Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

Tables of integrals

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

Have you ever felt that the very title, Progress in Optics, conjured an image in your mind? Don’t you see a row of handsomely printed books, bearing the editorial stamp of one of the most brilliant members of the optics community, and chronicling the field of optics since the invention of the laser? If so, you are certain to move the bookend to make room for Volume 16, the latest of this series. It contains seven chapters on widely diverging topics, written by well-known authorities in their fields. These are: 1) Laser Selective Photophysics and Photochemistry by V. S. Letokhov, 2) Recent Advances in Phase Profiles (sic) Generation by J. J. Clair and C. I. Abitbol, 3 ) Computer-Generated Holograms: Techniques and Applications by W.-H. Lee, 4) Speckle Interferometry by A. E. Ennos, 5 ) Deformation  Invariant, Space-Variant Optical  Pattern Recognition by D. Casasent and D. Psaltis, 6) Light Emission from High-Current Surface-Spark Discharges by R. E. Beverly, and 7) Semiclassical Radiation  Theory within a  QuantumMechanical Framework by I. R. Senitzkt. The  breadth of topic  matter  spanned  by  these  chapters makes it impossible, for this reviewer at least, to pass judgement on the comprehensiveness, relevance, and completeness of every chapter. With an editorial board as prominent as that of Progress in Optics, however, it seems hardly likely that such comments should be necessary. It should certainly be possible to take the authority of each author as credible. The only remaining judgment to be  made on these chapters is their readability. In short, what are they like to read? The first sentence of the first chapter greets the eye with an obvious typographical error: “The creation of coherent laser light source, that have tunable radiation, opened the . . . .” Two pages later we find: “When two types of atoms or molecules of different isotopic composition ( A and B ) have even one spectral line that does not overlap with others, it is pos-

Progress in optics

The authors review progress in understanding the nature of atomic collisions occurring at temperatures ranging from the millidegrees Kelvin to the nanodegrees Kelvin regime. The review includes advances in experiments with atom beams, light traps, and purely magnetic traps. Semiclassical and fully quantal theories are described and their appropriate applicability assessed. The review divides the subject into two principal categories: collisions in the presence of one or more light fields and ground-state collisions in the dark.

Experiments and theory in cold and ultracold collisions

We report the development of an atom interferometer that uses optical standing waves as phase gratings and operates in the time domain. The observed signal is entirely caused by the wave nature of the atomic center-of-mass motion. The opportunities to measure recoil frequency and gravity acceleration are demonstrated.

Time-Domain de Broglie Wave Interferometry

We study superfluorescence (SF) from spherical and cigar-shaped clouds of laser-cooled Rubidium atoms from the $5{D}_{5/2}$ level through the $6{P}_{3/2}$ level to the $5{S}_{1/2}$ ground level. The atomic system is initially excited to the $5{D}_{5/2}$ level from the ground state via two-photon excitation through the intermediate $5{P}_{3/2}$ level. The fluorescence on the $6P\text{\ensuremath{-}}5S$ transition at 420 nm is recorded using time-resolved measurements. The time delays of the observed SF emission peaks typically scale as $\ensuremath{\sim}{N}^{\ensuremath{-}1}$, where $N$ is the atom number, and are much smaller than the time delay expected for uncorrelated cascade fluorescence. Since $N$ is significantly smaller than the threshold number for SF on the 420 nm transition, and larger than the threshold number for the $5D\text{\ensuremath{-}}6P$ transition at $5.2\text{ }\ensuremath{\mu}\text{m}$, our observations suggest that the 420 nm SF emission is triggered by rapid deexcitation of the $5D$ to the $6P$ level via SF at $5.2\text{ }\ensuremath{\mu}\text{m}$. The observed SF time delays for 420 nm emission agree with SF time-delay estimates for the $5.2\text{ }\ensuremath{\mu}\text{m}$ transition. For spherical clouds, the SF is isotropic. For cigar-shaped clouds, the SF is highly anisotropic. Along the long axis of cigar-shaped atom clouds, SF and incoherent cascade fluorescence produce temporally well-resolved peaks in the detected signal. In this case, the SF component of the signal is highly concentrated along a direction in between the directions of the two almost parallel excitation beams. The observed SF intensities scale as $N$, suggesting that the $5D$ level is regeneratively pumped during the SF decay.

Observation of superfluorescent emissions from laser-cooled atoms

We have studied the temperature scaling laws for the conditions under which a cloud of trapped ^85Rb atoms in the sigma+/sigma- configuration makes the transition from the temperature-limited regime to the multiple-scattering regime. Our experimental technique for measuring temperature relies on measuring the ballistic expansion of the cloud after turning off the confining forces and imaging the cloud size as a function of time with two CCD cameras. In the transition regime, the temperature T is shown to depend on the number of atoms N and the peak density n as (T-T_0) proportional N^1/3 and as (T-T_0) proportional n^2/3, in a manner consistent with theoretical predictions. Here T_0 is defined as the equilibrium temperature of a low-density optical molasses. In the multiple-scattering regime we find that T proportional Omega^2/(delta Gamma), where Omega and delta are the Rabi frequency and the detuning of the trapping laser, respectively, and Gamma is the natural linewidth of the cycling transition. We have also measured the ratio of temperatures along the axial and radial directions of the magnetic field gradient coils and find that the temperature is isotropic only if the intensities of the three orthogonal trapping beams are equal, and that the ratio is generally independent of trapping laser intensity and magnetic field gradient. Finally we demonstrate a measurement of the gravitational acceleration precise to approximately 0.1% by tracking the center of the cloud during ballistic expansion.

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Measurements of temperature scaling laws in an optically dense magneto-optical trap

We have demonstrated a method of generation and real-time detection of nanostructures in a cold Rb cloud. These structures, which are periodic gratings of atomic density, appear as a result of interference of atoms diffracted by pulses of an optical standing wave of wavelength $\ensuremath{\lambda}.$ We have detected structures of period $\ensuremath{\lambda}/2$ and $\ensuremath{\lambda}/4.$ Calculations indicate that these density gratings have period $\ensuremath{\lambda}/2N$ for integer N. While the structures with the period $\ensuremath{\lambda}/2$ are easily detected by Bragg scattering of an optical probe beam, the shorter-period structures are not. For their detection we have developed a three-pulse echo method, in which the shorter-period gratings get converted into the structures with period $\ensuremath{\lambda}/2,$ readily detected in real time. Applications related to lithography are discussed.

/pdf/periodic-structures-generated-in-a-cloud-of-cold-atoms-26jxln5qmg.pdf

Periodic structures generated in a cloud of cold atoms

We describe how a lock-in amplifier can be used in a feedback loop to lock the frequency of a laser to an atomic transition in 85Rb. A simple physical explanation is presented to describe the shape...

/pdf/laser-frequency-stabilization-using-a-lock-in-amplifier-32r83nsg4l.pdf

A. Kumarakrishnan

Papers

Time-Domain de Broglie Wave Interferometry

Observation of superfluorescent emissions from laser-cooled atoms

Measurements of temperature scaling laws in an optically dense magneto-optical trap

Periodic structures generated in a cloud of cold atoms

Laser-frequency stabilization using a lock-in amplifier