Les photons sont d’excellents porteurs d’information, mais ils n’interagissent généralement pas entre eux.

Les atomes interagissent, mais ils sont difficiles à manipuler et ne bénéficient pas de l’arsenal de l’optique quantique pour détecter les fluctuations quantiques et l’intrication.

Notre approche pour marier ces deux systèmes pour la simulation quantique consiste à utiliser des exciton-polaritons dans des microcavités semi-conductrices.

\noindent Notre équipe utilise cette plateforme pour simuler des effets astrophysiques à proximité de trous noirs artificiels, avec de la lumière.

Description du stage

La gravité analogue permet d’étudier les champs dans des espaces courbés en laboratoire \cite{unruh1981experimental} : il est possible de créer des conditions dans lesquelles les ondes dans les milieux se propagent comme si elles étaient à proximité d’un trou noir \cite{jacquet2020polariton} ou dans un univers en expansion \cite{eckel2018rapidly}, par exemple.

Au sein du Groupe d’Optique Quantique du Laboratoire Kastler Brossel, en utilisant des exciton-polaritons dans des microcavités semi-conductrices et en les faisant se comporter comme des “fluides de lumière”, il est possible de simuler ces effets en laboratoire.

À l’heure actuelle, nous nous intéressons à la création d’une distribution de flux (vitesse) d’un fluide de lumière pour créer l’analogie d’un trou noir artificiel, caractérisé par une surface intangible appelée horizon (le point de non-retour qui délimite l’intérieur du trou noir).

Nous avons récemment démontré un contrôle total de l’espace-temps et nous étudions maintenant sur les corrélations découlant de l’effet Hawking dans cette expérience.

\noindent Le stage pourrait consister en un travail expérimental et/ou théorique.

Responsabilités clés

En tant que membre de l’équipe des fluides quantiques de lumière, vous serez chargé de divers objectifs (selon vos préférences).

Du côté théorique, l’étudiant utiliserait des méthodes numériques \cite{jacquet2023quantum} pour simuler l’hydrodynamique du fluide en rotation et calculer les corrélations Hawking.

Du côté expérimental, l’étudiant utiliserait notre nouvelle plateforme expérimentale pour collecter des données (densité du fluide et phase, spectre d’émission, corrélations de bruit) et analyser ces données en les comparant aux prédictions théoriques.

\end{itemize}

Impact du projet

Ce projet se situe à la croisée de la physique quantique et de la gravité analogue. Il nous permet de créer des conditions de laboratoire où les ondes dans les milieux imitent les comportements près des trous noirs ou des univers en expansion. Cette recherche implique une large gamme de connaissances et de techniques expérimentales que vous aurez l’opportunité d’apprendre pendant le stage.

Comment postuler – Contactez-nous

Nous offrons une opportunité de stage (suivie d’un doctorat si nécessaire)

Pour des questions ou plus d’informations sur ce stage ou pour postuler, veuillez nous contacter directement à l’adresse \href{mailto:maxime.jacquet@lkb.upmc.fr}{maxime.jacquet@lkb.upmc.fr}.

Groupe des fluides quantiques de lumière au LKB

Nous sommes un groupe de scientifiques accueillants-e-s, et nous visons à créer un environnement de recherche inclusif et de soutien.

Nous croyons fermement en la valeur de la diversité et de l’inclusion dans le domaine de la physique quantique, et nous encourageons les femmes et/ou les individus issus de groupes minoritaires sous-représentés à postuler pour ce stage.

phase-transition engineering in a Quantum Fluid of Light

**Overview**

Institution: Sorbonne University – Ecole Normale Sup´erieure – CNRS – Laboratoire Kastler Brossel

Team: Quantum Fluids of Light team – Alberto Bramati, Quentin Glorieux, Hanna Le Jeannic

Location: Jussieu campus. Paris, France

Duration: 3-6 months – followed by a ERC-funded PhD

Websites: www.quantumoptics.fr and www.quentinglorieux.fr

**Quantum fluids of light**

Photons are great carriers of information but they usually don’t interact with one another. Atoms in-

teract but are hard to manipulate and do not benefit from the toolbox of quantum optics for detecting

quantum fluctuations and entanglement. Many approaches have been proposed to marry these two

systems for quantum simulation of condensed matter with strongly interacting photons,

but to date, the realization of large-scale synthetic materials made of optical photons is still missing.

Our team targets this exciting goal, namely the creation of Synthetic Photonic Matter.

This ambitious goal relies on our original approach of engineering a quantum phase transition in a

quantum fluid of light. Indeed, 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 fluids of light. The current situation is then;

we have a superfluid of light (left part of the image below) and we want to create Syntehtic Photonic

Matter (right part of the image).

**Internship Description**

Building on these experiments done by the LKB group, we propose to use a platform based on atomic

cloud of Rubidium to study quantum fluids of light in a new regime. Specifically, we will investigate

the superfluid to Mott insulator transition for light propagating in a dense cold atomic

cloud. In this regime, photons will follow an evolution similar to ultracold atomic quantum gases and

our original hypothesis is that a fluid of light should undergo the same phase transition, driven by

quantum fluctuations, as quantum gases do, and therefore a many-body state of light will emerge from

this transition.

**Key Responsibilities**

As a member of the quantum fluids of light team you will be in charge to

• Design and build a novel cold-atoms setup to explore the physics of fluids of light in the strong

interaction regime.

• Collaborate with other team members to conduct experiments and data analysis on already working

setups in hot atomic vapors.

**Impact of the project**

At the fundamental level, a Mott insulator state of light allows for exploring truly quantum effects

such as the emergence of analogue of phase transition in non-equilibrium systems, the presence of quan-

tum depletion and pre-thermal states and the entanglement dynamics in many-body systems. On the

applied side, a photonic Mott insulator is a giant source of single photons (or any Fock state)

with potentially several hundreds of lattice sites delivering tunable photon number-states in parallel. It

will be a game changer for scalability issues in photonics quantum technologies.

**How to Apply – Contact Us**

We are offering an internship opportunity (followed by an ERC-funded PhD) to expand the

capabilities of this platform to a new level by increasing by many orders of magnitude the effective

photon-photon interactions and enter the strong interaction regime.

For inquiries or more information about this internship or to apply for this internship, please contact us

directly at quentin.glorieux@lkb.upmc.fr.

**Quantum fluids of light group at LKB**

We are a group of friendly and welcoming scientists and we aim to create an inclusive and supportive

research environment. We strongly believe in the value of diversity and inclusion in the field of

quantum physics and we encourage women and/or individuals from underrepresented minority

groups to apply for this internship.

The project aims at the experimental implementation of large and complex optical networks based on continuous-variable Gaussian correlations [1,2] and non-Gaussian operations [3,4]. The ultimate aims are the exploration of fundamental open questions in such large structures and/or their exploitation in optimized quantum information tasks. The post-doc will work on/supervise one of two cutting-edge setups at near infrared and telecom wavelengths where we recently demonstrated, for the first time, simultaneous multiplexing in time and frequency. This enable three-dimensional structures that are required to build a scalable quantum computer [5]. Protocols than can be addressed: quantum simulation [6], quantum reservoir computing [7], multiparty quantum communication [8] in complex networks [9,10].

The multimode quantum optics group at LKB carried out leading research in experimental generation of cluster states,i.e. large entangled networks useful in quantum information protocol on a large scale. The group has a strong experimental focus, but is also engaged in purely theoretical activities developing quantum optics in the continuous variable framework.

*Why to apply*:

-If you are passionate about quantum science, its fundamental aspect and/or real-world applications

-To join an international team of experts in Continuous Variable quantum information spanning both theory and experiments.

– To be part of a group that’s at the heart of national and international research networks, amplifying your impact and collaboration.

– Continuous variables are exploited to build deterministic and complex quantum networks [2, 9,10]

-We merge pulse-by-pulse temporal and multimode spectral encoding of femtosecond light sources in non-linear processes in waveguides [1,2]

-Measurement-based Gaussian and non-Gaussian operations [3,4] are used to shape quantum resources and perform protocols [6,7,8].

[1] V. Roman-Rodriguez, D. Fainsin, G. L Zanin, N. Treps, E. Diamanti, V. Parigi *Spectrally multimode squeezed states generation at telecom wavelengths*, arXiv:2306.07267 (2023)

[2] T. Kouadou, F. Sansavini, M. Ansquer, J. Henaff, N. Treps, V. Parigi, *Spectrally shaped and pulse-by-pulse multiplexed multimode squeezed states of light,* *APL Photonics* **8**, 086113 (2023)

[3] Ra, Y.-S., Dufour, A., Walschaers, M., Jacquard, C., Michel, T., Fabre, C., and Treps, N., *Non-Gaussian quantum states of a multimode light field*, Nat. Phys. **16**, 144–147 (2020)

[4] G. Roeland, S. Kaali, Vi. Roman Rodriguez, N. Treps, V. Parigi *Mode-selective single-photon addition to a multimode quantum field* New J. Phys. **24** 043031 (2022)

[5] J. E., Bourassa, et al. Quantum **5**, 392 (2021).

[6] P. Renault, J. Nokkala, G. Roeland, N. Joly, R. Zambrini, S. Maniscalco, J. Piilo, N. Treps, V. Parigi *Experimental optical simulator of reconfigurable and complex quantum environment* arXiv:2302.12674 (2023) accepted in PRX Quantum

[7] J. Nokkala, R. Martínez-Peña, G. L. Giorgi, V. Parigi, M. C Soriano, R. Zambrini, *Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing*, Communications Physics volume **4**, Article number: 53 (2021)

[8] O. Kovalenko, Y.-S. Ra, Y Cai, V. C. Usenko , C. Fabre N. Treps, and R. Filip, *Frequency-multiplexed entanglement for continuous-variable quantum key distribution* Photonics Research Vol. **9**, pp. 2351-2359 (2021)

[9] M. Walschaers, N. Treps, B. Sundar, L D Carr, V. Parigi *Emergent complex quantum networks in continuous-variables non-Gaussian states *Quantum Sci. Technol. **8** 035009 (2023)

[10] F. Centrone, F. Grosshans, and V.Parigi *Cost and routing of continuous variable quantum networks *arXiv:2108.08176

As a whole, the group has a tradition of working together with a diverse range of people from varied backgrounds. This diversity often leads to fruitful scientific input from different points of view, and it allows the group to explore new avenues. Furthermore, the moderate size of our group gives PhD students and postdocs the opportunity to discuss with PIs on a daily basis. This gives rise to a dynamical atmosphere with a lot of space for discussion.Your work fits in the ERC project COCQOoN, and can include the supervision of PhD students. The group is part of several other large research projects, among the most recent: the national acceleration strategy PEPR OQULUS, EIC Pathfinder VeriQub (European Innovation Council), EIC Pathfinder PANDA (European Innovation Council). This provides support to enlarge your scientific network and establish new international collaborations.

Laboratoire Kastler Brossel is one of the main worldwide leaders in the field of fundamental physics of quantum systems, covering a number of subjects spanning from fundamental tests of quantum theory to applications. It has an internationally recognized expertise throughout its 65 years history, including three Nobel Prize winners. The multimode quantum optics team explore both fundamental science and applications in CV quantum information. Based in Sorbonne Université in the Pierre and Marie Curie Campus in the center of Paris, it is part of the Quantum Information Center (QICS) in Sorbonne, hosting both quantum physicists and computer scientists. It is also part of the Paris Centre for Quantum Technologies (PCQT), a research, training and innovation network involving 22 research laboratories in Paris Region, 35 start-ups and larger industry groups.

The multimode quantum optics team has experience in technological transfer and collaboration with industrial partner, ongoing collaborations and projects involve Cailabs, Thales and PASQAL. Moreover, we are engaged in mentoring postdoctoral researchers in their actual and future career, both as independent academics or actors in the private sector.

*Candidates* must hold an internationally recognized PhD in a field related to experimental quantum physics.

A good background and past research track record in experimental optics, and quantum physics is required.

Euraxess link: https://euraxess.ec.europa.eu/jobs/142797

]]>Our group, the multimode quantum optics group of Laboratoire Kastler Brossel, pioneered many aspects of continuous variable (CV) approach to quantum optics. Our main objects of interest are the quadratures of the electric field, which are typically measured through homodyne detection. Our activities span both spatial and spectral modes, which we manipulate to develop tools for quantum computation, communication, and metrology.

Our general objective is the creation of multimode squeezed states of optical pulses, either by a synchronously pumped optical parametric oscillator (SPOPO) [1], or through nonlinear waveguides. As such, our sources can create big entangled Gaussian states, which can be probed in arbitrary modes by shaping the local oscillator of the homodyne detector. In recent years, we have gradually explored mode-selective photon subtraction and addition, which allows us to generate multimode non-Gaussian states of light in a highly versatile way [2].

Apart from our experimental focus, the group also has purely theoretical activities where the framework of CV quantum optics is further developed. In particular for non-Gaussian quantum states, there are still many fundamental questions that remain unanswered [3]. The interplay between theoretical work and experiments is a key element of our group.

** ****Project**

It is yet unclear exactly which types of quantum states should be created in experiments to drive quantum technologies. For quantum computation, one of the necessary resources is Wigner negativity [4]. In recent years, this motivated our group to produce a series of works on the measurement-based creation of Wigner-negative states [5, 6, 7, 8]. However, there are a multitude of other important properties that a quantum state can have, such as a high stellar rank [9], non-linear squeezing [10], and non-Gaussian entanglement [9].

The aim of the post-doc project is to design new protocols to generate quantum states with non-Gaussian entanglement. The primary approach will be focused on measurement-based protocols: assuming Alice, Bob, and Charlie share a quantum state, under which conditions can a measurement on Charlie’s subsystem create non-Gaussian entanglement between Alice and Bob? This question can be approached from a very fundamental point of view (e.g. what correlations are required between the three parties to achieve non-Gaussian entanglement), but also from a pragmatic point of view (e.g. how can we make sure that the procedure has a high success probability). As a secondary approach, you are encouraged to explore other techniques for engineering non-Gaussian quantum states of light, such as through light-atom interaction.

**Environment**

As a whole, the group has a tradition of working together with a diverse range of people from varied backgrounds. This diversity often leads to fruitful scientific input from different points of view, and it allows the group to explore new avenues. This has, for example, led to a growing activity in theoretical work over the past few years. The strength of our group is the constructive interplay between all these different points of view. Furthermore, the moderate size of our group gives PhD students and postdocs the opportunity to discuss with PIs on a daily basis. This gives rise to a dynamical atmosphere with a lot of space for discussion.

In your day to day activities, you will participate in the supervision of PhD students who work on theoretical topics and interact with the experimentalists in the group. Your work fits in the ANR project “NORDIC” and the group is part of several other large research projects (e.g. PEPR OQULUS, EIC Pathfinder VeriQub, etc.) which provide support to enlarge your scientific network and establish new international collaborations.

**Practical information**

** **

*Application process:***Apply via the CNRS portal***Application deadline:*Preferentially apply**before 10 July 2023**.*Starting date:*flexible*Duration :*18 months*Salary:*Monthly net salary between 2100€ and 2800€, depending on experience

**References**

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

[2] Y.-S. Ra, A. Dufour, M. Walschaers, C. Jacquard, T. Michel, C. Fabre, and N. Treps, Nature Physics **16**, 144–147 (2020).

[3] M. Walschaers, PRX Quantum **2**, 030204 (2021).

[4] A. Mari and J. Eisert, Phys. Rev. Lett. **109**, 230503 (2012).

[5] M. Walschaers and N. Treps, Phys. Rev. Lett. **124**, 150501 (2020).

[6] M. Walschaers, V. Parigi, and N. Treps, PRX Quantum **1**, 020305 (2020).

[7] Y. Xiang, S. Liu, J. Guo, Q. Gong, N. Treps, Q. He, and M. Walschaers, npj Quantum Inf **8**, 21 (2022).

[8] M. Walschaers, Quantum **7**, 1038 (2023).

[9] U. Chabaud and M. Walschaers, Phys. Rev. Lett. **130**, 090602 (2023).

[10] V. Kala, R. Filip, P. Marek, Optics Express **30**, 31456 (2022).

]]>

We are looking for an highly motivated postdoc to work on a novel experiment with quantum fluids of light: the creation of synthetic photonic matter by engineering a quantum phase transition for light.

Photons are great carriers of information but they usually don’t interact with one another. Atoms interact but are hard to manipulate and do not benefit from the toolbox of quantum optics for detecting quantum fluctuations and entanglement.

Many approaches have been proposed to marry these two systems for quantum simulation of condensed matter with strongly interacting photons, but to date, the realization of large-scale synthetic materials made of optical photons is still missing.

In this project, we will use the fluid of light approach to investigate the superfluid to Mott insulator transition for light propagating in a dense cold atomic cloud.

At the fundamental level, a Mott insulator state of light allows for exploring truly quantum effects such as the emergence of analogue of phase transition in non-equilibrium systems, the presence of quantum depletion and pre-thermal states and the entanglement dynamics in many-body systems.

On the applied side, a photonic Mott insulator is a giant source of single photons (or any Fock state) with potentiallyseveral hundreds of lattice sites delivering tunable photon number-states in parallel.

As a postdoc you will lead the construction of a new experimental apparatus for observing a quantum phase transition of light with the support of highly qualified PhD students. In parallel, you will be involved in the current activities of the team (Bose-bose mixture, 1D quantum fluid of light, quantum turbulence…)

We are looking for highly motivated candidate with an expertise in cold atoms, atomic physics and/or quantum optics. An experience in building a cold atoms setup is a plus. The offer is for 2 years with 2 years extension possible during the entire duration of the ERC Consolidator project.

We strongly encourage women to apply and we do our best to create a secure and welcoming environnement for women in science. Our group is currently composed of 4 men and 4 women.

]]>**Overview**

A fundamental task in quantum metrology is to identify the ultimate sensitivity limit in the estimation of a parameter encoded into a quantum state. Even under ideal conditions, when all technical noise sources are removed, quantum noise poses unavoidable limitations to such estimation. In spite of that, quantum parameter estimation theory provides the tools to reduce noise by optimizing the output measurements. This optimization leads to the quantum Cramér-Rao lower bound, which gives the minimal uncertainty of the estimator of a parameter, and that can be further optimized by finding quantum states that, for a given parameter, maximize the value of the quantum Fisher information.

In the optical scenario, would it be in imaging, remote sensing or interferometric measurement, the parameter of interest does not only modify the quantum state of the probe light, but also its spatio-temporal distribution. This distribution is conveniently described in terms of *modes* i.e. normalized solutions of Maxwell’s equations in vacuum [1]. Optimal quantum parameter estimation is thus at the crossroads between quantum information theory and optical mode manipulation, where only by taking into account both classical and quantum optimization one can derive efficient and practical estimators.

The multimode quantum optics group of Laboratoire Kastler Brossel, pioneered many aspects of optical quantum parameter estimation, in particular in the continuous variable (CV) approach [2,3]. Our activities generally span both spatial and spectral modes, which we manipulate to develop tools for quantum computation, communication, and metrology. The group has a strong experimental focus, but also has purely theoretical activities where the framework of CV quantum optics is further developed. The interplay between theoretical work and experiments is a key element of our group.

**Project**

When dealing with extracting a few parameters from an image, using prior information allows for going far beyond the Rayleigh limit. In practice, this can be achieved using the correlation of electromagnetic field amplitudes at different transverse positions of the image plane, and not only the intensity distribution. Technically, this involves decomposing the incoming field into an orthonormal basis of spatial modes (typically, Hermite-Gaussian) and measuring the amplitude (or intensity) of each basis component. This method of spatial demultiplexing, or SpaDe [4], enables us to not only achieve sub-Rayleigh precision, but also, in some cases, reach the ultimate resolution limits allowed by quantum mechanics [5,6]. The objectives of the group are to:

- Determine the physical limits of multi-parameter estimation to quantum estimation theory.
- Demonstrate practical parameter estimation with mode demultiplexing
- Implement a Bayesian framework for static and dynamic superresolution imaging.

Furthermore, the group has an ongoing collaboration with Thales Research and Technology to study distant imaging with frequency conversion, whose aim is to bring the system to new applications.

The postdoctoral fellow will have to coordinate the group activities in optical parameter estimation to reach the above objectives. She/He will have a background either in theoretical or experimental physics, but an interest to combine both in order to bring modal approach to parameter estimation to a practical device and to apprehend the fundamental limits imposed by the quantum nature of light in multi-parameter estimation in the presence of experimental imperfection. The work can have extension either in the more fundamental studies of the group, in particular regarding the link between Quantum Fisher information and quantum non-gaussian states of light [7], or to more practical considerations in particular within the framework of the collaboration with Thales.

**Environment**

As a whole, the group has a tradition of working together with a diverse range of people from very varied backgrounds. This diversity often leads to fruitful scientific input from different points of view, and it allows the group to explore new avenues. This has, for example, led to a growing activity in theoretical work over the past few years. The strength of our group is the constructive interplay between all these different points of view. Furthermore, the moderate size of our group gives PhD students and postdocs the opportunity to discuss with PIs on a daily basis. This gives rise to a dynamical atmosphere with a lot of space for discussion.

In your day-to-day activities, you will supervise PhD students who work on the same activity, and you are responsible for the everyday organization of the work. You will be involved in several European programs, which will enlarge your scientific network and provide opportunities for international collaborations.

*Application process:*Send CV and motivation letter to nicolas.treps@sorbonne-universite.fr*Application deadline:*Preferentially apply before 31^{st}of March 2023 (late application will be considered as long as the position has not been filled).

**References**

[1] C. Fabre and N. Treps, Modes and states in quantum optics. Rev. Mod. Phys. 92, 035005 (2020). https://doi.org/10.1103/RevModPhys.92.035005

[2] N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, A Quantum Laser Pointer, Science 301, 940 (2003).

[3] O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, C. Fabre, Ultimate sensitivity of precision measurements with in- tense Gaussian quantum light: a multi-modal approach, Phys. Rev. A 85, 010101(R) (2012). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.85.010101

[4] Labroille, G. et al. Efficient and mode selective spatial mode multiplexer based on multi-plane light conversion. Opt. Express 22, 15599–15607 (2014). https://doi.org/10.1364/OE.22.015599

[5] Tsang, M., Nair, R. & Lu, X.-M. Quantum theory of superresolution for two incoherent optical point sources. Phys. Rev. X 6, 031033 (2016). URL https://link.aps.org/doi/10.1103/PhysRevX.6.031033 .

[6] P. Boucher, C. Fabre, G. Labroille, and N. Treps, Spatial Optical Mode Demultiplexing as a Practical Tool for Optimal Transverse Distance Estimation, Optica, OPTICA **7**, 1621 (2020). https://doi.org/10.1364/OPTICA.404746

[7] C. E. Lopetegui, M. Gessner, M. Fadel, N. Treps, and M. Walschaers, Homodyne Detection of Non-Gaussian Quantum Steering, PRX Quantum 3, 030347 (2022). https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.030347

- Research Field
- Physics » Quantum mechanics
- Education Level
- PhD or equivalent

- Languages
- ENGLISH
- Level
- Good

Our group, the multimode quantum optics group of Laboratoire Kastler Brossel, pioneered many aspects of continuous variable (CV) approach to quantum optics. Our main objects of interest are the quadratures of the electric field, which are typically measured through homodyne detection. Our activities generally span both spatial and spectral modes, which we manipulate to develop tools for quantum computation, communication, and metrology.

Our general objective is the creation of multimode squeezed states of optical pulses, either by a synchronously pumped optical parametric oscillator (SPOPO) [1], or through nonlinear waveguides. As such, our sources can create big entangled Gaussian states, which can be probed in arbitrary modes by shaping the local oscillator of the homodyne detector. In recent years, we have gradually explored mode-selective photon subtraction and addition, which allows us to generate multimode non-Gaussian states of light in a highly versatile way [2].

Apart from our experimental focus, the group also has purely theoretical activities where the framework of CV quantum optics is further developed. In particular for non-Gaussian quantum states, there are still many fundamental questions that remain unanswered [3]. The interplay between theoretical work and experiments is a key element of our group.

**Project**

These theoretical activities are at the core the proposed post-doctoral project, which aim to unravel properties of non-Gaussian states. In particular, we focus on the study of non-Gaussian entanglement, i.e., quantum states where the quantum correlations themselves are of a non-Gaussian nature. This entanglement may be understood as a type of quantum correlations that cannot be witness based on the covariance matrix of the state. We previously showed the existence of such non-Gaussian quantum correlations in pure photon-subtracted states [4], but are currently lacking a more general theoretical framework to study its properties.

Your role as a post-doc is to help develop witnesses and measures for non-Gaussian entanglement, tailored towards multipartite systems ideally compatible with the group’s experimental capabilities. You will then apply these techniques to explore applications of non-Gaussian entanglement. Depending on your background, the applications could be aimed at various quantum technologies, ranging from quantum computing to quantum metrology.

Possible starting points for the work include the use of metrology-based entanglement witnesses [5], phase space methods [3], techniques from network theory [6,7], and more brute-force machine-learning techniques [8]. However, we encourage candidates to use their past experience the pursue alternative routes.

** **

**Environment**

As a whole, the group has a tradition of working together with a diverse range of people from very varied backgrounds. This diversity often leads to fruitful scientific input from different points of view, and it allows the group to explore new avenues. This has, for example, led to a growing activity in theoretical work over the past few years. The strength of our group is the constructive interplay between all these different points of view. Furthermore, the moderate size of our group gives PhD students and postdocs the opportunity to discuss with PIs on a daily basis. This gives rise to a dynamical atmosphere with a lot of space for discussion.

In your day to day activities, you will participate in the supervision of PhD students who work on theoretical topics and interact with the experimentalists in the group. Your work fits in the ANR project “NoRdiC”, which provides support to enlarge your scientific network and establish new international collaborations.

**Practical information**

*Application process:*CV and motivation letter to be uploaded to CNRS portal*Application deadline:*16/02/2022.*Starting date:*we aim for 01/06/2022 but are flexible*Duration of contract:*Two years*Salary:*Monthly net salary between 2100€ and 2800€, depending on experience*For more information:*walschaers@lkb.upmc.fr

**References**

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

[2] Y.-S. Ra, A. Dufour, M. Walschaers, C. Jacquard, T. Michel, C. Fabre, and N. Treps, Nature Physics **16**, 144–147 (2020).

[3] M. Walschaers, PRX Quantum 2, 030204 (2021).

[4] M. Walschaers, C. Fabre, V. Parigi, and N. Treps, Phys Rev Lett **119**, 183601 (2017).

[5] M. Gessner, L. Pezzè, and A. Smerzi, Quantum 1, 17 (2017).

[6] G. García-Pérez, M. A. C. Rossi, B. Sokolov, E.-M. Borrelli, and S. Maniscalco, Phys. Rev. Research 2, 023393 (2020).

[7] M. Walschaers, N. Treps, B. Sundar, L. D. Carr, V. Parigi arXiv:2012.15608

[8] V. Cimini, M. Barbieri, N. Treps, M. Walschaers, and V. Parigi, Phys. Rev. Lett. 125, 160504 (2020).

]]>Quantum communication experiments developed for communication networks require single photon sources with a tunable frequency and a narrow linewidth. Semiconductor quantum dots are good candidates for realizing such sources, but they need to be coupled to high finesse cavities to improve their coherence properties. Enhancement of light-matter interaction at the nanometer scale is a key issue of modern photonics. It is possible to tailor the properties of individual quantum emitters by modifying their electromagnetic environment. However, in order to achieve a strong influence of the environment on fluorescent emission, it is critical to control the position of the emitter with nanometer accuracy in the near field of a nanostructure. Our group is working to control the nano-positioning of single photon emitters on photonic nanostructures with high precision.

During the internship, the main goal will be to study experimentally a hybrid apparatus that couples the light from a single photon emitter to an optical nanofiber. In the long term, we will nano-position with an atomic-force microscope tip a single quantum emitter inside a cavity directly embedded in the nanofiber itself.

Optical cavities are often employed to increase the interaction between light and matter. A natural step forward for nanofiber-based hybrid systems is therefore the use of a cavity that can substantially enhance the coupling of the nano-emitter emission into the nanofiber. Indeed the interaction is enhanced by the transverse confinement of the field in the fiber core as well as the longitudinal confinement of the field between the mirrors. It has been theoretically predicted that the collection efficiency into the nanofiber guided modes can be enhanced up to 94% by incorporating a moderate finesse cavity structure to the nanofiber.

The nanofiber is home-made at LKB by heating up a commercial optical fiber that can be stretched in order to reduce its diameter down to 300 nm. This diameter is less than the wavelength of the light and will therefore induce an strong evanescent electromagnetic field around the nanofiber. An emitter placed on the nanofiber will then interact with this evanescent field and be coupled to the guided mode of the fiber.

Recent results [1] have been obtained on this topic and we are looking for a motivated, smart and curious candidate who wants to join the Quantum Optics group and to conduct high impact research in the field of NanoOptics.

1. S. Pierini, M. D’Amato, M. Goyal, Q. Glorieux, E. Giacobino, E. Lhuillier, C. Couteau, A. Bramati, ACS Photonics 7, 2265-2272 (2020),

Highly photo-stable Perovskite nanocubes: towards integrated single photon sources based on tapered nanofibers

Analogue gravity is a type of analogue quantum simulation that enables the study of gravitational effects in the laboratory [1]: it is possible to create conditions in which waves in media propagate as though they were in the vicinity of a black hole [2] or on an expanding universe [3], for example.

In the Quantum Optics Group at Laboratoire Kastler Brossel, we study excitons-polaritons in semiconductor microcavities and make them behave as “fluids of light”. At present, we are interested in engineering the flow profile of the fluid of light to create event horizon (the point of no-return that bounds the interior of the black hole) for excitations of the fluid. We aim to observe the Hawking effect at the horizon, that is the spontaneous emission of entangled pairs of excitations of the fluid at the horizon [4]. Specifically, the internship is concerned with setting up and using homodyne detection to this end.

We have recently obtained promising theoretical results and are currently assembling a new experiment to create the horizon and observe the Hawking effect. The M2 internship would consist in using this new experimental platform to collect data and in analysing this data by comparing it with theoretical predictions.

The student would work with the Polariton team (2 PhD students and a postdoc) under the supervision of Prof Alberto Bramati, who has strong expertise in quantum optics techniques like homodyne detection. This M2 internship could lead to a PhD project depending on funding availability. The research community at LKB is composed of people from all around the world and we strive to promote an inclusive environment. We encourage applications from female candidates and candidates from under-represented groups.

- [1] W. G. Unruh, Physical Review Letters 46, 1351 (1981).
- [2] L.-P. Euve ́, F. Michel, R. Parentani, T. Philbin, and G. Rousseaux, Physical Review Letters 117, 1079 (2016).
- [3] S. Eckel, A. Kumar, T. Jacobson, I. B. Spielman, and G. K. Campbell, Physical Review X 8, 021021 (2018).
- [4] M.J.Jacquet, T.Boulier,F.Claude, A.Maïtre, E.Cancellieri, C.Adrados, A.Amo, S.Pigeon, Q.Glorieux,

More details here

Analogue gravity enables the study of fields on curved spacetimes in the laboratory [1]: it is possible to create conditions in which waves in media propagate as though they were in the vicinity of a black hole [2] or on an expanding universe [3], for example.

In the Quantum Optics Group at Laboratoire Kastler Brossel, we study exciton- polaritons in semiconductor microcavities and make them behave as “fluids of light”. At present, we are interested in engineering the flow profile of the fluid of light to create the analogue of a rotating black hole — an effective spacetime characterised by two intangible surfaces: the event horizon (the point of no-return that bounds the interior of the black hole) and, further out, the ergosurface (a point beyond which waves and particles cannot remain at rest with respect to an outside observer).

This can be done by pumping the microcavity with a Laguerre-Gauss beam, thus inducing a vortex flow in the fluid of light [4]. We want to observe the propagation of small amplitude waves (e.g. density perturbations) as well as phase singularities (vortices and dark solitons) on this rotating spacetime. This could lead to the observation of effects such as the Hawking effect, rotational superradiance or the black hole bomb.

We have recently gathered promising preliminary experimental results with rotating spacetimes and are currently assembling a new experiment to push these investigations further.

We are looking for talented and motivated post-doc researchers. The selected candidate will work with the Polariton Team under the supervision of Prof Alberto Bramati.

Contact: Prof. Alberto Bramati, alberto.bramati@lkb.upmc.fr

[1] W. G. Unruh, Physical Review Letters 46, 1351 (1981).

[2] L.P. Euve, F. Michel, R. Parentani, T. Philbin, and G. Rousseaux, Physical Review Letters 117, 1079 (2016).

[3] S. Eckel, A. Kumar, T. Jacobson, I. B. Spielman, and G. K. Campbell, Physical Review X 8, 021021 (2018).

[4] M. J. Jacquet, T. Boulier, F. Claude, A. Maıtre, E. Cancellieri, C. Adrados, A. Amo, S. Pigeon, Q. Glorieux, A. Bramati, et al., Philosophical Transactions of the Royal Society A 378, 20190225 (2020), arXiv: 2002.00043.