In this thesis, we investigate polarised solitary waves, known as magnetic solitons and dark-antidark solitons, in binary (two-component) Bose-Einstein condensates in the miscible phase. These solitons have been recently realised in experiments and are predicted to form bound states. We calculate the interaction potentials between magnetic solitons with the same and opposite polarisation, uncovering the mechanisms underlying bound state formation. By considering two superimposed counter-propagating magnetic solitons with opposite polarisation, we analytically calculate the dissociation energy of the bound states and find good agreement with full numerical simulations. Furthermore, we show that the oscillation period of bound states depends on the maximum soliton separation. We subsequently extend these results to dark-antidark solitons. For binary dipolar Bose- Einstein condensates, we derive the dispersion relation of elementary excitations and find that, in the presence of a spin-roton, spin-density modulations form around dark-antidark solitons. These modulations lead to additional local maxima and minima in the inter-soliton potentials, enabling the formation of additional bound state regions. Additionally, we compare the collision characteristics of magnetic solitons in non-dipolar systems with dark-antidark solitons in dipolar–nondipolar condensate mixtures and explore the collisions between bound states in the non-dipolar case.
In this thesis, we investigate polarised solitary waves, known as magnetic solitons and dark-antidark solitons, in binary (two-component) Bose-Einstein condensates in the miscible phase. These solitons have been recently realised in experiments and are predicted to form bound states. We calculate the interaction potentials between magnetic solitons with the same and opposite polarisation, uncovering the mechanisms underlying bound state formation. By considering two superimposed counter-propagating magnetic solitons with opposite polarisation, we analytically calculate the dissociation energy of the bound states and find good agreement with full numerical simulations. Furthermore, we show that the oscillation period of bound states depends on the maximum soliton separation. We subsequently extend these results to dark-antidark solitons. For binary dipolar Bose- Einstein condensates, we derive the dispersion relation of elementary excitations and find that, in the presence of a spin-roton, spin-density modulations form around dark-antidark solitons. These modulations lead to additional local maxima and minima in the inter-soliton potentials, enabling the formation of additional bound state regions. Additionally, we compare the collision characteristics of magnetic solitons in non-dipolar systems with dark-antidark solitons in dipolar–nondipolar condensate mixtures and explore the collisions between bound states in the non-dipolar case.
We investigate the formation of bound states between dark-antidark solitary waves in two-component dipolar Bose-Einstein condensates. The excitation spectrum contains density and spin branches and a rotonic feature of the spin branch enables long-range soliton interactions, giving rise to multiple bound states for a single pair, each with a distinct separation. We show that these bound states originate from periodic modulations of the intersoliton potential, while individual solitons are surrounded by spatial spin-density oscillations. Both features provide direct signatures of the spin roton. Collisions between unbound solitons probe this potential, with dipolar interactions enforcing universal bouncing at low velocities, independent of soliton sign, whereas nondipolar solitons may either transmit or bounce. This distinct behavior offers a realistic path to confirming spin rotons experimentally.
Two-component Bose-Einstein condensates in the miscible phase can support polarization solitary waves, known as magnetic solitons. By calculating the interaction potential between two magnetic solitons, we elucidate the mechanisms and conditions for the formation of bound states—or —and support these predictions with dynamical simulations. We analytically determine the of bound states consisting of two oppositely polarized solitons and find good agreement with full numerical simulations. Collisions between bound states—either with other bound states or with individual solitons—produce intriguing dynamics. Notably, collisions between a pair of bound states exhibit a dipole-like behavior. We anticipate that such bound states, along with their rich collision dynamics, are within reach of current experimental capabilities.
Multicomponent Bose-Einstein condensates exhibit an intriguing variety of nonlinear structures. In recent theoretical work [C. Qu, L. P. Pitaevskii, and S. Stringari, Phys. Rev. Lett. 116, 160402 (2016)], the notion of magnetic solitons has been introduced. Here we examine a variant of this concept in the form of vector dark-antidark solitary waves in multicomponent Bose-Einstein condensates (BECs). We first provide concrete experimental evidence for such states in an atomic BEC and subsequently illustrate the broader concept of these states, which are based on the interplay between miscibility and intercomponent repulsion. Armed with this more general conceptual framework, we expand the notion of such states to higher dimensions presenting the possibility of both vortex-antidark states and ring-antidark-ring (dark soliton) states. We perform numerical continuation studies, investigate the existence of these states, and examine their stability using the method of Bogoliubov--de Gennes analysis. Dark-antidark and vortex-antidark states are found to be stable for broad parametric regimes. In the case of ring dark solitons, where the single-component ring state is known to be unstable, the vector entity appears to bear a progressively more and more stabilizing role as the intercomponent coupling is increased.
Spin mixing induced dynamics of spinor solitons in F=1 Bose Einstein condensates
We explore soliton interactions in a homogeneous spinor F=1 Bose Einstein Condensate (BEC) in the presence of a magnetic field, focusing on dark bright dark and bright dark bright configurations. We investigate how these interactions depend on the phase differences among bright solitons and their influence during the dynamics. Our findings align with prior non spinor results, i.e., repulsion among in phase bright solitons and attraction among out of phase pairs in self repulsive atomic BECs. The potential bright soliton attraction, added to the short range repulsion of dark dark soliton interactions, can lead to bound states. However, we find that these bound states break in the presence of spinor interactions due to the particle exchange dynamics between the hyperfine states of the components. Additonally, we develop an effective classical model to describe the soliton dynamics, using a Lagrangian approach. The accuracy of the model is tested by comparing it against numerical simulations. Our results suggest that the proposed model captures the essential features of soliton behavior in the presence of spin interactions, and provides congruent soliton trajectories and interspecies particle exchange dynamics in most of the cases.
This thesis examines two aspects of the non-equilibrium dynamics of Bose-Einstein condensates (BECs). Our particular interests are the relaxation of near-integrable systems, and the inter-particle correlations present in BECs, both in equilibrium and following an abrupt change in the Hamiltonian. In the first part of this thesis we investigate the stability of solitary wave solutions to a system of two coupled one-dimensional non-linear Schrodinger equations (CNLSE). This system has an integrable point known as the Manakov[1] model which has analytic dark-bright soliton solutions[2]. We break the integrability of this model by varying the inter-species interaction strength, and employ variational and numerical methods in order to find dark-bright solitary wave solutions, away from the integrable point. The time evolution of these states is calculated via numerical integration of the CNLSE, which allows us to assess the stability of these solutions in isolation and to quantify their robustness against collisions with a dark soliton. We find that there is a broad region of the parameter space in which solutions for black-bright (stationary) solitary waves can be found. In this domain, the integrability breaking is revealed only during collisions. Prior to a collision, the numerical solutions are indistinguishable from true solitons, however, the collisional stability of these solitary waves is significantly affected by the extent to which integrability is broken. We find that there is a smooth transition between the non-dispersive particle-like nature of soliton interactions for integrable systems, and the destructive collisions which take place when the system is perturbed far from the integrable point. In the case of moving (grey-bright) solitary waves, we find a more restricted region of the parameter space which admits solitary wave solutions. In this domain we are able to find approximately stable solitary wave solutions using a variational ansatz. The collisional stability of these grey-bright solitary waves is also found to depend upon the extent to which integrability is broken. We conclude that the observation of stable, long-lived dark-bright solitary waves is not sufficient to indicate near-integrability of the two-component system. However, near-integrability may inferred if dark-bright solitary waves are observed to survive multiple collisions. These results are not only of theoretical interest, but may also inform future experiments which explore the behaviour of solitary waves in two-component Bose-Einstein condensates. Following this we investigate the properties of magnetic solitary wave solutions to the CNLSE. We find that the analytic ‘magnetic soliton’ solutions derived in reference [3] are dynamically unstable and relax to non-stationary magnetic solitary wave states over a short timescale. We investigate the collisional dynamics of these magnetic solitary waves and find that these excitations are remarkably robust. In the second part of this thesis we calculate the fluctuations in the number difference between two sub-regions of a Bose-Einstein condensate. This study is motivated by recent experiments performed by the Truscott group at the Australian National University (ANU), which indicate sub- Poissonian fluctuations even for condensates with large thermal depletion. This result cannot easily be reconciled with existing literature, which predicts strongly super-Poissonian fluctuations below the critical temperature (Tc). We develop one-dimensional, and three-dimensional, models to describe these experiments and employ the Bogoliubov formalism to explore the quantum fluctuations of the condensate, which have not previously been studied in detail. We calculate the relative number fluctuations between two halves of the condensate, and also between multiple pairs of spatial bins. For harmonically confined condensates at zero temperature, quantum correlations result in a suppression of the relative number fluctuations between the two halves of the condensate below the shot-noise level. However, the presence of even a small thermal component results in strongly super-Poissonian fluctuations below Tc; this is in agreement with the existing theoretical and experimental results. In addition, we find that the fluctuations of the harmonically confined condensate are non-uniform, with the relative number fluctuations being peaked towards the edges of the condensate. The recent studies of the Truscott group measure the fluctuations after free expansion. We therefore calculate the propagation of correlations following a sudden removal of the harmonic confinement. We find that free expansion results in a strong decrease in the relative number fluctuations. Condensates which exhibit super-Poissonian fluctuations when harmonically confined may therefore display number- squeezing after expansion. A second set of experiments by the Truscott group measured the density fluctuations present in small ‘atom laser’ pulses of atoms out-coupled from their BEC. We also model this procedure and find that immediately after the out-coupling process, the number fluctuations of the out-coupled atomic pulse are approximately Poissonian, irrespective of the correlations present in the atomic reservoir. However, the competing effects of interactions between the atomic pulse and the condensate reservoir, and free expansion of the pulse after out-coupling, can result in the measured fluctuations being either number squeezed or super-Poissonian. Our results will guide future experiments planned by the Truscott group.
The interaction between two bright solitons in a one-dimensional dipolar Bose-Einstein condensate (BEC) is investigated, with the aim of finding the regimes where they form a stable bound state, known as the soliton molecule. To study soliton interactions in BECs we employed a method similar to that used in experimental investigation of the interaction between solitons in optical fibers. The idea consists in creating two solitons at some spatial separation from each other at initial time t0 and then measuring the distance between them at a later time t1>t0. Depending on whether the distance between solitons has increased, decreased, or remained unchanged, compared to its initial value at t0, we conclude that the soliton interaction was repulsive, attractive, or neutral, respectively. We propose an experimentally viable method for estimating the binding energy of a soliton molecule, based on its dissociation at critical soliton velocity. Our theoretical analysis is based on the variational approach, which appears to be quite accurate in describing the properties of soliton molecules in dipolar BECs, as reflected in the good agreement between the analytical and the numerical results.