Session P06: Generation, Detection and Dynamics of Solitons in Bose-Einstein Condensates

Live

Predicting the evolution of many-body systems under attractive interactions is a challenging task, owing to the instability to collapse. Bright solitons are remarkable stationary states, established when the self-focusing effect responsible for collapse is exactly compensated by the wave dispersion. In two-dimensional (2D) Bose gases, however, such intricate balance cannot be fulfilled except at a critical norm known as the Townes threshold – only at which matter-wave bright solitons can form. By quenching the atomic interaction from repulsive to attractive via a Feshbach resonance \footnote{Cheng-An Chen and Chen-Lung Hung, \textbf{arXiv}:1907.12550 (2019).}, we report the observation of Townes solitons formation through the manifestation of modulational instability that results in the amplification of density wave disturbances and fragmentation of a 2D sample. Our high-resolution density measurements in space and time domain reveal detailed information about the formation process, and demonstrate multiple universal behaviors in association with the formation of a stationary state in an attractive many-body system.   

Live

Solitons are non-dispersive wave packets that arise as solutions to the one-dimensional nonlinear Shr\"{o}dinger equation. Due to the integrability of the equation, after a specific interaction quench, a fundamental soliton may be transformed into a $n$th-order soliton composed of $n$ fundamental solitons, which are known as breathers.\footnote{V. E. Zakharov and A. B. Shabat, Soviet Physics JETP, 34, 1 (1972)}$^{,}$\footnote{J. Satsuma and N. Yajima, Prog. Theor. Phys. Supp. 55, 284 (1974)} The density profile oscillates in time, at a frequency determined by the chemical potential difference of the constituent solitons. A $n$-soliton breather is formed with the mass ratio of the constituent solitons of 1:3:...:2$n$-1, when the quench factor is $n^{2}$ where $n$ is an integer. In this work, we first form a soliton from a Bose-Einstein condensate of $^{7}$Li atoms in a quasi-1D harmonic potential formed from a single focused IR laser beam. We then quench the scattering length to form breathers. As we decrease the trap axial confinement strength sufficiently, the breathing frequency becomes independent of the axial confinement, which indicates that the geometry approaches the 1D-limit. We observe the density profiles of the $n$=2 and $n$=3 breathers.   

Live

A mean-field cold-atom breather, which can be formed by the application of a four-fold quench of the scattering length to the fundamental soliton in an attractive quasi-one-dimensional gas, is a nonlinear superposition of two solitons with the $1:3$ mass ratio and zero relative velocity. Formation of solitons with varying mass ratios and relative velocities, predicted by the Bethe-ansatz analysis [1] of the quench for up to $N=23$ atoms, is a manifestation of quantum fluctuations. The fluctuations are analyzed here [2] within the Bogoliubov approach in the limit of large $N$, using two models of the vacuum state: white noise and correlated noise. The latter model, closer to the ab initio by construction, leads to a better agreement, within 20\% accuracy, with the fluctuations estimated from the Bethe-ansatz results for small $N$. The variances of relative velocity, relative phase, initial distance, and soliton masses scale as $N$, $1/N$, $1/N^3$, and $N$, respectively. Effects of the trap potential on the quantum fluctuations are also analyzed. 1. V. A. Yurovsky, B. A. Malomed, R. G. Hulet, and M. Olshanii, Phys. Rev. Lett. 119, 220401 (2017). 2. O. V. Marchukov, B. A. Malomed, M. Olshanii, V. Dunjko, R. G. Hulet, and V. A. Yurovsky, arXiv:1911.01369.   

On Demand

Vector soliton are a type of solitary wave packet occurring in a nonlinear medium comprised of multiple components. They have been discovered in a variety of systems including ultracold atoms. In this talk, we report the observation of a new type of soliton, called a magnetic soliton, in a spinor BEC beyond the usual Manakov limit of the 1-dimensional Gross-Pitaevskii (GP) equations. By using a ``magnetic shadowing'' technique that only affects the spin and is therefore non-destructive, we created a pair of magnetic solitons in an antiferromagnetic spinor BEC. In addition, multiple solitons can be created by spatially modulating the pattern of the magnetic shadow, which allows the investigation of soliton interactions, collisions and possible bound states.   

On Demand

We present results on moving beyond the K-Harmonic approximation for the adiabatic hypervectorial surface of a Bose-Einstein condensate, which intuitively describes the longitudinal and transverse sizes of the collective system. The K-Harmonic approximation freezes the hyperangular behavior of the many-body wavefunction to be that of the non-interacting state. Previous works show that the approximation describes the ground-state and the first excitation frequency reasonably well but qualitatively differs from the Bogoliubov theory for most other collective modes. Therefore, we develop a method for using the stationary state of the Gross-Pitaevskii equation as an alternative ansatz for the dominant hyperangular behavior. Of importance are the Thomas-Fermi regime and the quasi-one-dimensional bright soliton, where the order parameter deviates significantly from a gaussian. In particular, for the bright soliton, the K-Harmonic approximation predicts that the many-body spectrum should comprise of different Rydberg series of very large effective angular momentum, converging to thresholds defined by the transverse trap eigenstates. We discuss how the new method modifies the simple analytic behavior of K-Harmonic surfaces, in comparison with the Bogoliubov theory.   

On Demand

Solitary waves (solitons) are non-dispersing localized traveling waves that retain their size, shape, and speed as they move, and even when they collide with one another. In a repulsively interacting 1D Bose-Einstein condensates (BEC), the soliton velocity governs the width, depth, and even stability of a soliton. To study solitons dynamics, a number of absorption images need to be manually analyzed to obtain the number of solitons present and their position. These solitons must be distinguished from a background of additional excitations. ~ We developed an automated two-step protocol for detecting dark solitons in two-component BECs. Our algorithm combines two neural networks pre-trained using simulated and real data to: (1) identify the number of solitons present in BEC and (2) determine their position. This automated detector highlights the applicability of machine learning-driven feature detection, rather than traditional curve fitting, to streamline cold atom research.   

Observation of quantum synchronization and blockade in spin-1 atom

synchronization between different physical systems has gained lots of attention in research. While in classical system, numerous research articles report the signature of synchronization, synchronization in the quantum regime has not been observed yet. We report the first observation of quantum synchronization in an ensemble of cold spin-1 $^{\mathrm{87}}$Rb atoms. In particular, when we store and destructively interfere two dark state polaritons, we observe an otherwise delocalized limit-cycle spin-1 state gets localized and entrained to classically controlled phases, only in presence of artificially engineered, anisotropic decay channels, These observations are in accordance with the recent predictions of Roulet and Bruder of quantum phase synchronization in the smallest quantum systems, spin-1 atoms, due to anisotropic internal decay channels. We numerically reconstruct the underlying quantum state and when viewed in phase space, in presence of artificially engineered asymmetric decay channels, we observe the state getting entrained even when the dark states interfere destructively. The corresponding relative phase difference of the dark state polaritons locks to a classical, controlled phase difference. Furthermore, we observe a blockade of synchronization due to quantum interference, a genuine quantum signature, which gets lifted due to increasing asymmetry in decays. When the system is driven harder, we observe emergence of Arnold tongue-like typical signatures of all synchronization.   

Quench-produced solitons in a box-trapped Bose-Einstein condensate

We describe a protocol to prepare solitons in a quasi-1d box-trapped Bose-Einstein condensate using only a quench of the isotropic s-wave scattering length. A quench to exactly four times the initial scattering length creates one soliton at each boundary of the box, which then propagate in a uniform background density. No additional excitations are created during the quench. We investigate the robustness of this procedure to the scattering length ramp rate and an mismatch of the final scattering length. We additionally investigate the 3d regime, where the quench may cause excitations along the transverse directions of the elongated box, and give a procedure for minimizing these excitations even far away from the quasi-1d regime via an additional quench of the transverse confining potential.   

Not Participating

We theoretically study the core structure of a stationary soliton, the building block of wall-vortex composite defects recently observed in the polar phase of spin-1 condensate [Seji Kang et. al., Phys. Rev. Lett. 122, 095301 (2019)], in the presence of quadratic Zeeman term. The phase diagram of such solitons is mapped out by locating the solutions of minimal soliton tension coefficient in the defining range of polar phase, and the states are distinguished into normal, anti-ferromagnetic, broken-axisymmetry, and ferromagnetic phases according to the number and spin densities of the core. Phase boundaries and the associated orders of phase transitions are determined and the critical behavior of the relevant continuous phase transitions is analyzed using Ginzburg-Landau theory.