# Master and PhD position : Superfluidity of light

## Superfluidity at room temperature and above

#### Quantum Hydrodynamics

Quantum fluids Physics is the study of hydrodynamic systems which demonstrate a quantum behavior. A large range of many-particle systems are currently under intense investigation, from liquid Helium, to electrons in solids, to quark-gluon plasma and trapped gases of ultra-cold atoms. Surprisingly, these very different systems show similar behavior when the thermal de Broglie wavelength becomes comparable or larger than the average inter-particle spacing. In this regime, the Bose versus Fermi statistics of the particules starts playing a critical role in determining the properties of the fluid. For exemple, in a non-interacting Bose gas a macroscopic fraction of the particules will accumulates in the lowest-energy state leading to a Bose-Einstein condensate. When interactions between particules are not negligible, the Physics become even more fascinating with the appearance of purely quantum effects such as supra-conductivity and superfluidity.

#### Quantum fluids of light

Historically, most work in many body-physics (theoretical and experimental) are dealing with massive material particules (atoms, electrons…). However, we know since the early days of quantum mechanics, that photons in a box can be interpreted as a massless Bose gas of non-interacting particules and this interpretation leads to a correct calculation of the black-body radiation. Recently, it has been realized that under suitable circumstances photons can acquire an effective mass and will behave as a quantum fluid of light with photon-photon interactions. Striking experimental demonstrations of superfluidity and other quantum hydrodynamics effects such as quantized vortices and solitons have been performed using semi-conductor planar micro-cavities. Building on these experiments done by the LKB group, we propose to use a different geometry (propagating light instead of confined) to study quantum fluids of light.

#### Superfluidity of light in propagating geometries

An alternative to the confined geometry is to use a non-linear χ(3) medium showing an intensity de- pendent index of refraction and a propagating monochromatic light field. Striking similarities appears under the paraxial approximation, where the electric field of the monochromatic light can be described by the formalism of the Gross-Pitaevskii equation for the order parameter of a superfluid or equiva- lently the macroscopic wave-function of a Bose-Einstein condensate. However, an important difference must be highlighted. As the Gross-Pitaevskii equation describes the evolution of superfluid Helium or ultra-cold atomic cloud macroscopic wave-function in real-time, the non-linear wave equation for the electric field refers to an evolution in space along the propagation direction. It is therefore crucial to have in mind this space-time mapping when discussing fluids of light in the propagating geometries. The actual Bose gas under investigation is a 2D quantum fluid of light in the transverse direction. In the propagation direction, imaging at different positions give direct access to the temporal evolution of the fluid in position and momentum space.

## Project : Quantum fluid of light in a atomic vapor cell

During this internship/PhD you will be investigating a new system based on photons propagating in a non-linear medium, for the study of interacting Bose gases with unique control of generation and manipulation.

To implement an experiment on quantum fluids of light in the propagating geometry, the most im- portant parameter is the choice of the non-linear medium, as it will drive the photon-photon interaction. In our group we use alkali-atomic vapor cells at room temperature or higher as the non-linear χ(3) medium needed for inducing photon-photon interactions. Rubidium or Cesium are commonly used, as they have transitions accessible in the near-infrared and a level structure which allows strongly enhanced non-linearity.

The most basic approach to benefit from a third order Kerr non-linearity is to set the excitation light field near an atomic resonance as the non-linear part of the index of refraction can be tuned from positive to negative depending on the detuning from resonance. This effect is known in Optics under the name of Kerr self-focusing or self-defocusing (depending on the sign of the non-linearity). Intuitively, we can make an analogy between an attractive (resp. repulsive) photon-photon interaction and Kerr self-focusing (resp. self-defocusing). In this regime the non-linearity increases with the atomic density (which itself grows with the temperature) and decreases with the detuning to resonance (which can be tune quickly during the experiment). This system therefore offers a great flexibility for tuning the non-linearity parameter.

The main objective of this internship is to demonstrate superfluidity of light in this configuration. This will be the first demonstration of superfluidity at room temperature or above as all the previous experiments need complex cryogenic systems. Numerical simulations on atomic systems could also be conducted if the candidate is interested, but the core part of the project is experimental. In the long term, we plan to study hydrodynamic generation of quantized vortices and solitons in quantum fluid of light and we will develop an experiment to see the opto-mechanical signature of superfluidity on a mechanical resonator.

Recent results have been obtained on this topic in collaboration with the group of Daniele Faccio in Edinburgh and we are looking for a motivated, smart and curious candidate who wants to join the Quantum Optics group to conduct these experiments.

Interested candidates should contact Quentin Glorieux (quentin.glorieux@lkb.upmc.fr) and Alberto Bramati (bramati@lkb.upmc.fr).

For more details, please check our website: www.quantumoptics.fr.Experimental internship.

Duration: 3 to 6 months. Possible PhD.