Applications of a Quantum Memory

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Table of contents

Introduction 
I Introduction to Quantum Optics 
1 Motivation for a Quantum Memory
1.1 Applications of a Quantum Memory
1.2 Research Avenues
1.3 Our Approach
2 Continuous Variable Quantum Optics
2.1 Quantum States
2.1.1 The Density Operator
2.1.1.1 Properties of the Density Operator
2.1.2 The Wigner Representation
2.1.2.1 Properties of the Wigner Function
2.2 Quantum States of the Electric Field
2.2.1 Vacuum States
2.2.2 Fock States
2.2.3 Coherent States
2.2.4 Squeezed States
2.2.5 Operator Linearization
2.2.6 Noise Characterization
2.3 Quantum Correlations
2.3.1 Separability Criterion
2.3.2 States Incident on a Beamsplitter
2.3.3 Effects of Optical Losses
II Squeezed Light Production With an OPO 
3 Squeezed Light Production With Nonlinear Optics
3.1 Nonlinear Optics
3.1.1 Propagation Equations
3.2 Nonlinear Processes
3.2.1 Coupled Wave Equations
3.2.2 Second-Harmonic Generation
3.2.2.1 Nonlinear Efficiency
3.2.2.2 Cavity-Enhanced SHG
3.2.3 Parametric Down-Conversion
3.2.4 Phase Matching
3.3 Optical Parametric Amplification and Oscillation
3.3.1 Below Threshold Parametric Gain
3.3.2 Quantum Noise Below Threshold
4 Experimental Setup of the OPO
4.1 Optical Setup
4.1.1 Laser Source
4.1.1.1 Optical Fibers
4.1.2 OPO Table
4.1.2.1 Cavity Generalities
4.2 Nonlinear Crystal
4.2.1 Selection Characteristics
4.2.1.1 Quasi-Phase Matching
4.2.1.2 Periodic-Poling
4.2.1.3 Phase-Matching Angle
4.2.1.4 Nonlinear Coefficient
4.2.1.5 Phase-Matching Temperature
4.2.1.6 Damage Threshold
4.2.1.7 Blue Light Induced Losses
4.2.2 Implementation Parameters
4.2.2.1 Optical Losses
4.2.2.2 Temperature Control
4.2.2.3 Optimal Focusing
4.3 Doubling Cavity
4.3.1 Intracavity Losses
4.3.2 Tilt Locking
4.3.3 Second-Harmonic Generation Results
4.3.3.1 Nonlinear Efficiency
4.3.3.2 Phase-Matching Temperature
4.3.3.3 SHG Efficiency
4.4 OPO Cavity
4.4.1 Cavity Locking
4.4.1.1 Tilt Locking Attempts
4.4.1.2 Pound-Drever-Hall Locking
4.4.1.3 Electronic Implementation
4.4.2 Pump Matching
4.4.3 Classical Observations
4.4.3.1 OPO Threshold
4.4.3.2 Type I OPO Degeneracy
4.4.3.3 OPO Above Threshold
4.4.3.4 OPO Injected Below Threshold
5 Detection and Characterization of Squeezed Light
5.1 Balanced Homodyne Detection
5.1.1 Measuring the Rejection Ratio of Subtraction
5.1.2 Electronic Noise Floor
5.1.3 Detector Balancing
5.1.4 Visibility
5.2 Continuous-Wave Squeezing Measurements
5.2.1 Comparison With Theory
5.2.2 Accounting for Losses
5.3 Quantum State Tomography
5.3.1 Homodyne Measurements
5.3.2 Tomographic Reconstruction
5.3.3 Maximum Likelihood Estimation
5.3.4 Experimental Implementation
5.4 Creation of Pulses of Squeezed Light
5.4.1 AOM Implementation
5.4.2 Optical Chopper Implementation
5.4.2.1 Optical Detection Losses Due To Pulse Edges
5.4.2.2 Real Pulse Envelope
5.4.2.3 Slit Selection
5.4.2.4 Beam Focusing
5.4.2.5 Chopper Selection
5.4.2.6 Rotating Disc
5.4.2.7 Disc Balancing
5.4.2.8 Disc Geometry
5.4.2.9 Pulse Measurements
5.4.2.10 Noise
5.4.2.11 Vibrations
xii Contents
5.4.2.12 Jitter
Publication
III Preparation of a Quantum Memory With Cold Atoms 
6 Experimental Tools for the Storage of Squeezed Light
6.1 Introduction
6.1.1 Optical Storage Through EIT
6.2 Phase Lock
6.2.1 Theory
6.2.1.1 Frequency Division
6.2.1.2 Phase-Frequency Detection
6.2.2 Experimental Setup
6.2.3 Analysis
6.3 The Magneto-Optical Trap
6.3.1 Basic Trapping Principles
6.3.2 MOT Characteristics
6.3.3 Laser Sources
6.3.3.1 Locking
6.3.4 Controlling the Magnetic Field
6.3.4.1 Control Signal
6.3.4.2 Labview Interface
6.3.4.3 Program Operation
6.3.4.4 Results
6.3.5 Timing
6.4 Optical Layout
6.4.1 Beam Displacers
6.4.2 Signal Beam
6.4.3 Local Oscillator
6.4.4 Control Beam
6.4.5 Auxiliary Beam
6.5 Optical Density Measurements
6.5.1 Implementation
6.6 Raman Scheme for the Compensation of the Magnetic Field
6.6.1 Raman Spectroscopy
6.6.2 Labview Interface
6.7 Conclusion
7 Usage of an FPGA for Timing Applications
7.1 Digital Timekeeping
7.1.1 Software Based Clocks
7.1.2 Hardware Based Clocks
7.1.2.1 RC Oscillators
7.1.2.2 Crystal Oscillators
7.1.3 Digitizing the Oscillator
7.2 FPGA Digital Circuits
7.2.1 Programming an FPGA
7.2.1.1 Higher Level Programming
7.2.1.2 NI Labview and Labview FPGA
7.2.2 The Labview FPGA Programming Model
7.3 Basics Concepts in Digital Logic
7.3.1 Data Representation
7.3.2 Digital Input and Output (DIO)
7.3.3 Integers
7.3.4 Floating Point Numbers
7.4 Basic Building Blocks for Timing Applications
7.4.1 Describing a Pulse
7.4.2 Labview Timer Implementation
7.4.2.1 Digital Input and Output
7.4.2.2 Detecting Edge Transitions
7.4.3 Labview Implementation
7.4.4 Implementing the Pulse generator
7.4.5 Putting the Blocks Together
7.5 Experimental Application
7.5.1 Laser Timing via Pulse Delay Generation
7.5.2 Chopper Period Measurement
7.6 Where to find Source Code
Conclusion 
Appendix 
A Matisse Laser
A.1 Laser Locking
A.1.1 Cavity Locking
A.1.2 Saturated Absorption
B Chopper Disc Diagram
C Electronic Diagrams
Bibliography