Symmetry breaking induced by random fluctuations for Bose-Einstein condensates in a double-well trap

This paper is devoted to the study of the dynamics of two weakly-coupled Bose-Einstein condensates confined in a double-well trap and perturbed by random external forces. Energy diffusion due to random forcing allows the system to visit symmetry-breaking states when the number of atoms exceeds a threshold value. The energy distribution evolves to a stationary distribution which depends on the initial state of the condensate only through the total number of atoms. This loss of memory of the initial conditions allows a simple and complete description of the stationary dynamics of the condensate which randomly visits symmetric and symmetry-breaking states.Comment: 12 pages, 6 figure

Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length

Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied analytically and numerically. The time-dependent variational approach is used for the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is invistigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevski equation.Comment: 17 pages, 10 figures, submitted to Journal of Physics

Dissipation-managed soliton in a quasi-one-dimensional Bose-Einstein condensate

We use the time-dependent mean-field Gross-Pitaevskii equation to study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose-Einstein condensate (BEC). Because of three-body recombination of bosonic atoms to molecules, atoms are lost (dissipated) from a BEC. Such dissipation leads to the decay of a BEC soliton. We demonstrate by a perturbation procedure that an alimentation of atoms from an external source to the BEC may compensate for the dissipation loss and lead to a dynamically-stabilized soliton. The result of the analytical perturbation method is in excellent agreement with mean-field numerics. It seems possible to obtain such a dynamically-stabilized BEC soliton without dissipation in laboratory.Comment: 5 pages, 3 figure

Adiabatic Compression of Soliton Matter Waves

The evolution of atomic solitary waves in Bose-Einstein condensate (BEC) under adiabatic changes of the atomic scattering length is investigated. The variations of amplitude, width, and velocity of soliton are found for both spatial and time adiabatic variations. The possibility to use these variations to compress solitons up to very high local matter densities is shown both in absence and in presence of a parabolic confining potential.Comment: to appear in J.Phys.

Collapse and revival of oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap

In this work, we study parametric resonances in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical and analytical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric resonances (collapse and revival of the oscillations of the BEC width). Parametric resonances disappear when one of the competing factors i.e strength of harmonic trap or the strength of optical lattice dominates. Parametric instabilities (exponential growth of Bogoliubov modes) arise for large variations in the strength of the optical lattice.Comment: 9 pages, 20 figure

Modulational instability in nonlocal Kerr-type media with random parameters

Modulational instability of continuous waves in nonlocal focusing and defocusing Kerr media with stochastically varying diffraction (dispersion) and nonlinearity coefficients is studied both analytically and numerically. It is shown that nonlocality with the sign-definite Fourier images of the medium response functions suppresses considerably the growth rate peak and bandwidth of instability caused by stochasticity. Contrary, nonlocality can enhance modulational instability growth for a response function with negative-sign bands.Comment: 6 pages, 12 figures, revTeX, to appear in Phys. Rev.

Effects of plant growth regulators on callogenesis and embryogenesis in sarnav and desiree potato (Solanum tuberosum L.) varieties

Somatic embryos play a pivotal role in the production of high-quality potatoes and seed breeding. This study focused on determining the concentrations of 1-naphthaleneacetic acid (NAA) and 6-benzyl amino purine (BAP) in the formation of callus tissue and callus induction. Our goal was to assess the efficiency of potato explants with the highest potential for somatic embryo production. To achieve this, we cultivated Sarnav and Desiree potato varieties under in vitro tissue culture conditions, utilizing the obtained tissue cultures for subsequent experiments. The MS nutrient media were enriched with NAA and BAP at ratios of 1.5: 1, 1: 1.5, and 1: 1 mg/L, along with NAA concentrations of 1.5, 1, or 2 mg/L. Somatic embryogenesis experiments were conducted using various MS nutrient media, enriched with BAP and GA3 at concentrations of 1: 0.5, 0.4: 0.1, 0.5: 0.2, and 0.1: 0.1 mg/L of plant growth regulators. During the course of the study, diverse callus formations were observed in both leaf and internodal stem explants. Among the nutrient media, the M2 medium enriched with 1: 1.5 mg/L of NAA and BAP yielded the highest callus formation rates: 92% for the Desiree variety and 100% for the Sarnav variety, specifically in internodal stem explants. Notably, the index of embryo formation in leaf explants selected for somatic embryogenesis within the SE4 medium was 70% for the Sarnav variety and 65% for the Desiree variety. The inclusion of BAP and GA3 at a ratio of 0.1: 0.1 mg/l in the SE4 nutrient medium resulted in somatic embryogenesis in 80% of calli for the Sarnav variety and 78% for the Desiree variety. These findings underscore the potential for regenerating plants through somatic embryogenesis in the Sarnav potato variety, a significant development with implications for genetic transformation studies involving this particular variety

PT{\cal PT}-symmetric coupler with χ(2)\chi^{(2)} nonlinearity

We introduce the notion of a ${\cal PT}$-symmetric dimer with a $\chi^{(2)}$ nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain/loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first or the second harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable.Comment: 12 pages, 11 figure