Photon Fluid Research Articles

Theory of interacting cavity Rydberg polaritons

Photonic materials are an emerging platform to explore quantum matter (Carusotto and Ciuti 2013 Rev. Mod. Phys. 85 299; Sommer et al 2015 arXiv:1506.00341) and quantum dynamics (Peyronel et al 2012 Nature 488 57). The development of Rydberg electromagnetically induced transparency (Weatherill et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 201002; Petrosyan et al 2011 Phys. Rev. Lett. 107 213601) provided a clear route to strong interactions between individual optical photons. In conjunction with carefully designed optical resonators, it is now possible to achieve extraordinary control of the properties of individual photons, introducing tunable gauge fields (Schine et al 2016 Nature 534 671) whilst imbuing the photons with mass and embedding them on curved spatial manifolds (Sommer et al 2016 New J. Phys. 18 035008). Building on work formalizing Rydberg mediated interactions between propagating photons (Gorshkov et al 2011 Phys. Rev. Lett. 107 133602; Gullans et al 2016 Phys. Rev. Lett. 117 113601), we develop a theory of interacting Rydberg polaritons in multimode optical resonators, where the strong interactions are married with tunable single particle properties to build and probe exotic matter. In the presence of strong coupling between the resonator field and a Rydberg-dressed atomic ensemble, a quasiparticle called the ‘cavity Rydberg polariton’ emerges. We investigate its properties, finding that it inherits both the fast dynamics of its photonic constituents and the strong interactions of its atomic constituents. We develop tools to properly renormalize the interactions when polaritons approach each other, and investigate the impact of atomic motion on the coherence of multi-mode polaritons, showing that most channels for atom-polariton cross-thermalization are strongly suppressed. Finally, we propose to harness the repeated diffraction and refocusing of the optical resonator to realize interactions which are local in momentum-space. This work points the way to efficient modeling of polaritonic quantum materials in properly renormalized strongly interacting effective theories, thereby enabling experimental studies of photonic fractional quantum Hall fluids and crystals (Sommer et al 2015 arXiv:1506.00341; Umucalılar et al 2014 Phys. Rev. A 89 023803; Grusdt and Fleischhauer 2013 Phys. Rev. A 87 043628), plus photonic quantum information processors and repeaters (Jaksch et al 2000 Phys. Rev. Lett. 85 2208; Saffman et al 2010 Rev. Mod. Phys. 82 2313; Han et al 2010 Phys. Rev. A 81, 052311).

Coherently driven microcavity-polaritons and the question of superfluidity

Due to their driven-dissipative nature, photonic quantum fluids present new challenges in understanding superfluidity. Some associated effects have been observed, and notably the report of nearly dissipationless flow for coherently driven microcavity-polaritons was taken as a smoking gun for superflow. Here, we show that the superfluid response—the difference between responses to longitudinal and transverse forces—is zero for coherently driven polaritons. This is a consequence of the gapped excitation spectrum caused by external phase locking. Furthermore, while a normal component exists at finite pump momentum, the remainder forms a rigid state that is unresponsive to either longitudinal or transverse perturbations. Interestingly, the total response almost vanishes when the real part of the excitation spectrum has a linear dispersion, which was the regime investigated experimentally. This suggests that the observed suppression of scattering should be interpreted as a sign of this new rigid state and not a superfluid.

Rotating black hole geometries in a two-dimensional photon superfluid

Photon fluids have recently found applications in the simulation of a variety of physical phenomena such as superfluidity, vortex instabilities, and artificial gauge theories. Here we experimentally demonstrate the use of a photon fluid for analog gravity, i.e., the study of the physics of curved spacetime in the laboratory. While most analog gravity experiments are performed in 1+1 dimensions (one spatial plus time) and thus can only mimic 1+1D spacetime, we present a (room-temperature) photon superfluid where the geometry of a rotating acoustic black hole can be realized in 2+1D dimensions by an optical vortex. By measuring the local flow velocity and speed of waves in the photon superfluid, we identify a 2D region surrounded by an ergosphere and a spatially separated horizon.

Biological tissue-inspired tunable photonic fluid

Inspired by how cells pack in dense biological tissues, we design 2D and 3D amorphous materials that possess a complete photonic bandgap. A physical parameter based on how cells adhere with one another and regulate their shapes can continuously tune the photonic bandgap size as well as the bulk mechanical properties of the material. The material can be tuned to go through a solid-fluid phase transition characterized by a vanishing shear modulus. Remarkably, the photonic bandgap persists in the fluid phase, giving rise to a photonic fluid that is robust to flow and rearrangements. Experimentally this design should lead to the engineering of self-assembled nonrigid photonic structures with photonic bandgaps that can be controlled in real time via mechanical and thermal tuning.

Stimuli-Driven Control of the Helical Axis of Self-Organized Soft Helical Superstructures.

Supramolecular and macromolecular functional helical superstructures are ubiquitous in nature and display an impressive catalog of intriguing and elegant properties and performances. In materials science, self-organized soft helical superstructures, i.e., cholesteric liquid crystals (CLCs), serve as model systems toward the understanding of morphology- and orientation-dependent properties of supramolecular dynamic helical architectures and their potential for technological applications. Moreover, most of the fascinating device applications of CLCs are primarily determined by different orientations of the helical axis. Here, the control of the helical axis orientation of CLCs and its dynamic switching in two and three dimensions using different external stimuli are summarized. Electric-field-, magnetic-field-, and light-irradiation-driven orientation control and reorientation of the helical axis of CLCs are described and highlighted. Different techniques and strategies developed to achieve a uniform lying helix structure are explored. Helical axis control in recently developed heliconical cholesteric systems is examined. The control of the helical axis orientation in spherical geometries such as microdroplets and microshells fabricated from these enticing photonic fluids is also explored. Future challenges and opportunities in this exciting area involving anisotropic chiral liquids are then discussed.

Block Copolymer Micelles for Photonic Fluids and Crystals.

Block copolymer micelles (BCMs) are self-assembled nanoparticles in solution with a collapsed core and a brush-like stabilizing corona typically in the size range of tens of nanometers. Despite being widely studied in various fields of science and technology, their ability to form structural colors at visible wavelength has not received attention, mainly due to the stringent length requirements of photonic lattices. Here, we describe the precision assembly of BCMs with superstretched corona, yet with narrow size distribution to qualify as building blocks for tunable and reversible micellar photonic fluids (MPFs) and micellar photonic crystals (MPCs). The BCMs form free-flowing MPFs with an average interparticle distance of 150-300 nm as defined by electrosteric repulsion arising from the highly charged and stretched corona. Under quiescent conditions, millimeter-sized MPCs with classical FCC lattice grow within the photonic fluid-medium upon refinement of the positional order of the BCMs. We discuss the generic properties of MPCs with special emphasis on surprisingly narrow reflected wavelengths with full width at half-maximum (fwhm) as small as 1 nm. We expect this concept to open a generic and facile way for self-assembled tunable micellar photonic structures.

Riemann problem for the photon fluid: Self-steepening effects

We consider the Riemann problem of evolution of initial discontinuities for the photon fluid propagating in a normal dispersion fiber with account of self-steepening effects. The dynamics of light field is described by the nonlinear Schroedinger (NLS) equation with self-steepening term appearing due to retardation of the fiber material response to variations of the electromagnetic signal. It is shown that evolution dynamics in this case is much richer than that for the NLS equation. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity.

Analog curved spacetimes in the reversed dissipation regime of cavity optomechanics

In this paper, we theoretically propose an optomechanical scheme to explore the possibility of simulating the propagation of the collective excitations of the photon fluid in a curved spacetime. For this purpose, we introduce two theoretical models for two-dimensional photon gas in a planar optomechanical microcavity and a two-dimensional array of coupled optomechanical systems. In the reversed dissipation regime (RDR) of cavity optomechanics where the mechanical oscillator reaches equilibrium with its thermal reservoir much faster than the cavity modes, the mechanical degrees of freedom can adiabatically be eliminated. The adiabatic elimination of the mechanical mode provides an effective nonlinear Kerr-type photon-photon interaction. Using the nonlinear Schr\"{o}dinger equation (NLSE), we show that the phase fluctuations in the two-dimensional photon fluid obey the Klein-Gordon equation for a massless scalar field propagating in a curved spacetime. The results reveal that the photon fluid as well as the corresponding metric can be controlled by manipulating the system parameters.

Squeezing in a nonlocal photon fluid

Quantum fluids of light are an emerging tool employed in quantum many-body physics. Their amazing properties and versatility allow using them in a wide variety of fields including gravitation, quantum information and simulation. However the implications of the quantum nature of light in the nonlinear optical propagation are still missing many features. We theoretically predict classical spontaneous squeezing of a photon fluid in a nonlocal nonlinear medium. By using the so called Gamow vectors, we show that the quadratures of a coherent state get squeezed and that a maximal squeezing power exists. Our analysis holds true for temporal and spatial optical propagation in highly nonlocal regime. These results open a new scenario in quantum photon fluids and may lead to novel applications in fields like metrology and analogues of quantum gravity.

The dawn of FIMP Dark Matter: A review of models and constraints

We present an overview of scenarios where the observed Dark Matter (DM) abundance consists of Feebly Interacting Massive Particles (FIMPs), produced nonthermally by the so-called freeze-in mechanism. In contrast to the usual freeze-out scenario, frozen-in FIMP DM interacts very weakly with the particles in the visible sector and never attained thermal equilibrium with the baryon–photon fluid in the early Universe. Instead of being determined by its annihilation strength, the DM abundance depends on the decay and annihilation strengths of particles in equilibrium with the baryon–photon fluid, as well as couplings in the DM sector. This makes frozen-in DM very difficult but not impossible to test. In this review, we present the freeze-in mechanism and its variations considered in the literature (dark freeze-out and reannihilation), compare them to the standard DM freeze-out scenario, discuss several aspects of model building, and pay particular attention to observational properties and general testability of such feebly interacting DM.

Stabilizing strongly correlated photon fluids with non-Markovian reservoirs

We introduce a novel frequency-dependent incoherent pump scheme with a square-shaped spectrum as a way to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a non-equilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-Insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or non-integer densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic non-equilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero temperature many-body physics is highlighted.

Phase diagram of incoherently driven strongly correlated photonic lattices

We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator coupled to a two-level emitter, which is pumped incoherently. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of such a system. We find that, at a critical value of the inter-cavity photon hopping rate, a second-order nonequilibrium phase transition associated with the spontaneous breaking of the $U(1)$ symmetry occurs. The transition from an incompressible Mott-like photon fluid to a coherent delocalized phase is driven by commensurability effects and not by the competition between photon hopping and optical nonlinearity. The essence of the mean-field predictions is corroborated by finite-size simulations obtained with matrix product operators and corner-space renormalization methods.

Dispersive Dam-Break Flow of a Photon Fluid.

We investigate the temporal photonic analogue of the dam-break phenomenon for shallow water by exploiting a fiber optics setup. We clearly observe the decay of the steplike input (photonic dam) into a pair of oppositely propagating rarefaction wave and dispersive shock wave. Our results show evidence for a critical transition of the dispersive shock into a self-cavitating state. The detailed observation of the cavitating state dynamics allows for a fully quantitative test of the Whitham modulation theory applied to the universal defocusing nonlinear Schrödinger equation.

Autonomous stabilizer for incompressible photon fluids and solids

We suggest a simple approach to populate photonic quantum materials at non-zero chemical potential and near-zero temperature. Taking inspiration from forced evaporation in cold-atom experiments, the essential ingredients for our low-entropy thermal reservoir are (a) inter-particle interactions, and (b) energy-dependent loss. The resulting thermal reservoir may then be coupled to a broad class of Hamiltonian systems to produce low-entropy quantum phases. We present an idealized picture of such a reservoir, deriving the scaling of reservoir entropy with system parameters, and then propose several practical implementations using only standard circuit quantum electrodynamics tools, and extract the fundamental performance limits. Finally, we explore, both analytically and numerically, the coupling of such a thermalizer to the paradigmatic Bose-Hubbard chain, where we employ it to stabilize an $n=1$ Mott phase. In this case, the performance is limited by the interplay of dynamically arrested thermalization of the Mott insulator and finite heat capacity of the thermalizer, characterized by its repumping rate. This work explores a new approach to preparation of quantum phases of strongly interacting photons, and provides a potential route to topologically protected phases that are difficult to reach through adiabatic evolution.

Lasing in dark and bright modes of a finite-sized plasmonic lattice

Lasing at the nanometre scale promises strong light-matter interactions and ultrafast operation. Plasmonic resonances supported by metallic nanoparticles have extremely small mode volumes and high field enhancements, making them an ideal platform for studying nanoscale lasing. At visible frequencies, however, the applicability of plasmon resonances is limited due to strong ohmic and radiative losses. Intriguingly, plasmonic nanoparticle arrays support non-radiative dark modes that offer longer life-times but are inaccessible to far-field radiation. Here, we show lasing both in dark and bright modes of an array of silver nanoparticles combined with optically pumped dye molecules. Linewidths of 0.2 nm at visible wavelengths and room temperature are observed. Access to the dark modes is provided by a coherent out-coupling mechanism based on the finite size of the array. The results open a route to utilize all modes of plasmonic lattices, also the high-Q ones, for studies of strong light-matter interactions, condensation and photon fluids.

Bosonic lasing and trapping of a dressed photon fluid in InGaN at room temperature

The generation of a quantum fluid of dressed photons at room temperature is experimentally demonstrated in an InGaN microcavity which is divided into two- and one-dimensional sections, resulting in single- and switchable multilevel coherent light emission. Ultra-low-threshold operation is attributed to the slight but robust excitonic fraction of the photonic condensate representing a bosonic laser working below the Mott transition (polariton laser). In contrast to equilibrium Bose-Einstein condensates, the nonequilibrium driven-dissipative nature enables the population of higher orbitals if any confinement potential is present to induce enhanced quantum correlations. Trapping inside microwire spacers leads to a polariton harmonic oscillator resulting in discrete states in an equidistant ladder of photonic orbitals. Level occupation and selection of a specific wave function is managed via optical control, mimicking a quantum emitter on a macroscopic level. It shows that exotic states of matter can be realized in rather simple structures at room temperature directly visible to the human eye. It represents also an excellent opportunity to study basic many-body dynamics in one-dimensional bosonic matter by simultaneously settling an optimized fabrication technique for devices enabling practical Boolean quantum logic gates for optical computing.

Synthetic magnetism for photon fluids

We develop a theory of artificial gauge fields in photon fluids for the cases of both second-order and third-order optical nonlinearities. This applies to weak excitations in the presence of pump fields carrying orbital angular momentum, and is thus a type of Bogoliubov theory. The resulting artificial gauge fields experienced by the weak excitations are an interesting generalization of previous cases and reflect the PT-symmetry properties of the underlying non-Hermitian Hamiltonian. We illustrate the observable consequences of the resulting synthetic magnetic fields for examples involving both second-order and third-order nonlinearities.

Role of geometry in the superfluid flow of nonlocal photon fluids

Recent work has unveiled a new class of optical systems that can exhibit the characteristic features of superfluidity. One such system relies on the repulsive photon-photon interaction that is mediated by a thermal optical nonlinearity and is therefore inherently nonlocal due to thermal diffusion. Here we investigate how such a nonlocal interaction, which at a first inspection would not be expected to lead to superfluid behavior, may be tailored by acting upon the geometry of the photon fluid itself. Our models and measurements show that restricting the laser profile and hence the photon fluid to a strongly elliptical geometry modifies thermal diffusion along the major beam axis and reduces the effective nonlocal interaction length by two orders of magnitude. This in turn enables the system to display a characteristic trait of superfluid flow: the nucleation of quantized vortices in the flow past an extended physical obstacle. These results are general and apply to other nonlocal fluids, such as dipolar Bose-Einstein condensates, and show that "thermal" photon superfluids provide an exciting and novel experimental environment for probing the nature of superfluidity, with applications to the study of quantum turbulence and analogue gravity.

Circuit quantum electrodynamics simulator of flat band physics in a Lieb lattice

The concept of flat band plays an important role in strongly-correlated many-body physics. However, the demonstration of the flat band physics is highly nontrivial due to intrinsic limitations in conventional condensed matter materials. Here we propose a circuit quantum electrodynamics simulator of the 2D Lieb lattice exhibiting a flat middle band. By exploiting the simple parametric conversion method, we design a photonic Lieb lattice with \textit{in situ} tunable hopping strengths in a 2D array of coupled superconducting transmissionline resonators. Moreover, the flexibility of our proposal enables the immediate incorporation of both the artificial gauge field and the strong photon-photon interaction in a time- and site-resolved manner. To unambiguously demonstrate the synthesized flat band, we further investigate the observation of the flat band localization of microwave photons through the pumping and the steady-state measurements of only few sites on the lattice. Requiring only current level of technique and being robust against imperfections in realistic circuits, our scheme can be readily tested in experiments and may pave a new way towards the future realization of exotic photonic quantum Hall fluids including anomalous quantum Hall effect and bosonic fractional quantum Hall states without magnetic fields.

Synthetic Landau levels for photons.

Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties. Photons experiencing a Lorentz force develop handedness, providing opportunities to study quantum Hall physics and topological quantum science. Here we present an experimental realization of a magnetic field for continuum photons. We trap optical photons in a multimode ring resonator to make a two-dimensional gas of massive bosons, and then employ a non-planar geometry to induce an image rotation on each round-trip. This results in photonic Coriolis/Lorentz and centrifugal forces and so realizes the Fock–Darwin Hamiltonian for photons in a magnetic field and harmonic trap. Using spatial- and energy-resolved spectroscopy, we track the resulting photonic eigenstates as radial trapping is reduced, finally observing a photonic Landau level at degeneracy. To circumvent the challenge of trap instability at the centrifugal limit, we constrain the photons to move on a cone. Spectroscopic probes demonstrate flat space (zero curvature) away from the cone tip. At the cone tip, we observe that spatial curvature increases the local density of states, and we measure fractional state number excess consistent with the Wen–Zee theory, providing an experimental test of this theory of electrons in both a magnetic field and curved space. This work opens the door to exploration of the interplay of geometry and topology, and in conjunction with Rydberg electromagnetically induced transparency, enables studies of photonic fractional quantum Hall fluids and direct detection of anyons.