**This project is a collaboration between the NANOST team at the Institute of NanoSciences of Paris (INSP) and the Quantum Optics Group of the Kastler-Brossel Laboratory (LKB)**. The INSP, a founding member of the Labex “**Materials, InterfaceS, Surfaces, Environment**” (MATISSE), is a leading player in Pierre et Marie Curie University (UPMC) in Physics and Materials Science, particularly at the nanoscopic level. The NANOST team’s concerns are in cutting-edge fields (exciton and spin physics in semiconductor or magnetic nanostructures) where electronic properties are studied by advanced optical spectroscopies.

The LKB is a major international player in the fundamental fields of atomic physics, quantum optics and related fields (metrology, quantum information, …). The LKB partner team in the project focuses on the quantum properties of light produced by different model systems, with study themes related to quantum fluctuations, generation of entangled states, light-matter states (polaritons ) and quantum metrology.

The project is funded by SU Emergence

Salary: 2200 €/month.

Starting date (flexible between March and June 2017)

**Contact: **

- Prof. Maria Chamarro: maria.chamarro@insp.jussieu.fr,
- Prof. Alberto Bramati: alberto.bramati@lkb.upmc.fr

**More information here**

**Arrays of Cold Atoms Coupled to Nanoscale Waveguides: Towards Quantum Non-Linear Optics**

**Deterministic interactions between single photons, i.e. quantum non-linear optics,** is a long-standing goal in optical physics, with applications to quantum optics and quantum information science. However, single photons usually do not interact with each other and the interaction needs to be **mediated by an atomic system**. Enhancing this coupling has been the driving force for a large community over the past two decades. One pioneering approach is known as cavity quantum electrodynamics (CQED), where a single atom and a single photon can be strongly coupled via a high-finesse cavity. Cavity-QED led to a better understanding of fundamental aspects of light-matter interaction and to various seminal demonstrations.

Strong **transverse confinement in** **single-pass nanoscale waveguide** recently triggered various investigations for coupling **guided light** **and cold atoms, **without a cavity. Specifically, a subwavelength waveguide can provide a large evanescent field that can interact with atoms trapped in the vicinity. An atom close to the surface can absorb a fraction of the guided light as the effective mode area is comparable with the atom cross-section due to the tight transverse confinement.

The LKB team recently developed an experiment in this direction. Using a **nanofiber with a 400-nm diameter and a few thousands atoms trapped around**, the team recently realized a first all-fibered quantum memory for light. The team also demonstrated the very efficient reflection of single photons by an ordered one-dimensional array of trapped atoms.

The goal is now to **push further the accessible non-linearity** and to demonstrate in such waveguided-configuration quasi-deterministic single-photon emission and single-photon controlled optical switches and transistors, with applications to quantum state engineering and quantum networks.

*References:
*

Contact: Prof. Julien Laurat, julien.laurat at upmc.fr

In analogy to what has happened for classical signals with the **digital and analog paradigms**, quantum information has developed along **two traditionally** **separated lines**, known as the **discrete- and the continuous-variable approaches**.

In the optical approach, the **wave-particle duality of light** has naturally led to this distinction. The discrete-variable approach involves for instance **single photons** and the states live in a finite-dimensional space spanned, among others, by orthogonal polarizations or the presence and absence of single photons. In the continuous-variable alternative, the encoding is realized in the **amplitude or phase of a light field**, in an inherently infinite-dimensional space. The typical detection and processing tools are different, based either on photon counting or homodyne detection. A variety of groundbreaking experiments have been realized using one or the other paradigm.

However, in recent years, few groups, including the LKB team, have tackled the effort to **combine the two approaches**, integrating continuous- and discrete-variable tools and concepts in **optical hybrid realizations**. These protocols can overcome some limitations of the schemes taken individually or provide novel capabilities. An illustrative protocol realized at LKB consisted in witnessing single-photon entanglement up to 100 km using only homodyne measurements, an example of realization where the combination of the toolboxes can be an enabling pathway. Recently the team also demonstrated for the first time a so-called **hybrid entanglement of light** between particle-like and wave-like qubits to bridge the two approaches.

The team aims now at exploring the **uniqueness and benefits of hybrid entanglement light** **and at harnessing this yet unexplored photonic resource to realize first advanced protocols**. This resource opens up the promise of heterogeneous quantum protocols and networks where the two encodings can be combined or interconverted in the form best suited for a particular process. The experimental effort will include for instance the realization of an analog-to-digital converter for quantum information via teleportation. Hybrid entanglement of light can be also be seen by itself as a novel type of qubit with a double encoding and first principles of quantum computing with this resource will be explored.

*These researches involve non-linear optics, quantum state generation and characterization, superconducting single-photon detectors (in collaboration with NASA and NIST)…*

Contact: Prof. Julien Laurat, julien.laurat at upmc.fr

Optical frequency combs have revolutionized frequency metrology and found application from fundamental constants measurements and optical clocks, to spectroscopy and telecommunications. They are becoming key elements of more and more advanced experiments as they offer unprecedented properties in terms of spectral purity, pulse repetition rate stability and spectrum spanning. It is thus crucial to get a better understanding of the noise sources and coupling mechanisms that directly impact the performances.

On the other hand, quantum optics has been, from its beginning, the driving force both for the exploration of fundamental limits of the quantum world and for conceiving seminal ideas and applications of the so-called quantum technologies. The last 20 years have seen a rapid development of ideas and proof-of-principle experiments involving the fields of quantum communication, quantum computation, quantum metrology and quantum simulation.

In the photonic scenario single photons are the traditional carriers of quantum information, but the scalability and adaptability of quantum resources is still an open problem. The system developed in the Quantum Optics group of the Laboratoire Kastler Brossel is based on a complementary approach where the information is not encoded on discrete variables, like the number of photons, but in continuous variable of the electromagnetic field, i.e. its amplitude and phase. In our approach, in the case of Gaussian quantum states, the resource to be scaled-up is the number of modes in which these states of light are simultaneously and deterministically generated[1].

This project is based on ultra stable femtosecond mode locked laser (∼ 30 fs pulses, repetition rate of 150 MHz). We first apply the quantum optics tools to give a modal description of classical femtosecond lasers, shining new light on laser dynamics[2]. This study will be pursued and applied to other type of lasers, using further developments achieved in a quantum context. This part of the project is supported by an ANR-DGA project in collaboration with Thales and Laboratoire Aimé Coton.

In order to develop quantum complex network, we use this laser to pump a non-linear crystal. Each pump pulse generates a couple of entangled pulses in two separate spatial channels. While the two will maintain the spectral multi-mode decomposition that can already be arranged as a quantum network, one of the two channels will be delayed in the temporal domain by the time between two consecutive pulses, before being mixed with the other channel on a 50:50 beam-splitter. This will create a dual-rail temporal structure characterized by non-trivial entanglement, which can involve up to 10^{6} temporal-modes. The interplay between the spectral and the temporal structure of entanglement connections will be used for generating quantum networks[3] with more elaborated geometry involving community structures. Optimization of quantum information protocols and quantum transport phenomena will be studied. Beyond the already identified quantum strategies involving multi-mode quantum states, the variety of experimental implementations opens new fundamental questions on how to describe the quantum nature of a large multiple system and which kind of advantages can be obtained from these resources.

We specifically propose an internship on the detection, at the quantum level, of single pulses with a 150MHz repetition rate. The general aim is being able, in real time, to extract the multimode quantum structure in time and frequency of both the classical and quantum sources available.

- [1] J. Roslund, R. M. De Araujo, S. Jiang, and C. Fabre, Nature Photonics
**8**, 109 (2014). - [2] R. Schmeissner, J. Roslund, C. Fabre, and N. Treps, Phys Rev Lett
**113**, 263906 (2014). - [3] J. Nokkala, F. Galve, R. Zambrini, S. Maniscalco, and J. Piilo, Sci. Rep.
**6**, 26861 (2016).

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.

* *

The last 20 years have seen a rapid development of ideas and proof-of-principle experiments regarding the so-called quantum technologies involving the fields of 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 experimental quantum resources based on an Optical Parametric Oscillator Synchronously Pumped by a mode-locked femtosecond laser (SPOPO). The spectrum of this lasers is constituted of hundreds thousands of frequency component. The parametric process couples all these optical frequencies in a non-linear crystal, and generates highly multimode quantum states [1,2]. This resource can be described as quantum networks, where the nodes are different spectral/temporal modes of the e.m. field and the links are given by entanglement properties. The use of ultrafast pulse shaping combined with multi-homodyne-based projective measurements allows the on-demand construction of various quantum networks useful for the implementation of measurement based quantum computing [3] or to simulate complex quantum network [4].

The intrinsic number of modes that are involved in the generated network could be of the order of 50, but up to now the projective measurements are able to address a maximum of 16 modes. The multimode homodyne detection technique is in fact based on the interferometric measurement of the signal with a strong local oscillator. The used local oscillator is a portion of the original laser source; whose spectral extension is unfortunately not large enough to efficiently interact with all the generated quantum modes.

The internship project proposed by the group consists in the experimental study of the coherent expansion of the bandwidth of our local oscillator. The process that will be investigated is the self-phase modulation in a short photonic crystal (PC) fiber [5], with the aim of expanding the spectrum of the original laser by a factor of two.

The internship could be followed by a PhD project based on the developed technique, which combined with controlled pulse shaping of the pump in the parametric process, will give direct access to a large class of Gaussian quantum networks.

The realization of a mode-selective single-photon subtraction, which is currently under implementation in the experimental setup [6], will also pave the way for non-Gaussian resources that are necessary for the implementation of universal quantum information protocols. The characterization of this new multimode non-Gaussian states will be part of the project, finally followed by the implementation of specific protocols where we will exploit a genuine quantum advantage.

- [1] J. Roslund, R. Medeiros de Araujo, S. Jiang, C. Fabre and N. Treps, 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. Fabreand N. Treps arXiv 1605.02303v1
- [4] J. Nokkala, F. Galve , R. Zambrini, S. Maniscalco and J. Piilo, Scientific Reports 6, 26861 (2016).
- [5] Xin Jiang, Nicolas Y Joly, Martin A Finger, Fehim Babic, Meng Pang, Rafal Sopalla, Michael H Frosz, Samuel Poulain, Marcel Poulain, Vincent Cardin, John C Travers, Philip St J Russell, Optics Letters 41, 4245-4248 (2016).
- [6]V. A. Averchenko, V. Thiel, N. Treps, Phys. Rev. A 89, 063808 (2014). V. A. Averchenko, C. Jacquard,V. Thiel, C. Fabre, and N. Treps arXiv :1510.04217

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.

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.

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.

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.

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.