Complete report - Donostia International Physics Center - Euskal ...

2011 DIPC Highlight
One dimensional bosons:
from condensed matter systems
to ultracold gases
M.A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol
Reviews of Modern Physics 83, 1405-1466 (2011)
We review a century of both experimental and theoretical results on interacting bosons systems
in one dimensions. We also discuss current problems and future challenges.
When matter is forced to move predominantly on a line, qualitatively new kinds of behavior emerge. At
the individual level, we are all painfully familiar with this situation, as we experience it every time we are
ourselves trapped in a traffic jam or we have to queue to buy movie tickets, for example. However, if we
forget about the individual aspect of being forced to move on a line, we can easily grasp its collective
side: in order to move (forward or backward), all individuals in the queue must agree to do so. This collectivizes
any motion and turns it into a highly correlated phenomenon: if one individual moves, it is because
all the others also do to some degree.
Indeed, microscopic particles like atoms or electrons, which behave according to the laws of Quantum
Mechanics, also experience this kind of collectivization when they are confined to move on a line. Although
this was theoretically discovered very early in the history of Quantum Physics, but for a long time
the study of models of systems of quantum particles interacting on the line was regarded as a theorists'
playground; It was a field for the more or less mathematically inclined theoretical physicists to occupy
themselves trying to solve toy models, which -it was hoped- could shed light into the complexities of real
materials where particles move in all three familiar dimensions of space.
Understanding the properties of matter confined in narrow channels is becoming more and more necessary
as the size of elements of microchips is pushed towards the limits of miniaturization by the electronics
industry. In the future, the properties of electronic devices, as well as the wires connecting them, will be
strongly affected by quantum effects. This will lead to electronic “traffic jams”, which make it difficult the
transmission of currents in such devices, and which will also require the development of new devices that
exploit the properties of one dimensional systems. Moreover, new materials with strong direction-properties
may be created: For example, heat conductors that conduct heat very efficiently in only one direction
while remaining cool (due to a poor heat conductivity) in the other directions.
Figure 1. Phase diagram of a coupled 1D Boson system. K is a dimensionless
parameter that Measures the strength of the interactions
amongst the bosons in 1D. J is the strength of the Josephson coupling
(quantum tunneling) between the the 1D systems.
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