ICTS

We study self-gravitating bosonic systems, candidates for dark-matter halos, by carrying out a suite of direct numerical simulations designed to investigate the formation of finite-temperature, compact objects in the three-dimensional (3D) Fourier-truncated Gross-Pitaevskii-Poisson equation (GPPE). This truncation allows us to explore the collapse and fluctuations of compact objects and show the following:

1) The statistically steady state of the GPPE, in the large-time limit and for the system sizes we study, can also be obtained efficiently by tuning the temperature in an auxiliary stochastic Ginzburg-Landau-Poisson equation.
2) Over a wide range of model parameters, this system undergoes a thermally driven first-order transition from a collapsed, compact, Bose-Einstein condensate to a tenuous Bose gas (that is not gravitationally condensed).
3) By a suitable choice of initial conditions in the GPPE, we also obtain a binary condensate that comprises a pair of collapsed objects rotating around their center of mass.
4) We use a generalised GPPE to study the collapse of an axion star.
5) By introducing a solid-crust potential and rotation in the GPPE, we develop a minimal model for pulsars and their glitches.

References:
1. A.K. Verma, R. Pandit, and M.E. Brachet, The formation of compact objects at finite temperatures in a dark-matter-candidate self-gravitating bosonic system, Phys. Rev. Research 3 (2), L022016 (2021).
2. A.K. Verma, R. Pandit, and M.E. Brachet, Rotating self-gravitating Bose-Einstein condensates with a crust: a minimal model for pulsar glitches, Physical Review Research 4 (1), 013026 (2022).
3. S. Shukla, A.K. Verma, M.E. Brachet, and R. Pandit, Gravity- and temperature-driven phase
transitions in a model for collapsed axionic condensates, submitted for publication (November 2023).

We present experimental and theoretical results on formation of quantum vortices in a laser beam propagating in a nonlinear medium. Topological constrains richer that the mere conservation of vorticity impose an elaborate dynamical behaviour to the formation and annihilation of vortex/anti-vortex pairs. We identify two such mechanisms, both described by the same fold-Hopf bifurcation. One of them has been first proposed more than 30 years ago but had not been observed experimentally so far. The other one is new and appears particularly efficient. These results suggest new (experimentally relevant) observables for studying the transition to turbulence.
T. Congy, P. Azam, R. Kaiser, N. Pavloff, Phys. Rev. Lett. 132 033804 (2024)

Dissipation mechanisms play an important role in superfluid dynamics in general, and a central role in the dynamics of high energy turbulent superfluids. While the need to understand condensate formation stimulated a solid foundation for reservoir theory of matter wave Bose-Einstein condensates, its standard incarnation - a damped Gross-Pitaevskii equation closely related to the imaginary time treatment of nonlinear ground states - fails spectacularly to describe the damping timescales of quantum vortices in experiments. I will describe an effective point vortex theory of 2D matter waves at finite temperature derived from open systems (c-field) theory in which number-conserving energy exchange with the reservoir determines the mutual friction coefficient, in agreement with experiments, and in stark contrast to the standard damped Gross-Pitaevskii treatment. Our results indicate the general significance of energy damping in cold quantum gases and we will briefly discuss implications for other systems where energy damping may be important.

First, I will give a short review of the numerical [Phil. Trans. R. Soc. A 380: 20210090, (2022)] and functional renormalization group results [PHYSICAL REVIEW LETTERS 131, 247101 (2023)] on the unpredicted crossover from Kardar-Parisi-Zhang to inviscid scaling in the 1D Galerkin-truncated Burgers equation. Then I will discuss the possibility of observing a similar crossover in 2D, in particular in the Gross-Pitaevskii equation.

Photons confined in optical cavities acquire an effective mass and behave like matter particles. Moreover, an effective photon-photon interaction can be engineered when the photons propagate in a nonlinear medium, resulting in collective fluid-like behaviors of light, such as superfluidity [1].
First, I will show how, in a resonantly driven 2D polariton superfluid, the combination of the bistability behaviour of the system with flexible all-optical methods allows to control the formation and the propagation of a new class of dark solitons [2]. Due to the onset of the snake instabilities these topological defects evolve in stationary symmetric or anti-symmetric arrays of vortex streets, straightforwardly observable in CW experiments [3]. 
Then I will present a novel coherent probe spectroscopy technique allowing to observe spontaneous symmetry breaking in a parametrically driven microcavity, revealing the appearance of a diffusive Goldstone mode; a phenomenology stemming from the out of equilibrium nature of the system [4].
Finally, I will show how the properties of polariton quantum fluids can be used to simulate astrophysical objects like Black Holes and I will discuss our progresses on the experimental investigation of the Hawking effect in a quantum fluid of polaritons.
In the last part of the talk, I will introduce a new kind of quantum fluid of light, obtained on a nonlinear hot Rb vapor, in a paraxial geometry and briefly discuss our recent results on 2D-turbulent dynamics in such a system [5]. 

[1] I. Carusotto and C. Ciuti, Quantum Fluids of Light, Rev. Mod. Phys. 85, 299 (2013)
[2] A. Maître, G. Lerario, A. Medeiros, F. Claude, Q. Glorieux, E. Giacobino, S. Pigeon, and A. Bramati, Phys. Rev. X 10, 041028 (2020)
[3] F. Claude, S. V. Koniakhin, A. Maître, S. Pigeon, G. Lerario, D. D. Stupin, Q. Glorieux, E. Giacobino, D. Solnyshkov, G. Malpuech, and A. Bramati, Optica, 7, 1660 (2020)
[4] F. Claude, M. Jacquet, R. Usciati, I. Carusotto, E. Giacobino, A. Bramati, Q. Glorieux, Phys. Rev. Lett. 129, 103601 (2022)
[5] M. Baker-Rasooli, W. Liu, T. Aladjidi, A. Bramati and Q. Glorieux, Phys. Rev. A 108, 063512 (2023)

Understanding many-body systems far-from equilibrium is an outstanding challenge in physics. It was proposed that such systems generically feature dynamic scaling while approaching non-thermal fixed points and the associated scaling exponents would provide a classification of the nonequilibrium phenomena analogously to the equilibrium universality classes. 

I will present our experimental results with homogeneous two-dimensional Bose gas on two prototypical far-from-equilibrium problems: driven turbulence (1) and isolated-system coarsening (2). For the turbulence, we have observed two key phenomena associated with its development – the emergence of statistical isotropy under anisotropic forcing, and the spatiotemporal scaling of the momentum spectrum.

For the coarsening we have observed universal dynamic scaling with exponents that match analytical nonequilibrium field theory predictions. For different initial states we reveal universal dynamics by accounting for state-dependent prescaling effects. The methods we introduce should be applicable to any quantitative study of universality far from equilibrium.

1.    M. Galka, P. Christodoulou, M. Gazo, A. Karailiev, N. Dogra, J. Schmitt, and Z. Hadzibabic, Emergence of Isotropy and Dynamic Scaling in 2D Wave Turbulence in a Homogeneous Bose Gas, Phys. Rev. Lett. 129, 190402 (2022)
2.    M. Gazo, A. Karailiev, T. Satoor, C. Eigen, M. Galka, and Z. Hadzibabic, Universal Coarsening in a Homogeneous Two-Dimensional Bose Gas, arXiv:2312.09248 (2023)

Motivated by experiments studying 2D vortex dynamics in BECs, we illustrate that, by considering these vortices as quasi-particles, one can describe their dynamics using reduced ODE models. It is then possible to study in detail the dynamics, stability, and bifurcations of vortex configurations and match the ensuing results to experimental observations. We will also explore extensions of the quasi-particle approach for 3D vortex rings which are formed when a vortex line is looped back onto itself creating a close ring that carries vorticity. We focus, in particular, on vortex rings interactions, collisions, and scattering scenarios.These reduced ODE models might serve as a platform to study some basic properties (inc. turbulence) when considering large collections of these quasi-particles.

Bose-Einstein condensation has been observed with cold atomic gases, exciton-polaritons, and more recently also with low-dimensional photon gases e.g. in a dye solution-filled optical microcavity. I here report on experiments observing a non-Hermitian phase transition in a photon Bose-Einstein condensate realized in the dye-microcavity platform. The dissipative phase transition occurs due to an exceptional point in the condensate that is associated with the (small) system losses. While usually Bose-Einstein condensation is separated by a smooth crossover to lasing, the presence of the here observed phase transition reveals a state of the light field characterized by a bi-exponential second order coherence that is separated by a phase transition from lasing [1]. In more recent work, we have performed a critical test of the thermal nature of the photon condensate coupled to the reservoir of photo-excitable dye molecules by probing the fluctuation-dissipation theorem in this system [2].

[1] F. Öztürk, T. Lappe, G. Hellmann, J. Schmitt, J. Klaers, F. Vewinger, J. Kroha, and M. Weitz, Science 372, 6537 (2021). 
[2] F. Öztürk, F. Vewinger, M. Weitz, and J. Schmitt, Phys. Rev. Lett. 130, 033602 (2023).

Exciton-polaritons, resulting from the strong coupling of photons and excitons in semiconductor microcavities, have demonstrated their potential for exploring quantum fluids in optical systems over the past two decades. This study presents the initial evidence of turbulent dynamics and vortex clustering within 2D exciton-polariton fluids, focusing on the statistical properties of velocity and vorticity fields. By directly measuring the phase of the polariton fluid, we can identify and categorize vortices, revealing the emergence of an inverse energy cascade. Simultaneously, this measurement facilitates the extraction of complete statistics regarding the velocity field, establishing connections with classical turbulence and the universal behavior of critical systems.

Quantum vortices are a core element of superfluid dynamics and elusively hold the keys to our understanding of energy dissipation in these systems. We show that we can visualize these vortices in the canonical and higher-symmetry case of a stationary rotating superfluid bucket. Using direct visualization, we quantitatively verify Feynman’s rule linking the resulting quantum vortex density to the imposed rotational speed. We make the most of this stable configuration by applying an alternative heat flux aligned with the axis of rotation. Moderate amplitudes led to the observation of collective wave mode propagating along the vortices, and high amplitudes led to quantum vortex interactions. When increasing the heat flux, this ensemble of regimes defines a path toward quantum turbulence in rotating 4He and sets a baseline to consolidate the descriptions of all quantum fluids. REF: https://doi.org/10.1126/sciadv.adh2899

This talk will be in the classical limit. Inertial particles are thought to evacuate the neighborhood of vortices and collect in strain regions. We will discuss how, in rotating flow, the simplest of which is just a co-rotating vortex pair, particles can remain for long periods in the neighborhood, display extreme clustering and bifurcations from fixed points to limit cycles to chaos.

We numerically study a turbulent flow of a classical incompressible fluid in a two-dimensional, so-called, lid-driven cavity. The cavity here is square and the top side (lid)  moves with a prescribed horizontal velocity. Other three sides stay still (zero velocity). The boundary condition is no-slip. It is known that, at a moderate Reynolds number such as $Re=1000$, the lid-driven cavity flow is stationary.  It is a nontrivial nonlinear stationary solution of the incompressible Navier--Stokes equations. These stationary solutions have been used as benchmarks for various numerical methods. 
In this study, we increase the Reynolds numbers more than $10^5$ using a standard Chebyshev-tau method with a suitable regularization of the lid corners. Accordingly, the flow becomes turbulent. Our objective here is to characterize this turbulence. To our knowledge, such a study of 2D lid-driven cavity turbulence is not common. Our numerical findings suggest that the mean enstrophy dissipation rate increases as $Re^{1/2}$. Also we study the mean velocity profile near the center of the bottom wall to see if it is similar to the logarithmic law of the wall. We then discuss how we can understand some of the findings.

Dynamical quenches across phase transitions and subsequent relaxation into a steady-state represent an exciting field of non-equilibrium many-body quantum physics: during such evolution, turbulent-like dynamics are induced featuring the relevant quantum vortical (or more broadly nonlinear macroscopic) excitations, whose evolution obeys scaling laws in the appropriate regimes. In this talk I will discuss examples of the emergence of such scaling laws in 2D and 3D systems, both for open and closed quantum systems [1].

Recently, the potential role of a cosmological-size Bose-Einstein condensate as an alternative `fuzzy’ model for dark matter has been gaining traction: within such framework – which will be briefly motivated on observational grounds – we showcase the qualitative analogy of a single galaxy to trapped laboratory-based quantum gases, revealing a fully-coherent galactic core surrounded by a turbulent vortex tangle [2].

[1] N.P. Proukakis, Universality of Bose-Einstein Condensation and Quenched Formation Dynamics, arXiv:2304.09541 (Encyclopedia of Condensed Matter Physics (2nd Edition), Elsevier, 2023).
[2] I.K. Liu, N.P. Proukakis and G. Rigopoulos, Coherent and incoherent structures in fuzzy dark matter halos, arXiv:2211.02565 (Monthly Notices of the Royal Astronomical Society, 521, 3625 (2023).