Dynamics Of Condensate Research Articles

Quantum Time Crystals and Interacting Gauge Theories in Atomic Bose-Einstein Condensates.

We study the dynamics of a Bose-Einstein condensate trapped circumferentially on a ring, and which is governed by an interacting gauge theory. We show that the associated density-dependent gauge potential and concomitant current nonlinearity permits a ground state in the form of a rotating chiral bright soliton. This chiral soliton is constrained to move in one direction by virtue of the current nonlinearity, and represents a time crystal in the same vein as Wilczek's original proposal.

Collective excitation profiles and the dynamics of photonic condensates

Photonic condensates are complex systems exhibiting phase transitions due to the interaction with their molecular environment. Given the macroscopic number of molecules that form a reservoir of excitations, numerical simulations are expensive, even for systems with few cavity modes. We present a systematic construction of molecular excitation profiles with a clear hierarchical ordering, such that only modes in the lowest order in the hierarchy directly affect the cavity photon dynamics. In addition to a substantial gain in computational efficiency for simulations of photon dynamics, the explicit spatial shape of the mode profiles offers a clear physical insight into the competition among the cavity modes for access to molecular excitations.

The ground state and the tunnelling dynamics of the Bose-Einstein condensate in a tilted shallow trap

The ground state and the tunnelling dynamics of the Bose-Einstein condensate (BEC) loaded in a tilted shallow trap is studied analytically and numerically. The stable bound state, the quasi-bound state and the diffusion state are predicted. The thresholds for transition between the different states are obtained and the stability diagram in parameter space is presented. The tunnelling dynamics of the system in different states is revealed. The shape of the potential well and the atomic interaction play important role and have coupled effect on the tunnelling dynamics of the system. Furthermore, the resonant tunnelling phenomenon in the parametrically modulated shallow trap is observed. The results show that when the modulating frequency approaches the dipolar mode of the system, resonant tunnelling occurs and the whole system is unstable. Our results provide a theoretical evidence for studying the tunnelling dynamics of the ultracold atomic system.

Ultrafast Dynamics of Nonequilibrium Organic Exciton-Polariton Condensates.

Exciton–polariton condensation in organic materials, arising from the coupling of Frenkel excitons to the electromagnetic field in cavities, is a phenomenon resulting in low-threshold coherent light emission among other fascinating properties. The exact mechanisms leading to the thermalization of organic exciton–polaritons toward condensation are not yet understood, partly due to the complexity of organic molecules and partly to the canonical microcavities used in condensation studies, which limit broadband studies. Here, we exploit an entirely different cavity design, i.e., an array of plasmonic nanoparticles strongly coupled to organic molecules, to successfully measure the broadband ultrafast dynamics of the strongly coupled system. Sharp features emerge in the transient spectrum originating from the formation of a condensate with a well-defined molecular vibrational composition. These measurements represent the first direct experimental evidence that molecular vibrations drive condensation in organic systems and provide a benchmark for modeling the dynamics of organic-based exciton–polariton condensates.

Fluctuation dynamics of an open photon Bose-Einstein condensate

Bosonic gases coupled to a particle reservoir have proven to support a regime of operation where Bose-Einstein condensation coexists with unusually large particle-number fluctuations. Experimentally, this situation has been realized with two-dimensional photon gases in a dye-filled optical microcavity. Here, we investigate theoretically and experimentally the open-system dynamics of a grand canonical Bose-Einstein condensate of photons. We identify a regime with temporal oscillations of the second-order coherence function $g^{(2)}(\tau)$, even though the energy spectrum closely matches the predictions for an equilibrium Bose-Einstein distribution and the system is operated deeply in the regime of weak light-matter coupling. The observed temporal oscillations are attributed to the nonlinear, weakly driven-dissipative nature of the system which leads to time-reversal symmetry breaking.

Collective modes of a photon Bose–Einstein condensate with thermo-optic interaction

Although for photon Bose–Einstein condensates the main mechanism of the observed photon–photon interaction has already been identified to be of a thermo-optic nature, its influence on the condensate dynamics is still unknown. Here a mean-field description of this effect is derived, which consists of an open-dissipative Schrödinger equation for the condensate wave function coupled to a diffusion equation for the temperature of the dye solution. With this system at hand, the lowest-lying collective modes of a harmonically trapped photon Bose–Einstein condensate are calculated analytically via a linear stability analysis. As a result, the collective frequencies and, thus, the strength of the effective photon–photon interaction turn out to strongly depend on the thermal diffusion in the cavity mirrors. In particular, a breakdown of the Kohn theorem is predicted, i.e. the frequency of the centre-of-mass oscillation is reduced due to the thermo-optic photon–photon interaction.

Quantum Quench and Nonequilibrium Dynamics in Lattice-Confined Spinor Condensates.

We present an experimental study on nonequilibrium dynamics of a spinor condensate after it is quenched across a superfluid to Mott insulator (MI) phase transition in cubic lattices. Intricate dynamics consisting of spin-mixing oscillations at multiple frequencies are observed in time evolutions of the spinor condensate localized in deep lattices after the quantum quench. Similar spin dynamics also appear after spinor gases in the MI phase are suddenly moved away from their ground states via quenching magnetic fields. We confirm these observed spectra of spin-mixing dynamics can be utilized to reveal atom number distributions of an inhomogeneous system, and to study transitions from two-body to many-body dynamics. Our data also imply the nonequilibrium dynamics depend weakly on the quench speed but strongly on the lattice potential. This enables precise measurements of the spin-dependent interaction, a key parameter determining the spinor physics.

Anomalous phase ordering of a quenched ferromagnetic superfluid

Coarsening dynamics, the canonical theory of phase ordering following a quench across a symmetry breaking phase transition, is thought to be driven by the annihilation of topological defects. Here we show that this understanding is incomplete. We simulate the dynamics of an isolated spin-1 condensate quenched into the easy-plane ferromagnetic phase and find that the mutual annihilation of spin vortices does not take the system to the equilibrium state. A nonequilibrium background of long wavelength spin waves remain at the Berezinskii-Kosterlitz-Thouless temperature, an order of magnitude hotter than the equilibrium temperature. The coarsening continues through a second much slower scale invariant process with a length scale that grows with time as t^{1/3}t1/3. This second regime of coarsening is associated with spin wave energy transport from low to high wavevectors, bringing about the the eventual equilibrium state. The transport displays features of a spin wave energy cascade, providing a potential profitable connection with the emerging field of spin wave turbulence. Strongly coupling the system to a reservoir destroys the second regime of coarsening, allowing the system to thermalise following the annihilation of vortices.

Localization of a Bose-Einstein condensate in a two-leg ladder subject to an artificial magnetic field

We investigate the localization of a Bose-Einstein condensate trapped in a two-leg ladder in the presence of an artificial magnetic field via Bose-Hubbard model and discuss its abundant localized phenomena using variational approximation and direct numerical simulation. A two-leg bosonic ladder provides an ideal platform to study the complex dynamics of Bose-Einstein condensates in an optical lattice subject to an artificial magnetic field. As a main result, the system displays rich interesting localized states including self-trapping, soliton and breather. The coupling of the repulsive atomic interaction, artificial magnetic field, the rung-to-leg coupling ratio of the ladder, and the initial population difference of atoms between the two legs of the ladder results in the transitions between the localized states. The critical conditions for the transitions between the localized states are given analytically and are intuitively demonstrated in the phase diagram. Particularly, when the rung-to-leg coupling radio of the ladder satisfies a critical condition, we have the localized states with no local atomic currents between the two legs, otherwise, we observe the localized states with local atomic currents between the two legs. Finally, the results obtained via variational method are confirmed by the numerical simulations of the full discrete nonlinear Schrödinger equation describing the system.

Quantifying Dynamics in Phase-Separated Condensates Using Fluorescence Recovery after Photobleaching

Cells contain numerous membraneless organelles that assemble by intracellular liquid-liquid phase separation. The viscous properties and associated biomolecular mobility within these condensed phase droplets, or condensates, are increasingly recognized as important for cellular function and also dysfunction, for example, in protein aggregation pathologies. Fluorescence recovery after photobleaching (FRAP) is widely used to assess condensate fluidity and to estimate protein diffusion coefficients. However, the models and assumptions utilized in FRAP analysis of protein condensates are often not carefully considered. Here, we combine FRAP experiments on both in vitro reconstituted droplets and intracellular condensates with systematic examination of different models that can be used to fit the data and evaluate the impact of model choice on measured values. A key finding is that model boundary conditions can give rise to widely divergent measured values. This has important implications, for example, in experiments that bleach subregions versus the entire condensate, two commonly employed experimental approaches. We suggest guidelines for determining the appropriate modeling framework and highlight emerging questions about the molecular dynamics at the droplet interface. The ability to accurately determine biomolecular mobility both in the condensate interior and at the interface is important for obtaining quantitative insights into condensate function, a key area for future research.

Dynamics of excited-state condensate for optically confined exciton-polaritons.

We report experimental studies on the dynamics of excited-state condensate for exciton-polaritons confined in an optically generated trap. The three-dimensionally confined trap was realized by imposing two optical barriers onto a one-dimensional ZnO whispering gallery microcavity. Experimentally, we characterized the confined polariton condensate by varying the trap width and the barrier height. Theoretically, we calculated the spatial overlap between the polariton wavefunction and the excitonic reservoir. Direct comparison of these results verified that such polariton-reservoir overlap was responsible for the observed excited-state polariton condensate.

Monitoring currents in cold-atom circuis

Complex circuits of cold atoms can be exploited to devise new protocols for the diagnostics of cold-atoms systems. Specifically, we study the quench dynamics of a condensate confined in a ring-shaped potential coupled with a rectilinear guide of finite size. We find that the dynamics of the atoms inside the guide is distinctive of the states with different winding numbers in the ring condensate. We also observe that the depletion of the density, localized around the tunneling region of the ring condensate, can decay in a pair of excitations experiencing a Sagnac effect. In our approach, the current states of the condensate in the ring can be read out by inspection of the rectilinear guide only, leaving the ring condensate minimally affected by the measurement. We believe that our results set the basis for definition of new quantum rotation sensors. At the same time, our scheme can be employed to explore fundamental questions involving dynamics of bosonic condensates.

Simulation of the quantum dynamics of indistinguishable bosons with the method of coupled coherent states

Computer simulations of many-body quantum dynamics of indistinguishable particles is a challenging task for computational physics. In this paper we demonstrate that the method of coupled coherent states (CCS) developed previously for multidimensional quantum dynamics of distinguishable particles can be used to study indistinguishable bosons in the second quantisation formalism. To prove its validity, the technique termed here coupled coherent states for indistinguishable bosons (CCSB) is tested on two model problems. The first is a system-bath problem consisting of a tunnelling mode coupled to a harmonic bath, previously studied by CCS and other methods in distinguishable representation in 20 dimensions. The harmonic bath is comprised of identical oscillators, and may be second quantised for use with CCSB, so that this problem may be thought of as a bosonic bath with an impurity. The cross-correlation function for the dynamics of the system and Fourier transform spectrum compare extremely well with a benchmark calculation, which none of the prior methods of studying the problem achieved. The second model problem involves 100 bosons in a shifted harmonic trap. Breathing oscillations in the 1-body density are calculated and shown to compare favourably to a multiconfigurational time-dependent Hartree for bosons calculation, demonstrating the applicability of the method as a new formally exact way to study the quantum dynamics of Bose-Einstein condensates.

Defective ribosomal products challenge nuclear function by impairing nuclear condensate dynamics and immobilizing ubiquitin

Nuclear protein aggregation has been linked to genome instability and disease. The main source of aggregation‐prone proteins in cells is defective ribosomal products (DRiPs), which are generated by translating ribosomes in the cytoplasm. Here, we report that DRiPs rapidly diffuse into the nucleus and accumulate in nucleoli and PML bodies, two membraneless organelles formed by liquid–liquid phase separation. We show that nucleoli and PML bodies act as dynamic overflow compartments that recruit protein quality control factors and store DRiPs for later clearance. Whereas nucleoli serve as constitutive overflow compartments, PML bodies are stress‐inducible overflow compartments for DRiPs. If DRiPs are not properly cleared by chaperones and proteasomes due to proteostasis impairment, nucleoli undergo amyloidogenesis and PML bodies solidify. Solid PML bodies immobilize 20S proteasomes and limit the recycling of free ubiquitin. Ubiquitin depletion, in turn, compromises the formation of DNA repair compartments at fragile chromosomal sites, ultimately threatening cell survival.

Squeezed-field path-integral description of second sound in Bose-Einstein condensates

We propose a generalization of the Feynman path integral using squeezed coherent states. We apply this approach to the dynamics of Bose-Einstein condensates, which gives an effective low energy description that contains both a coherent field and a squeezing field. We derive the classical trajectory of this action, which constitutes a generalization of the Gross Pitaevskii equation, at linear order. We derive the low energy excitations, which provides a description of second sound in weakly interacting condensates as a squeezing oscillation of the order parameter. This interpretation is also supported by a comparison to a numerical c-field method.

Dissipation-Induced Instabilities of a Spinor Bose-Einstein Condensate Inside an Optical Cavity.

We investigate the dynamics of a spinor Bose-Einstein condensate inside an optical cavity, driven transversely by a laser with a controllable polarization angle. We focus on a two-component Dicke model with complex light-matter couplings, in the presence of photon losses. We calculate the steady-state phase diagram and find dynamical instabilities in the form of limit cycles, heralded by the presence of exceptional points and level attraction. We show that the instabilities are induced by dissipative processes that generate nonreciprocal couplings between the two collective spins. Our predictions can be readily tested in state-of-the-art experiments and open up the study of nonreciprocal many-body dynamics out of equilibrium.

Probing Inhomogeneous Diffusion in the Microenvironments of Phase-Separated Polymers under Confinement

Biomolecular condensates formed by liquid-liquid phase separation of proteins and nucleic acids have been recently discovered to be prevalent in biology. These dynamic condensates behave like biochemical reaction vessels, but little is known about their structural organization and biophysical properties, which are likely related to condensate size. Thus, it is critical that we study them on scales found in vivo. However, previous in vitro studies of condensate assembly and physical properties have involved condensates up to 1000 times larger than those found in vivo. Here, we apply confinement microscopy to visualize condensates and control their sizes by creating appropriate confinement length scales relevant to the cell environment. We observe anomalous diffusion of probe particles embedded within confined condensates, as well as heterogeneous dynamics in condensates formed from PEG/dextran and in ribonucleoprotein complexes of RNA and the RNA-binding protein Dhh1. We propose that the observed non-Gaussian dynamics indicate a hopping diffusion mechanism inside condensates. We also observe that, for dextran-rich condensates, but not for ribonucleo condensates, probe particle diffusion depends on condensate size.

Time‐Dependent Density Functional Theory for Fermionic Superfluids: From Cold Atomic Gases − To Nuclei and Neutron Stars Crust

In cold atoms and in the crust of neutron stars, the pairing gap can reach values comparable with the Fermi energy. While in nuclei the neutron gap is smaller, it is still of the order of a few percent of the Fermi energy. The pairing mechanism in these systems is due to short range attractive interactions between fermions and the size of the Cooper pair is either comparable to the inter‐particle separation or it can be as big as a nucleus, which is still relatively small in size. Such a strong pairing gap is the result of the superposition of a very large number of particle–particle configurations, which contribute to the formation of the Cooper pairs. These systems have been shown to be the host of a large number of remarkable phenomena, in which the large magnitude of the pairing gap plays an essential role: quantum shock waves, quantum turbulence, Anderson–Bogoliubov–Higgs mode, vortex rings, domain walls, soliton vortices, vortex pinning in neutron star crust, unexpected dynamics of fragmented condensates and role of pairing correlations in collisions on heavy‐ions, Larkin–Ovchinnikov phase as an example of a Fermi supersolid, role of pairing correlations in controlling the dynamics of fissioning nuclei.

Bloch oscillations of multidimensional dark soliton wave packets and light bullets.

The robust propagation of dark solitonic waves featuring Bloch oscillations (BOs) in media with a Kerr nonlinearity is demonstrated. The models considered have a discrete refractive index gradient in one dimension and are continuous in the orthogonal direction or directions. Such systems can be realized in photonic settings, where temporal dispersion of a normal type is able to support dark solitons. The demonstrated effects may also appear in the dynamics of Bose-Einstein condensates (BECs), where dark solitons appear due to the joint action of diffraction and a self-defocusing nonlinearity. Furthermore, our analysis shows that a periodic variation of the refractive index gradient in the propagation direction allows us to realize the spatial analog of dynamical localization. In addition, we demonstrate that dark solitons serve as excellent supporters for light bullets of a peculiar dark-bright type that can also feature robust BOs.

Nonlinear waves of Bose-Einstein condensates in rotating ring-lattice potentials

We analyze the dynamics of Bose-Einstein condensates loaded in rotating ring lattices made of a few sites, and show how rotation maps the states found in this finite system into those belonging to a static infinite lattice. Ring currents and soliton states in the absence of a lattice find their continuation in the presence of the lattice as nonlinear Bloch waves and soliton-like states connecting them. Both bright gap solitons and dark-soliton trains are shown to connect continuously to linear solutions. The existence of adiabatic paths upon varying rotation frequency between states with quantized supercurrents suggests highly controllable methods for the experimental generation of persistent currents.