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

This paper presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the focus issue of New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few-body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. Ultracold molecules offer promising applications such as new platforms for quantum computing, precise control of molecular dynamics, nanolithography and Bose-enhanced chemistry. The discussion is based on recent experimental and theoretical work and concludes with a summary of anticipated future directions and open questions in this rapidly expanding research field.

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Cold and ultracold molecules: science, technology and applications

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

The feasibility of a novel technique for efficient and selective population transfer from a thermally populated level 1 via an intermediate state 2 to level 3 is experimentally demonstrated. It is shown for sodium dimers that the process of on‐ or near‐resonance stimulated Raman scattering with only partially overlapping laser beams is, in particular, useful for the selective population of high vibrational levels of particles in a molecular beam. This is achieved when the interaction with the Stokes laser, coupling levels 2 and 3, begins earlier than the interaction with the pump laser. The phenomenon, which is closely related to the formation of ‘‘trapped states,’’ is quantitatively explained using the basis of eigenstates of molecules strongly coupled to the radiation fields. The similarity and difference to related techniques such as rapid adiabatic passage phenomena in two‐level systems, off‐resonant stimulated Raman scattering, or stimulated emission pumping is briefly discussed.

Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results

Recent advances1,2,3,4,5 in the magnetic trapping and evaporative cooling of atoms to nanokelvin temperatures have opened important areas of research, such as Bose–Einstein condensation and ultracold atomic collisions. Similarly, the ability to trap and cool molecules should facilitate the study of ultracold molecular physics and collisions6; improvements in molecular spectroscopy could be anticipated. Also, ultracold molecules could aid the search for electric dipole moments of elementary particles7. But although laser cooling (in the case of alkali metals1,8,9) and cryogenic surface thermalization (in the case of hydrogen10,11) are currently used to cool some atoms sufficiently to permit their loading into magnetic traps, such techniques are not applicable to molecules, because of the latter's complex internal energy-level structure. (Indeed, most atoms have resisted trapping by these techniques.) We have reported a more general loading technique12 based on elastic collisions with a cold buffer gas, and have used it to trap atomic chromium and europium13,14. Here we apply this technique to magnetically trap a molecular species—calcium monohydride (CaH). We use Zeeman spectroscopy to determine the number of trapped molecules and their temperature, and set upper bounds on the cross-sectional areas of collisional relaxation processes. The technique should be applicable to many paramagnetic molecules and atoms.

Magnetic trapping of calcium monohydride molecules at millikelvin temperatures

A novel scheme is proposed for sequential cooling of rotation, translation, and vibration of molecules. More generally, this scheme manipulates and controls the states and energies of molecules. The scheme, while somewhat complex, is simpler and more feasible than simply providing a large number of synchronously but independently tunable lasers. The key component is a multiple single frequency laser (MSFL) in which a single narrow band pump laser generates an ensemble of resonant ‘‘stimulated Raman’’ (RSR) sidebands (subsequently amplified and selected) in a sample of the molecules to be cooled. Starting with a relatively cold molecular sample (e.g., a supersonic beam of Cs2), the rotation of molecules is cooled by sequential application of P branch electronic transition frequencies transverse to the molecular beam beginning at higher rotational angular momentum J. Then translation of molecules is cooled by application of multiple low J, P, and R branch transition frequencies which counterpropagate with t...

Laser cooling of molecules : a sequential scheme for rotation, translation, and vibration

We report an interesting spectrum of Na2 excited by a Kr+ (5682 A) laser which shows a long series of R–P doublets in the region 5600–8000 A and a continuum with three very broad maxima beyond 8000 A. Our spectral analysis reveals that the laser populates the v′=34, J′=50 level in the A1Σ+u state from where Na2 molecules fluoresce not only to the bound vibrational levels of the entire ground state potential well (3≤v″≤56) but also to the continuum levels above the well. We have made an independent theoretical quantitative prediction of the continuous emission and the agreement between experiment and theory is found to be excellent. Almost the entire (99.6%) ground state RKR potential is constructed using the bound state experimental data which leads to a more accurate value of the dissociation energy (D″e=6024±6 cm−1). The feasibility of a continuously tunable near infrared Na2 laser based upon this radiative dissociation process is discussed. Finally, we present a comprehensive bibliography for the Na2 m...

First observation of bound–continuum transitions in the laser‐induced A 1Σ+u–X 1Σ+g fluorescence of Na2

Publisher Summary This chapter illustrates that the formation of low-temperature molecules with translational energy distributions characterized by T ≤ K is reviewed. Such molecules can in principle be produced optically or nonoptically or by photoassociation of ultracold atoms. Recent results producing cold - and especially ultracold - alkali metal dmers and producing cold paramagnetic molecules are highlighted, along with their potential applications and scientific significance. It clarifies and summarizes the many proposals for formation of gas-phase molecules with subKelvin translational and internal temperatures (or average energies (divided by Boltzmann's constant k) if not in a thermal distribution) and to discuss the exciting and very recent results achieved in implementing these proposals. However, for low-density, low-temperature atomic and molecular gases, the time required to reach true equilibrium (a solid) can be much longer than the corresponding experimental studies. Only the translational degrees of freedom clearly equilibrate thermally on a short time scale. The possibilities for nonthermal distributions among other (internal) degrees of freedom are great, as discussed in the chapter.

Formation of Cold (T ⩽ 1 K) Molecules

Electronic assignments of the violet bands of sodium

We report our observations attributable to optical gain through stimulated emission in the violet when sodium vapor is optically pumped with the 350.7‐nm line of a krypton ion laser. In addition we present the accompanying fluorescence spectrum which shows previously unreported discrete structure on the short wavelength side of the violet bands.

John T. Bahns

Papers

Laser cooling of molecules : a sequential scheme for rotation, translation, and vibration

First observation of bound–continuum transitions in the laser‐induced A 1Σ+u–X 1Σ+g fluorescence of Na2

Formation of Cold (T ⩽ 1 K) Molecules

Electronic assignments of the violet bands of sodium

Observation of gain in the violet bands of sodium vapor