The dynamics of atomic gases at ultracold temperatures are a particular challenge for scientists. Researchers from the Center for Optical Quantum Technologies at Universität Hamburg have developed an approach that describes correlations between many particles and helps to develop new techniques. The scientists report their findings in the journal Physical Review A.
Simulating accurately the dynamics of atomic gases out of equilibrium at ultracold temperatures constitutes a great challenge. This is due to two major obstacles, Dr. Sven Krönke from the group of Professor Peter Schmelcher, explains: “First, collisions of atoms lead to correlations which are in general difficult to describe. Second, at such low temperatures the dynamics of gases is governed by quantum mechanics.” Simulating a gas with all details, that is resolving the state of each and every atom, becomes extremely difficult and eventually impossible if one considers more and more atoms, the scientist concludes.
Approaches which directly address coarse-grained quantities
In praxis, however, this fully detailed view on such a quantum gas is often not needed. Typically, scientists are mainly interested in coarse-grained quantities such as the spatial density or velocity distribution. Schmelcher: “Thus, it is very appealing to develop theoretical approaches which directly address such coarse-grained quantities without explicitly describing the state of each and every atom.” The so-called Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations belongs to this kind of theoretical approaches and aims at describing only the dynamics of low-dimensional effective properties of gas instead of resolving each atom’s motion individually.
The scientists developed a BBGKY approach which is tailored to so-called bosonic quantum gases, that is gases of atoms with integer spin. For this purpose, they carefully constructed a corresponding truncation approximation for the BBGKY hierarchy and worked out striking differences to the case of fermionic gases. Fermionic gases are gases of atoms with half-integer spin and have been much more in the focus of previous research.
Describing correlations between many particles
By using a highly efficient representation of the underlying mathematical approach, the researchers could truncate the hierarchy of equations of motion at very high orders. Krönke: “This means that our theoretical approach can describe correlations between many particles.” They applied their approach to two typical scenarios, namely tunneling dynamics and collective oscillations, and found that it accurately describes the short-time dynamics. At longer times, however, the BBGKY hierarchy is plagued by instabilities and gives inaccurate predictions. “We analyze this behavior in detail and develop techniques to mitigate those instabilities”, Krönke concludes.
The research was supported by the cluster of excellence CUI. Text: CUI
S. Krönke and P. Schmelcher
“The BBGKY Hierarchy for Ultracold Bosonic Systems”
Physical Review A 98, 013629 (2018)