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Quantum frontiers: Quantum simulation
At a glance: Quantum simulation
● The idea of quantum simulation originated in a 1981 lecture
by Richard Feynman, in which he suggested that simple,
controllable quantum systems could be used to simulate the
quantum dynamics of problems that cannot be modelled by a
conventional computer
● Ultracold atoms trapped in optical lattices are a good candidate
for performing such simulations, thanks to the high degree of
control that experimentalists have over important parameters
such as the position of the atoms and the geometry of the lattice
● Recent experiments have obtained high-resolution images of
atoms trapped in these optical lattices, and also used laser
beams to flip the spins of individual atoms in a controlled way
● Future experiments with ultracold atoms may enable us to
simulate the effects of very high magnetic fields on real
materials, and perhaps even observe new phases of matter
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allow them to work around this fundamental problem,
and in many cases these techniques have given
us good answers to specific problems. However, in
other systems, especially where the electrons interact
strongly with each other, these approximations
fail or become invalid as a result of the rapid growth
of entanglement effects in many-body systems. This
rapid growth can be especially severe for a system
that has been pushed far from equilibrium and then
allowed to evolve. But does this mean we have to give
up on trying to understand how these quantum manybody
problems work? Or is there another solution?
Richard Feynman certainly thought there was. In
his visionary 1981 lecture “Simulating physics with
computers” Feynman outlined a radically different
approach to this fundamental problem: he suggested
that it might be possible to use highly controllable
quantum systems to simulate the quantum dynamics
of other – classically intractable – problems. The
idea of a “quantum simulator” was born – a “quantum
machine that could imitate any quantum system,
including the physical world”.
As with many of Feynman’s brilliant ideas, this one
has taken some time to take shape in practice. Within
the past few years, however, groups around the world
have begun to build such quantum simulators in
many different physical implementations, including
Bose–Einstein condensates, degenerate Fermi gases,
photons, trapped ions and arrays of superconducting
qubits or quantum dots. These systems all have
the virtue of being tunable, meaning that all their
interactions, potentials and other parameters can be
engineered to suit a certain model. Thanks to this
property, there is a very good chance that we will be
able to use such model systems to realize completely
new forms of matter under extreme conditions that
cannot be achieved in any other system – and in the
process, start to investigate some previously intractable
problems.
Trapped in a lattice
The root of many condensed-matter problems lies in
understanding the behaviour of electrons in a solid.
In the simplest approximation, such electrons can
be described as moving through a periodic potential
physicsworld.com
Simulations machine Christof Weitenberg working on the experimental set-up at MPQ.
generated by the positively charged ionic cores of the
atoms that make up the solid, which are arranged in
a lattice structure. One way to create such a periodic
potential in the laboratory is to use an “optical lattice”
formed by laser beams. When the beams are
superimposed on each other, their optical interference
generates a pattern of regularly spaced potential
wells. These wells are deep enough that atoms
that have been cooled to temperatures just above
absolute zero can be trapped in them, like eggs in
an egg carton. These ultracold atoms then experience
the lattice pattern of dark and bright regions
as a perfect, defect-free, periodic potential and can
move from one lattice site to the next via quantummechanical
tunnelling.
The great advantage of such a set-up is that many
parameters of this periodic potential are under the
complete control of the experimentalist. For example,
the depth of the wells can be easily changed by
adjusting the intensity of the laser beams, and the
lattice’s geometry can be shaped by interfering laser
beams under different angles. This flexibility allows
researchers to create any geometrical pattern, from a
simple cubic-type lattice structure to triangular and
hexagonal lattices like those found in graphene.
In recent years, the collective behaviour of interacting
bosonic and fermionic atoms in such optical
lattices has been a major focus of investigations with
ultracold atoms. Then, in 2011, prospects for using
ultracold atoms to perform quantum simulations
took a dramatic step forward when two research
teams (led by Markus Greiner at Harvard University
and Stefan Kuhr and myself in Munich) reported
that we had successfully obtained high-resolution
images of individual atoms in an optical lattice. The
resolution of the imaging in these so-called “quantum
gas microscopes” is so good that we can discern
the occupation of neighbouring lattice sites. To put
that into perspective, if we had this kind of resolution
in a real electronic material, we would be able to take
single snapshots of the position of all the electrons in
the material.
The way the experiments work is that ultracold
atoms in a Bose–Einstein condensate (BEC) – an
exotic state of matter in which all the component
Physics World March 2013
Thorsten Naeser, MPQ