# Quantum gases and ultracold atoms

We study gases of cold and ultracold atoms, their physics and features for the sake of quantum technology. Here are the areas we are involved into:

- Detection of correlations in optical lattices

We proposed a setup for detecting quantum correlations in strongly correlated states in optical lattices. The idea is based on the quantum polarization spectroscopy which employs Faraday rotation: the polarization of a beam of light passing through a magnetic sample is rotated by a quantity proportional to the magnetic moment of the sample. By using a standing wave configuration, as the one shown above, in which a laser illuminates ultracold atoms in optical lattices, we can characterise the state of the atoms by analysing the light polarisation at the output. We showed how to link order parameters of certain quantum phases with the output light by changing the periodicity of the standing wave.

*Further reading:*

G. De Chiara, O. Romero-Isart, A. Sanpera:

Probing magnetic order in ultracold lattice gases - Quantum impurities in degenerate gasesWe analyse the dynamics of two-level impurities immersed in a BEC. The two levels of each impurity represent the occupancy of the left and right well of a double well. We study the properties of the BEC as an environment. We show that it behaves as a Markovian and non-Markovian bath depending on its dimensionality and on the interaction strength of atoms in the BEC. We further show that multiple impurities immersed in the BEC, when close enough, they will decohere collectively and that the BEC can induce entanglement between two non interacting impurities.

*Further reading:*

P. Haikka, S. McEndoo, G. De Chiara, G. M. Palma, S. Maniscalco:

Quantifying, characterizing, and controlling information flow in ultracold atomic gases - Bosonic gases in optical cavities

We study the state of bosonic atoms trapped in an optical lattice generated by a cavity light field:

The atoms are illuminated by a transversal laser and photons are scattered by the atoms into the cavity mode. The cavity field in turn provides a trapping potential for the atoms which self-organize in a regular pattern. Depending on the strength of the pumping laser the atoms are in a Mott-insulating state or a superfluid.

*Further reading:*

S. Fernández-Vidal, G. De Chiara, J. Larson, and G. Morigi:

Quantum ground state of self-organized atomic crystals in optical resonators - Orthogonality catastrophe as a consequence of qubit embedding in an ultra-cold Fermi gas

We investigate the behaviour of a single qubit coupled to a low-dimensional, ultra-cold Fermi gas. The scattering between the system and the fermions leads to the loss of any coherence in the initial state of the qubit and we show that the exact dynamics of this process is strongly influenced by the effect of the orthogonality catastrophe within the gas. We highlight the relationship between the Loschmidt echo and the retarded Green’s function – typically used to formulate the dynamical theory of the catastrophe – and demonstrate that the effect can be triggered and characterized via local operations on the qubit. We demonstrate how the expected broadening of the spectral function can be observed using Ramsey interferometry on the qubit.

*Further reading:*

J. Goold, T. Fogarty, N. Lo Gullo, M. Paternostro, Th. Busch:

Orthogonality catastrophe as a consequence of qubit embedding in an ultracold Fermi gas - Non-locality of ultracold trapped atoms

We study the non-local properties of the fundamental problem of two trapped, distinguishable neutral atoms which interact with a short range potential characterised by an s-wave scattering length. We show that this interaction generates continuous variable (CV) entanglement between the external degrees of freedom of the atoms and consider its behaviour as a function of both, the distance between the traps and the magnitude of the inter-particle scattering length. We first quantify the entanglement in the ground state of the system at zero temperature and then, adopting a phase-space approach, test the violation of the Clauser-Horn-Shimony-Holt inequality at zero and non-zero temperature and under the effects of general dissipative local environments.

*Further reading:*

J. Goold, T. Fogarty, N. Lo Gullo, M. Paternostro, Th. Busch:

Non-locality of two ultracold trapped atoms