Degenerate Quantum Gases (BEC, DFG)

• Bose-Einstein condensate (BEC)
• Degenerate Fermi gas (DFG)
• Tuning interactions in degenerate gases
• BEC of molecules
• Degenerate gases in optical lattices simulating solid state physics

General understanding 

The general understanding of nature involves three, sometimes four states of matter. We all are well aware of solids, liquids and gases, plus – if we think about stars – plasmas. The state in which a specific “matter” is found depends on the relation between interaction energy and temperature. In 1924, a revolutionary article was published by Bose and Einstein theoretically describing that particles should undergo a phase transition at low temperatures even if there is no or negligible interaction between them. This phase transition would not rely on an interaction between the particles but occur only due to quantum statistical effects relying on the indistinguishable nature of particles with integer spin (called bosons). This was a striking prediction and it took 71 years until this phase transition could clearly be observed in dilute atomic gases by three research groups in 1995.  Only 6 years later, the Nobel Prize in physics was awarded to E. A. Cornell, W. Ketterle and C. E. Wieman “for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates”. The headline was simpler: “New state of matter revealed: Bose-Einstein condensate”. This was just a beginning of a still exploding research field. Not only are Bose-Einstein condensate the coldest things in universe – temperatures below one nK (1 billionth of a K above absolute zero) have been observed, they also show unique properties, e.g. behave as one giant matter wave. Weakly interacting particles with half integer spin (Fermions) do not undergo a phase transition to a Bose-Einstein condensate (BEC). Still one can cool them so far that quantum statistical effects dominate. The system is called degenerate Fermi gas (DFG) and again strange behavior occurs. Both types of degenerate quantum gases, BEC and DFG,  are investigated in optical lattices to study solid state physics. New methods for precise tuning of the atomic interaction were used to study effects of High-Tc super conductivity, to create molecular BECs or to investigate dipolar BECs.

Formation of Bose-Einstein condensates

Bose-Einstein condensates (BECs) are formed if the phase space density of the atom gas becomes greater than an integer number of order one. Above this point more and more atoms occupy the lowest energy state available leading to macroscopically occupied lowest energy quantum state. A more intuitive picture is based on the wave nature of the atoms. Atoms are not point like particles. They show wave-like behavior especially at low temperature. At the transition from a thermal gas to a Bose-Einstein condensate, the size of the atomic wave packet becomes comparable to the mean distance between atoms so all atoms start to feel their common identity. In order to increase the phase space density of a laser cooled atom cloud – that is making it colder and/or more dense - one transfers the atoms into a magnetic or optical dipole trap. Further cooling is achieved by evaporative cooling taking away high energy atoms and letting the remaining ones rethermalize, quite similar to the cooling of a hot cup of coffee or tea. Typically, Bose-Einstein condensation then occurs at temperatures on the order of 0.1 µK and is observed by a characteristic change in the shape of an atom cloud that was released from the trap, illuminated with a resonant laser beam and its shadow then observed with a CCD camera.

Degenerate Fermi gases

Degenerate Fermi gases (DFGs) are typically achieved under similar conditions as BEC. The main difference is Fermi gases can only be cooled to low temperature if two different “kinds of atoms” (different elements, different isotopes or different internal states) are simultaneously trapped. The typical shape of a degenerate Fermi gas is significantly different from the BEC shape and so are the physical properties. Unlike Bosons identical Fermions can not occupy a quantum state with more than one particle. So there is no macroscopic occupation of the lowest energy state with fermions. While BECs are not observed in nature, degenerate Fermi gases of non-atomic particles are present in neutron stars or in metals. Thanks to atom cooling results neutral atoms can now be studied as model systems for these systems or degenerate Fermi gases in general. 

Bose-Einstein condensates or degenerate Fermi gases were realized with the following atomic elements sorted by atomic number with year of first production: (feel free to inform us about missing species and win a TOPTICA cup)

H (1998), He* (2001), Li (1995), Na (1995), K (2001), Ca (2009), Cr (2004), Rb (1995), Sr (2009), Cs (2002), Dy (2011), Er (2012) and Yb (2003).

Tuning of interactions gives not only a new twist to the physics of degenerate quantum gases but pushes the door open wide for many fundamental studies. Most of the BEC (or degenerate Fermi gase) species show only weak interaction between the atoms (“weakly interacting BEC”).  This interaction is the standard “molecular” interaction which at low temperatures can be modeled as a hard sphere interaction. Two atoms behave as if they were “billiard” balls feeling the presence of each other only if they approach very closely (typ. 10-100 nm). This short range interaction, called contact interaction, is isotropic and the dominant interaction in BECs. Close to a “Feshbach resonance”, where a molecular bound state is magnetically shifted to the energy of the two free atoms, things can change dramatically. With tiny changes in the magnetic field, one can control the strength and the sign of this interaction, e.g. have strong repulsive, zero or even attractive interaction. Using this Feshbach resonances, one could observe interaction induced collapse of BECs, dipolar BECs and transition between molecular BECs to “High Tc super conducting” degenerate Fermi gases.  

Molecular BECs so far have been achieved starting from atomic BECs or DFGs gases. Direct trapping of molecules and cooling them down to sub-µK temperatures has not been achieved so far. Having a optically trapped atomic BEC or DFG, one can coherently transform pairs of unbound atoms into a vibrationally highly excited molecules by sweeping the magnetic field over a Feshbach resonance.  Applying laser pulses, one can then disexcite the molecules until they are in the lowest energy state. Especially interesting are diatomic molecules with a large electric dipole moment confined in optical lattices. They allow one to study or simulate unique quantum phases like super solid or checker board.

Degenerate quantum gases in optical lattices can be used to investigate solid state physics. While the atoms play the role of electrons, the optical lattice takes the part of the periodic potentials in solid states stemming from the ions. The advantages of the degenerate quantum gases are that one can tune the interaction between the particles and that one can generate very clean potentials of many different kinds and strengths. This way, one can study theoretically predicted phenomena (e.g. transition between superfluid and Mott-Insulator, Anderson localization, High Tc super conductivity) or even “quantum simulate” solid state problems which do not have an analytical solution and can not be treated numerically.

TOPTICA’s added value 

Lasers are the key instruments for degenerate quantum gases experiments. They are needed to laser cool, optically pump, optically trap, resonantly illuminate and coherently transfer the atoms. Usually, one experimental apparatus needs many lasers at different wavelengths, most of them locked very precisely with respect to atomic resonances. Research can only lead to results if all lasers are operating at the same time with the desired characteristics (e.g. linewidth, power, frequency). 
TOPTICA has always developed special lasers, e.g. diode based tunable lasers at exotic wavelength, for these applications carefully listening to scientists’ demands. As a consequence, most research groups around the world successfully use our lasers. They know that inside TOPTICA there is a big lobby for this field of research. We understand the language and the needs of scientists working with degenerate quantum gases. You will find experts at TOPTICA that are happy to find together with you laser solutions for your application, now and in the future. Feel free to contact us to discuss details of your experiment.