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.

/pdf/observation-of-bose-einstein-condensation-in-a-dilute-atomic-2wpb5ks2pi.pdf

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.

/pdf/quantum-dynamics-of-single-trapped-ions-5b12pz9r16.pdf

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].

/pdf/optics-and-interferometry-with-atoms-and-molecules-1vnuwajb51.pdf

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

The frequency instabilities of precision bulk acoustic wave (BAW) quartz crystal oscillators are reviewed. The fundamental limits on the achievable frequency stabilities, and the degree to which the fundamental limits have been approached to date are examined. Included are the instabilities as a function of time, temperature, acceleration, ionizing radiation, electromagnetic fields, humidity, atmospheric pressure, power supply, and load impedance. Most of the fundamental limits are zero or negligibly small, a few are finite. We speculate about the progress which may be achievable in the future with respect to approaching the fundamental limits. Suggestions are provided about the paths that may lead to significant stability improvements. >

Fundamental limits on the frequency stabilities of crystal oscillators

A new technique is presented which makes it possible to measure the inherent short-term stability of quartz crystal resonators in a passive circuit. Comparisons with stability measurements made on crystal controlled oscillators indicate that noise in the electronics of the oscillators very seriously degrades the inherent stability of the quartz resonators for times less than 1 s. A simple model appears to describe the noise mechanism in crystal controlled oscillators and points the way to design changes which should improve their short-term stability by two orders of magnitude. Calculations are outlined which show that with this improved short-term stability it should be feasible to multiply a crystal controlled source to 1 THz and obtain a linewidth of less than 1 Hz. In many cases, this improved short-term stability should also permit a factor of 100 reduction in the length of time necessary to achieve a given level of accuracy in frequency measurements.

Measurement of the Short-Term Stability of Quartz Crystal Resonators and the Implications for Crystal Oscillator Design and Applications

The characterization of frequency stability in the time domain and frequency domain are briefly defined and their relationships explained. Techniques for making precise measurements of frequency fluctuations in oscillators, multipliers, dividers, amplifiers, and other components are discussed. Particular attention is given to methods of calibration which permit accuracies of 1 dB or better to be achieved when measuring in the frequency domain. Common pitfalls to avoid are also covered, and efficient time-domain techniques are explained.

Measurements of frequency stability

We have achieved a stability of 3/spl middot/10/sup -13/ /spl tau//sup -1/2/ for 3</spl tau/<30 s with a laser-pumped rubidium gas-cell frequency standard by reducing the effects due to noise in the microwave and laser sources. This result is one order of magnitude better than the best present performance of lamp-pumped devices.

https://doc.rero.ch/record/28622/files/Mileti_Gaetano_-_Laser-Pumped_Rubidium_Frequency_Standards_20120229.pdf

Laser-pumped rubidium frequency standards: new analysis and progress

The frequency, amplitude, and noise of the output signal of a quartz oscillator are affected by a large number of environmental effects. The physical basis for the sensitivity of precision oscillators to temperature, humidity, pressure, acceleration and vibration, magnetic field, electric field, load, and radiation is examined. The sensitivity of quartz oscillators to radiation is a very complex topic and poorly understood. Therefore, only a few general results are mentioned. The sensitivity to most external influences often varies significantly both from one oscillator type to another and from one unit of a given type to another. For a given unit, the sensitivity to one parameter often depends on the value of other parameters and on history. Representative sensitivity to the above parameters is given. >

Fred L. Walls

Papers

Fundamental limits on the frequency stabilities of crystal oscillators

Measurement of the Short-Term Stability of Quartz Crystal Resonators and the Implications for Crystal Oscillator Design and Applications

Measurements of frequency stability

Laser-pumped rubidium frequency standards: new analysis and progress

Environmental sensitivities of quartz oscillators