malcolm jardine internship poster - 2016-2
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Background
Results
Conclusions
Quantum optics is the field of research in which the interaction of light and matter at the atomic scale is investigated.
Theory
Transport Dynamics in Quantum
Gas Microscopes
Major experimental and
computational advances
have been made recently
which have allowed
many new, radical
experiments to be
undertaken (Figure [1])
and new theories to be
tested.
Figure [1]
Aims
Laser beam
Optical lattice
Particles `hopping’ Figure [2]
at the university of strathclyde
department of
physics Malcolm Jardine | Supervisors: Andrew J. Daley, Anton Buyskikh
Special thanks: Jorge Yago
Funded by: Interns@Strathclyde
Any further questions please contact: malcolm.jardine.2013@uni.strath.ac.uk
Quantum optics experiments can be undertaken by creating an optical
lattice using counter-propagating laser beams. This is an artificial crystal
of light that physicists can insert particles into, where there is single
particle control and resolution.
Goal of project was to simulate the dynamics of a large number of
atoms in an optical lattice.
Allows us to emulate electron transport in materials such as high
temperature superconductors and address fundamental ideas about
matter.
Method
Particles interacting
In response to the inability of the Hubbard model to be calculated, the
technique of using Matrix Product States (MPS) [2] was developed. This
represents the system in a different way: instead of all possible
combinations, only the most relevant ones are used. This information is
then broken into small pieces that are affordable to compute.
Quantum mechanics has to consider all possible
combinations of particles on lattice.
Lattice of 300 particles on 100 lattice sites has more configurations
than there are particles in the universe.
Conventional methods on computers cannot solve worthwhile sized
Hubbard model systems.
Log 1
0(E
xact
—M
PS)
Time
Site occupation
allowed
Difference in hopping between exact and MPS calculations
Figure [3]
The Hubbard model was solved numerically using standard methods but
could only be solved for small systems, which is not useful for
experiments. Therefore MPS was needed to go to bigger systems.
The Hubbard Model provides an effective mathematical description of
an optical lattice
This model accounts for atoms `hopping’ between neighbouring sites,
or interacting if they are on the same site
Problem arises trying to solve this computationally
Hubbard Model Challenges
Single atoms in an optical lattice
in a quantum gas microscope
We computationally model these many-particle
interacting systems to study matter at a
fundamental level where quantum physics
dominates, accessing properties such as
movement of atoms along the lattice.
Figure 3 shows the difference in the magnitude of hopping that was
predicted by the MPS and exact calculations. The two solutions should
converge, and this is seen up to certain degree of accuracy.
Using these results it is now possible to start going beyond what is
possible via standard techniques. Therefore more realistic and useful
systems can be simulated.
MPS technique can be used on much larger quantum optics systems than exact calculations are able to do.
Investigated this by showing MPS techniques can replicate the result of a Hubbard model simulation which used conventional methods.
The future steps will be to take the MPS code and apply it to more interesting systems and geometries, with the possibility that these can be
replicated with experiments.
[1] Haller, E., Hudson, J., Kelly, A., Cotta, D.A., Peaudecerf, B., Bruce, G.D. and Kuhr, S. (2015) ‘Single-atom imaging of fermions in a quan-
tum-gas microscope’, Nature Physics, 11(9), pp. 738–742. doi: 10.1038/nphys3403
[2] Schollwöck, U. (2011) ‘The density-matrix renormalization group in the age of matrix product states’, Annals of Physics, 326(1)
i1
i2
iN
. . . i1
i2
A1 A2 . . .
iN
AN MPS
construction
What information is kept? The information that is most important for
the low energy dynamics.
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