# INTERNSHIP: Bell inequality in superfluid of light

# INTERNSHIP: Bell inequality in superfluid of light

When light propagates in linear medium (vacuum, air etc), photon behaves as a non-interacting gas, but when the medium is non-linear (atomic vapor or semiconductor microcavity for examples), they start flowing as a liquid called fluid of light. From the medium, photons acquire an effective interaction that may lead to macroscopic coherent behavior such as superfluidity [1,2]. This surprising behavior connected to quantum states of matter raises the question about the quantumness in fluids of light. Among the features of quantum mechanics, quantum entanglement is surely one of the most infringing and most promising. It is the fundamental resource to quantum technologies mandatory to quantum computation or quantum cryptography.

Despite its importance, determining if fluids of light encompass some form of quantum entanglement remains elusive until now. Entanglement in its most intricate version was only recently evidenced in atomic superfluids through the violation of a Bell’s inequality [3.4]. Here we want to determinate if same results can be obtained in a superfluid of light?

To that purpose, the student will have to reformulate the Bell’s inequality used in atomic context to fluids of light context. After that tow option are available depending on the student wish : (i) performing a realistic quantum Monte Carlo simulation to evaluate Bell’s inequality or (ii) used a simplified model to calculate if Bell’s inequality is violated in fluids of light context.

[1] A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,”*Nature Physics*

**5**, 805 (2009). [2] I. Carusotto and C. Ciuti “Quantum fluids of light,”

*Review of Modern Physics*

**85**, 299 (2013). [3] R. Schmied, J.-D. Bancal, B. Allard, M. Fadel, V. Scarani, P. Treutlein, and N. Sangouard, “Bell correlations in a Bose–Einstein condensate,”

*Science*

**352**, 441 (2016). [4] N. J. Engelsen, R. Krishnakumar, O. Hosten, and M. A. Kasevich, “Bell correlations in spin-squeezed states of 500 000 atoms,”

*Physical Review Letters*

**118**, 140401 (2017)

Interested candidates should contact Simon Pigeon (simon.pigeon@lkb.upmc.fr)

Numerical and/or Theoretical internship.

Duration: 3 to 6 months