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 realization of superfluidity in a dilute gas of fermionic atoms, analogous to superconductivity in metals, represents a long-standing goal of ultracold gas research. In such a fermionic superfluid, it should be possible to adjust the interaction strength and tune the system continuously between two limits: a Bardeen–Cooper–Schrieffer (BCS)-type superfluid (involving correlated atom pairs in momentum space) and a Bose–Einstein condensate (BEC), in which spatially local pairs of atoms are bound together. This crossover between BCS-type superfluidity and the BEC limit has long been of theoretical interest, motivated in part by the discovery of high-temperature superconductors. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created. Here we report the direct observation of a molecular Bose–Einstein condensate created solely by adjusting the interaction strength in an ultracold Fermi gas of atoms. This state of matter represents one extreme of the predicted BCS–BEC continuum.

Emergence of a molecular Bose-Einstein condensate from a Fermi gas

Photoassociation is the process in which two colliding atoms absorb a photon to form an excited molecule. The development of laser-cooling techniques for producing gases at ultracold !!1 mK" temperatures allows photoassociation spectroscopy to be performed with very high spectral resolution. Of particular interest is the investigation of molecular states whose properties can be related, with high precision, to the properties of their constituent atoms with the “complications” of chemical binding accounted for by a few parameters. These include bound long-range or purely long-range vibrational states in which two atoms spend most or all of their time at large internuclear separations. Low-energy atomic scattering states also share this characteristic. Photoassociation techniques have made important contributions to the study of all of these. This review describes what is special about photoassociation spectroscopy at ultracold temperatures, how it is performed, and a sampling of results including the determination of scattering lengths, their control via optical Feshbach resonances, precision determinations of atomic lifetimes from molecular spectra, limits on photoassociation rates in a Bose-Einstein condensate, and briefly, production of cold molecules. Discussions are illustrated with examples on alkali-metal atoms as well as other species. Progress in the field is already past the point where this review can be exhaustive, but an introduction is provided on the capabilities of photoassociation spectroscopy and the techniques presently in use.

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Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering

The development of Doppler laser cooling techniques allowed unprecedented access to ultracold temperatures of less 1 millikelvin. The motion of particles effectively ceases at such temperatures, enabling physical phenomena to be studied and controlled in extraordinary detail. Although laser cooling of atoms was demonstrated about 30 years ago, these techniques had not previously been extended to molecules. Ultracold molecules may prove even more interesting than ultracold atoms, because their greater internal complexity can potentially be exploited to investigate and manipulate a wide variety of physical phenomena, ranging from quantum information processing to chemical reactions and particle physics. Currently the only technique for producing ultracold molecules is by binding together ultracold alkali atoms to produce bi-alkali molecules. A team from Yale University now presents an experimental demonstration of laser cooling of a diatomic molecule — the polar molecule strontium monofluoride (SrF). With further refinement, the technique should enable the production of large samples of molecules at ultracold temperatures for species that are chemically distinct from bi-alkalis. Laser cooling has not yet been extended to molecules because of their complex internal structure. At present, the only technique for producing ultracold molecules is to bind ultracold alkali atoms to produce bialkali molecules. These authors experimentally demonstrate laser cooling of the polar molecule strontium monofluoride, reaching temperatures of a few millikelvin or less. The technique should allow the production of molecules at microkelvin temperatures for species that are chemically distinct from bialkalis. It has been roughly three decades since laser cooling techniques produced ultracold atoms1,2,3, leading to rapid advances in a wide array of fields. Laser cooling has not yet been extended to molecules because of their complex internal structure. However, this complexity makes molecules potentially useful for a wide range of applications4. For example, heteronuclear molecules possess permanent electric dipole moments that lead to long-range, tunable, anisotropic dipole–dipole interactions. The combination of the dipole–dipole interaction and the precise control over molecular degrees of freedom possible at ultracold temperatures makes ultracold molecules attractive candidates for use in quantum simulations of condensed-matter systems5 and in quantum computation6. Also, ultracold molecules could provide unique opportunities for studying chemical dynamics7,8 and for tests of fundamental symmetries9,10,11. Here we experimentally demonstrate laser cooling of the polar molecule strontium monofluoride (SrF). Using an optical cycling scheme requiring only three lasers12, we have observed both Sisyphus and Doppler cooling forces that reduce the transverse temperature of a SrF molecular beam substantially, to a few millikelvin or less. At present, the only technique for producing ultracold molecules is to bind together ultracold alkali atoms through Feshbach resonance13 or photoassociation14. However, proposed applications for ultracold molecules require a variety of molecular energy-level structures (for example unpaired electronic spin5,9,11,15, Omega doublets16 and so on). Our method provides an alternative route to ultracold molecules. In particular, it bridges the gap between ultracold (submillikelvin) temperatures and the ∼1-K temperatures attainable with directly cooled molecules (for example with cryogenic buffer-gas cooling17 or decelerated supersonic beams18). Ultimately, our technique should allow the production of large samples of molecules at ultracold temperatures for species that are chemically distinct from bialkalis.

Laser cooling of a diatomic molecule

Collisions of molecules in a thermal gas are difficult to control. Thermal motion randomizes molecular encounters and diminishes the effects of external radiation or static electromagnetic fields on intermolecular interactions. The effects of the thermal motion can be reduced by cooling molecular gases to low temperatures. At temperatures near or below 1 K, the collision energy of molecules becomes less significant than perturbations due to external fields. At the same time, inelastic scattering and chemical reactions may be very efficient in low-temperature molecular gases. The purpose of this article is to demonstrate that collisions of molecules at temperatures below 1 K can be manipulated by external electromagnetic fields and to discuss possible applications of cold controlled chemistry. The discussion focuses on molecular interactions at cold (0.001-2 K) and ultracold (<0.001 K) temperatures and is based on both recent theoretical and experimental work. The article concludes with a summary of current challenges for theory and experiment in the research of cold molecules and cold chemistry.

Cold controlled chemistry.

The ability to cool and slow atoms with light for subsequent trapping allows investigations of the properties and interactions of the trapped atoms in unprecedented detail. By contrast, the complex structure of molecules prohibits this type of manipulation, but magnetic trapping of calcium hydride molecules thermalized in ultra-cold buffer gas and optical trapping of caesium dimers generated from ultra-cold caesium atoms have been reported. However, these methods depend on the target molecules being paramagnetic or able to form through the association of atoms amenable to laser cooling, respectively, thus restricting the range of species that can be studied. Here we describe the slowing of an adiabatically cooled beam of deuterated ammonia molecules by time-varying inhomogeneous electric fields and subsequent loading into an electrostatic trap. We are able to trap state-selected ammonia molecules with a density of 10(6) cm(-3) in a volume of 0.25 cm3 at temperatures below 0.35 K. We observe pronounced density oscillations caused by the rapid switching of the electric fields during loading of the trap. Our findings illustrate that polar molecules can be efficiently cooled and trapped, thus providing an opportunity to study collisions and collective quantum effects in a wide range of ultra-cold molecular systems.

Electrostatic trapping of ammonia molecules

A polar molecule experiences a force in an inhomogeneous electric field. Using this force, neutral molecules can be decelerated and trapped. It is shown here that this can in principle be done without loss in phase-space density. Using a series of 64 pulsed inhomogeneous electric fields a supersonic beam of ammonia molecules ${(}^{14}{\mathrm{NH}}_{3},$ ${}^{14}{\mathrm{ND}}_{3},$ ${}^{15}{\mathrm{ND}}_{3})$ is decelerated. Subsequently, the decelerated molecules are loaded into an electrostatic quadrupole trap. Densities on the order of ${10}^{7} {\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}/\mathrm{c}\mathrm{m}}^{3}$ at a temperature of 25 mK are obtained for ${}^{14}{\mathrm{ND}}_{3}$ and ${}^{15}{\mathrm{ND}}_{3}$ separately and simultaneously. This corresponds to a phase-space density in the trap of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13},$ 50 times less than the initial phase-space density in the beam.

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Deceleration and trapping of ammonia using time-varying electric fields

The ability to cool and manipulate atoms with light has yielded atom interferometry, precision spectroscopy, Bose–Einstein condensates and atom lasers. The extension of controlled manipulation to molecules is expected to be similarly rewarding, but molecules are not as amenable to manipulation by light owing to a far more complex energy-level spectrum. However, time-varying electric and magnetic fields have been successfully used to control the position and velocity of ions, suggesting that these schemes can also be used to manipulate neutral particles having an electric or magnetic dipole moment1,2,3,4. Although the forces exerted on neutral species are many orders of magnitude smaller than those exerted on ions, beams of neutral dipolar molecules have been successfully slowed down in a series of pulsed electric fields5,6 and subsequently loaded into an electrostatic trap7. Here we extend the scheme to include a prototype electrostatic storage ring made of a hexapole torus with a circumference of 80 cm. After injection, decelerated bunches of deuterated ammonia molecules, each containing about 106 molecules in a single quantum state and with a translational temperature of 10 mK, travel up to six times around the ring. Stochastic cooling8 might provide a means to increase the phase-space density of the stored molecules in the storage ring, and we expect this to open up new opportunities for molecular spectroscopy and studies of cold molecular collisions9,10.

A prototype storage ring for neutral molecules

A series of pulsed electric fields can be arranged such that it creates a traveling potential well in which neutral dipolar molecules can be confined. This provides a method to transport, to decelerate, and to cool a sample of neutral molecules while maintaining the initial phase-space density. This method is described using the concept of phase stability. The oscillating motion of molecules in the traveling potential well, reaching a minimum velocity spread corresponding to a translational temperature of 4 mK, is experimentally observed.

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Trapping neutral molecules in a traveling potential well.

A neutral polar molecule experiences a force in an inhomogeneous electric field. This electric field can be designed such that a beam of polar molecules is exposed to a harmonic potential in the forward direction. In this potential the longitudinal phase-space distribution of the ensemble of molecules is rotated uniformly. This property is used to longitudinally focus a pulsed beam of ammonia molecules and to produce a beam with a longitudinal velocity spread of $0.76\text{ }\text{ }\mathrm{m}/\mathrm{s}$, corresponding to a temperature of $250\text{ }\ensuremath{\mu}\mathrm{K}$.

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Floris M. H. Crompvoets

Papers

Electrostatic trapping of ammonia molecules

Deceleration and trapping of ammonia using time-varying electric fields

A prototype storage ring for neutral molecules

Trapping neutral molecules in a traveling potential well.

Longitudinal Focusing and Cooling of a Molecular Beam