Readings

No textbook was used during the course. References provided below supplement the lecture notes.

[GK] = Buy at Amazon Gerry, Christopher C., and Peter L. Knight. Introductory Quantum Optics. New York, NY: Cambridge University Press, 2004. ISBN: 9780521527354.

[Loudon] = Buy at Amazon Loudon, Rodney. The Quantum Theory of Light. Oxford, United Kingdom: Clarendon Press, 1973. ISBN: 9780198511304.

[Louisell] = Buy at Amazon Louisell, William H. Quantum Statistical Properties of Radiation. New York, NY: McGraw-Hill, 1973. Reprint, New York, NY: Wiley-Interscience, 1990. ISBN: 9780471523659.

[MW] = Buy at Amazon Mandel, Leonard, and Emil Wolf. Optical Coherence and Quantum Optics. New York, NY: Cambridge University Press, 1995. ISBN: 9780521417112.

[NC] = Buy at Amazon Nielsen, Michael A., and Isaac L. Chuang. Quantum Computation and Quantum Information. New York, NY: Cambridge University Press, 2000. ISBN: 9780521635035.

SES # TOPICS READINGS
1

Introduction

Optical eavesdropping tap, action at a distance, and long-distance quantum state transmission

  
2

Dirac-notation quantum mechanics

Quantum systems, states as ket vectors, state evolution via Schrödinger's equation, and quantum measurements

  
3

Dirac-notation quantum mechanics (cont.)

Quantum measurement statistics, Schrödinger picture versus Heisenberg picture, and Heisenberg Uncertainty Principle

  
4

Quantum harmonic oscillator

Quantization of a classical LC circuit, annihilation and creation operators, and energy eigenstates

The quantum harmonic oscillator and its energy eigenkets

[GK] pp. 10-15.

[Louisell] sections 2.1 to 2.5.

[Loudon] pp. 128-133.
5

Quantum harmonic oscillator (cont.)

Measurement statistics and transition to the classical limit of noiseless oscillation

Coherent states and minimum uncertainty states and minimum uncertainty states

[GK] sections 3.1, 3.5, and 3.6.

[Loudon] chapter 7.

[MW] sections 11.1 to 11.6.
6

Quantum harmonic oscillator (cont.)

Quadrature-representation wave functions, minimum uncertainty-product states, squeezed states and their measurement statistics

Squeezed states

[GK] section 7.1.

Yuen, H. P. "Two-Photon Coherent States of the Radiation Field." Physical Review A 13 (1976): 2226-2243.

[MW] sections 21.1 to 21.6.

Continuous-spectrum eigenkets

[Louisell] section 1.10.
7

Quantum harmonic oscillator (cont.)

Quadrature measurement statistics and phase space, characteristic functions and Wigner distribution, and positive operator-valued measurement of â

Quantum characteristic functions

[GK] section 3.8.

[Louisell] section 3.4.

For positive operator-valued measurements

[NC] section 2.2.6.
8

Quantum harmonic oscillator (cont.)

Positive operator-valued measurement

Single-mode photodetection

Contrasting semiclassical and quantum theories of direct detection and balanced homodyne detection in ideal photodetectors

Eigenkets for joint measurement

Shapiro, J. H., and S. S. Wagner. "Phase and Amplitude Uncertainties in Heterodyne Detection." IEEE Journal of Quantum Electronics QE-20 (1984): 803-813.

Quantum photodetection

[GK] section 5.2.

[MW] sections 12.1 to 12.4, 12.9, and 12.10.

Yuen, H. P., and J. H. Shapiro. "Optical Communication with Two-Photon Coherent States-Part III: Quantum Measurements Realizable with Photoemissive Detectors." IEEE Transactions on Information Theory IT-26 (1980): 78-92.

Semiclassical photodetection

[MW] sections 9.1 to 9.8.

Buy at Amazon Gagliardi, Robert M., and Sherman Karp. Optical Communications. New York, NY: John Wiley and Sons, 1976, chapter 2. ISBN: 9780471289159.
9

Single-mode photodetection (cont.)

Optical heterodyne detection and the â positive operator-valued measurement

  
10

Single-mode photodetection (cont.)

Signatures of non-classical light and the squeezed-state waveguide tap

  
11

Single-mode photodetection (cont.)

Single-mode photodetection with inefficient detectors

Single-mode linear systems

Classical and quantum theories of linear attenuation and linear amplification

The quantum theory of beam splitters

[GK] section 6.2.

The quantum theory of linear amplifiers

Caves, C. M. "Quantum Limits on Noise in Linear Amplifiers." Physical Review D 26 (1982): 1817-1839.

[MW] chapter 20.

Buy at Amazon Haus, Herman A. Electromagnetic Noise and Quantum Optical Measurements. New York, NY: Springer Verlag, 2000, chapter 11. ISBN: 9783540652724.
12

Single-mode and two-mode linear systems

Quantum mechanics of attenuators and amplifiers; phase-insensitive and phase-sensitive amplifiers

  
13

Two mode linear systems (cont.)

Dual parametric amplifier, photon twins, and entanglement

Four-mode quantum systems

Polarization entanglement and qubit teleportation

  
14

Teleportation

Polarization entanglement and qubit teleportation; quadrature entanglement and continuous-variable teleportation

  
15

Teleportation (cont.)

Continuous-variable teleportation

  
16

Quantum cryptography

One-time pad classical cryptography, Bennett-Brassard 1984 quantum key distribution protocol, Clauser-Home-Shimony-Holt form of Bell's inequality, and Ekert protocol quantum key distribution

Quantum key distribution

Buy at Amazon Bouwmeester, Dirk, Artur Ekert, and Anton Zeilinger, eds. The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, and Quantum Computation. New York, NY: Springer Verlag, 2000, chapter 2. ISBN: 9783540667780.

[NC] chapter 2.
17

Quantization of the electromagnetic field

Maxwell's equations, plane-wave mode expansions, and multi-mode number states and coherent states

Electromagnetic field quantization

[Louisell] sections 4.3 and 4.4.

[MW] sections 10.1 to 10.3.
18

Continuous-time photodetection

Poisson shot-noise semiclassical model, photon-flux operator measurement quantum model, and direct-detection signatures of non-classical light

Random processes

Shapiro, J. H. Optical Propagation, Detection, and Communication. Unpublished manuscript, chapter 4.

Continuous-time photodetection

Shapiro, J. H., H. P. Yuen, and J. A. Machado Mata. "Optical Communication with Two-Photon Coherent States-Part II: Photoemissive Detection and Structured Receiver Performance." IEEE Transactions on Information Theory IT-25 (1979): 179-192.

Yuen, H. P., and J. H. Shapiro. "Optical Communication with Two-Photon Coherent States-Part III: Quantum Measurements Realizable with Photoemissive Detectors." IEEE Transactions on Information Theory IT-26 (1980): 78-92.

Shapiro, J. H. "Quantum Noise and Excess Noise in Optical Homodyne and Heterodyne Receivers." IEEE Journal of Quantum Electronics QE-21 (1985): 237-250.

[MW] sections 9.1 to 9.8, 12.1 to 12.4, 12.9, and 12.10.
19

Continuous-time photodetection (cont.)

Noise spectral densities in direct detection, semiclassical and quantum theories of coherent detection, and coherent-detection signatures of non-classical light

  
20

Nonlinear Optics

Maxwell's equations with a nonlinear polarization, coupled-mode equations for parametric downconversion, phase-matching for efficient interactions, and classical theory of optical parametric amplification in second-order nonlinear crystals

Classical coupled-mode equations for parametric interactions

Buy at Amazon Saleh, Bahaa E. A., and Malvin C. Teich. "Coupled- Wave Theory of Three-Wave Mixing." Section 19.4 in Fundamentals of Photonics. New York, NY: John Wiley and Sons, 1991. ISBN: 9780471839651.
21

Nonlinear optics (cont.)

Coupled-mode equations for parametric downconversion, continuous-time field operator theory of spontaneous parametric downconversion and Gaussian-state characterization

Nonclassical light generation from parametric downconversion

[MW] sections 21.7 and 22.4.

Wong, F. N. C., J. H. Shapiro, and T. Kim. "Efficient Generation of Polarization-Entangled Photons in a Nonlinear Crystal." Laser Physics 16, no. 11 (November 2006): 1517-1524.

Gaussian-state theory of parametric amplifier noise and its quantum signatures

Shapiro, J. H., and K.-X. Sun. "Semiclassical versus Quantum Behavior in Fourth-Order Interference." Journal of the Optical Society of America B Optical Physics 11, no. 6 (1994): 1130-1141.

Shapiro, J. H. "Quantum Gaussian Noise." Proceedings of SPIE—the International Society for Optical Engineering 5111 (2003): 382-395.
22

Quantum signatures from parametric interactions

Quantum interference, photon indistinguishability, Hong-Ou-Mandel interferometry, the biphoton, generation of polarization entanglement, photon twins from an optical parametric amplifier

  
23

More quantum optical applications

Binary optical communication with squeezed states, phase-sensing interferometry with squeezed states, super-dense coding with entangled states, and quantum lithography with "N00N" states

Binary optical-communication with squeezed-state light

Shapiro, J. H., H. P. Yuen, and J. A. Machado Mata. "Optical Communication with Two-Photon Coherent States-Part II: Photoemissive Detection and Structured Receiver Performance." IEEE Transactions on Information Theory IT-25 (1979): 179-192.

Squeezed-state interferometry

Caves, C. M. "Quantum-Mechanical Noise in an Interferometer." Physical Review D 23, no. 8 (1981): 1693-1708.

Bondurant, R. S., and J. H. Shapiro. "Squeezed States in Phase Sensing Interferometers." Physical Review D 30, no. 12 (1984): 2548-2556.

Super-dense coding

[NC] section 2.3.

Quantum lithography

Boto, A. N., P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling. "Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit." Physical Review Letters 85, no. 13 (2000): 2733-2736.