PW_mar13_sample_issue

physicsworld.com
This is an unparalleled
glimpse into the inner
workings and dynamics of
many-body systems
netic field on the electron is thus to introduce a phase
shift φ on a closed-loop trajectory. Hence, if we are
able to engineer such a phase shift in the wavefunction
of a neutral atom by other means, we will have
simulated essentially the same effect.
Several possibilities have been outlined for doing
this using quantum optical control techniques. One
can, for example, engineer a Hamiltonian such that
when an atom, initially prepared in a single quantum
state, is moved slowly in space in a way that does not
induce heating (adiabatically), no quantum jumps
to other energy levels occur. For a suitable choice
of Hamiltonian, the particle can pick up a phase
during this state evolution – the so-called Berry’s
phase – which depends on the geometric properties
of the Hamiltonian. The Berry’s phase acquired
in this adiabatic state evolution then formally corresponds
to the Aharonov–Bohm phase shift of a
charged particle.
Another possibility is to use laser-assisted hopping
of particles in an optical lattice to achieve the
same net phase shift. Imagine two neighbouring lattice
sites that are shifted in energy relative to each
other, such that a single particle cannot move to
the next site without some additional help, owing to
energy conservation. Laser light tuned to the right
frequency can provide this missing energy, allowing
the particle to hop to the next site. Crucially, during
this hopping process, the matter wave of the atoms
inherits the phase of the optical wave. Laser-assisted
hopping thus allows one to tune almost at will the
phase shift produced when an atom hops from one
lattice site to the next, and to render this phase shift
position-dependent. For example, an atom hopping
around a 2 × 2 plaquette in a lattice (figure 4) thus
picks up a phase shift of φ = φ 1–φ 2 corresponding to
the Aharonov–Bohm phase shift an electron would
pick up when hopping around a lattice plaquette
while being exposed to a magnetic field.
The interesting thing about this second possibility
is that in real materials, the achieved phase shift is
limited by the strength of the applied magnetic field
and is typically small. For ultracold atoms, however,
such phase shifts can be tuned to any value between
φ = 0 and π. In a real material, one would need to
apply a magnetic field of several thousands of tesla –
some two orders of magnitude greater than the fields
generated by today’s strongest research magnets – to
achieve the same effect. How will matter behave
under such extreme field strengths? The answer is
that we don’t really know – we cannot calculate it,
which is why it is worth doing the simulations. Some
theorists have predicted that one might encounter
states that are closely related to those of the frac-
Quantum frontiers: Quantum simulation
4 Realization of artificial magnetic fields
a b
tional quantum Hall effect in 2D electron gases.
However, there is also real potential for discovering
new phases of matter.
As you might imagine, there are plenty of pathways
ahead for future research. One possibility would
be to extend high-resolution imaging techniques
to fermionic atoms, or even to polar molecules,
which have strong electric dipole moments that give
rise to long-range interactions. Being able to study
such interactions at high resolution might bring an
intriguing new perspective to our understanding of
quantum matter. Topological phases of matter with
new forms of excitations, such as Majorana fermions
– an elusive particle that is its own anti-particle, and
has only recently been discovered in a condensedmatter
setting – could be realized and probed with
ultracold atoms.
Another fundamental topic that is currently much
debated concerns how isolated quantum systems
come into thermal equilibrium; more specifically,
it would be interesting to know which observables
show thermal-like behaviour after a certain evolution
time. Being able to probe, with high spatial
resolution, how non-local correlations in the system
evolve in time would offer an exciting new way to
unravel the secrets of these dynamics. One can only
speculate, but I am sure Feynman would have been
fascinated to see how far we have come in realizing
his vision of a quantum simulator and the possibilities
it offers for future research.
n
More about: Quantum simulation
2012 Nature Physics Insight: Quantum simulation Nature
Phys. 8 263
J Dalibard, F Gerbier, G Juzeliu − nas and P Öhberg 2011
Colloquium: Artificial gauge potentials for neutral atoms
Rev. Mod. Phys. 83 1523
R P Feynman 1982 Simulating physics with computers Int. J.
Theor. Phys. 21 467
D Jaksch and P Zoller 2005 The cold atoms Hubbard toolbox
Ann. Phys. 315 52
Physics World March 2013 51
B
e –
eiφ AB
y
e iφ 1
φ
e –iφ 2
(a) An electron in a magnetic field B experiences a phase shift φ AB caused by the Aharonov–
Bohm effect as it traverses a closed loop. (b) A similar phase shift can be achieved for
neutral atoms in an optical lattice by using a laser to make them “hop” around a 2 × 2 region
of the lattice. Each hop along the x-direction imprints a phase shift φ i that depends on the
y-position of the particle. The net phase shift of the neutral atom hopping around the closed
path shown is then given by φ = φ 1 – φ 2, corresponding to an “effective magnetic field”.
x