Study of ultra-cold degenerate Bosons and ultra-cold degenerate Fermions – Part 8

Physics Comments (0)

What is Feshbach resonances?

One of the properties of Bose-Einstein condensates or Fermi degenerate gases is the existence of interactions between the constituent atoms. Although these ultra-cold gases are typically 5 orders of magnitude less dense than air, the inter-atomic interactions strongly affect a number of their properties. A well-known feature of such low energy scattering from an attractive potential well (i.e. scattering between a molecular bound state and a colliding pair of atoms) is resonance scattering. Resonance scattering occurs when a bound state of the potential is very close to the collision energy of the atoms. The presence of the bound state near zero energy profoundly affects the scattering physics. This is because the colliding atoms can make a transition to the bound state and dwell there briefly before moving apart again after the collision. The biggest effect on the scattering occurs when the two levels have exactly the same energy, which causes the elastic cross section and scattering length to reach infinite values.

For controlling the interactions between the constituent atoms in these ultra-cold gases, it was suggested almost one decade ago, that the scattering length could be influenced using an external magnetic field. The magnetic field would allow one to shift the energy of a molecular bound state to near-degeneracy with the energy of a colliding pair of atoms, thereby altering the elastic scattering properties. Such an effect is called a Feshbach resonance and was first studied in nuclear scattering. Feshbach resonances are quantum mechanical scattering resonances. Hence a Feshbach resonance occurs when the state of two free colliding atoms couples to a molecular bound state, and can be induced by an external magnetic field.

Rovibrational coupling

Rovibrational coupling is a coupled rotational and vibrational excitation of a molecule. Generally vibrational transitions occur in conjunction with rotational transitions. Rovibrational states correspond to simultaneous rotation and vibration of the molecule.

Photoassociation

When two colliding atoms separated by distances of a few Angstroms (interatomic distances of tens to hundreds of Angstroms) absorb a photon, from an applied laser field, they could fuse together to form a molecule. This process is known as photoassociation.  Here the molecule is electronically excited and will subsequently decay either back to a pair of free atoms or to a ground-state molecule. This downward decay process generally leads to a range of ground rovibrational states being populated. The downward decay can be controlled in a “pump-dump” scheme by using a second photon of different energy. Using this kind of “pump-dump” scheme on ultra cold atoms held in a magneto-optical trap can produce tightly bound ultracold molecules. But the production rate is often very low and the state selectivity can be poor. Recently in a variety of atomic gases molecules in the absolute (singlet) rovibrational ground state have been produced.

Formation of ultracold molecules

Following the realization of Bose–Einstein condensates in atomic gases, the formation of ultracold molecules is a new and rapidly developing area in the physics of quantum degenerate gases.

The advent of laser cooling and evaporative cooling has resulted in the realization of quantum degenerate Boson gases in the form of Bose-Einstein condensates (BEC) and Fermi-degenerate gases. However, the laser cooling techniques used to realize quantum degeneracy in case of dilute atomic gases do not work for molecules due to the complicated level structure of molecules i.e. their complex internal rotational and vibrational structure. The evaporative cooling requires the preparation of a dense gas of molecules, where elastic collisions dominate inelastic collisions.

Initially a wide range of techniques were pursued, including Stark deceleration, buffer gas cooling, electrostatic velocity selection, optical Stark deceleration, Zeeman deceleration, and collisional cooling in crossed molecular beams. Now they have succeeded in cooling molecules by creating ultracold molecules from quantum-degenerate atomic samples. This is accomplished either by photoassociation or by ‘‘tuning’’ a molecular state via a Feshbach resonance to be degenerate with the atomic state. A Feshbach resonance occurs when an applied magnetic field Zeeman shifts a molecular state to zero binding energy. By ramping an external field across a Feshbach resonance from negative to positive scattering length, translationally cold molecules in high vibrational states can be created adiabatically. For example, bosonic atoms in a Bose-Einstein condensate have been coupled to electronic ground-state molecules through photoassociation or a magnetic field Feshbach resonance. Also when fermionic atoms are coupled to bosonic molecules the quantum statistics of the system alters. Such a coupling would be closely related to the pairing mechanism in a fermionic superfluid, predicted to occur near a Feshbach resonance, for example the creation of ultracold ⁴⁰K₂ molecules.

The realization of a molecular condensate can be used in the study of quantum gases with anisotropic dipolar interactions, tests of fundamental symmetries such as the search for a permanent electric dipole moment, study of rotational and vibrational energy transfer processes, and coherent chemistry, where reactants and products are in coherent quantum superposition states.

Here we shall discuss the work done by two groups who have reported in Physical Review Letters to have created ultracold molecular gases. F. Lang, K. Winkler, C. Strauss, R. Grimm, and J. Hecker Denschlag at the University of Innsbruck reported their successful creation of an ultracold gas of ground-state Rb₂ molecules close to quantum degeneracy and , J. Deiglmayr, A. Grochola, M. Repp, K. Mörtlbauer, C. Glück, J. Lange, O. Dulieu, R. Wester, and M. Weidemüller at the University of Freiburg have successfully created ultracold LiCs molecules.

Work done by F. Lang, K. Winkler, C. Strauss, R. Grimm, and J. Hecker Denschlag

In their quest to create ultracold molecules Lang and his group combined optical transfer techniques with the production of Feshbach molecules. They used an optical scheme to selectively produce cold and dense samples of deeply bound molecules in a rovibrational ground state.

First they used an atomic 87Rb Bose- Einstein condensate to produce a 50 μm-size pure ensemble of 3 x 10⁴  weakly bound Rb₂ Feshbach molecules using a Feshbach resonance at a magnetic field of 1007.4 G (1 G = 10^-4T). Then they optically transferred the dense ensemble of Feshbach molecules to a single quantum level in the rovibrational ground (the absolute lowest quantum state) state of the Rb₂ triplet potential. The transfer was carried out in a single step using stimulated Raman adiabatic passage (STIRAP). This required the application of two laser fields that couple the initial and final molecular states to a common electronically excited state i.e. STIRAP converts the initial Feshbach molecular state into the final ground molecular state upon the application of the appropriate sequence of laser pulses. They found this technique to be extremely efficient with an efficiency of almost 90%. Also the STIRAP uses a counterintuitive pulse sequence during which molecules are kept in a dynamically changing dark superposition state that avoids populating the short-lived excited state thereby suppressing losses due to spontaneous emission.

In all of these experiments the molecular fraction is detected by simply repeating the STIRAP process in reverse and then dissociating the Feshbach molecules.

The molecules are held in the lowest Bloch band of a cubic 3D optical lattice with no more than a single molecule per lattice site and an effective lattice filling factor of about 0.3. The molecules exhibit a trap lifetime exceeding 200 ms, after an initial relaxation within 50 ms. The optical lattice was formed by the interference of several laser beams.

They also observed coherent motional dynamics of the molecules in the lattice potential. From this they concluded that besides the internal degrees of freedom, the external degrees of freedom are also precisely defined after transfer. The transfer of molecules into a single Bloch band was possible, either by matching the lattice depths of weakly and deeply bound molecules, or by spectroscopically resolving the Bloch bands. The latter involves longer STIRAP pulses and more tightly phase-locked Raman lasers, with the added benefit of increasing the transfer efficiency further.

December 15, 2008