The Jaynes-Cummings model (JCM), a soluble fully quantum mechanical model of an atom in a field, was first used (in 1963) to examine the classical aspects of spontaneous emission and to reveal the existence of Rabi oscillations in atomic excitation probabilities for fields with sharply defined energy (or photon number). For fields having a statistical distributions of photon numbers the oscillations collapse to an expected steady value. In 1980 it was discovered that with appropriate initial conditions (e.g. a near-classical field), the Rabi oscillations would eventually revive, only to collapse and revive repeatedly in a complicated pattern. The existence of these revivals, present in the analytic solutions of the JCM, provided direct evidence for discreteness of field excitation (photons) and hence for the truly quantum nature of radiation. Subsequent study revealed further non-classical properties of the JCM field, such as a tendency of the photons to antibunch. Within the last two years it ha...

The Jaynes-Cummings Model

Seventy five years ago, three remarkable papers by Schr¨ odinger, Kennard and Darwin were published. They were devoted to the evolution of Gaussian wave packets for an oscillator, a free particle and a particle moving in uniform constant electric and magnetic fields. From the contemporary point of view, these packets can be considered as prototypes of the coherent and squeezed states, which are, in a sense, the cornerstones of modern quantum optics. Moreover, these states are frequently used in many other areas, from solid state physics to cosmology. This paper gives a review of studies performed in the field of so-called ‘nonclassical states’ (squeezed states are their simplest representatives) over the past seventy five years, both in quantum optics and in other branches of quantum physics. My starting point is to elucidate who introduced different concepts, notions and terms, when, and what were the initial motivations of the authors. Many new references have been found which enlarge the ‘standard citation package’ used by some authors, recovering many undeservedly forgotten (or unnoticed) papers and names. Since it is practically impossible to cite several thousand publications, I have tried to include mainly references to papers introducing new types of quantum states and studying their properties, omitting many publications devoted to applications and to the methods of generation and experimental schemes, which can be found in other well known reviews. I also mainly concentrate on the initial period, which terminated approximately at the border between the end of the 1980s and the beginning of the 1990s, when several fundamental experiments on the generation of squeezed states were performed and the first conferences devoted to squeezed and ‘nonclassical’ states commenced. The 1990s are described in a more ‘squeezed’ manner: I have confined myself to references to papers where some new concepts have been introduced, and to the most recent reviews or papers with extensive bibliographical lists.

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'Nonclassical' states in quantum optics: a 'squeezed' review of the first 75 years

Squeezed light generation has come of age. Significant advances on squeezed light generation have been made over the last 30 years—from the initial, conceptual experiment in 1985 till today’s top-tuned, application-oriented setups. Here we review the main experimental platforms for generating quadrature squeezed light that have been investigated in the last 30 years.

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30 years of squeezed light generation

We apply a generalization of the time-dependent density matrix renormalization group (DMRG) to study finite-temperature properties of several quantum spin chains, including the frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. We discuss several practical issues with the method, including use of quantum numbers and finite-size effects. We compare with transfer-matrix DMRG, finding that both methods produce excellent results.

https://arxiv.org/pdf/cond-mat/0510124.pdf

Finite-temperature density matrix renormalization using an enlarged Hilbert space

Publisher Summary This chapter discusses the quantum interference, superposition states of light and the nonclassical effects. The superposition principle is at the heart of quantum mechanics. The coherent state forms a position-momentum, phase-space patch of minimum area, and is the quantum analog of the classical point in phase space. The chapter discusses how quantum interference between coherent states results in nonclassical effects, and associates quantum coherences between coherent states with quantum interference in the phase space. Schrodinger's argument is based on stability and invariance of Gaussian wavepackets of an isolated quantum harmonic oscillator. The effect of coarsening is identical to the influence of reservoirs on quantum interference. The chapter describes several methods proposed for the generation of quantum-mechanical superposition states of light. The methods for the detection of schrodinger cats include homodyne detection, DAP-QND detection scheme and optical homodyne tomography method. These methods provide a complete quantum mechanical description of the measured mode and therefore, can be applied for characterization of quantum-mechanical superposition states, providing these fields are directly measureable.

I: Quantum Interference, Superposition States of Light, and Nonclassical Effects

The fully quantum-electrodynamical model of a two-level atom interacting with a single-cavity mode predicts an atomic evolution whose form is dictated by the discrete nature of the field energy and its statistical distribution. We demonstrate that the revivals of atomic excitation which are the signature of the quantum nature of the evolution are strongly affected by field dissipation even when the damping hardly affects the underlying Rabi oscillations.

Dissipation in a fundamental model of quantum optical resonance

We present a new class of radiation field states which exhibit squeezed fluctuations. This new class of states are formed by a simple implementation of the superposition principle and are fundamentally different from the conventional two-photon coherent squeezed states. We demonstrate the importance of these states as the natural product of the resonant interaction of suitably prepared atoms with the radiation field. We establish a general relationship between reduced quantum fluctuations of these field states and the dipole fluctuations of the atoms which produce them.

Squeezing and superposition states.

Yurke and Potasek [Phys. Rev. A 36, 3464 (1987)] have shown that pure states of correlated pairs of quantum systems can lead to mixed-state behavior if only one of the systems is observed. We note that such behavior is well known and describe how the mixed-state properties of these states have led to their application in thermodynamical problems via the thermofield formalism. The correlations have been found to lead to manifestly nonclassical behavior (such as squeezing) if both systems are observed.

P. L. Knight

Papers

Dissipation in a fundamental model of quantum optical resonance

Squeezing and superposition states.

Comment on "Obtainment of thermal noise from a pure quantum state"