Spin-orbit coupled ultra-cold atoms provide an intriguing new avenue for the study of rich spin dynamics in superfluids. In this Letter, we observe Zitterbewegung, simultaneous velocity (thus position) and oscillations, neutral between two spin-orbit bands a Bose-Einstein condensate (BEC) through sudden quantum quenches Hamiltonian. The observed Zitterbewegung oscillations are perfect on short time scale but gradually damp out long scale, followed by strong heating BEC. As application, also...

Spin-orbit coupling is an essential ingredient in topological materials, conventional and quantum-gas-based alike. Engineered spin-orbit ultracold-atom systems-unique their experimental control measurement opportunities-provides a major opportunity to investigate understand phenomena. Here we experimentally demonstrate theoretically analyze technique for controlling two-component Bose-Einstein condensate using amplitude-modulated Raman coupling.

An analytic solution for a moving magnetic soliton in spinor condensate shows that the width and velocity of these solitons are directly linked to spin healing length sound condensate.

Spin-orbit coupling (SOC) plays a crucial role in many branches of physics. In this context, the recent experimental realization between spin and linear momentum ultracold atoms opens completely new avenue for exploring spin-related superfluid Here we propose that another important fundamental SOC, orbital angular (SOAM), can be implemented using higher-order Laguerre-Gaussian laser beams to induce Raman two hyperfine states atoms. We study ground-state phase diagrams SOAM-coupled...

The recent experimental realization of spin-orbit (SO) coupling for spin-1 ultracold atoms opens an interesting avenue exploring SO-coupling-related physics in large-spin systems, which is generally unattainable electronic materials. In this paper, we study the effects interactions between on ground states and collective excitations SO-coupled Bose-Einstein condensates (BECs) presence a spin-tensor potential. We find that ferromagnetic interaction can induce stripe phase exhibiting in-phase...

We report on the single-atom-resolved measurement of distribution momenta $\hbar k$ in a weakly interacting Bose gas after 330 ms time-of-flight. investigate it for various temperatures and clearly separate two contributions to depletion condensate by their $k$-dependence. The first one is thermal depletion. second contribution falls as $k^{-4}$, its magnitude increases with in-trap density predicted Bogoliubov theory at zero temperature. These observations suggest associating quantum How...

We investigate many-body spin squeezing dynamics in an XXZ model with interactions that fall off distance $r$ as $1/r^\alpha$ $D=2$ and $3$ spatial dimensions. In stark contrast to the Ising model, we find a broad parameter regime where comparable infinite-range $\alpha=0$ limit is achievable even when are short-ranged, $\alpha>D$. A region of "collective" behavior which optimal grows system size extends all way $\alpha\to\infty$ nearest-neighbor interactions. Our predictions, made using...

The spin dynamics of a harmonically trapped Bose-Einstein condensed binary mixture sodium atoms is experimentally investigated at finite temperature. In the collisional regime motion thermal component shown to be damped because drag, while two condensates exhibit counterflow oscillation without friction, thereby providing direct evidence for superfluidity. Results are also reported in collisionless where components both condensate and part oscillate damping, their relative being driven by...

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, a superconducting state with nonzero total momentum Cooper pairs in large magnetic field, was first predicted about 50 years ago and has since become an important concept many branches of physics. Despite intensive search various materials, unambiguous experimental evidence for the FFLO phase is still lacking experiments. In this paper we show that both Fulde-Ferrell (FF) (a uniform order parameter plane-wave phase) Larkin-Ovchinnikov (LO)...

Current approaches for training Process Reward Models (PRMs) often involve breaking down responses into multiple reasoning steps using rule-based techniques, such as predefined placeholder tokens or setting the step's length a fixed size. These overlook fact that specific words do not typically mark true decision points in text. To address this, we propose AdaptiveStep, method divides based on model's confidence predicting next word. This division provides more decision-making information at...

We study the collective oscillations of spin-orbit-coupled Bose-Einstein condensates in presence position-dependent detuning. Specifically, we explore quadrupole modes system using both numerical and analytical approaches based on Gross-Pitaevskii equation hydrodynamic theory. Due to spin-orbit coupling synthetic magnetic field, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>x</a:mi><a:mi>y</a:mi></a:mrow></a:math> scissors mode couples with a superposition three diagonal...

The experimental realization of emergent spin-orbit coupling through laser-induced Raman transitions in ultracold atoms paves the way for exploring novel superfluid physics and simulating exotic many-body phenomena. A recent proposal with use Laguerre-Gaussian lasers enables another fundamental type between spin orbital angular momentum (SOAM) atoms. We hereby study quantum phases a realistic Bose-Einstein condensate (BEC) this synthetic SOAM disk-shaped geometry, respecting radial...

We report on the measurement of spin-dipole (SD) polarizability and frequency SD oscillation a two-component Bose-Einstein condensate sodium atoms occupying $|3{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2},F=1,{m}_{F}=\ifmmode\pm\else\textpm\fi{}1\ensuremath{\rangle}$ hyperfine states. This binary spin mixture presents important properties being, at same time, fully miscible rid limit set by buoyancy. It is also characterized huge enhancement consequent softening oscillation, due to vicinity...

We study magnetic solitons, solitary waves of spin polarization (i.e., magnetization), in binary Bose-Einstein condensates the presence Rabi coupling. show that system exhibits two types called $2\pi$ and $0\pi$ characterized by a different behavior relative phase between components. solitons exhibit jump phase, independent their velocity, static domain wall explored Son Stephanov being an example such with vanishing velocity magnetization. instead do not any asymptotic phase. Systematic...

The recent experimental realization of a three-dimensional (3D) optical lattice clock not only reduces the influence collisional interactions on clock's accuracy but also provides promising platform for studying dipolar many-body quantum physics. Here, by solving governing master equation, we investigate role both elastic and dissipative long-range in dynamics study its dependence spacing, dimensionality, orientation. For small i.e., ${k}_{0}a\ensuremath{\ll}1$, where $a$ is constant...

Understanding the effects of spin-orbit coupling (SOC) and many-body interactions on spin transport is important in condensed matter physics spintronics. This topic has been intensively studied for carriers such as electrons but barely explored charge-neutral bosonic quasiparticles (including their condensates), which hold promises coherent over macroscopic distances. Here, we explore synthetic SOC (induced by optical Raman coupling) atomic an Bose-Einstein condensate (BEC), where...

Abstract The quantum emulation of spin-momentum coupling, a crucial ingredient for the emergence topological phases, is currently drawing considerable interest. In previous gas experiments, typically two atomic hyperfine states were chosen as pseudospins. Here, we report observation coupling achieved by loading Bose-Einstein condensate into periodically driven optical lattices. s and p bands static lattice, which act pseudospins, are coupled through an additional moving lattice that induces...

Abstract Optical Ising machines promise to solve complex optimization problems with an optical hardware acceleration advantage. Here we study the ground state properties of a nonlinear machine realized by spatial light modulator, Fourier optics, and second-harmonic generation in crystal. By tuning ratio intensities at fundamental frequencies, experimentally observe two distinct ferromagnetic-to-paramagnetic phase transitions: second-order transition where magnetization changes zero...

We investigate the expansion dynamics of spin-orbit-coupled Bose-Einstein condensates subjected to a synthetic magnetic field, after their release from an external harmonic trap. Our findings reveal that condensate experiences spin-dependent rotation and separation due rigid-like rotational velocity which leads spin-density deflection. The deflection angle reaches peak at time is inversely related trap frequency. When detuning gradient below critical value for vortex nucleation, our...

The recent experimental realization of spin-orbit (SO) coupling for ultracold atoms opens a completely new avenue exploring quantum matters. In experiments, the SO is implemented simultaneously with Zeeman field. Such SO-coupled Fermi gases are predicted to support Majorana fermions non-Abelian exchange statistics in one dimension (1D). However, as shown theory and experiments 1D spin-imbalanced gases, field can lead long-sought Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids nonzero...

We study the expansion of an interacting atomic system at zero temperature, following its release from isotropic three-dimensional harmonic trap and calculate time dependence density momentum distribution, with special focus on behavior contact parameter. consider different quantum systems, including unitary Fermi gas infinite scattering length, weakly Bose gas, two particles highly asymmetric mass imbalance. In all cases analytic results can be obtained, which show that initial value...

Spin-imbalanced ultracold Fermi gases have been widely studied recently as a platform for exploring the long-sought Fulde-Ferrell-Larkin-Ovchinnikov superfluid phases, but so far conclusive evidence has not found. Here we propose to realize an Fulde-Ferrell (FF) without spin imbalance in three-dimensional fermionic cold atom optical lattice, where s- and p-orbital bands of lattice are coupled by another weak moving lattice. Such coupling leads spin-independent asymmetric surface, which,...

We investigate the effect of a periodic potential generated by one-dimensional optical lattice on magnetic properties an $S=1/2$ spin-orbit-coupled Bose gas. By increasing strength one can achieve phase transition between polarized and unpolarized Bloch wave phase, characterized significant enhancement contrast density fringes. If vector is chosen close to roton momentum, could take place at very small intensities, revealing strong response system weak perturbation. solving Gross-Pitaevskii...