We study a circularly moving impurity in an atomic condensate for the realisation of superradiance phenomena in tabletop experiments. The impurity is coupled to the density fluctuations of the condensate and, in a quantum field theory language, it serves as an analog of a detector for the quantum phonon field. For sufficiently large rotation speeds, the zero-point fluctuations of the phonon field induce a sizeable excitation rate of the detector even when the condensate is initially at rest in its ground state. For spatially confined condensates and harmonic detectors, such a superradiant emission of sound waves provides a dynamical instability mechanism leading to a new concept of phonon lasing. Following an analogy with the theory of rotating black holes, our results suggest a promising avenue to quantum simulate basic interaction processes involving fast moving detectors in curved space-times.
Dynamical instabilities at the interface between two Bose--Einstein condensates that are moving relative to each other are investigated using mean-field and Bogoliubov analyses. Kelvin--Helmholtz instability is dominant when the interface thickness is much smaller than the wavelength of the unstable interface mode, whereas the counter-superflow instability becomes dominant in the opposite case. These instabilities emerge not only in an immiscible system but also in a miscible system where an interface is produced by external potential. Dynamics caused by these instabilities are numerically dem…
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 which generate non-reciprocal couplings between the two collective spins. Our predic…
Motivated by a recent demonstration of cyclic addition of quantized vorticity into a Bose-Einstein condensate, the vortex pump, we study dynamical instabilities and core sizes of giant vortices. The core size is found to increase roughly as a square-root function of the quantum number of the vortex, whereas the strength of the dynamical instability either saturates to a fairly low value or increases extremely slowly for large quantum numbers. Our studies suggest that giant vortices of very high angular momenta may be achieved by gradually increasing the operation frequency of the vortex pump.
Motivated by recent experiments, we analyse the stability of a three-dimensional Bose-Einstein condensate (BEC) loaded in a periodically driven one-dimensional optical lattice. Such periodically driven systems do not have a thermodynamic ground state, but may have a long-lived steady state which is an eigenstate of a "Floquet Hamiltonian". We explore collisional instabilities of the Floquet ground state which transfer energy into the transverse modes. We calculate decay rates, finding that the lifetime scales as the inverse square of the scattering length and inverse of the peak three- dimensi…
We study fingering instabilities and pattern formation at the interface of an oppositely polarized two-component Bose-Einstein condensate with strong dipole-dipole interactions in three dimensions. It is shown that the rotational symmetry is spontaneously broken by fingering instability when the dipole-dipole interactions are strengthened. Frog-shaped and mushroom-shaped patterns emerge during the dynamics due to the dipolar interactions. We also demonstrate the spontaneous density modulation and domain growth of a two-component dipolar BEC in the dynamics. Bogoliubov analyses in the two-dimen…
We demonstrate spontaneous generation of spatially-periodic supersolid-like super-lattice and stripe solitons in Rashba spin-orbit (SO) coupled spin-1 and spin-2 quasi-two-dimensional nonmagnetic Bose-Einstein condensates (BECs). The solitons in a weakly SO-coupled spin-1 BEC are circularly-symmetric of $(-1, 0, +1)$ and $(0, +1, +2)$ types and have inherent vorticity; the numbers in the parentheses are the winding numbers in hyper-spin components $+1, 0, -1$, respectively. The circularly-symmetric solitons in an SO-coupled spin-2 BEC are of types $(-2, -1, 0, +1, +2)$ and $(-1, 0, +1, +2, +3)…
Periodically-driven quantum systems are currently explored in view of realizing novel many-body phases of matter. This approach is particularly promising in gases of ultracold atoms, where sophisticated shaking protocols can be realized and inter-particle interactions are well controlled. The combination of interactions and time-periodic driving, however, often leads to uncontrollable heating and instabilities, potentially preventing practical applications of Floquet-engineering in large many-body quantum systems. In this work, we experimentally identify the existence of parametric instabiliti…
Shaking optical lattices in a resonant manner offers an efficient and versatile method to devise artificial gauge fields and topological band structures for ultracold atomic gases. This was recently demonstrated through the experimental realization of the Harper-Hofstadter model, which combined optical superlattices and resonant time-modulations. Adding inter-particle interactions to these engineered band systems is expected to lead to strongly-correlated states with topological features, such as fractional Chern insulators. However, the interplay between interactions and external time-periodi…
Instabilities of vortex-ring-bright coherent structures in harmonically trapped two-component three-dimensional Bose-Einstein condensates are studied numerically within the coupled Gross-Pitaevskii equations and interpreted analytically. Interestingly, the filled vortex core with a sufficiently large amount of the bright component is observed to reduce the parametric interval of stability of the vortex ring. We have identified the mechanisms of several linear instabilities and one nonlinear parametric instability in this connection. Two of the linear instabilities are qualitatively different f…
We propose to probe the quantum ground state of a spin-1 Bose-Einstein condensate with the transmission spectra of an optical cavity. By choosing a circularly polarized cavity mode with an appropriate frequency, we can realize coupling between the cavity mode and the magnetization of the condensate. The cavity transmission spectra then contain information of the magnetization statistics of the condensate and thus can be used to distinguish the ferromagnetic and antiferromagnetic quantum ground states. This technique may also be useful for continuous observation of the spin dynamics of a spinor…
In the study of trapped two-component Bose gases, a widely used dynamical protocol is to start from the ground state of a one-component condensate and then switch half the atoms into another hyperfine state. The slightly different intra-component and inter-component interactions can then lead to highly nontrivial dynamics. We study and classify the possible subsequent dynamics, over a wide variety of parameters spanned by the trap strength and by the inter- to intra-component interaction ratio. A stability analysis suited to the trapped situation provides us with a framework to explain the var…
We theoretically investigate four types of dynamical instability, in particular the periodic and oscillatory type $I_O$, in an anti-ferromagnetic spin-1 Bose-Einstein condensate in a nonzero magnetic field, by employing the coupled-mode theory and numerical method. This is in sharp contrast to the dynamical stability of the same system in zero field. Remarkably, a pattern transition from a periodic dynamical instability $I_O$ to a uniform one $III_O$ occurs at a critical magnetic field. All the four types of dynamical instability and the pattern transition are ready to be detected in $^{23}$Na…
We investigate the stability of vortices in two-dimensional Bose--Einstein condensates. In analogy with rotating spacetimes and with a careful account of boundary conditions, we show that the dynamical instability of multiply quantized vortices in trapped condensates persists in untrapped, spatially homogeneous geometries and has an ergoregion nature with some modification due to the peculiar dispersion of Bogoliubov sound. Our results open new perspectives to the physics of vortices in trapped condensates, where multiply quantized vortices can be stabilized by interference effects and singly …
We investigate the stability of Bloch waves for a Bose-Einstein condensate moving through a periodic lattice created by another condensate modulated by an optical lattice. We show that the coupling of phonon-antiphonon modes of the two species give rise to a very rich structure of the regimes for dynamical instability, with significant differences with respect to the case of a single condensate in an optical lattice. We characterize the relative weight of each condensate in the mixing and discuss an analytic limit that accounts for the bare structure of the instability diagrams.
A two-component Bose-Einstein condensate of cold atoms with a strong intercomponent repulsion leading to the spatial separation of the components has been numerically studied. Configurations with a multiple quantized vortex in one component, where the vortex core is filled with the other component, are considered. The effective radius of the core can exceed the width of the transition layer between components, and then an analogy with a filled cylindrical vortex in the classical hydrodynamics of two immiscible ideal fluids appears. This analogy allows one to analyze the longitudinal "sausage" …
We investigate the stability of vortices in two-dimensional Bose--Einstein condensates. In analogy with rotating spacetimes and with a careful account of boundary conditions, we show that the dynamical instability of multiply quantized vortices in trapped condensates persists in untrapped, spatially homogeneous geometries and has an ergoregion nature with some modification due to the peculiar dispersion of Bogoliubov sound. Our results open new perspectives to the physics of vortices in trapped condensates, where multiply quantized vortices can be stabilized by interference effects and singly …
The paper is devoted to numerical study of stability of nonlinear localized modes ("gap solitons") for the spatially one-dimensional Gross-Pitaevskii equation (1D GPE) with periodic potential and repulsive interparticle interactions. We use the Evans function approach combined with the exterior algebra formulation in order to detect and describe weak oscillatory instabilities. We show that the simplest ("fundamental") gap solitons in the first and in the second spectral gaps can undergo oscillatory instabilities for certain values of the frequency parameter (i.e., the chemical potential). The …
We study the stability and dynamics of an ultra-cold bosonic gas trapped in a toroidal geometry and driven by rotation, in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a "disorder" potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the sy…
We present a theoretical study on the origin of some findings of recent experiments on sonic analogs of gravitational black holes. We focus on the realization of a black-hole lasing configuration, where the conclusive identification of stimulated Hawking radiation requires dealing with the implications of the nonstationary character of the setup. To isolate the basic mechanisms responsible for the observed behavior, we use a toy model where nonstationarity can be described in terms of departures from adiabaticity. Our approach allows studying which aspects of the characterization of black-hole…
Quantum turbulence (QT) generated by the Rayleigh-Taylor instability in binary immiscible ultracold 87Rb atoms at zero temperature is studied theoretically. We show that the quantum vortex tangle is qualitatively different from previously considered superfluids, which reveals deep relations between QT and classical turbulence. The present QT may be generated at arbitrarily small Mach numbers, which is a unique property not found in previously studied superfluids. By numerical solution of the coupled Gross-Pitaevskii equations we find that the Kolmogorov scaling law holds for the incompressible…
We investigate the various physical mechanisms that underlie the dynamical instability of a quantized vortex array at the interface between two counter-propagating superflows in a two-dimensional Bose--Einstein condensate. Instabilities of markedly different nature are found to dominate in different flow velocity regimes. For moderate velocities where the two flows are subsonic, the vortex lattice displays a quantized version of the hydrodynamic Kelvin--Helmholtz instability (KHI), with the vortices rolling up and co-rotating. For supersonic flow velocities, the oscillation involved in the KHI…
Suppressing Parametric Instabilities in Driven Bosonic Lattices through Multi-tone Control
University of Strathclyde（斯特拉斯克莱德大学）；University of Birmingham（伯明翰大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；ETH Zürich（苏黎世联邦理工学院）；Collège de France（法兰西公学院）；CNRS（法国国家科学研究中心）；ENS-Université PSL（巴黎文理研究大学）；Sorbonne Université（索邦大学）；International Solvay Institutes（国际索尔维研究所）；Université Libre de Bruxelles（布鲁塞尔自由大学）
We theoretically propose a finite-size quasi-one-dimensional Bose-Einstein condensate with coherent source and drain placed at its two ends, which can in principle sustain a stationary sonic black hole with a single event horizon. Our analysis is focused on the condensate persistence against quantum fluctuations. We show that similar to white hole-black hole pairs, dynamical instabilities occur. Investigating in detail the instabilities' dependence on the system parameters, we also identify windows of formally infinite black hole lifetimes. By using quantum depletion of the condensate as a dia…
We explore prethermal Floquet steady states and instabilities of the weakly interacting two-dimensional Bose-Hubbard model subject to periodic driving. We develop a description of the nonequilibrium dynamics, at arbitrary drive strength and frequency, using a weak-coupling conserving approximation. We establish the regimes in which conventional (zero-momentum) and unconventional [$(π,π)$-momentum] condensates are stable on intermediate time scales. We find that condensate stability is \emph{enhanced} by increasing the drive strength, because this decreases the bandwidth of quasiparticle excita…
Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this work, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters y…
We theoretically investigate superradiance effects in quantum field theories in curved space-times by proposing an analogue model based on Bose--Einstein condensates subject to a synthetic vector potential. The breaking of the irrotationality constraint of superfluids allows to study superradiance in simple planar geometries and obtain intuitive insight in the amplified scattering processes at ergosurfaces. When boundary conditions are modified allowing for reflections, dynamical instabilities are found, similar to the ones of ergoregions in rotating space-times. Their stabilization by horizon…
We study the stability, form and interaction of single and multiple dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates. The solitons are found numerically as stationary solutions in the moving frame of a non-local Gross Pitaevskii equation, and characterized as a function of the key experimental parameters, namely the ratio of the dipolar atomic interactions to the van der Waals interactions, the polarization angle and the condensate width. The solutions and their integrals of motion are strongly affected by the phonon and roton instabilities of the system. Dipolar matter…
We analyze sound waves (phonons, Bogoliubov excitations) propagating on continuous wave (cw) solutions of repulsive $F=1$ spinor Bose-Einstein condensates (BECs), such as $^{23}$Na (which is antiferromagnetic or polar) and $^{87}$Rb (which is ferromagnetic). Zeeman splitting by a uniform magnetic field is included. All cw solutions to ferromagnetic BECs with vanishing $M_F=0$ particle density and non-zero components in both $M_F=\pm 1$ fields are subject to modulational instability (MI). MI increases with increasing particle density. MI also increases with differences in the components' wavenu…
We numerically obtain the full time-evolution of a parametrically-driven dissipative Bose-Einstein condensate in an optical cavity and investigate the implications of driving for the phase diagram. Beyond the normal and superradiant phases, a third nonequilibrium phase emerges as a manybody parametric resonance. This dynamical normal phase switches between two symmetry-broken superradiant configurations. The switching implies a breakdown of the system's mapping to the Dicke model. Unlike the other phases, the dynamical normal phase shows features of nonintegrability and thermalization.
We develop theory for a two-component miscible dipolar condensate in a planar trap. Using numerical solutions and a variational theory we solve for the excitation spectrum and identify regimes where density- and spin-roton excitations are favored. We characterize the various instabilities that can emerge in this system over a wide parameter regime and present results for the stability phase diagram. Importantly this allows us to identify the parameter regimes where a novel roton-immiscibility transition can occur, driven by the softening of the spin roton excitation.
The dynamical stability of nonstationary states of homogeneous spin-2 rubidium Bose-Einstein condensates is studied. The states considered are such that the spin vector remains parallel to the magnetic field throughout the time evolution, making it possible to study the stability analytically. These states are shown to be stable in the absence of an external magnetic field, but they become unstable when a finite magnetic field is introduced. It is found that the growth rate and wavelength of the instabilities can be controlled by tuning the strength of the magnetic field and the size of the co…
We calculate analytically the Bogoliubov excitation spectrum of a toroidal spin-1 Bose-Einstein condensate that is subjected to a homogeneous magnetic field and contains vortices with arbitrary winding numbers in the $m_F=\pm 1$ components of the hyperfine spin. We show that a rotonlike spectrum can be obtained, or an initially stable condensate can be made unstable by adjusting the magnitude of the magnetic field or the trapping frequencies. The structure of the instabilities can be analyzed by measuring the particle densities of the spin components. We confirm the validity of the analytical …
We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrastedto the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of {\em stable} nonlinear single or multi-vortex excitations. The potential i…
The dynamics of deformations of a quantum vortex ring in a Bose-Einstein condensate with periodic equilibrium density $ρ(z)= 1-ε\cos z$ has been considered within the local induction approximation. Parametric instabilities of the normal modes with azimuthal numbers $\pm m$ have been revealed at the energy integral $E$ near values $E_m^{(p)}=2m\sqrt{m^2-1}/p$, where $p$ is the resonance order. Numerical simulations have shown that already at $ε\sim 0.03$ a rapid growth of unstable modes with $m=2$, $p=1$ to magnitudes of order of unity is typical, which is then followed, after a few large oscil…
We study the stability of collective amplitude excitations in non-equilibrium polariton condensates. These excitations correspond to renormalized upper polaritons and to the collective amplitude modes of atomic gases and superconductors. They would be present following a quantum quench or could be created directly by resonant excitation. We show that uniform amplitude excitations are unstable to the production of excitations at finite wavevectors, leading to the formation of density-modulated phases. The physical processes causing the instabilities can be understood by analogy to optical param…
We demonstrate the feasibility of generation of quasi-stable counter-propagating solitonic structures in an atomic Bose-Einstein condensate confined in a realistic toroidal geometry, and identify optimal parameter regimes for their experimental observation. Using density engineering we numerically identify distinct regimes of motion of the emerging macroscopic excitations, including both solitonic motion along the azimuthal ring direction, such that structures remain visible after multiple collisions even in the presence of thermal fluctuations, and snaking instabilities leading to the decay o…
The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the t…
We present a stability analysis on a driven-dissipative electron-hole condensate in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-condensation)-crossover region. Extending the combined BCS-Leggett theory with the generalized random phase approximation (GRPA) to the non-equilibrium case by employing the Keldysh formalism, we show that the pumping-and-decay of carriers causes a depairing effect on excitons. This phenomenon gives rise to an attractive interaction between excitons in the BEC regime, as well as a supercurrent that anomalously flows anti-parallel to $\nabla θ({\bf r})$ (whe…
