscopy and atomic coherence -- 15.1. Moving two-level atoms in a travelling wave field -- 15.2. Moving atoms in a standing wave -- 15.3. Lamb dip -- 15.4. Crossover resonances -- 15.5. Atomic coherence phenomena -- 15.6. EIT Hamiltonian of the system -- 15.7. Dressed states picture -- 15.8. Coherent population trapping -- 15.9. Electromagnetically induced absorption (EIA) -- 15.10. Further reading -- 15.11. Problems
16. Quantum theory of radiation -- 16.1. Maxwell's equations -- 16.2. The electromagnetic field in a cavity -- 16.3. Quantization of a single mode -- 16.4. Multimode radiation field -- 16.5. Coherent states -- 16.6. Squeezed states of light -- 16.7. Further reading -- 16.8. Problems
17. Interaction of an atom with a quantized field -- 17.1. Interaction Hamiltonian in terms of Pauli operators -- 17.2. Absorption and emission phenomena -- 17.3. Dressed states -- 17.4. Jaynes-Cummings model -- 17.5. Theory of spontaneous emission : Wigner-Weisskopf model -- 17.6. Further reading -- 17.7. Problems
18. Photon statistics -- 18.1. Young's double-slit experiment -- 18.2. Hanbury Brown-Twiss experiment -- 18.3. Photon counter -- 18.4. Outcome of the photon counter -- 18.5. Photon statistics of a perfectly coherent light -- 18.6. Photon statistics of a thermal light -- 18.7. Classification of light by second-order correlation function and photon statistics. -- 18.8. Photon bunching and anti-bunching -- 18.9. Further reading -- 18.10. Problems.
Abstract: This book studies the application of quantum mechanics to some of the most current and notable concepts in the area, such as quantum optics, cryptography, teleportation, and computing. Written as a complete and comprehensive course text, this book works through mathematically rigorous material using a clear and practical approach that facilitates student engagement, and highlights the fundamental principles of quantum physics used to develop quantum computing.
    average rating: 0.0 (0 votes)
No physical items for this record

"Version: 202201"--Title page verso.

Includes bibliographical references.

1. Bra ket algebra of Dirac -- 1.1. The bra and ket notation of Dirac -- 1.2. Hermitian conjugation -- 1.3. Definition of inner product (also called overlap) -- 1.4. Definition of outer product -- 1.5. Eigenvalue equation -- 1.6. Linear vector space -- 1.7. Linear independence -- 1.8. Linear dependence -- 1.9. Span (expansion of an arbitrary ket)/expansion postulate -- 1.10. Ket space, bra space, dual space -- 1.11. Physical significance of inner product <m|n> -- 1.12. Norm and the process of normalization -- 1.13. Ortho-normalization (orthogonal + normalized) -- 1.14. Orthonormal basis (orthogonal + normalized + linearly independent + span) -- 1.15. Expansion postulate -- 1.16. Projection operator -- 1.17. Normal matrix -- 1.18. Spectral theorem -- 1.19. Elements of a matrix in Bra Ket notation -- 1.20. Hermitian matrix operator -- 1.21. Unitary matrix -- 1.22. Diagonalization of a matrix--change of basis -- 1.23. Triangle laws (inequality and equality) -- 1.24. Cauchy-Schwarz laws (inequality and equality) -- 1.25. Commutator bracket -- 1.26. Trace -- 1.27. Pauli spin matrices -- 1.28. Orthogonal matrix operator -- 1.29. Standard method of ortho-normalization Graham-Schmidt ortho-normalization procedure -- 1.30. Definition of average value -- 1.31. Some definitions -- 1.32. Kroneckar product (symbol [Kronecker product]) or direct product or tensor product -- 1.33. Further reading -- 1.34. Problems

2. Postulates of quantum mechanics -- 2.1. First postulate : observables are replaced by operators -- 2.2. Second postulate : state vector and wave function -- 2.3. Third postulate : process of measurement -- 2.4. Fourth postulate : Time evolution of a state -- 2.5. Solution of the Schr�odinger equation -- 2.6. Unitary operator keeps the length of state vector constant -- 2.7. Heisenberg's uncertainty principle or principle of indeterminism -- 2.8. Further reading -- 2.9. Problems

3. Introduction to quantum computing -- 3.1. Introduction -- 3.2. Some basic ideas about classical and quantum computing -- 3.3. Definition of certain terms relating to quantum computing -- 3.4. Journey towards quantum computing -- 3.5. Need for quantum computers -- 3.6. Landauer's principle -- 3.7. Quantum computing -- 3.8. Bits 0 and 1 -- 3.9. A bit of Boolean algebra -- 3.10. Gate -- 3.11. Computational complexity -- 3.12. Further reading -- 3.13. Problems

4. Quantum bits -- 4.1. Qubits and comparison with classical bits -- 4.2. Qubit model applied to the Stern-Gerlach experiment -- 4.3. Qubit model applied to polarized photon (computational and Hadamard basis introduced) -- 4.4. Bloch sphere representation of a qubit -- 4.5. Multiple qubits -- 4.6. Explicit representation of the basis states -- 4.7. Bell state or EPR pair (or state) -- 4.8. Global phase and relative phase -- 4.9. Measurement depends on choice of basis -- 4.10. Further reading -- 4.11. Problems

5. Quantum circuits -- 5.1. Quantum gate and quantum circuit -- 5.2. Single-qubit gates -- 5.3. Quantum NOT gate or Pauli �X gate (�[sigma]x) -- 5.4. �Z gate or Pauli �Z gate (�[sigma]z) -- 5.5. Pauli �Y gate or �[sigma]y -- 5.6. Phase shift gates (�P gate, �S gate, �T gate) -- 5.7. Hadamard gate �H, Hadamard basis |+>, | - > -- 5.8. Unitary matrix as length preserving matrix -- 5.9. Rotation gates �RX([theta]), �RY([theta]), �RZ([theta]) -- 5.10. Multi-qubit gates -- 5.11. Controlled-NOT gate or CNOT gate -- 5.12. Preparing Bell states -- 5.13. Swap gate -- 5.14. Controlled U gates -- 5.15. Toffoli quantum gate or CCNOT gate (controlled controlled NOT gate) -- 5.16. Controlled SWAP gate or CS gate or Fredkin gate -- 5.17. Deutsch gate -- 5.18. Implementing classical computation by quantum gates -- 5.19. Plan of a quantum circuit -- 5.20. Quantum half adder circuit -- 5.21. Quantum full adder circuit -- 5.22. Oracle (black box) in quantum computer -- 5.23. Hadamard transformation on each of n qubits leads to a linear superposition of 2n states -- 5.24. Process of measurement -- 5.25. Quantum coin flipping -- 5.26. Further reading -- 5.27. Problems

6. Teleportation and super dense coding -- 6.1. Quantum no-cloning theorem -- 6.2. Teleportation -- 6.3. Super dense coding (or dense coding) (of Bennett and Wiesner) -- 6.4. Further reading -- 6.5. Problems

7. Pure and mixed state -- 7.1. Pure state -- 7.2. Mixed state -- 7.3. Density operator (introduced by Von Neumann) -- 7.4. Density operator for a pure state -- 7.5. Average -- 7.6. Density operator of a mixed state (or an ensemble) -- 7.7. Quantum mechanics of an ensemble -- 7.8. Density matrix for a two-level spin system (Stern-Gerlach experiment) -- 7.9. Single-qubit density operator in terms of Pauli matrices -- 7.10. Some illustration of density matrix for pure and mixed states -- 7.11. Partially mixed, completely mixed, maximally mixed states -- 7.12. Time evolution of density matrix : Liouville-Von Neumann equation -- 7.13. Partial trace and the reduced density matrix -- 7.14. Measurement theory of mixed states -- 7.15. Positive operator valued measure (POVM) -- 7.16. Further reading -- 7.17. Problems

8. Quantum algorithms -- 8.1. Quantum parallelism -- 8.2. Reversibility -- 8.3. XOR is addition modulo 2 -- 8.4. Quantum arithmetic and function evaluations -- 8.5. Deutsch algorithm -- 8.6. Deutsch-Jozsa (DJ) algorithm -- 8.7. Bernstein-Vazirani algorithm -- 8.8. Simon algorithm -- 8.9. Grover's search algorithm -- 8.10. Discrete integral transform -- 8.11. Quantum Fourier transform -- 8.12. Finding period using QFT -- 8.13. Implementation of QFT -- 8.14. Some definitions and GCD evaluation -- 8.15. Inverse modulo -- 8.16. Shor's algorithm -- 8.17. Further reading -- 8.18. Problems

9. Quantum error correction -- 9.1. Error in classical computing -- 9.2. Errors in quantum computing/communication -- 9.3. The phase flip -- 9.4. Qubit transmission from Alice to Bob -- 9.5. Converting a phase flip error to qubit flip error -- 9.6. Shor's nine-qubit error code -- 9.7. Further reading -- 9.8. Problems

10. Quantum information -- 10.1. Classical information theory -- 10.2. Decision tree -- 10.3. Measure of information : Shannon's entropy -- 10.4. Statistical entropy and Shannon's information entropy -- 10.5. Communication system -- 10.6. Shannon's noiseless coding theorem -- 10.7. Prefix code, binary tree -- 10.8. Quantum information theory, Von Neumann entropy -- 10.9. Further reading -- 10.10. Problems

11. EPR paradox and Bell inequalities -- 11.1. EPR paradox -- 11.2. David Bohm's version of EPR paradox (1951) -- 11.3. Bell's (Gedanken) experiment : EPR and Bell's inequalities -- 11.4. Clauser, Horne, Shimony and Holt's inequality -- 11.5. Further reading -- 11.6. Problems

12. Cryptography--the art of coding -- 12.1. A bit of history of cryptography -- 12.2. Essential elements of cryptography -- 12.3. One-time pad -- 12.4. RSA cryptosystem -- 12.5. Fermat's little theorem -- 12.6. Euler theorem -- 12.7. Chinese remainder theorem -- 12.8. RSA algorithm -- 12.9. Quantum cryptography -- 12.10. Protocol of quantum cryptography -- 12.11. Further reading -- 12.12. Problems

13. Experimental aspects of quantum computing -- 13.1. Basic principle of nuclear magnetic resonance quantum computing -- 13.2. Further reading

14. Light-matter interactions -- 14.1. Interaction Hamiltonian -- 14.2. Rabi oscillations -- 14.3. Weak field case -- 14.4. Strong field case : Rabi oscillations -- 14.5. Damping phenomena -- 14.6. The density matrix -- 14.7. Pure and mixed states -- 14.8. Equation of motion of the density operator -- 14.9. Inclusion of decay phenomena -- 14.10. Vector model of density matrix equations of motion -- 14.11. Power broadening and saturation of the spectrum -- 14.12. Spectral line broadening mechanism -- 14.13. Natural broadening -- 14.14. Collision or pressure broadening -- 14.15. Inhomogeneous broadening or Doppler broadening -- 14.16. Further reading -- 14.17. Problems

15. Laser spectroscopy and atomic coherence -- 15.1. Moving two-level atoms in a travelling wave field -- 15.2. Moving atoms in a standing wave -- 15.3. Lamb dip -- 15.4. Crossover resonances -- 15.5. Atomic coherence phenomena -- 15.6. EIT Hamiltonian of the system -- 15.7. Dressed states picture -- 15.8. Coherent population trapping -- 15.9. Electromagnetically induced absorption (EIA) -- 15.10. Further reading -- 15.11. Problems

16. Quantum theory of radiation -- 16.1. Maxwell's equations -- 16.2. The electromagnetic field in a cavity -- 16.3. Quantization of a single mode -- 16.4. Multimode radiation field -- 16.5. Coherent states -- 16.6. Squeezed states of light -- 16.7. Further reading -- 16.8. Problems

17. Interaction of an atom with a quantized field -- 17.1. Interaction Hamiltonian in terms of Pauli operators -- 17.2. Absorption and emission phenomena -- 17.3. Dressed states -- 17.4. Jaynes-Cummings model -- 17.5. Theory of spontaneous emission : Wigner-Weisskopf model -- 17.6. Further reading -- 17.7. Problems

18. Photon statistics -- 18.1. Young's double-slit experiment -- 18.2. Hanbury Brown-Twiss experiment -- 18.3. Photon counter -- 18.4. Outcome of the photon counter -- 18.5. Photon statistics of a perfectly coherent light -- 18.6. Photon statistics of a thermal light -- 18.7. Classification of light by second-order correlation function and photon statistics. -- 18.8. Photon bunching and anti-bunching -- 18.9. Further reading -- 18.10. Problems.

This book studies the application of quantum mechanics to some of the most current and notable concepts in the area, such as quantum optics, cryptography, teleportation, and computing. Written as a complete and comprehensive course text, this book works through mathematically rigorous material using a clear and practical approach that facilitates student engagement, and highlights the fundamental principles of quantum physics used to develop quantum computing.

Primary market Students, upper-level undergrad and graduate in optics, quantum optics, quantum computing, light-matter interaction.

Also available in print.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Dr. Dipankar Bhattacharyya is an Associate Professor of Physics, Department of Physics, Santipur College, Nadia, W.B. India. He completed his PhD at the University of Calcutta, India on Laser Spectroscopy and later went to the Weizmann Institute of Science, Israel for Postdoctoral research work with a Feinberg Graduate School Fellowship. Dr. Jyotirmoy Guha is an Associate Professor of Physics and currently Head of the Department of Physics, Santipur College, West Bengal.

Title from PDF title page (viewed on February 11, 2022).

There are no comments for this item.

Log in to your account to post a comment.