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 superconductors1,2,3,4,5,6,7,8,9,10. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created11,12,13,14,13. 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.

https://zenodo.org/record/1233267/files/article.pdf

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

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

Following the realization of Bose–Einstein condensates in atomic gases, an experimental challenge is the production of molecular gases in the quantum regime. A promising approach is to create the molecular gas directly from an ultracold atomic gas; for example, bosonic atoms in a Bose-Einstein condensate have been coupled to electronic ground-state molecules through photoassociation1 or a magnetic field Feshbach resonance2. The availability of atomic Fermi gases offers the prospect of coupling fermionic atoms to bosonic molecules, thus altering the quantum statistics of the system. Such a coupling would be closely related to the pairing mechanism in a fermionic superfluid, predicted to occur near a Feshbach resonance3,4. Here we report the creation and quantitative characterization of ultracold 40K2 molecules. Starting with a quantum degenerate Fermi gas of atoms at a temperature of less than 150 nK, we scan the system over a Feshbach resonance to create adiabatically more than 250,000 trapped molecules; these can be converted back to atoms by reversing the scan. The small binding energy of the molecules is controlled by detuning the magnetic field away from the Feshbach resonance, and can be varied over a wide range. We directly detect these weakly bound molecules through their radio-frequency photodissociation spectra; these probe the molecular wavefunction, and yield binding energies that are consistent with theory.

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Creation of ultracold molecules from a Fermi gas of atoms

The electronic transport properties of conventional three-dimensional metals are successfully described by Fermi-liquid theory. But when the dimensionality of such a system is reduced to one, the Fermi-liquid state becomes unstable to Coulomb interactions, and the conduction electrons should instead behave according to Tomonaga-Luttinger-liquid (TLL) theory. Such a state reveals itself through interaction-dependent anomalous exponents in the correlation functions, density of states and momentum distribution of the electrons. Metallic single-walled carbon nanotubes (SWNTs) are considered to be ideal one-dimensional systems for realizing TLL states. Indeed, the results of transport measurements on metal-SWNT and SWNT-SWNT junctions have been attributed to the effects of tunnelling into or between TLLs, although there remains some ambiguity in these interpretations. Direct observations of the electronic states in SWNTs are therefore needed to resolve these uncertainties. Here we report angle-integrated photoemission measurements of SWNTs. Our results reveal an oscillation in the pi-electron density of states owing to one-dimensional van Hove singularities, confirming the one-dimensional nature of the valence band. The spectral function and intensities at the Fermi level both exhibit power-law behaviour (with almost identical exponents) in good agreement with theoretical predictions for the TLL state in SWNTs.

Direct observation of Tomonaga–Luttinger-liquid state in carbon nanotubes at low temperatures

The core–valence correlation is introduced into ab initio relativistic pseudopotential calculations by modifying the existing core polarization potential. The salient feature of the method presented here is the use of an l‐dependent cutoff parameter (which is related to spherical harmonic functions) for solving the multicenter integrals over the 1/r4 ‐ and r/r3 ‐type operators. The method is tested on the Rb2 and Cs2 molecules considered as two valence‐electron problems. Reliable results for the molecular spectroscopic constants (Re, Te, De, and ωe ) are obtained for the ground state and the lowest excited states. Deviation from the experimental values ranges from 0.05 to 0.1 A for Re, seldom exceeds 2 cm−1 for ωe, and is of the order of 100 cm−1 for De for most of the excited states.

Nonperturbative method for core–valence correlation in pseudopotential calculations: Application to the Rb2 and Cs2 molecules

The molecular electronic structure of the twenty-six lowest lying states of Li2 at short and intermediate internuclear separations

Long-range interactions of Li(n = 2) states with each other and the long-range interaction of Li(2s2S) with Li(3s2S)

Electronic transition dipole moment functions for transitions among the twenty-six lowest-lying states of Li2

Low-lying electronic states of Li2+ and Li2−

The outer limb of the potential energy curve for the second excited 1Σg+ state of Li2 is dominated by the Li+–Li− ion–pair interaction. Consequently, the curve has a double minimum and has an unusual pattern of vibrational energy levels. We obtain excellent agreement with the vibrational levels 0⩽v⩽12 deduced from optical double resonance spectra.

James L. Fish

Papers

The molecular electronic structure of the twenty-six lowest lying states of Li2 at short and intermediate internuclear separations

Long-range interactions of Li(n = 2) states with each other and the long-range interaction of Li(2s2S) with Li(3s2S)

Electronic transition dipole moment functions for transitions among the twenty-six lowest-lying states of Li2

Low-lying electronic states of Li2+ and Li2−

The effect of Li+Li− ion‐pair interaction on the vibrational energy spectrum of the second excited state of Li2 of 1Σg+ symmetry