Observation of Sine-Gordon-like Solitons in a Spinor Bose-Einstein Condensate
Anonymous, Alexander Schmutz, Raphael Schäfer, Alexander Flamm, Florian Schmitt, Ido Siovitz, Thomas Gasenzer, P. G. Kevrekidis, Helmut Strobel, Markus K. Oberthaler
We experimentally generate sine-Gordon-like solitons in a spin-1 spinor BEC utilizing a robust and reproducible local phase-imprinting scheme. We find that the soliton velocity can be tuned by the effective quadratic Zeeman shift. This enables the investigation of controlled soliton interactions, in which we observe the characteristic elastic collision behavior of the integrable sine-Gordon model. The spatial displacement-the so-called phase shift-between incoming and outgoing solitons, the signature of their pairwise interaction, is found to be in quantitative agreement with numerical spin-1 simulations within the error bars. These results establish spinor BECs as a highly controllable experimental platform for studying aspects of the dynamics of sine-Gordon-like models.
We experimentally generate sine-Gordon-like solitons in a spin-1 spinor BEC utilizing a robust and reproducible local phase-imprinting scheme. We find that the soliton velocity can be tuned by the effective quadratic Zeeman shift. This enables the investigation of controlled soliton interactions, in which we observe the characteristic elastic collision behavior of the integrable sine-Gordon model. The spatial displacement-the so-called phase shift-between incoming and outgoing solitons, the signature of their pairwise interaction, is found to be in quantitative agreement with numerical spin-1 simulations within the error bars. These results establish spinor BECs as a highly controllable experimental platform for studying aspects of the dynamics of sine-Gordon-like models.
Quantum mechanical many-body systems are inherently hard to describe microscopically due to the exponential scaling of their state space with the number of particles. Progress in many-body physics is therefore often facilitated by identifying the relevant degrees of freedom of a system and constructing an effective field theory containing the dominant physical processes for the phenomena one would like to understand. Universal dynamics far from equilibrium, which has first been experimentally observed in a spinor Bose-Einstein condensate, has emerged as an im- portant concept which so far has eluded a comprehensive theoretical explanation. In this thesis, we experimentally test the validity of the sine-Gordon model, a paradigmatic integrable model in non-linear physics that describes the low energy behavior of a multitude of physical systems, as the effective field theory for our experimental platform, which is a spinor Bose-Einstein conden- sate. We find qualitative agreement in a first set of quench experiments between the late-time dynamics of the condensate and the effective theory for a wide range of parameters. The presence of topological excitations is conjectured to have an influence on the universal dy- namics exhibited by many-body systems. We develop a novel phase imprinting scheme in order to locally manipulate the degree of freedom of the effective sine-Gordon theory. We use the imprinting scheme to deterministically generate sine-Gordon-type solitons in the spinor con- densate, and characterize their behavior. The ability to control the velocity of the solitons with an experimental parameter opens up the study of collisions of the sine-Gordon-type solitons. We characterize the interaction of the solitons during collision, finding quantitative agreement with numerical simulations. We furthermore find that the solitons display even richer behavior than in the integrable sine-Gordon model, opening up the study of non-integrable effects such as energy transfer between internal and external modes. Observing the full spin-1 nature of the solitons during collisions additionally reveals that the solitons are a special case of a larger family of solitonic solutions. These results lay the foundation for the experimental exploration of uni- versal dynamics and its physical mechanisms through an effective field theory. The investigation of the sine-Gordon-type solitons furthermore constitutes the first experimental study of solitons in multicomponent Bose-Einstein condensates that go beyond the so-called Manakov regime.
Bose-Einstein condensates (BECs), a quantum state of matter formed when bosonic atoms are cooled close to absolute zero, have become the premier platform for investigating fundamental physics with atomic vapours. Experiments on Bose-Einstein condensates now achieve exquisite control over many aspects of the system, including interactions, trapping potential, and dynamics. This has precipitated a new wave of research into many-body quantum phenomena and, in particular, solitons. These structures are fundamental excitations of an interacting non-linear medium, of interest to a multitude of scientific disciplines from non-linear optics to financial markets. The highly controllable environment of BECs form an attractive playground for the study of solitons allowing the non-linearity to be dynamically tuned, facilitating deeper investigations into these structures. Consistently generating and analysing solitons in BEC experiments continues to be problematic. In particular, the non-linear dynamics of BECs, though required for the generation of solitons, produce particularly challenging control and optimization problems. These control problems must be solved before further investigations into the fundamental physics of soliton dynamics can be answered. This thesis makes three important advances in the control and measurement of BECs that will lead to better generation and observation of solitons. (1) a theoretical model for a control scheme capable of highly precise wavefunction engineering, (2) the experimental implementation of a machine learning algorithm for online optimisation, and (3) a continuous non-destructive imaging system capable of directly observing soliton dynamics in real-time. Together, these advances provide a suite of tools for manipulating and exploiting solitons in Bose-Einstein condensates. A novel technique was developed theoretically, offering control of the macroscopic wavefunction of a Bose-Einstein condensate with unprecedented spatial resolution and speed. The ability to control the atomic wavefunction at the fundamental length scale is key to the advancement of many quantum technologies such as quantum simulators. The magnetic resonance control scheme is demonstrated through simulation of a 87Rb condensate with the exemplar model generating a single dark soliton with corresponding π phase kink. The soliton represents a structure at the fundamental length scale of the system, and demonstrates the potential of the scheme for precision state engineering. The scheme is extended to generate higher-order soliton modes which are yet to be experimentally realised. A machine learning algorithm based on Gaussian processes was developed and implemented on the evaporative cooling stage of the production of a 87Rb Bose-Einstein condensate, successfully demonstrating fast optimisation to condensation. The Gaussian process develops a statistical model based on the data that enables the characterisation of the relationship between the experimental controls and resultant quality of the BEC. This relationship is often obfuscated through technical details of the apparatus, frustrating the use of theoretical models to design optimal evaporation ramps. These models often only consider ergodic dynamics with two-body s-wave interactions and no other loss rates with better ramps likely exploiting more complex interactions. The internal model generated from the Gaussian process utilised uncertainty in measured data, making the optimisation more robust to experimental noise than alternate methods. The algorithm is shown to produce high quality Bose-Einstein condensates in 10 times fewer experimental iterations than previously used online optimisation techniques. By exploiting information on the sensitivity of each control, the model can be used to aid experimental design. The convergence of the optimisation is further improved by eliminating a superfluous parameter identified by the model. The general usefulness of machine learning compared with bespoke optimisation algorithms has seen machine learning approach ubiquity. Finally, an experimentally straightforward technique for continuous non-destructive imaging of matter-wave solitons was developed and implemented, facilitating measurements of stochastic phenomena. The technique is readily practicable on any ultracold atom experiment with an existing absorption imaging system, simply requiring the probe laser be far-detuned from resonance. With a signal-to-noise of ∼ 33 at 1.25 GHz detuning, the technique is capable of producing 100 images with no observable heating or atom loss. Coupled with a fast optical phase locked loop, the technique can be used in conjunction with absorption imaging to generate a series of non-destructive images followed by a final high signal-to-noise absorption image solely through moving the laser on resonance for the final image. The high performance and utility of this imaging setup make it a powerful tool for ultra-cold atom experiments.
Established techniques for deterministically creating dark solitons in repulsively interacting atomic Bose-Einstein condensates (BECs) can only access a narrow range of soliton velocities. Because velocity affects the stability of individual solitons and the properties of soliton-soliton interactions, this technical limitation has hindered experimental progress. Here we create dark solitons in highly anisotropic cigar-shaped BECs with arbitrary position and velocity by simultaneously engineering the amplitude and phase of the condensate wave function, improving upon previous techniques which explicitly manipulated only the condensate phase. The single dark soliton solution present in true one-dimensional (1D) systems corresponds to the kink soliton in anisotropic three-dimensional systems and is joined by a host of additional dark solitons, including vortex ring and solitonic vortex solutions. We readily create dark solitons with speeds from zero to half the sound speed. The observed soliton oscillation frequency suggests that we imprinted solitonic vortices, which for our cigar-shaped system are the only stable solitons expected for these velocities. Our numerical simulations of 1D BECs show this technique to be equally effective for creating kink solitons when they are stable. We demonstrate the utility of this technique by deterministically colliding dark solitons with domain walls in two-component spinor BECs.
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.
The analogy between nonlinear optics and Bose-Einstein condensates (BECs) is a fascinating area of study due to the similarities in their underlying physical principles. Both systems are governed by similar nonlinear partial differential equations, which allow researchers to draw parallels between the behaviors observed in these two distinct fields. Among the phenomena observed, the soliton is of particular interest. In this chapter, we demonstrate the possibility of controlling the formation and dynamics of soliton molecules in binary dipolar Bose-Einstein condensates (BECs) with spin-orbit (SO) coupling. The study is carried out analytically using the variational approach and validated numerically through split-step Fourier simulations. Our results reveal that the integrity and stability of the soliton molecules are highly sensitive to the system’s physical parameters, particularly the interplay between local (contact) and nonlocal (dipolar) interactions in the presence of SO coupling. By appropriately tuning these interactions, one can effectively control the binding, oscillatory dynamics, and potential dissociation of the soliton molecules.
Ultracold gases provide an unprecedented level of control for the investigation of soliton dynamics and collisions. We present a scheme for deterministically preparing pairs of three-component solitons in a Bose-Einstein condensate. Our method is based on local spin rotations which simultaneously imprint suitable phase and density distributions. This enables us to observe striking collisional properties of the vector degree of freedom which naturally arises for the coherent nature of the emerging multicomponent solitons. We find that the solitonic properties in the quasi-one-dimensional system are quantitatively described by the integrable repulsive three-component Manakov model.