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].

/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 Time and Frequency Division of the National Institute of Standards and Technology (NIST) begun operation of a laser-cooled cesium atomic fountain for evaluation as a possible primary frequency standard. This device is conceptually similar to the Zacharias caesium fountain and is similar in layout to the BNM-LPTF (Observatoire de Paris) caesium fountain. This paper gives a brief description of the NIST Time and Frequency Division's caesium fountain and presents some preliminary data.

NIST caesium fountain frequency standard: preliminary results

Experimental results are presented on a hybrid optical/electronic oscillator which uses an optical delay line to generate high spectral purity microwave signals. At Fourier frequencies above 10 kHz, the single sideband (SSB) phase noise spectrum decreases as roughly 1/f/sup 2/ attaining a value of -138 dB below the carrier in a 1 Hz bandwidth (dBc/Hz) at 20 kHz offset. The origin of this noise is in part the fundamental shot noise on the light itself, although other optical noise sources such as double Rayleigh scattering and stimulated Brillouin scattering also appear to be important under certain operating conditions. The frequency stability over several hours is dominated by changes in the fiber ambient temperature with a coefficient of about 10/sup -5//K originating mostly from changes in the fiber refractive index with temperature.

A 1 GHz optical-delay-line oscillator driven by a diode laser

This paper presents state-of-the-art results on 1 GHz surface transverse wave (STW) power oscillators running at extremely high loop power levels. High-Q single-mode STW resonators used in these designs have an insertion loss of 3.6 dB, an unloaded Q of 8000, a residual phase noise of -142 dBc/Hz at 1 Hz intercept and operate at an incident power of up to 31 dBm in the loop. Other low-Q STW resonators and coupled resonator filters (CRF) with an insertion loss in the 5-9 dB range can conveniently handle power levels in excess of 2 W. These devices were implemented in voltage controlled oscillators (VCO's) running from a 9.6 V source at an output power of 23 dBm and a RF/dc efficiency of 28%. Their tuning range was 750 kHz and the noise floor -180 dBc/Hz. The oscillators, stabilized with the high-Q devices, use specially designed AB-class power amplifiers, deliver an output power of 29 dBm and demonstrate a noise floor of -184 dBc/Hz and a 1 Hz intercept of -17 dBc/Hz. The 1 Hz intercept was improved to -33 dBc/Hz using the UTO-1023 as a loop amplifier. In this case the output power was 22 dBm. In all cases the loop amplifier was the limiting factor for the close-to-carrier oscillator phase noise performance. >

Surface transverse wave oscillators with extremely low thermal noise floors

We present experimental results on intrinsic 1/f frequency modulation (FM) noise in high-overtone thin-film sapphire resonators that operate at 2 GHz. The resonators exhibit several high-Q resonant modes approximately 100 kHz apart, which repeat every 13 MHz. A loaded Q of approximately 20000 was estimated from the phase response. The results show that the FM noise of the resonators varied between S/sub y/(10 Hz)=-202 dB relative (rel) to 1/Hz and -210 dB rel to 1/Hz. The equivalent phase modulation (PM) noise of an oscillator using these resonators (assuming a noiseless amplifier) would range from L(10 Hz)=-39 to -47 dBc/Hz.

1/f frequency noise of 2-GHz high-Q thin-film sapphire resonators

The parametric oscillation of a single trapped electron is studied and used to measure enhanced spontaneous emission. Hysteresis in this motion provides a 1-bit memory to store information about excitations made with the electron ``in the dark.'' The time dependence and stability criteria for the parametric excitation are examined. The cyclotron motions for one and two electrons are also studied.

/pdf/1-bit-memory-using-one-electron-parametric-oscillations-in-a-285a2q4cpr.pdf

Fred L. Walls

Papers

NIST caesium fountain frequency standard: preliminary results

A 1 GHz optical-delay-line oscillator driven by a diode laser

Surface transverse wave oscillators with extremely low thermal noise floors

1/f frequency noise of 2-GHz high-Q thin-film sapphire resonators

1-bit memory using one electron: Parametric oscillations in a Penning trap