PW_mar13_sample_issue

Quantum frontiers: Quantum simulation
3 Controlling single spins in an optical lattice
50
a b
y
x
addressing laser beam
atoms in 2D optical lattice
microwave
6.8 GHz
For example, if we send a laser beam in the reverse
direction through the high-resolution microscope
objective, we can focus the beam onto single sites of
the lattice and selectively flip the spin states of each
atom (in other words, between different hyperfine
spin states) in the microscopic array. By moving the
beam along a controlled pathway, an arbitrary spin
pattern can thereby be imprinted onto the gases.
The spin-flipped atoms can be made visible by first
removing the unaffected (non-addressed) atoms
and then imaging the remaining (addressed) ones.
Examples of such single-atom spin orderings can be
seen in figure 3. Once these spin patterns have been
prepared, they could form the initial conditions for
observing interesting non-equilibrium dynamics.
For example, one can track the motion of a singleparticle
impurity in the many-body system, observe
the dynamics of domain walls between regions of
different magnetization, or track the collision of two
spins at energies of a few pico-electron volts. The
possibilities for interesting configurations abound.
Artificial fields
Another condensed-matter problem that ultracoldatom
researchers have long wanted to simulate concerns
the effect of a magnetic field on the electrons
in a 2D electron gas. For a single electron moving in
free space, the presence of a magnetic field with a
component perpendicular to the electron’s direction
of motion creates a Lorentz force that pulls the electron
into a circular “cyclotron” orbit. If the electron
y
x
physicsworld.com
(a) Controlling the spins of atoms in an optical lattice requires a laser beam to “address” the atoms as well as a microwave field. When this addressing laser beam is
focused onto a single atom, it shifts the frequency of a transition between two spin states of the atom. If the frequency of the microwave field is set so that it is
resonant with this shifted transition frequency, only the addressed atoms will have their spins flipped when the field is applied. By moving the addressing beam to
different lattice sites, arbitrary spin patterns at the single-spin level can be prepared (b–c). Such precise control of spin patterns is a crucial first step to a number of
interesting experiments, including the creation of a practical, scalable quantum computer using ultracold atoms.
c
2 μm
is instead moving through a conductor, this same
Lorentz force produces a voltage difference across
the conductor – the Hall effect. But when a 2D electron
gas in a very pure semiconductor at very low
temperatures is exposed to a magnetic field, something
more dramatic can happen: the Hall effect
becomes a quantum phenomenon, with the conductance
in the semiconductor equal to ν e 2 /h. The coefficient
ν can take either integer or fractional values,
and the fractional quantum Hall effect, in particular,
remains a hot topic in condensed-matter research
more than 30 years after its discovery. However, a
severe problem exists in trying to simulate such physics
with ultracold atomic gases: because atoms are
neutral, they do not experience any Lorentz force in
a magnetic field. One might expect that this would
prevent quantum-Hall-type effects from being realized
in an ultracold-atom system, but in fact there
may be a way around this problem.
To understand how we might overcome such an
apparently fundamental difficulty, let us take a closer
look at what, on a quantum-mechanical level, the
effect of a magnetic field, B, on a charged particle
really is. When an electron encircles an area with an
enclosed magnetic flux, its wavefunction acquires a
phase shift. This is known as the Aharonov–Bohm
phase, and its value is given by φ AB = 2π Φ/Φ 0 where
Φ is the flux enclosed in the trajectory of the electron
and Φ 0, the magnetic flux quantum, is equal to the
ratio of Planck’s constant to the charge on an electron.
The quantum-mechanical effect of the mag-
Physics World March 2013
I Bloch, MPQ