Model Of Bose-Einstein Condensate Research Articles

Efficient manipulation of Bose–Einstein Condensates in a double-well potential

We pose the problem of transferring a Bose–Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the time-dependent form of the potential. We derive a reduced dynamical system using a Galerkin truncation onto a finite set of eigenfunctions and find that including three modes suffices to effectively control the full dynamics, described by the Gross–Pitaevskii model of BEC. The functional form of the control is reduced to finite dimensions by using another Galerkin-type method called the chopped random basis (CRAB) method, which is then optimized by a genetic algorithm called differential evolution (DE). Finally, we discuss the extent to which the reduction-based optimal control strategy can be refined by means of including more modes in the Galerkin reduction.

Modulation instability of two-dimensional Bose-Einstein condensates with helicoidal and a mixture of Rashba-Dresselhaus spin-orbit couplings

The modulational instability (MI) process is exclusively studied in a two-component Bose-Einstein condensate (BEC) which includes Rashba-Dresselhaus (RD) spin-orbit (SO) and helicoidal SO couplings. A generalized set of two-dimensional (2D) Gross-Pitaevskii (GP) equations is derived. The tunability of the helicoidal gauge potential is exploited to address BECs dynamics in a square lattice. The MI growth rate is derived, and parametric analyses of MI show the dependence of the instability on interatomic interaction strengths, the RD SO coupling, and helicoidal SO coupling, which combines the gauge amplitude and the helicoidal gauge potential. Direct numerical simulations are carried out to confirm the analytical predictions. Trains of solitons are obtained, and their behaviors are debated when the RD SO parameters are varied under different combinations between the gauge amplitude and the helicoidal gauge potential. The latter gives a potential way to manipulate the trapping capacities of the proposed BEC model.

Bose–Einstein Condensate dark matter models in the presence of baryonic matter and random confining potentials

We consider the effects of an uncorrelated random potential on the properties of Bose–Einstein Condensate (BEC) dark matter halos, which acts as a source of disorder, and which is added as a new term in the Gross–Pitaevskii equation, describing the properties of the halo. By using the hydrodynamic representation we derive the basic equation describing the density distribution of the galactic dark matter halo, by also taking into account the effects of the baryonic matter, and of the rotation. The density, mass and tangential velocity profiles are obtained exactly in spherical symmetry by considering a simple exponential density profile for the baryonic matter, and a Gaussian type disorder potential. To test the theoretical model we compare its predictions with a set of 39 galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database. We obtain estimates of the relevant astrophysical parameters of the dark matter dominated galaxies, including the baryonic matter properties, and the parameters of the random potential. The BEC model in the presence of baryonic matter and a random confining potential gives a good statistical description of the SPARC data. The presence of the condensate dark matter could also provide a solution for the core/cusp problem.

Reduction-based strategy for optimal control of Bose-Einstein condensates.

Applications of Bose-Einstein condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal control is a reliable framework to prepare such a state while avoiding undesirable excitations, and, when applied to the time-dependent Gross-Pitaevskii equation(GPE) model of BEC in multiple space dimensions, results in a large computational problem. We propose a control method based on first reducing the problem, using a Galerkin expansion, from a partial differential equationto a low-dimensional Hamiltonian ordinary differential equationsystem. We then apply a two-stage hybrid control strategy. At the first stage, we approximate the control using a second Galerkin-like method known as the chopped random basis to derive a finite-dimensional nonlinear programing problem, which we solve with a differential evolution algorithm. This search method then yields a candidate local minimum which we further refine using a variant of gradient descent. This hybrid strategy allows us to greatly reduce excitations both in the reduced model and the full GPE system.

Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential

We pose the problem of transferring a Bose-Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the time-dependent form of the potential. We derive a reduced dynamical system using a Galerkin truncation onto a finite set of eigenfunctions and find that including three modes suffices to effectively control the full dynamics, described by the Gross-Pitaevskii model of BEC. The functional form of the control is reduced to finite dimensions by using a Galerkin-type method called the chopped random basis (CRAB) method, which is then optimized by a genetic algorithm called differential evolution (DE). Finally, we discuss the the extent to which the reduction-based optimal control strategy can be refined by means of including more modes in the Galerkin reduction.

Is a Bose–Einstein condensate a good candidate for dark matter? A test with galaxy rotation curves

We analyze the rotation curves that correspond to a Bose–Einstein Condensate (BEC)-type halo surrounding a Schwarzschild-type black hole to confront predictions of the model upon observations of galaxy rotation curves. We model the halo as a BEC in terms of a massive scalar field that satisfies a Klein–Gordon equation with a self-interaction term. We also assume that the bosonic cloud is not self-gravitating. To model the halo, we apply a simple form of the Thomas–Fermi approximation that allows us to extract relevant results with a simple and concise procedure. Using galaxy data from a subsample of SPARC data base, we find the best fits of the BEC model by using the Thomas–Fermi approximation and perform a Bayesian statistics analysis to compare the obtained BEC’s scenarios with the Navarro–Frenk–White (NFW) model as pivot model. We find that in the centre of galaxies, we must have a supermassive compact central object, i.e. supermassive black hole, in the range of [Formula: see text] which condensate a boson cloud with average particle mass [Formula: see text] eV and a self-interaction coupling constant [Formula: see text], i.e. the system behaves as a weakly interacting BEC. We compare the BEC model with NFW concluding that in general the BEC model using the Thomas–Fermi approximation is strong enough compared with the NFW fittings. Moreover, we show that BECs still well-fit the galaxy rotation curves and, more importantly, could lead to an understanding of the dark matter nature from first principles.

Slowly rotating Bose–Einstein condensate compared with the rotation curves of 12 dwarf galaxies

Context.The high plateaus of the rotation curves of spiral galaxies suggest either that there is a dark component or that the Newtonian gravity requires modifications on galactic scales to explain the observations. We assemble a database of 12 dwarf galaxies, for which optical (R-band) and near-infrared (3.6 μm) surface brightness density together with spectroscopic rotation curve data are available, in order to test the slowly rotating Bose–Einstein condensate (BEC) dark matter model.Aims.We aim to establish the angular velocity range compatible with observations, bounded from above by the requirement of finite-size halos, to check the model fits with the dataset, and the universality of the BEC halo parameter ℛ.Methods.We constructed the spatial luminosity density of the stellar component of the dwarf galaxies based on their 3.6 μm andR-band surface brightness profiles, assuming an axisymmetric baryonic mass distribution with arbitrary axis ratio. We built up the gaseous component of the mass by employing an inside-truncated disk model. We fitted a baryonic plus dark matter combined model, parametrized by theM/Lratios of the baryonic components and parameters of the slowly rotating BEC (the central densityρc, size of the BEC halo ℛ in the static limit, angular velocityω) to the rotation curve data.Results.The 3.6 μm surface brightness of six galaxies indicates the presence of a bulge and a disk component. The shape of the 3.6 μm andR-band spatial mass density profiles being similar is consistent with the stellar mass of the galaxies emerging wavelength-independent. The slowly rotating BEC model fits the rotation curve of 11 galaxies out of 12 within the 1σsignificance level, with the average of ℛ as 7.51 kpc and standard deviation of 2.96 kpc. This represents an improvement over the static BEC model fits, also discussed. For the 11 best-fitting galaxies the angular velocities allowing for a finite-size slowly rotating BEC halo are less then 2.2 × 10−16s−1.For a scattering length of the BEC particle ofa ≈ 106fm, as allowed by terrestrial laboratory experiments, the mass of the BEC particle is slightly better constrained than in the static case asm ∈ [1.26 × 10−17 ÷ 3.08 × 10−17] (eV c−2).

Dark Matter as a Non-Relativistic Bose–Einstein Condensate with Massive Gravitons

We confront a non-relativistic Bose–Einstein Condensate (BEC) model of light bosons interacting gravitationally either through a Newtonian or a Yukawa potential with the observed rotational curves of 12 dwarf galaxies. The baryonic component is modeled as an axisymmetric exponential disk and its characteristics are derived from the surface luminosity profile of the galaxies. The purely baryonic fit is unsatisfactory, hence a dark matter component is clearly needed. The rotational curves of five galaxies could be explained with high confidence level by the BEC model. For these galaxies, we derive: (i) upper limits for the allowed graviton mass; and (ii) constraints on a velocity-type and a density-type quantity characterizing the BEC, both being expressed in terms of the BEC particle mass, scattering length and chemical potential. The upper limit for the graviton mass is of the order of 10 − 26 eV / c 2 , three orders of magnitude stronger than the limit derived from recent gravitational wave detections.

Rydberg dressing of a one-dimensional Bose-Einstein condensate

We study the influence of Rydberg dressed interactions in a one-dimensional (1D) Bose-Einstein Condensate (BEC). We show that a 1D geometry offers several advantages over 3D for observing BEC Rydberg dressing. The effects of dressing are studied by investigating collective BEC dynamics after a rapid switch-off of the Rydberg dressing interaction. The results can be interpreted as an effective modification of the s-wave scattering length. We include this modification in an analytical model for the 1D BEC, and compare it to numerical calculations of Rydberg dressing under realistic experimental conditions.

Bose-Einstein Condensate Dark Matter Halos Confronted with Galactic Rotation Curves

We present a comparative confrontation of both the Bose-Einstein Condensate (BEC) and the Navarro-Frenk-White (NFW) dark halo models with galactic rotation curves. We employ 6 High Surface Brightness (HSB), 6 Low Surface Brightness (LSB), and 7 dwarf galaxies with rotation curves falling into two classes. In the first class rotational velocities increase with radius over the observed range. The BEC and NFW models give comparable fits for HSB and LSB galaxies of this type, while for dwarf galaxies the fit is significantly better with the BEC model. In the second class the rotational velocity of HSB and LSB galaxies exhibits long flat plateaus, resulting in better fit with the NFW model for HSB galaxies and comparable fits for LSB galaxies. We conclude that due to its central density cusp avoidance the BEC model fits better dwarf galaxy dark matter distribution. Nevertheless it suffers from sharp cutoff in larger galaxies, where the NFW model performs better. The investigated galaxy sample obeys the Tully-Fisher relation, including the particular characteristics exhibited by dwarf galaxies. In both models the fitting enforces a relation between dark matter parameters: the characteristic density and the corresponding characteristic distance scale with an inverse power.

Nonlinear clustering during the BEC dark matter phase transition

Spherical collapse of the Bose-Einstein Condensate (BEC) dark matter model is studied in the Thomas Fermi approximation. The evolution of the overdensity of the collapsed region and its expansion rate are calculated for two scenarios. We consider the case of a sharp phase transition (which happens when the critical temperature is reached) from the normal dark matter state to the condensate one and the case of a smooth first order phase transition where there is a continuous conversion of "normal" dark matter to the BEC phase. We present numerical results for the physics of the collapse for a wide range of the model's space parameter, i.e. the mass of the scalar particle $m_{\chi}$ and the scattering length $l_s$. We show the dependence of the transition redshift on $m_{\chi}$ and $l_s$. Since small scales collapse earlier and eventually before the BEC phase transition the evolution of collapsing halos in this limit is indeed the same in both the CDM and the BEC models. Differences are expected to appear only on the largest astrophysical scales. However, we argue that the BEC model is almost indistinguishable from the usual dark matter scenario concerning the evolution of nonlinear perturbations above typical clusters scales, i.e., $\gtrsim 10^{14}M_{\odot}$. This provides an analytical confirmation for recent results from cosmological numerical simulations [H.-Y. Schive {\it et al.}, Nature Physics, {\bf10}, 496 (2014)].

Quantum information approach to Bose–Einstein condensation of composite bosons

We consider composite bosons (cobosons) comprised two elementary particles, fermions or bosons, in an entangled state. First, we show that the effective number of cobosons implies the level of correlation between the two constituent particles. For the maximum level of correlation, the effective number of cobosons is the same as the total number of cobosons, which can exhibit the original Bose–Einstein condensation (BEC). In this context, we study a model of BEC for indistinguishable cobosons with a controllable parameter, i.e., entanglement between the two constituent particles. We find that bi-fermions behave in a predictable way, i.e., the effective number of the ground state coboson is an increasing function of entanglement between a pair of constituent fermions. Interestingly, bi-bosons exhibit the opposite behavior—the effective number of the ground state coboson is a decreasing function of entanglement between a pair of constituent bosons.

Partially relativistic self-gravitating Bose-Einstein condensates with a stiff equation of state

Because of their superfluid properties, some compact astrophysical objects such as neutron stars may contain a significant part of their matter in the form of a Bose-Einstein condensate (BEC). We consider a partially-relativistic model of self-gravitating BECs where the relation between the pressure and the rest-mass density is assumed to be quadratic (as in the case of classical BECs) but pressure effects are taken into account in the relation between the energy density and the rest-mass density. At high densities, we get a stiff equation of state similar to the one considered by Zel'dovich (1961) in the context of baryon stars in which the baryons interact through a vector meson field. We determine the maximum mass of general relativistic BEC stars described by this equation of state by using the formalism of Tooper (1965). This maximum mass is slightly larger than the maximum mass obtained by Chavanis and Harko (2012) using a fully-relativistic model. We also consider the possibility that dark matter is made of BECs and apply the partially-relativistic model of BECs to cosmology. In this model, we show that the universe experiences a stiff matter phase, followed by a dust matter phase, and finally by a dark energy phase (equivalent to a cosmological constant). The same evolution is obtained in Zel'dovich (1972) model which assumes that initially, near the cosmological singularity, the universe is filled with cold baryons. Interestingly, the Friedmann equations can be solved analytically in that case and provide a simple generalization of the $\Lambda$CDM model. We point out, however, the limitations of the partially-relativistic model for BECs and show the need for a fully-relativistic one.

Thermal conductivity ofIPA-CuCl3: Evidence for ballistic magnon transport and the limited applicability of the Bose-Einstein condensation model

The heat transport of the spin-gapped material (CH_3)_2CHNH_3CuCl_3 (IPA-CuCl_3), a candidate quantum magnet with Bose-Einstein condensation (BEC), is studied at ultra-low temperatures and in high magnetic fields. Due to the presence of the spin gap, the zero-field thermal conductivity (\kappa) is purely phononic and shows a ballistic behavior at T < 1 K. When the gap is closed by magnetic field at H = H_{c1}, where a long-range antiferromanetic (AF) order of Cu^{2+} moments is developed, the magnons contribute significantly to heat transport and exhibit a ballistic T^3 behavior at T < 600 mK. In addition, the low-T \kappa(H) isotherms show sharp peaks at H_{c1}, which indicates a gap re-opening in the AF state (H > H_{c1}) and demonstrates limited applicability of the BEC model to IPA-CuCl_3.

Study of Localized Solutions of the Nonlinear Discrete Model for Dipolar BEC in an Optical Lattice by the Homoclinic Orbit Method

We use homoclinic orbits to find solutions of a dynamical system of the dipolar Bose Einstein Condensate (BEC) in a deep optical lattice. The equation of motion is transformed to a two-dimensional map and its homoclinic orbits are computed numerically. Each homoclinic orbit leads to a different solution. These different solutions lead to different types of solitons. We also analyse the stability of the solutions.

Extended JC-Dicke model for two-component atomic BEC inside a cavity

We consider a trapped two-component atomic Bose-Einstein condensate (BEC), where each atom with three energy-levels is coupled to an optical cavity field and an external classical optical field as well as a microwave field to form the so-called $\Delta$-type configuration. After adiabatically eliminating the atomic excited state, an extended JC-Dicke model is derived under the rotating-wave approximation. The scaled ground-state energy and the phase diagram of this model Hamiltonian are investigated in the framework of mean-field approach. A new phase transition is revealed when the amplitude of microwave field changes its sign.

Polynomial algebras and exact solutions of general quantum nonlinear optical models I: two-mode boson systems

We introduce higher order polynomial deformations of A1 Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe ansatz) solutions to a class of two-mode boson systems, including the Bose–Einstein condensate (BEC) models as special cases. Up to an overall factor, the eigenfunctions of the two-mode boson systems are given by polynomials whose roots are solutions of the associated Bethe ansatz equations. The corresponding eigenvalues are expressed in terms of these roots. We also establish the spectral equivalence between the BEC models and certain quasi-exactly solvable Schördinger potentials.

Mismatch management for optical and matter-wave quadratic solitons

We propose a way to control solitons in chi(2) (quadratically nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter ("mismatch management," MM). It may be realized in the cotransmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. In an altogether different physical setting, the MM may also be implemented by dint of the Feshbach resonance in a harmonically modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. Accordingly, the problem is analyzed in two different ways. First, in the optical model, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially inhomogeneous configurations. In particular, an instability enclave is found inside the stability area. The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of the power. Interactions between stable solitons are virtually unaffected by the MM. The second method (parametric approximation), going beyond the MF description, is developed for spatially homogeneous states in the BEC model. It demonstrates that the MF description is valid for large modulation periods, while, at smaller periods, non-MF components acquire gain, which implies destruction of the MF under the action of the high-frequency MM.

CHAOTIC DYNAMICS OF N-DEGREE OF FREEDOM HAMILTONIAN SYSTEMS

We investigate the connection between local and global dynamics of two N-degree of freedom Hamiltonian systems with different origins describing one-dimensional nonlinear lattices: The Fermi–Pasta–Ulam (FPU) model and a discretized version of the nonlinear Schrödinger equation related to Bose–Einstein Condensation (BEC). We study solutions starting in the vicinity of simple periodic orbits (SPOs) representing in-phase (IPM) and out-of-phase motion (OPM), which are known in closed form and whose linear stability can be analyzed exactly. Our results verify that as the energy E increases for fixed N, beyond the destabilization threshold of these orbits, all positive Lyapunov exponents Li, i = 1,…, N - 1, exhibit a transition between two power laws, Li ∝ EBk, Bk &gt; 0, k = 1, 2, occurring at the same value of E. The destabilization energy Ec per particle goes to zero as N → ∞ following a simple power-law, Ec/N ∝ N-α, with α being 1 or 2 for the cases we studied. However, using SALI, a very efficient indicator we have recently introduced for distinguishing order from chaos, we find that the two Hamiltonians have very different dynamics near their stable SPOs: For example, in the case of the FPU system, as the energy increases for fixed N, the islands of stability around the OPM decrease in size, the orbit destabilizes through period-doubling bifurcation and its eigenvalues move steadily away from -1, while for the BEC model the OPM has islands around it which grow in size before it bifurcates through symmetry breaking, while its real eigenvalues return to +1 at very high energies. Furthermore, the IPM orbit of the BEC Hamiltonian never destabilizes, having finite-size islands around it, even for very high N and E. Still, when calculating Lyapunov spectra, we find for the OPMs of both Hamiltonians that the Lyapunov exponents decrease following an exponential law and yield extensive Kolmogorov–Sinai entropies per particle h KS /N ∝ const., in the thermodynamic limit of fixed energy density E/N with E and N arbitrarily large.

Fidelity for the quantum evolution of a Bose-Einstein condensate

We investigate fidelity for the quantum evolution of a Bose-Einstein condensate (BEC) and reveal its general property with a simple two-component BEC model. We find that, when the initial state is a coherent state, the fidelity decays with time in the ways of exponential, Gaussian, and power law, depending on the initial location, the perturbation strength, as well as the underlying mean-field classical dynamics. In this case we find a clear correspondence between the fast quantum fidelity decay and the dynamical instability of the mean-field system. With the initial state prepared as a maximally entangled state, we find that the behavior of fidelity has no classical correspondence and observe an interesting behavior of the fidelity: periodic revival, where the period is inversely proportional to the number of bosons and the perturbation strength. An experimental observation of the fidelity decay is suggested.