We will deal with Continuous Variables Quantum Complex Networks.

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This project concerns the implementation of complex quantum networks, i.e. quantum systems organized in a complex structure depicted as networks, and their exploitation for quantum simulations and optimized quantum information technologies.

The experimental implementation is based on multimode quantum process based on parametric interaction and time/frequency modes of femtosecond lasers (near-infrared and telecom wavelengths). Networks structures are encoded in the quantum correlations of continuous variables of the involved fields.

Candidates must hold an internationally recognized PhD in a field related to experimental quantum physics. A good background and past research/publication track record in experimental optics, and quantum physics is required. Knowledge of quantum information would be an advantage.

Application procedure: Inquiries and applications should be sent by email to Valentina Parigi (valentina.parigi@lkb.upmc.fr). Applications should include a detailed CV, a brief statement of research interests and two names of potential referees.

The position is founded by the ERC grant COQCOoN (COntinuous variables Quantum COmplex Networks) of Valentina Parigi, expected starting date: June 2019.

The team is part of the Multimode Quantum Optic team at Laboratoire Kastler Brossel (PIs: Nicolas Treps, Valentina Parigi and Claude Fabre)

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.

We will address a new way of testing light superfluidity by studying the drag force that a photon fluid exerts on a mobile obstacle. This experiment is based on a movable defect, a nanofiber, immersed in an atomic vapor so that the refractive-index mismatch provides a constant potential.

A light beam hitting the nanofiber tip at a small angle, will create a flow around the impurity, or in optics language, a radiation pressure force resulting in the opto-mechanical deformation of the obstacle. We expect to observe a cancellation of this “optical drag force” at high intensity indicating a superfluid flow of photons around the obstacle.

In terms of optics, this leads to a non-intuitive cancellation of the radiation pressure thanks to non-linear interactions.

We are currently building a setup to detect with very high precision (about 20 nm) the position of the nanofiber. By monitoring the position of the nanofiber, we will measure the small radiation pressure force exerted by a laser beam on the nano-object. First, we are going to perform preliminary measurements with light propagating in air (linear medium). In this condition, the radiation pressure force should be an increasing function of the incident laser power. The second step of the project will be to immerse the nanofiber in an atomic vapor. When light propagates through this nonlinear medium, it becomes superfluid above a critical laser power (i.e. above a critical photon density). In that case, we will measure the force acting on the the nanofiber as a function of the incident laser power. Contrary to air, we expect that, above a critical value of the intensity, the force is going to vanish, revealing the superfluid nature of light.

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

PDF Version : Mechanical_Signature_Superfluidity_2017

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.

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.

Quantum wells embedded in microcavities are systems where the interaction between matter (excitons) and the light (photons) exhibits unusual characteristics. In the regime of strong coupling between excitons and the photons, the fields can be described as a pseudo-particle, which is a mixed state of light and matter. These pseudo-particles are called polaritons.

These polaritons are bosons that are confined in a 2D structure (transverse plane of the microcavity). Due to Coulombian interactions, fascinating phenomena such as superfluidity and Bose-Einstein condensation can be observed.

The LKB Quantum Optics group has a recognize expertise in this domain and is looking forward on developing a new experimental setup to study the propagation of polariton superfluids in an optically controlable potential landscape. As we already demonstrated in the group, a defect in the microcavity acts like a potential well and induces the formation of vortices, anti-vortices and solitons. With a non-resonant light source, one can induce artificial defects in the cavity by injecting excitons. We aim at building an experiment in which the transverse beam profile can be set arbitrarily and reconfigure easily. This can be achieved using a Spatial Light Modulator (SLM) in addition with an algorithm that generate a numerical hologram in the Fourier plan.

The internship is proposed to Master 2 students and can be followed by a PhD in the group.

Interested candidates should contact Quentin Glorieux (quentin.glorieux@lkb.upmc.fr) and Alberto Bramati (bramati@lkb.upmc.fr) for more details. For more details, please check our website: www.quantumoptics.fr.

** **The last 20 years have seen a rapid development of ideas and proof-of-principle experiments regarding quantum technologies: quantum communication, quantum computation, quantum metrology and quantum simulation. If it is already clear that in principle the quantum world can provide useful advantages in terms of security, efficiency, speed, and sensitivity, we still need to solve the scalability problem. Indeed, generating simple systems for coding and manipulating quantum information is relatively easy. However, it is still not evident how to handle large quantum systems involving many degrees of freedom, in order, for instance, to implement a complete architecture where the quantum approach provides a real advantage compared to conventional systems.

The Quantum Optics group at Laboratoire Kastler Brossel developed in the last years an all-optical solution using the different wavelengths of light as quantum channels and, within each quantum channel, the optical field quadratures to encode quantum information. In this regime, we demonstrated the scalability of multimode entanglement[1,2]. Furthermore, this resource can be tuned at the measurement stage to allow for the on-demand construction of quantum networks suitable for measurement based quantum computing[3,4].

This highly scalable entanglement is of Gaussian nature, in the sense that all measured quantities display Gaussian statistics. While this is sufficient for quantum metrology, it can be proved that any calculation performed using these states can be efficiently simulated using a classical computer. Thus, moving away from Gaussian statistics is a requirement to demonstrate quantum supremacy. We have implemented this *de-gaussification* operation using mode dependent photon subtraction[5], while demonstrated theoretically that it can lead to a type of entanglement fundamentally different from the Gaussian one[6].

*Internship project*

The internship will aim at characterizing spectrally broaden femtosecond pulses and use them to perform quantum measurements demonstrating large multimode entanglement compatible with measurement based quantum computing protocols.

In the current experimental setup, the intrinsic number of modes are involved in the generated network could be of the order of 50. All measurements we have implemented so far are able to address a maximum of 16 modes. These are performed using multimode homodyne detection, which is based on the interferences between the signal beam and an intense local oscillator. The oscillator originates from the ultrafast laser source, whose spectral extension is not large enough to efficiently interact with all the generated quantum modes.

We have recently implemented spectral broadening of the local oscillator using self-phase modulation in a short photonic crystal (PC) fiber, expanding the spectrum of the original laser by a factor of two. This source will be characterized, improved, and used for multimode measurement to demonstrated unprecedented number of quantum channels simultaneously available.

*PhD project*

The internship can be naturally followed by a PhD project that will be based on this experimental setup. The main objectives are to, on the one hand, explore the possibilities of highly multimode non-Gaussian light, a largely unknown regime so far both theoretically and experimentally, and on the other hand to implement non-Gaussian quantum protocols, as for instance quantum verification. This last part could be performed within the collaboration of the group with ATOS Company, in the quest of the future quantum computing architecture.

[1] J. Roslund, R. M. De Araujo, S. Jiang, and C. Fabre, Nature Photonics **8**, 109 (2014).

[2] S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, Phys Rev Lett **114**, 050501 (2015).

[3] Y. Cai, J. Roslund, G. Ferrini, F. Arzani, X. Xu, C. Fabre, and N. Treps, Nat Comms **8**, 15645 (2017).

[4] G. Ferrini, J. Roslund, F. Arzani, C. Fabre, and N. Treps, Phys Rev A **94**, 062332 (2016).

[5] Y.-S. Ra, C. Jacquard, A. Dufour, C. Fabre, and N. Treps, Phys. Rev. X **7**, 031012 (2017).

[6] M. Walschaers, C. Fabre, V. Parigi, and N. Treps, *Entanglement and Wigner function negativity of multimode non-Gaussian states,* arXiv **quant-ph**, (2017).

Interested candidates should contact Nicolas Treps (nicolas.treps@lkb.upmc.fr), Claude Fabre (claude.fabre@lkb.upmc.fr) or Valentina Parigi (valentina.parigi@lkb.upmc.fr)

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

Experimental internship.

Duration: 3 to 6 months. Possible PhD.

Contact: Julien Laurat

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