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=Nh  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).