The elementary excitations in weakly interacting quantum fluids have a non-trivial nature which is at the basis of defining quantum phenomena such as superfluidity. These excitations and the physics they lead to have been explored in closed quantum systems at thermal equilibrium both theoretically within the celebrated Bogoliubov framework, and experimentally in quantum fluids of ultracold atoms. Over the past decade, the relevance of Bogoliubov excitations has become essential to understand quantum fluids of interacting photons. Their driven-dissipative character leads to distinct properties with respect to their equilibrium counterparts. For instance, the condensate coupling to the photonic vacuum environment leads to a non-zero generation rate of elementary excitations with many striking implications. In this work, considering that quantum fluids of light are often hosted in solid-state systems, we show within a joint theory-experiment analysis that the vibrations of the crystal constitute another environment that the condensate is fundamentally coupled to. This coupling leads to a unique heat transfer mechanism, resulting in a large generation rate of elementary excitations in typical experimental conditions, and to a fundamental non-zero contribution at vanishing temperatures. Our work provides a complete framework for solid-embedded quantum fluids of light, which is invaluable in view of achieving a regime dominated by photon vacuum fluctuations.
The elementary excitations in weakly interacting quantum fluids have a non-trivial nature which is at the basis of defining quantum phenomena such as superfluidity. These excitations and the physics they lead to have been explored in closed quantum systems at thermal equilibrium both theoretically within the celebrated Bogoliubov framework, and experimentally in quantum fluids of ultracold atoms. Over the past decade, the relevance of Bogoliubov excitations has become essential to understand quantum fluids of interacting photons. Their driven-dissipative character leads to distinct properties with respect to their equilibrium counterparts. For instance, the condensate coupling to the photonic vacuum environment leads to a non-zero generation rate of elementary excitations with many striking implications. In this work, considering that quantum fluids of light are often hosted in solid-state systems, we show within a joint theory-experiment analysis that the vibrations of the crystal constitute another environment that the condensate is fundamentally coupled to. This coupling leads to a unique heat transfer mechanism, resulting in a large generation rate of elementary excitations in typical experimental conditions, and to a fundamental non-zero contribution at vanishing temperatures. Our work provides a complete framework for solid-embedded quantum fluids of light, which is invaluable in view of achieving a regime dominated by photon vacuum fluctuations.
The elementary excitations in weakly interacting quantum fluids have a nontrivial nature which is at the basis of defining quantum phenomena such as superfluidity.These excitations and the physics they lead to have been explored in closed quantum systems at thermal equilibrium both theoretically within the celebrated Bogoliubov framework and experimentally in quantum fluids of ultracold atoms.Over the past decade, the relevance of Bogoliubov excitations has become essential to understand quantum fluids of interacting photons.Their driven-dissipative character leads to distinct properties with respect to their equilibrium counterparts.For instance, the condensate coupling to the photonic vacuum environment leads to a nonzero generation rate of elementary excitations with many striking implications.In this work, considering that quantum fluids of light are often hosted in solid-state systems, we show within a joint theory-experiment analysis that the vibrations of the crystal constitute another environment that the condensate is fundamentally coupled to.This coupling leads to a unique heat transfer mechanism, resulting in a large generation rate of elementary excitations in typical experimental conditions, and to a fundamental nonzero contribution at vanishing temperatures.Our work provides a complete framework for solidembedded quantum fluids of light, which is invaluable in view of achieving a regime dominated by photonvacuum fluctuations.
In this work we give an overview on a couple of decades of theoretical and experimental research on the many-body physics of driven-dissipative quantum fluids of light in optical cavities. These systems consist of a large number of photons enclosed in a cavity device where spatial confinement induces a finite photon mass and the Kerr optical nonlinearity of the cavity material mediates finite photon-photon interactions. Differently from standard Bose gases of material particles like liquid Helium or ultracold atomic gases, photons are inevitably subject to radiative and/or non-radiative losses, which must be compensated by some pumping mechanism. As a result, the properties of the steady state are not imposed by a thermal equilibrium condition, but are determined by a dynamical interplay of pumping and losses. Among the many collective phenomena that are observed in these systems, we focus here on the collective excitations around the steady state and we characterize the impact of the driven-dissipative nature of the gas on their properties, in particular on their dispersion relation. Different pumping configurations give very different behaviors: a specific discussion is provided for the most important configurations used in the experiments. Observable consequences of the various forms of the dispersion -gapped, gapless, sonic, band-sticking, diffusive Goldstone- are illustrated with a special eye towards their consequences on the superfluidity properties. We conclude the article with a presentation of a few research avenues that we personally find most exciting for the next years, namely the osbervable consequences of the concurrently superfluid and solid nature of supersolid states of light and the collective dynamics of quantum correlated states of strongly interacting photon gases in the presence of strong nonlinearities, in particular Mott insulator states.
Collective quantum phenomena are fascinating, as they repeatedly challenge our comprehension of nature and its underlying mechanisms. The qualification ``quantum'' can be attributed to a generic many-body system whenever the interference effects related to the underlying wave nature of its elementary constituents can not be neglected anymore, and a naive classical description in terms of interacting billiard balls fails to catch its most essential features. This interference phenomenon called ``quantum degeneracy'' which occurs at weak temperatures, leads to spectacular collective behaviours such as the celebrated Bose-Einstein Condensation (BEC) phase transition, where a macroscopic fraction of a bosonic system of particles collapses below a critical temperature T_c on a single-particle state. Quantum coherence, when combined with inter-particle interactions, gives rise to highly non-classical frictionless hydrodynamic behaviours such as superfluidity (SF) and superconductivity (SC). \nEven more exotic quantum phases emerge in presence of important interactions as matter reaches a ``strongly correlated regime'' dominated by quantum fluctuations, where each particle is able to affect significantly the surrounding fluid: characteristic examples are the so-called Mott-Insulator (MI) quantum phase where particles are localized on a lattice due to a strong interaction-induced blockade, along with the Tonks-Girardeau (TG) gas where impenetrable bosons in one-dimension acquire effective fermionic statistics up to a unitary transformation, and the Fractional Quantum Hall (FQH) effect which occurs in presence of a gauge field, and features a special type of elementary excitation possessing a fractional charge and obeying to fractional statistics called `anyon'. \nThese quantum many-body effects were explored in a first place in systems well isolated from the external environment such as ultra-cold atomic gases or electrons in solid-state systems, within a physical context well described by ``equilibrium statistical mechanics''. Yet, over the last two decades a broad community has started investigating the possibility of stabilizing interacting quantum phases in novel nonlinear quantum optics architectures, where interacting photons have replaced their atomic and electronic counterpart. Thanks to their high level of controllability and flexibility, and the possibility of reaching the quantum degeneracy regime at exceptionally high temperatures, these platforms appear as extremely promising candidates for the ``quantum simulation'' of the most exotic many-body quantum problems: while the precursors experiments in semiconductor exciton-polariton already allow to reach the Bose-Einstein Condensation and superfluid regimes, novel platforms such as superconducting circuits, coupled cavity arrays or photons coupled to Rydberg EIT (Electromagnetically induced Transparency) atoms have entered the so-called `photon blockade' where photons behave as impenetrable particles, and open a encouraging pathway toward the future generation of strongly correlated phases with light. \nA specificity of quantum optics devices is their intrinsic ``non-equilibrium'' nature: the interplay between the practically unavoidable radiative and non-radiative losses and the external drive needed to replenish the photon gas leads the many-body system toward a steady-state presenting important non-thermal features. One one hand, an overwhelmingly large quantity of novel quantum phenomena is expected in the non-equilibrium framework, as breaking the thermal equilibrium condition releases severe constraints on the state of a quantum system and on the nature of its surrounding environment. On the other hand, we do not benefit yet of an understanding of non-equilibrium statistical mechanics comparable with its well-established equilibrium counterpart, which relies on strong historical foundations. Understanding how to tame (and possibly exploit) non-equilibrium effects in order to stabilize interesting quantum phases in a controlled manner often reveals a hard challenge. \nIn that prospect, an important conceptual issue in the non-equilibrium physics of strongly interacting photons regards the possibility of stabilizing ``incompressible quantum phases'' such as the Mott-Insulator or Fractional Quantum Hall states, and more generally to stabilize the ground-state of a given particle-number conserving Hamiltonian, in a physical context where dissipative losses can not be neglected. While being able to quantum simulate those emblematic strongly correlated quantum phases in this novel experimental context would strongly benefit to the quantum optics community, gaining such a kind of flexibility would also contribute to fill an important bridge between the equilibrium and the non-equilibrium statistical physics of open quantum systems, allowing to access in a controlled manner a whole new phenomenology at the interface between the two theories. \nIn this thesis I address those questions, which I reformulate in the following manner: \n \n-What are the conditions for the emergence of analogue equilibrium properties in open quantum systems in contact with a non-thermal environment ? \n \n-In particular, is it possible to stabilize strongly correlated quantum phases with a perfectly defined particle number in driven-dissipative photonic platforms, in spite of environment-induced losses and heating effects ? \n \nThe structure of the thesis is the following. \n \n \n[Chapter 1.] We give an overview of the physics of many-body photonic systems. As a first step we address the weakly interacting regime in the physical context of exciton-polaritons: after describing the microscopic aspects of typical experiments, we move to the discussion of non-equilibrium Bose-Einstein Condensation and the various mechanisms related to the emergence of thermal signatures at steady-state. The second part of this Chapter is dedicated to strongly interacting fluids. After drawing a quick overview of several experimental platforms presenting a good potential for the study of such physics in a near future, we discuss the relative performance of several schemes proposed in order to replenish the photonic population \n \n[Chapter 2.] We investigate the potential of a non-Markovian pump scheme with a narrow bandpass (Lorentzian shaped) emission spectrum for the generation of strongly correlated states of light in a Bose-Hubbard lattice. Our proposal can be implemented by mean of embedded inverted two-level emitters with a strong incoherent pumping toward the excited state. Our study confirms in a single cavity the possibility of stabilizing photonic Fock states in a single configuration, and strongly localized n=1 Mott-Insulator states in a lattice with n=1 density. We show that a relatively moderate hopping is responsible for a depletion of the Mott-state, which then moves toward a delocalized state reminiscent of the superfluid regime. Finally, we proceed to a mean-field analysis of the phase diagram, and unveil a Mott-to-Superfluid transition characterized by a spontaneous breaking of the U(1) symmetry and incommensurate density. The results of this Chapter are based on the following publications: \n- J. Lebreuilly, M. Wouters and I. Carusotto, ``Towards strongly correlated photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping'', C. R. Phys., 17(8), 836, 2016. \n- A. Biella, F. Storme, J. Lebreuilly, D. Rossini, R. Fazio, I. Carusotto and C. Ciuti, ``Phase diagram of incoherently driven strongly correlated photonic lattice'', Phys. Rev. A, 96, 023839, 2017. \n \n[Chapter 3.] In view of improving the performance of the scheme introduced in last chapter, and reproducing in particular the equilibrium zero temperature phenomenology in driven-dissipative photonic lattices, we develop a fully novel scheme based on the use of non-Markovian reservoirs with tailored broadband spectra which allows to mimick the effect of tunable chemical potential. Our proposal can be implemented by mean of a small number of emitters and absorbers and is accessible to current technologies. \n \nWe first analyse the case of a frequency-dependent emission with a square spectrum and confirm the possibility of stabilizing Mott insulator states with arbitrary integer density. Unlike the previous proposal the Mott state is robust against both losses and tunneling. A sharp transition toward a delocalized superfluid-like state can be induced by strong values of the tunneling or a change in the effective chemical potential. While an overall good agreement is found with the T=0 predictions, our analysis highlights small deviations from the equilibrium case in some parts of the parameters space, which are characterized by a non-vanishing entropy and the kinetic generation of doublon excitations. We finally consider an improved scheme involving additional frequency-dependent losses, and show in that case that the Hamiltonian ground-state is fully recovered for any choice of parameters. Our proposal, whose functionality relies on generic energy relaxation mechanisms and is not restricted to the Bose-Hubbard model, appears as a promising quantum simulator of zero temperature physics in photonic devices. The results of this Chapter are based on the following publication: \n- J. Lebreuilly, A. Biella, F. Storme, D. Rossini, R. Fazio, C. Ciuti and I. Carusotto, ``Stabilizing strongly correlated photon fluids with non-Markovian reservoirs'', Phys. Rev. A 96, 033828 (2017). \n \n[Chapter 4.] We adopt a broader perspective, and analyse the conditions for the emergence of analogous thermal properties in driven-dissipative quantum systems. We show that the impact of an equilibrated environment can be mimicked by several non-Markovian and non-equilibrated reservoirs. Chapter 2 already f
As quantum-driven processes and properties start to shape the future of technology, quantum simulations appear as a crucial piece of the puzzle, acting both as building blocks and catalysts for the improvement of the understanding of unique quantum features. In essence, they can be understood as a class of prototype experiments that allow a study of quantum properties in a controllable environment. In this context, quantum fluids of light are one of the strongest candidates for this role as coherent behavior is easily accessible and not hidden by detrimental thermal noise usually present in more common quantum systems. In this work we explore the underlying theory of quantum fluids of light in propagating geometries through the hydrodynamic interpretation of light, where photons behave as interacting particles in the presence of a nonlinear medium. Exploiting the highly controllable optical properties of atomic systems and their enhanced nonlinear properties related to quantum coherence phenomena, we discuss how they can be used to set a tunable platform for quantum simulations. As examples, we demonstrate a series of quantum features of this light fluid in the form of super fluidic-like behaviors, ranging from the more common and experimentally confirmed suppressed scattering, drag-force cancellation and Bogoliubov-like dispersion relation for the elementary excitations, to other interesting phenomena yet to be explored, such as the case of persistent currents.
Superfluidity and Bose–Einstein condensation are usually considered as two closely related phenomena. Indeed, in most macroscopic quantum systems, like liquid helium, ultracold atomic Bose gases, and exciton-polaritons, condensation and superfluidity occur in parallel. In photon Bose–Einstein condensates realized in the dye microcavity system, thermalization does not occur by direct interaction of the condensate particles as in the above described systems, i.e. photon–photon interactions, but by absorption and re-emission processes on the dye molecules, which act as a heat reservoir. Currently, there is no experimental evidence for superfluidity in the dye microcavity system, though effective photon interactions have been observed from thermo-optic effects in the dye medium. In this work, we theoretically investigate the implications of effective thermo-optic photon interactions, a temporally delayed and spatially non-local effect, on the photon condensate, and derive the resulting Bogoliubov excitation spectrum. The calculations suggest a linear photon dispersion at low momenta, fulfilling the Landau's criterion of superfluidity. We envision that the temporally delayed and long-range nature of the thermo-optic photon interaction offer perspectives for novel quantum fluid phenomena.
Bogoliubov's description of Bose gases relies on the linear dynamics of noninteracting quasiparticles on top of a homogeneous condensate. Here, we theoretically explore the weakly nonlinear regime of a one-dimensional photon superfluid in which phononlike elementary excitations interact via their backreaction on the background flow. The generalized dispersion relation extracted from spatiotemporal intensity spectra reveals additional branches that correspond to Bogoliubov quasiparticles—phase-locked collective excitations originating from nonresonant harmonic generation and wave-mixing processes. These mechanisms are inherent to fluctuation dynamics and highlight nontrivial scattering channels other than resonant interactions that could be relevant in the emergence of dissipative and turbulent phenomena in superfluids. Published by the American Physical Society 2024