Dynamics Of Condensate Research Articles

Metastable hard-axis polar state of a spinor Bose-Einstein condensate under a magnetic field gradient

We investigate the stability of a hard-axis polar state in a spin-1 antiferromagnetic Bose-Einstein condensate under a magnetic field gradient, where the easy-plane spin anisotropy is controlled by a negative quadratic Zeeman energy $q<0$. In a uniform magnetic field, the axial polar state is dynamically unstable and relaxes into the planar polar ground state. However, under a field gradient $B'$, the excited spin state becomes metastable down to a certain threshold $q_{th}$ and as $q$ decreases below $q_{th}$, its intrinsic dynamical instability is rapidly recalled. The incipient spin excitations in the relaxation dynamics appear with stripe structures, indicating the rotational symmetry breaking by the field gradient. We measure the dependences of $q_{th}$ on $B'$ and the sample size, and we find that $q_{th}$ is highly sensitive to the field gradient in the vicinity of $B'=0$, exhibiting power-law behavior of $|q_{th}|\propto B'^{\alpha}$ with $\alpha \sim 0.5$. Our results demonstrate the significance of the field gradient effect in the quantum critical dynamics of spinor condensates.

Stability and instability properties of rotating Bose–Einstein condensates

We consider the mean-field dynamics of Bose-Einstein condensates in rotating harmonic traps and establish several stability and instability properties for the corresponding solution. We particularly emphasize the difference between the situation in which the trap is symmetric with respect to the rotation axis and the one where this is not the case.

Nonequilibrium polariton dynamics in a Bose-Einstein condensate coupled to an optical cavity

We study quasiparticle scattering effects on the dynamics of a homogeneous Bose-Einstein condensate of ultracold atoms coupled to a single mode of an optical cavity. The relevant excitations, which are polaritonlike mixed excitations of photonic and atomic density-wave modes, are identified. All the first-order correlation functions are presented by means of the Keldysh Green's function technique. Beyond confirming the existence of the resonant enhancement of Beliaev damping, we find a very structured spectrum of fluctuations. There is a spectral hole burning at half of the recoil frequency reflecting the singularity of the Beliaev scattering process. The effects of the photon-loss dissipation channel and that of the Beliaev damping due to atom-atom collisions can be well separated. We show that the Beliaev process does not influence the properties of the self-organization criticality.

Theory of relaxation oscillations in exciton-polariton condensates

We provide an analytical and numerical description of relaxation oscillations in the nonresonantly pumped polariton condensate. The presented considerations are based on the open dissipative Gross-Pitaevskii equation coupled to a pair of rate equations. The evolution of the condensate density can be explained qualitatively by studying the topology of the trajectory in phase space. We use a fixed points analysis for the classification of the different regimes of condensate dynamics, including fast stabilization, slow oscillations and ultrashort pulse emission. We obtain an analytical condition for the occurrence of relaxation oscillations. Continuous and pulsed condensate excitation considered and we demonstrate that in the latter case the existence of the second reservoir is necessary for the emergence of oscillations. We show that relaxation oscillations should be expected to occur in systems with relatively short polariton lifetime.

Nonlinear mixing of Bogoliubov modes in a bosonic Josephson junction

We revisit the dynamics of a Bose-Einstein condensate in a double-well potential, from the regime of Josephson plasma oscillations to the self-trapping regime, by means of the Bogoliubov quasiparticle projection method. For very small imbalance between left and right wells only the lowest Bogoliubov mode is significantly occupied. In this regime the system performs plasma oscillations at the corresponding frequency, and the evolution of the condensate is characterized by a periodic transfer of population between the ground and the first excited state. As the initial imbalance is increased, more excited modes -- though initially not macroscopically occupied -- get coupled during the evolution of the system. Since their population also varies with time, the frequency spectrum of the imbalance turns out to be still peaked around a single frequency, which is continuously shifted towards lower values. The nonlinear mixing between Bogoliubov modes eventually drives the system into the the self-trapping regime, when the population of the ground state can be transferred completely to the excited states at some time during the evolution. For simplicity, here we consider a one-dimensional setup, but the results are expected to hold also in higher dimensions.

Gain through losses in nonlinear optics

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. These instabilities are at the heart of symmetry breaking, condensate dynamics, self-organisation, pattern formation, and noise amplification across diverse disciplines, including physics, chemistry, engineering, and biology. In nonlinear optics, modulation instabilities are generally linked to the so-called parametric amplification process, which occurs when certain phase-matching or quasi-phase-matching conditions are satisfied.In the present review article, we summarise the principle results on modulation instabilities and parametric amplification in nonlinear optics, with special emphasis on optical fibres. We then review state-of-the-art research about a peculiar class of modulation instabilities (MIs) and signal amplification processes induced by dissipation in nonlinear optical systems. Losses applied to certain parts of the spectrum counterintuitively lead to the exponential growth of the damped mode themselves, causing gain through losses. We discuss the concept of imaging of losses into gain, showing how to map a given spectral loss profile into a gain spectrum. We demonstrate with concrete examples that dissipation-induced MI, apart from being of fundamental theoretical interest, may pave the way towards the design of a new class of tuneable fibre-based optical amplifiers, optical parametric oscillators, frequency comb sources, and pulsed lasers.

Non-linear relaxation of interacting bosons coherently driven on a narrow optical transition

We study the dynamics of a two-component Bose-Einstein condensate (BEC) of 174Yb atoms coherently driven on a narrow optical transition. The excitation transfers the BEC to a superposition of states with different internal and momentum quantum numbers. We observe a crossover with decreasing driving strength between a regime of damped oscillations, where coherent driving prevails, and an incoherent regime, where relaxation takes over. Several relaxation mechanisms are involved: inelastic losses involving two excited atoms, leading to a non-exponential decay of populations; Doppler broadening due to the finite momentum width of the BEC and inhomogeneous elastic interactions, both leading to dephasing and to damping of the oscillations. We compare our observations to a two-component Gross-Pitaevskii (GP) model that fully includes these effects. For small or moderate densities, the damping of the oscillations is mostly due to Doppler broadening. In this regime, we find excellent agreement between the model and the experimental results. For higher densities, the role of interactions increases and so does the damping rate of the oscillations. The damping in the GP model is less pronounced than in the experiment, possibly a hint for many-body effects not captured by the mean-field description.

Time-dependent Ginzburg-Landau approach to the dynamics of inhomogeneous chiral condensates in a nonlocal Nambu–Jona-Lasinio model

We study the dynamics of inhomogeneous scalar and pseudoscalar chiral order parameters within the framework of the time-dependent Ginzburg-Landau equations. We utilize a nonlocal chiral quark model to obtain the phase diagram of the model as function of temperature and baryon chemical potential and study the formation of metastable spatial domains of matter where the order parameters acquire a spatial modulation in the course their dynamical evolution. We found that, before reaching the expected equilibrium homogeneous state, both scalar and pseudoscalar chiral condensates go through long-lived metastable inhomogeneous structures. For different initial configurations of the order parameters, the lifetimes of the inhomogeneous structures are compared to timescales in a relativistic heavy-ion collision.

From octopus to dendrite-Semiflexible polyelectrolyte brush condensates in trivalent counterion solution.

Interplay between counterion-mediated interaction and stiffness inherent to polymer chain can bring substantial complexity to the morphology and dynamics of polyelectrolyte brush condensates. Trivalent counterions induce collapse of flexible polyelectrolyte brushes, over a certain range of grafting density, into octopus-like surface micelles; however, if individual chains are rigid enough, the ion-mediated local nematic ordering assembles the brush chains into fractal-like dendritic condensates whose relaxation dynamics is significantly slower than that in the surface micelles. Notably, the trivalent ions condensed in the dendritic condensates are highly mobile displaying quasi-one-dimensional diffusion in parallel along the dendritic branches. Our findings in this study are potentially of great significance to understanding the response of cellular organization such as chromosomes and charged polysaccharides on membranes to the change in ionic environment.

Interplay of coherent and dissipative dynamics in condensates of light**This paper is dedicated to the memory of Tobias Brandes

Based on the Lindblad master equation approach we obtain a detailed microscopic model of photons in a dye-filled cavity, which features condensation of light. To this end we generalise a recent non-equilibrium approach of Kirton and Keeling such that the dye-mediated contribution to the photon–photon interaction in the light condensate is accessible due to an interplay of coherent and dissipative dynamics. We describe the steady-state properties of the system by analysing the resulting equations of motion of both photonic and matter degrees of freedom. In particular, we discuss the existence of two limiting cases for steady states: photon Bose–Einstein condensate and laser-like. In the former case, we determine the corresponding dimensionless photon–photon interaction strength by relying on realistic experimental data and find a good agreement with previous theoretical estimates. Furthermore, we investigate how the dimensionless interaction strength depends on the respective system parameters.

Dressed state dynamics of two-component Bose-Einstein Condensates in state-dependent potentials

Dressed potentials realized by coupling state-dependent bare potentials with external fields have important applications in trapping and manipulating atoms. Here, we study the dynamics of dressed states for coupled two-component Bose-Einstein condensates (BECs) in state-dependent potentials. Through both analytical and numerical methods, we find that the dressed state dynamics sensitively depend on both the inter-component coupling strength and the initial state. If the inter-component coupling is strong enough and the initial wave packet is located at the potential minimum, the dressed states can be decoupled and the Josephson oscillations and macroscopic quantum self-trapping appear. However, if the initial wave packet is located far away from the potential minimum, the wave packet will acquire a large kinetic energy and Landau-Zener transitiozs between the dressed states occur at the avoided-crossing point. Further, we give the validity ranges and conditions for the formation of adiabatic potentials, where the influences of Landau-Zener transitions can be ignored. Our results give an insight on how the inter-component coupling affects the dressed state dynamics and how to realize adiabatic potentials with BECs in state-dependent potentials.

Suppressing Ice Nucleation of Supercooled Condensate with Biphilic Topography

Preventing or minimizing ice formation in supercooled water is of prominent importance in many infrastructures, transportation, and cooling systems. The overall phase change heat transfer on icephobic surfaces, in general, is intentionally sacrificed to suppress the nucleation of water and ice. However, in a condensation frosting process, inhibiting freezing without compromising the water condensation has been an unsolved challenge. Here we show that this conflict between anti-icing and efficient condensation cooling can be resolved by utilizing biphilic topography with patterned high-contrast wettability. By creating a varying interfacial thermal barrier underneath the supercooled condensate, the biphilic structures tune the nucleation rates of water and ice in the sequential condensation-to-freezing process. Our experimental and theoretical investigation of condensate freezing dynamics further unravels the correlation between the onset of droplet freezing and its characteristic radius, offering a new insight for controlling the multiphase transitions among vapor, water, and ice in supercooled conditions.

Spinor dynamics in a mixture of spin-1 and spin-2 Bose-Einstein condensates

The spinor dynamics of Bose-Einstein condensates of 87Rb atoms with hyperfine spins 1 and 2 were investigated. A technique of simultaneous Ramsey interferometry was developed for individual control of the vectors of two spins with almost the same Zeeman splittings. The mixture of spinor condensates is generated in the transversely polarized spin-1 and the longitudinally polarized spin-2 states. The time evolution of the spin-1 condensate exhibits dephasing and rephasing of the Larmor precession due to the interaction with the spin-2 condensate. The scattering lengths between spin-1 and -2 atoms were estimated by comparison with the numerical simulation using the Gross-Pitaevskii equation. The proposed technique is expected to facilitate the further study of multiple spinor condensates.

Fluctuations and temperature effects in bose-einstein condensation

The modeling of cold atoms systems has known an increasing interest in the theoretical physics community, after the first experimental realizations of Bose Einstein condensates, some twenty years ago. We here review some analytical and numerical results concerning the influence of fluctua-tions, either arising from fluctuations of the confining parameters, or due to temperature effects, in the models describing the dynamics of such condensates.

Generation of twin-Fock states for precision measurement beyond the standard quantum limit

The highest precision achievable for a two-mode (two-path) classical interferometer is bounded by 1/√N (with NN&lt;/span/2) in each mode). In the past, either through optical spontaneous parametric-down-conversion or through quantum-gate operations on trapped ions, twin-Fock states consisting of no more than 10 photons or ions have been realized. In recent years, twin-Fock states made up of a few thousand atoms have been generated using spin-mixing dynamics in spinor Bose-Einstein condensates (BECs). However, these twin-Fock states exhibit huge fluctuation in particle numbers, thereby limiting their potential applications. We recently generated twin-Fock states of about 11000 atoms in a deterministic manner by driving a spin-1 BEC through quantum critical points (QCPs) slowly. Even though substantial excitations occur while crossing the QCP regions during the drive, this method is capable of generating highly entangled twin-Fock states because of the very different structures of the system's low-lying eigenstates across the QCPs. The samples we prepare feature a number squeezing of 10.7±0.6 decibels and a normalized collective spin length of 0.99±0.01. Together, they infer a minimum entanglement cluster (or entanglement breadth) of 910 atoms. This article introduces the background and advancement of this research.

Dynamics of inhomogeneous chiral condensates

We study the dynamics of the formation of inhomogeneous chirally broken phases in the final stages of a heavy-ion collision, with particular interest on the time scales involved in the formation process. The study is conducted within the framework of a Ginzburg-Landau time evolution, driven by a free energy functional motivated by the Nambu–Jona-Lasinio model. Expansion of the medium is modeled by one-dimensional Bjorken flow and its effect on the formation of inhomogeneous condensates is investigated. We also use a free energy functional from a nonlocal Nambu–Jona-Lasinio model which predicts metastable phases that lead to long-lived inhomogeneous condensates before reaching an equilibrium phase with homogeneous condensates.

Mathematical Models and Numerical Methods for Spinor Bose-Einstein Condensates.

In this paper, we systematically review mathematical models, theories and numerical methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We start with a pseudo spin-1/2 BEC system with/without an internal atomic Josephson junction and spin-orbit coupling including (i) existence and uniqueness as well as non-existence of ground states under different parameter regimes, (ii) ground state structures under different limiting parameter regimes, (iii) dynamical properties, and (iv) efficient and accurate numerical methods for computing ground states and dynamics. Then we extend these results to spin-1 BEC and spin-2 BEC. Finally, extensions to dipolar spinor systems and/or general spin-F (F>=3) BEC are discussed.

Solitons in multi-body interactions for a fully modulated cubic–quintic Gross–Pitaevskii equation

• Dynamics of solitons in a fully modulated cubic–quintic Gross–Pitaevskii equation is analyzed. • Role of quintic parameter on the size of wave numbers of carrier and envelope is analyzed. • Lax-pair for the model with varying coefficients and external potential is given. • Regions of modulational instability and linear and nonlinear stabilities are investigated. A phase imprint approach is applied to a cubic Gross–Pitaevskii equation (GPE) in order to obtain a modified non-autonomous derivative cubic–quintic nonlinear GPE with fully variable coefficients. This model describes the dynamics of condensates in Bose–Einstein condensates, with both two- and three-body interatomic interactions with an external potential when the coefficient of the dispersion term is constant. This model is also applicable to fiber optics media in the absence of external potential. We show that this modified GPE model has a Lax-pair when all of its coefficients depend on time. However, the external potential depends on both the time and space variables. We obtain two classes of exact analytical solutions. These classes of solutions contain four different types of solitary-like wave solutions in the form of kink, anti-kink, bright, dark solitary, and periodic wave solutions. We reveal the effects of a quintic term on wave numbers, for both the carrier and envelope waves. Stability analysis is carried out, and conditions on parameters that determine regions with linear stability are discussed. Graphical analysis of some solutions are presented.

Higher-order stochastic differential equations and the positive Wigner function

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and $\ensuremath{\gamma}$ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

Effective two-mode model in Bose-Einstein condensates versus Gross-Pitaevskii simulations

We study the dynamics of three-dimensional Bose-Einstein condensates confined by double-well potentials using a two-mode model with an effective on-site interaction energy parameter. The effective on-site interaction energy parameter is evaluated for different numbers of particles ranging from a low experimental value to larger ones approaching the Thomas-Fermi limit, yielding important corrections to the dynamics. We analyze the time periods as functions of the initial imbalance and find a closed integral form that includes all interaction-driven parameters. A simple analytical formula for the self-trapping period is introduced and shown to accurately reproduce the exact values provided by the two-mode model. Systematic numerical simulations of the problem in 3D demonstrate the excellent agreement of the two-mode model for experimental parameters.