Entanglement with quantum gates in an optical lattice

The concept of a "quantum computer" has attracted much attention in
recent years. Many research groups around the world are studying
the extraordinary potential of quantum computers and attempting
their realisation. Current fundamental experiments are directed
towards the individual building blocks of such a computer. The
concept of using quantum mechanical systems to calculate complex
problems was created in 1982 with Feynmans proposal of the quantum
simulator. This concept represents a well controlled framework of
interacting quantum systems. The intention is to map a different
system of interest not mastered in the lab onto the quantum
simulator. From the behaviour of the quantum simulator the
behaviour of the system of interest can be deduced. A quantum
mechanical measurement on the quantum simulator is thus comparable
to one run of a numerical simulation of the system of interest. The
difference is that a numerical simulation can often only be run
under severe simplifications that then challenge the practical
relevance of the result. Only very small quantum systems can be
calculated on today's computers without simplifications. In this
work a system of ground state atoms stored in a 3D optical lattice
is presented. Each of the up to 100,000 atoms is stored in its own
potential minimum, isolated from the other atoms. This state is a
formidable starting point for the realisation of a quantum
simulator: every atom is considered the information carrier of a
spin-1/2 system. Only very few of the other concepts currently
under investigation have as many information carriers as a
Mott-Insulator state in an optical lattice. We have already shown
in preparatory experiments a long storage time and good coherence
times. Here this system is extended by a major prerequisite for a
quantum simulator: controllable interactions between individual
atoms are essential in order to model the interaction terms of the
system of interest. These interactions are realised by a
state-selective in the optical lattice by state-selective trapping
potentials. If the states of an atom are called |0> and |1>,
then there are two distinct potentials V0 and V1 that each act on
only one of the states. The two potentials are shifted with respect
to each other and thus allow bringing neighbouring atoms into
contact. Since the shifting is always performed along one of the
three lattice axes, the interaction is not confined to a single
pair of atoms, but all pairs of neighbouring atoms along a lattice
axis interact. This inherent parallelism has allowed us to create
entanglement in large systems in just a single operation. The
entanglement has then been measured in a Ramsey interferometer. A
sequence of one nearest-neighbour interaction produces the cluster
state, a maximally entangled state. More recent proposals suggest
to use a cluster state as the basis for a new kind of quantum
computer. As opposed to today's computers, this quantum computer
would not be a Touring machine whose working algorithm is only
controlled by programming. Instead the wiring of the quantum gates
would have to be changed in order to solve a new problem. This is
loosely comparable to today's FPGA (Field Programmable Gate Arrays
- programmable logic chips). Until these quantum computers are
built, quite some improvements on the experimental techniques will
be necessary. But the first quantum simulators are now practically
within reach.