A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled. The condensate fraction first appeared near a temperature of 170 nanokelvin and a number density of 2.5 x 10 12 per cubic centimeter and could be preserved for more than 15 seconds. Three primary signatures of Bose-Einstein condensation were seen. (i) On top of a broad thermal velocity distribution, a narrow peak appeared that was centered at zero velocity. (ii) The fraction of the atoms that were in this low-velocity peak increased abruptly as the sample temperature was lowered. (iii) The peak exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.

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Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor

Single trapped ions represent elementary quantum systems that are well isolated from the environment. They can be brought nearly to rest by laser cooling, and both their internal electronic states and external motion can be coupled to and manipulated by light fields. This makes them ideally suited for quantum-optical and quantum-dynamical studies under well-controlled conditions. Theoretical and experimental work on these topics is reviewed in the paper, with a focus on ions trapped in radio-frequency (Paul) traps.

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Quantum dynamics of single trapped ions

https://link.aps.org/pdf/10.1103/RevModPhys.70.721

Nobel Lecture: Laser cooling and trapping of neutral atoms

The development of wave optics for light brought many new insights into our understanding of physics, driven by fundamental experiments like the ones by Young, Fizeau, Michelson-Morley and others. Quantum mechanics, and especially the de Broglie’s postulate relating the momentum p of a particle to the wave vector k of an matter wave: k = 2 λ = p/ℏ, suggested that wave optical experiments should be also possible with massive particles (see table 1), and over the last 40 years electron and neutron interferometers have demonstrated many fundamental aspects of quantum mechanics [1].

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Optics and interferometry with atoms and molecules

A single charged particle in a Penning trap is a bound system that rivals the hydrogen atom in its simplicity and provides similar opportunities to calculate and measure physical quantities at very high precision. We review the theory of this bound system, beginning with the simple first-order orbits and progressively dealing with small corrections which must be considered owing to the experimental precision that is being achieved. Much of the discussion will also be useful for experiments with more particles in the trap, and several of the mathematical techniques have a wider applicability.

Geonium theory: Physics of a single electron or ion in a Penning trap

Acoustic sensor sensitivity is often reported in units of Hz per unit of measurand. It has been frequently stated or implied in the sensor literature that higher-frequency sensors are preferable to lower frequency sensors because the frequency change per unit of measurand is higher, i.e., the higher-frequency sensors are more "sensitive". This paper reviews the resonator instabilities that lead to the conclusions that: 1) sensitivity expressed as Hz per unit of measurand is not a good measure of sensor quality, and 2) when compared on the bases of accuracy, reproducibility and resolution capability, "good" low frequency sensors are often superior to "good" high frequency ones.

A review of sensor sensitivity and stability

Recent progress in extending high-accuracy measurements of phase noise in oscillators and other devices are described for carrier frequencies from the RF to the millimeter region and Fourier frequencies up to 10% of the carrier (or a maximum of about 1 GHz). A brief survey of traditional precision techniques for measuring phase noise is included as a basis for comparing relative performance and limitations. Several calibration techniques are developed which, when combined with two previous oscillator techniques, permit one to calibrate all factors affecting the measurements of phase noise of oscillator pairs to an accuracy which typically exceeds 1 dB and in favorable cases can approach 0.4 dB. >

Extending the range and accuracy of phase noise measurements

A novel experimental technique is introduced and used to measure the effect of frequency multiplication on the RF spectrum of an oscillator. This technique makes it possible to produce the RF spectrum at X band?where measurements are relatively straightforward?that would have been produced by frequency multiplication of the 5-MHz source to any frequency from 9.2 GHz to 100 THz (1014 Hz). A simplified theory is developed and shown to reproduce the experimental results for the relative power in the carrier and noise pedestal, and the shape and the width of the carrier and noise pedestal, to within the measurement uncertainty of 2 or 3 dB, from 5 MHz to 10 THz. The calculations are easily made using analytical techniques from the measurement of the spectral density of phase fluctuations of the source, the effective input spectrum density and the bandwidth of the multiplier chain, and the frequency multiplication factor. It is shown that present 5-MHz-crystal-controlled oscillators are useful as a precision source to ~500 GHz. Suggestions for extending their range to ~100 THz are made.

/pdf/rf-spectrum-of-a-signal-after-frequency-multiplication-4ocau30fs4.pdf

RF Spectrum of a Signal after Frequency Multiplication; Measurement and Comparison with a Simple Calculation

In this paper we report the results of extensive research on phase modulation (PM) and amplitude modulation (AM) noise in linear bipolar junction transistor (BJT) amplifiers. BJT amplifiers exhibit 1/f PM and AM noise about a carrier signal that is much larger than the amplifiers thermal noise at those frequencies in the absence of the carrier signal. Our work shows that the 1/f PM noise of a BJT based amplifier is accompanied by 1/f AM noise which can be higher, lower, or nearly equal, depending on the circuit implementation. The 1/f AM and PM noise in BJTs is primarily the result of 1/f fluctuations in transistor current, transistor capacitance, circuit supply voltages, circuit impedances, and circuit configuration. We discuss the theory and present experimental data in reference to common emitter amplifiers, but the analysis can be applied to other configurations as well. This study provides the functional dependence of 1/f AM and PM noise on transistor parameters, circuit parameters, and signal frequency, thereby laying the groundwork for a comprehensive theory of 1/f AM and PM noise in BJT amplifiers. We show that in many cases the 1/f PM and AM noise can be reduced below the thermal noise of the amplifier.

Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers

Phase noise measurements of an optoelectronic oscillator (OEO) at frequencies less than 10 Ha from the carrier (10.6 GHz) as well as the measured Allan variance are presented for the first time. The system has a measured single-side-band (SSB) phase-noise of -123 dB/Hz at 10 kHz from the carrier and a /spl sigma//sub y/(/spl tau/)=10/sup -10/ for an integration time between 1 and 10 seconds. The importance of amplifier phase-noise and environmental fluctuations in determining the noise of the oscillator at these low Fourier frequencies is verified experimentally and analyzed using a generalized model of noise sources in the OEOs. This analysis then allows prediction of the oscillator performance from measured parameters of individual components in the system.

Fred L. Walls

Papers

A review of sensor sensitivity and stability

Extending the range and accuracy of phase noise measurements

RF Spectrum of a Signal after Frequency Multiplication; Measurement and Comparison with a Simple Calculation

Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers

Performance evaluation of an optoelectronic oscillator