Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.

/pdf/electromagnetically-induced-transparency-optics-in-coherent-2dhges92td.pdf

Electromagnetically induced transparency : Optics in coherent media

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.

/pdf/nonclassical-states-in-quantum-optics-a-squeezed-review-of-1899ims4cu.pdf

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

The authors review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. They begin by describing the pioneering work of Macaluso and Corbino over a century ago on linear magneto-optical effects (in which the properties of the medium do not depend on the light power) in the vicinity of atomic resonances. These effects are then contrasted with various nonlinear magneto-optical phenomena that have been studied both theoretically and experimentally since the late 1960s. In recent years, the field of nonlinear magneto-optics has experienced a revival of interest that has led to a number of developments, including the observation of ultranarrow (1-Hz) magneto-optical resonances, applications in sensitive magnetometry, nonlinear magneto-optical tomography, and the possibility of a search for parity- and time-reversal-invariance violation in atoms.

Resonant nonlinear magneto-optical effects in atoms

The paper gives an overview of the use of the coherent population trapping phenomenon (CPT) in alkali-metal atoms in the implementation of atomic frequency standards. Several avenues are examined. These include: the approach using a combination of the CPT phenomenon and the Ramsey separated interaction field technique on an atomic beam; the passive approach in a cell in which the microwave hyperfine resonance excited by the CPT phenomenon is detected directly on the transmitted radiation; the maser approach in which the same resonance is observed by means of stimulated emission in a microwave cavity-cell arrangement; and, finally, the proposed approach using pulses in a time sequence that implements the combined CPT–Ramsey separated interaction field technique in time rather than in space. A review of field and laboratory implementations using these approaches is made.

Atomic clocks based on coherent population trapping: a review

Semiconductors have uniquely attractive properties for electronics and photonics. However, it has been difficult to find a highly coherent quantum state in a semiconductor for applications in quantum sensing and quantum information processing. We report coherent population trapping, an optical quantum interference effect, on a single hole. The results demonstrate that a hole spin in a quantum dot is highly coherent.

https://science.sciencemag.org/content/sci/325/5936/70.full.pdf

A coherent single-hole spin in a semiconductor.

Precision spectroscopy with coherent dark states

When neon is introduced as a buffer gas the interaction time of cesium atoms in a vapor cell with resonant laser beams is drastically increased. Using a pair of phase-locked lasers we have observed linewidths as narrow as $42 $Hz for coherent dark resonances in a cesium vapor cell. We study the influence of power and pressure broadening and systematic shifts of the resonance frequency. Our experiments demonstrate that coherent dark resonances could rival direct radio-frequency precision measurements, which have a wide range of applications in physics.

Buffer-gas-induced linewidth reduction of coherent dark resonances to below 50 Hz

Coherent population trapping resonances in cesium vapor can be used to determine DC flux densities in the range from 1 μT to 1 mT with typically 3·10−5 relative uncertainty. For fields modulated at a few kHz, we find sensitivities of below 10 pT within 0.5 s integration time. From the signal-to-noise ratio the sensitivity can be extrapolated to 500 fT/√Hz. A quantitative understanding of the lineshape allows to detect DC fields of several nT even when the Zeeman components of the resonance are not resolved.

/pdf/experimental-realization-of-coherent-dark-state-3scc2q3nmv.pdf

Experimental realization of coherent dark-state magnetometers

We have evaluated the suitability of a vertical-cavity surface-emitting laser diode (VCSEL) for spectroscopic applications. Despite its low output power it is possible to observe narrow resonances in a saturated absorption spectroscopy experiment on the cesium D
2 transition at 852 nm, limited in width by the laser linewidth of several tens of MHz. High modulation efficiency of the VCSEL allows us to create modulation sidebands at 9.2 GHz frequency via direct modulation of the laser injection current. Using the carrier and either one of the sidebands coherent population trapping (CPT) resonances in a buffered cesium vapor can be prepared with linewidths below 130 Hz. With this very compact setup we have studied the dependence of CPT resonance position and linewidth as a function of optical detuning and find evidence of the influence of the excited state hyperfine structure.

Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL)

In a weak magnetic field coherent dark resonances in cesium vapor are split into up to 15 resolved components, depending on field direction and laser polarizations. We find that the selection rules are different for vapor cells with and without buffer gas due to a change in multipolarity of the two-photon coupling. At low laser intensities or sufficiently high buffer-gas pressure optical pumping between different dark resonances can be neglected so that a simple model allows one to calculate the relative line strengths, giving complete agreement with the experimental spectra. @S1050-2947~98!00907-X#

/pdf/selection-rules-and-line-strengths-of-zeeman-split-dark-4113bu61ex.pdf

A. Nagel

Papers

Precision spectroscopy with coherent dark states

Buffer-gas-induced linewidth reduction of coherent dark resonances to below 50 Hz

Experimental realization of coherent dark-state magnetometers

Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL)

Selection rules and line strengths of Zeeman-split dark resonances