Russian and German physicists developed a mathematical model of trapped atoms and ions

September 13, 2018, RUDN University
Atoms in a trap. Credit: RUDN University

A team of physicists from RUDN, JINR (Dubna), and the University of Hamburg (Germany) developed a mathematical model for describing physical processes in hybrid systems that consists of atoms and ions cooled down to temperatures close to absolute zero. Such atom-ionic systems might serve as a basis for the elements of the quantum computer—a device operating on quantum phenomena and exceeding regular computers by calculation speed. Right now, this is just a hypothetical concept, but the new development could make it reality sooner. The results of the study were presented at the 22nd International Conference on Few-Body Systems in Physics that took place in Caen (France) in July 9-13.

It is difficult to study processes at the level of and ions at room temperature due to their , which causes disturbances that lead to considerable inaccuracy of measurements. The main cause of observation errors is the Doppler effect. However, if the atoms are cooled down, reducing the speed of their thermal motion, this effect can be suppressed.

Atoms can be cooled using a laser, but it's important to select the proper frequency and direction. The same laser can create a so-called trap for cooled atoms—a standing light wave (i.e. a wave that does not move but fluctuates in one place) keeps the atoms fixed in a confined region of space. This trap can be compared to an egg case that prevents the eggs from moving around. Such a trap can be used as a model system for studying processes including and . However, it is quite difficult to give a detailed mathematical description of systems of trapped quantum particles.

"The two-body problem (e.g. a hydrogen atom or two colliding atoms) is the basis of quantum mechanics. Each body has three coordinates (X, Y, and Z). In free space, this problem may be reduced to relative motion of two particles by separation of their center-of-mass. The number of variables left in the problem is now three instead of six. The absence of a preferred direction helps reduce this problem to an even simpler one-dimensional radial equation (i.e. an equation with one variable) by separation of angular variables. But when two are trapped, an additional condition appears, which is preferential direction. In this case, the problem cannot be reduced to a one-dimensional equation. It becomes two-dimensional if the atoms are identical and six-dimensional if they are distinguishable or if an atom-ionic system is considered. Many scientists are able to solve two-dimensional equations, but three-dimensional ones are already quite a complicated problem for modern numerical mathematics. This is the area where new methods have to be developed," said Vladimir Melezhik, the author of the study.

Together with physicists from the University of Hamburg, Melezhik developed a mathematical method reducing multi-dimensional calculations to a system of one-dimensional equations to simplify and speed up the calculations. The authors used it to describe atomic systems with different parameters (intensity of effective interparticle interaction, initial state population, and particle energy). The method also proved applicable to hybrid atom-ionic systems. If ions are trapped, new complex quantum effects can be studied. The developed algorithm provides for the calculation of collisions of and ions to each other and the laser trap. In the future, such hybrid structures can potentially help to model the elements of quantum computers.

Explore further: Theoretical physicists model complex quantum processes with cold atoms and ions

More information: The author acknowledges the support by the Russian Foundation for Basic Research, Grant No. 18-02-00673.
22nd International Conference on Few-Body Systems in Physics:
Abstracts: … ook_fb22_caen_en.pdf

Related Stories

Quantum mechanics: entanglements in ultracold atomic clouds

June 27, 2018

A system's state is characterised as entangled or quantum correlated if two or more particles cannot be described as a combination of separate, independent states but only as a whole. Researchers at the Kirchhoff Institute ...

Ions in the spotlight

November 2, 2017

The results of a research group from the Institute of Physics at the University of Freiburg has been given a special place in Nature Photonics. An accompanying "News & Views" article in the print version of the science journal ...

Physicists find evidence of an exotic state of matter

December 22, 2017

Using ultracold atoms, researchers at Heidelberg University have found an exotic state of matter where the constituent particles pair up when limited to two dimensions. The findings from the field of quantum physics may hold ...

Recommended for you

How heavy elements come about in the universe

March 19, 2019

Heavy elements are produced during stellar explosion or on the surfaces of neutron stars through the capture of hydrogen nuclei (protons). This occurs at extremely high temperatures, but at relatively low energies. An international ...

Trembling aspen leaves could save future Mars rovers

March 18, 2019

Researchers at the University of Warwick have been inspired by the unique movement of trembling aspen leaves, to devise an energy harvesting mechanism that could power weather sensors in hostile environments and could even ...

Quantum sensing method measures minuscule magnetic fields

March 15, 2019

A new way of measuring atomic-scale magnetic fields with great precision, not only up and down but sideways as well, has been developed by researchers at MIT. The new tool could be useful in applications as diverse as mapping ...


Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.