## Quantum SqueezingPeter D. Drummond, Zbigniew Ficek The concept of squeezing is intimately related to the idea of vacuum fluctu ations, once thought to place an absolute limit to the accuracy of measure ment. However, vacuum fluctuations are not unchangeable. By recognizing that these quantum fluctuations always occur in two complementary observ ables, physicists have been able to make an intriguing trade-off. Reduced fluctuations in one variable can be realized - at the expense of increased fluctuations in another, according to Heisenberg. This Heisenberg 'horse-trade' - originally predicted by theorists - was first accomplished experimentally by R. Slusher in 1985. Since then, the var ious techniques and applications of quantum squeezing have metamorphosed into a central tool in the wider field of quantum information. This book is a summary of the main ideas, methods and applications of quantum squeezing, written by those responsible for some of the chief developments in the field. The book is divided into three parts, to recognize that there are three areas in this research. These are the fundamental physics of quantum fluc tuations, the techniques of generating squeezed radiation, and the potential applications. Part I of the book, giving the fundamentals, is arranged as follows. • Chapter 1 introduces the basic ideas about what squeezing of quantum fluctuations is from the quantized free-field perspective. This chapter es tablishes the definitions and notations used throughout. • Chapter 2 explains how to quantize radiation in a dielectric, which is the basic technique that is used to make squeezed radiation. |

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### Contents

3 | |

EinsteinPodolskyRosen Correlations Entanglement | 10 |

Department of Physics H Wisemangu edu | 31 |

Nonlinear Dielectrics | 33 |

InputOutput Theory | 52 |

References | 95 |

References | 137 |

References | 169 |

References | 222 |

Quantum Cryptography | 239 |

References | 258 |

References | 305 |

Bernard Yurke Northwestern University Evanston | 333 |

References | 362 |

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absorption amplifier amplitude annihilation operators anomalous features approximation assume bandwidth beam splitter canonical commutation relations channel classical coherent commutation relations consider corresponding coupling D.F. Walls decay rate defined density described detector dipole discussed driving field effects EPR correlations EPR paradox equations of motion experimental feedback loop Ficek finite Fock Gaussian given H.P. Yuen Hamiltonian homodyne detection ideal squeezed vacuum in-loop squeezing input interaction intracavity Langevin equations laser Lett limit linear linewidth lower lasing level master equation modulation nonclassical nonlinear nonlinear optical obtained output field P.D. Drummond parameter parametric oscillator phase phase space photocurrent photon number Phys predicted propagation pump quantization quantum measurement quantum mechanics quantum noise Rabi frequency resonance fluorescence result Sect signal spectra spectrum squeezed field squeezed light squeezed vacuum statistics stochastic theory threshold tion transmission line two-level atom two-mode squeezed uncertainty variable variance vector Wigner function zero