9/7/16 September 20, 2016 6.453 Quantum Optical Communication - - PDF document

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Optical and Quantum Communications Group www.rle.mit.edu/qoptics September 20, 2016

6.453 Quantum Optical Communication Lecture 4 Jeffrey H. Shapiro

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6.453 Quantum Optical Communication — Lecture 4 § Handouts

§ Lecture notes, slides

§ Quantum Harmonic Oscillator

§ Quantization of a classical LC circuit § Annihilation and creation operators § Energy eigenstates — number-state kets

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Classical LC Circuit: Undriven, Lossless Oscillation

§ State Variables capacitor charge: inductor flux: § Stored Energy (Hamiltonian) § Hamilton’s Equations

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Classical LC Circuit: Undriven, Lossless Oscillation § Nonzero Initial Conditions: § Oscillation Frequency: § Solutions for :

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Classical LC Circuit: Dimensionless Reformulation § Assume § Define Complex Envelope (Phasor): § Simple Harmonic Motion at Constant Energy

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Quantum LC Circuit: Quantum Harmonic Oscillator § Postulate: Become Observables § Canonical Commutation Relation: § Dimensionless Reformulation:

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Quantum Harmonic Oscillator: Commutators § Dimensionless Reformulation of Canonical Commutators: § Hamiltonian: § Heisenberg Uncertainty Principle:

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Classical versus Quantum Behavior

§ Classical Oscillator: Noiseless § Quantum Oscillator: Noisy

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Energy Eigenvalues and Eigenkets § Notation: § Annihilation and Creation Operations

§ is energy eigenket with eigenvalue § is energy eigenket with eigenvalue

§ Minimum Energy State: such that § Energy Eigenvalues:

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Number Operator and Number States § Oscillator Energy is Quantized in Increments § (Photon) Number Operator:

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Coming Attractions: Lectures 5 and 6 § Lecture 5: Quantum Harmonic Oscillator

§ Number measurements versus quadrature measurements § Coherent states and their measurement statistics

§ Lecture 6: Quantum Harmonic Oscillator

§ Minimum uncertainty-product states § Squeezed states and their measurement statistics

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6.453 Quantum Optical Communication

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