Quantum Optics with Bose-Einstein condensates?

A Bose-Einstein condensate (BEC) is an ensemble of identical atoms
(boson having integer total spin) where almost all of the atoms occupy the same
ground state. A BEC forms as a second order phase transition (jump in the heat
capacity) below a critical temperature that is in the order of nanoKelvin (10^{-9}
K).

Below the
transition temperature, the wavelength of the atoms (due to the temperature
fluctuations) becomes longer than the mean separation between the individual
atoms. Since the wave function of the atoms overlap significantly, now, the
atoms are impossible to be distinguished from each other. The whole ensemble
behaves as a single wave (so called matter waves) and hence can be described
with a single wavefunction. BEC is not only a statistical phase transition, but
also a quantum many body phase transition. The entanglement among all of the
constituent atoms resists decoherence and randomized temperature fluctuations. Therefore,
the motion of one of the condensate atoms is correlated with the remaining
number of atoms. Due to such quantum correlations, condensate behaves as a
superfluid. A superfluid, a frictionless fluid, cannot be rotated unless each
of the ingredient atoms has angular momentum at least in the amount of *h* (Planck constant) —unless
the total angular momentum L=N*h * is supplied.

BECs are
idealized samples which are used in research to understand certain features of
manybody systems. These samples are harder to obtain experimentally, but easier
to treat theoretically. After gaining the understanding on a manybody (a new)
feature for a BEC, one can try to generalize the feature principle to higher
temperature devices. For example, BECs trapped in optical lattices (ideal
lattices obtained by standing wave laser pulses) are being studied intensively
to gain understanding on the manybody properties of crystal lattices, e.g.
metals, semiconductors. The insulator to conduction transition are investigated
using BEC in optical perfect lattices.

In our institute, we conduct active
research on the optical and quantum optical (entanglement, correlations)
features of Bose-Einstein condensates. We theoretically, as the first time,
showed that the rotational superradiant phase
transition
of a BEC —illuminated with a Laguerre-Gaussian mode
laser— can be transferred **completely**
to a vortex state. In other methods, used to pump BEC to a vortex state, only a
part of the BEC can be carried to vortex state, which are not useful
considering the BEC-pulse entanglement aspects.

In a sample of
normal phase (not superradiant), atoms radiate independently from each other.
In a sample of superradiant phase (above a critical laser pumping strength),
all of the ensemble atoms radiate all together (collectively). Above the
threshold for superradiance, ensemble atoms are mode entangled [Phys. Rev.
Lett. 92, 073602 (2004)]. Thus, the superradiant pulse emitted from the BEC
sample is also mode-entangled
with the BEC. What this means is that the electromagnetic
field measurements of superradiant pulse and the matter waves of BEC are
correlated.

Therefore, the rotatory superradiance is a fundamental
mechanism for mode entangling a BEC and pulses carrying orbital angular
momentum (e.g. Laguerre-Gaussian modes).