MIT OpenCourseWarehttp://ocw.mit.edu 6.453 Quantum Optical Communication Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.September 23, 2008Optical and Quantum Communications Groupwww.rle.mit.edu/qoptics6.453 Quantum Optical CommunicationLecture 6Jeffrey H. Shapiro2www.rle.mit.edu/qoptics6.453 Quantum Optical Communication — Lecture 6! Announcements! Pick up problem set 2 graded, lecture notes, slides! Quantum Harmonic Oscillator! Quadrature-representation wave functions! Minimum uncertainty-product (MUP) states! Squeezed states and their measurement statistics3www.rle.mit.edu/qopticsCoherent States: Reprise! Quantum Harmonic Oscillator:! Heisenberg Uncertainty Principle:! Eigenkets of the Annihilation Operator:! Quadrature Measurement Statistics:4www.rle.mit.edu/qopticsClassical versus Quantum Quadrature Behavior! Classical Oscillator: Noiseless ! Quantum Oscillator: State5www.rle.mit.edu/qopticsThe Vacuum State is Special!! It’s a number state:! Zero-uncertainty number operatormeasurement outcome:! Zero-point energy:! It’s a coherent state:! Minimum uncertainty-productquadrature measurements! Zero-point fluctuations:6www.rle.mit.edu/qopticsQuadrature-Operator Eigenkets! On Problem Set 4 You Will Find Quadrature Eigenkets:! Orthonormal:! Complete:! Fourier-kernel relation:7www.rle.mit.edu/qopticsQuadrature Representations: Wave Functions! Wave Function Representations of Arbitrary Ket! Fourier-Transform Duality8www.rle.mit.edu/qopticsMUP States with Zero-Mean Quadratures! Quadrature Variances From Wave Functions! Minimum Uncertainty-Product Wave Functions9www.rle.mit.edu/qopticsMinimum Uncertainty-Product States! Minimum Uncertainty-Product Wave Functionswhere! Coherent-State Wave Functions10www.rle.mit.edu/qopticsSqueezed States: Connection to MUP States! Equality Condition for Quadratures Uncertainty Principle:! Equivalent to Bogoliubov-Transformation Eigenket:where real and11www.rle.mit.edu/qopticsSqueezed States: Dynamics! Bogoliubov Transformation with complexwhere! Quadrature-Measurement Mean Values and Variances12www.rle.mit.edu/qopticsQuadrature-Measurement Statistics! Amplitude-Squeezed State ! Phase-Squeezed State13www.rle.mit.edu/qopticsComing Attractions: Lectures 7 and 8! Lecture 7:Quantum Harmonic Oscillator! Wigner distribution and phase space! Probability operator-valued measurement of! Lecture 8:Single-Mode Photodetection! Direct Detection! Homodyne
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