Session C09: Spinor Gases and Magnetic Phenomena

Sudden Quench non-Equilibrium Dynamics of Spinor Condensates

We classify the diverse dynamical behaviour of spin-1 Bose-Einstein condensates through sudden quenches. The observed behavior can be summarized under well-defined quantum collapse and revivals, thermalization, and certain special cases. These special cases are either nonthermal equilibration with no revival but a collapse even though the system has finite degrees of freedom or no equilibration with no collapse and revival. We explain why and when eigenstate thermalization hypothesis (ETH) holds for spinor condensates via numerical scaling arguments and showing the equivalence between microcanonical and diagonal ensemble predictions in long-time limit. The reason behind both thermalizing and nonthermalizing behaviours in the same model under different initial conditions is linked to the discussion of `rare' nonthermal states existing in the spectrum. By expanding the analysis to the participation ratio calculations of the spectrum, we make a link between the thermalization and localization properties of the spinor condensates. Furthermore, we present an explanation to the behaviours of the special cases demonstrated in the model.   

Magnetic phases in a spinor Bose-Einstein condensate subject to weak measurement

Nondestructive imaging of spinor Bose-Einstein condensates (BEC) presents new opportunities for observing and manipulating macroscopic quantum phenomena in real time. In this talk I theoretically study harmonically trapped two-component BECs subject to weak measurement via phase contrast imaging. I discuss the application of weak measurement theory to spatially extended condensates and present a stochastic Gross-Pitaevskii equation for the condensate order parameter. I then examine the stability of spin-polarized and spin-unpolarized phases of the condensate subject to continuous weak measurement. Additionally, I demonstrate how weak measurement can be used to track the position of a domain wall between spin-polarized regions. I quantify the effects of measurement backaction on the stochastic dynamics of the domain wall and discuss how domain wall dynamics could be observed in experiment.   

A spinor Bose-Einstein condensate phase-sensitive amplifier for SU(1,1) interferometry

A spinor Bose-Einstein condensate in the $m_F=0$ hyperfine sublevel can be manipulated to spontaneously produce pairs of entangled atoms in the $m_F=\pm 1$ sublevels. These pairs of entangled atoms serve as a resource for building an interferometer with phase sensitivity beyond the standard quantum limit, such as the SU(1,1) interferometer. Here we use simulations to extend the usual model of the spinor SU(1,1) interferometer to include the case of initial coherent seeds in the $m_F=\pm1$ modes, which make the input a phase-sensitive amplifier. We show that for the ideal case such a spinor interferometer not only retains Heisenberg-limited scaling but also has absolute sensitivity greater than what could be achieved with the same number of atoms in a coherent state input Mach-Zehnder interferometer.   

Sensitive detection of spin flip using spin-mixing dynamics of $^{87}$Rb Bose-Einstein condensates

We revisit experimentally the spin-mixing dynamics in $^{87}$Rb spinor Bose-Einstein condensates, starting with all atoms in the $F=1$, $m_F=0$ Zeeman sublevel. We show that the short-time dynamics in the parametric amplification regime [1] is extremely sensitive to the initial number of atoms in the $m_F=\pm1$ state. This behavior is utilized to precisely characterize the degree of spin flip down to a few atoms. The longer-time evolution beyond the undepleted approximation is also investigated both experimentally and theoretically by considering the atom loss, as well as background radio-frequency noise. \\\\ {[1] D. Linnemann et al., Phys. Rev. Lett. 117, 013001 (2016)}   

Resonant spin exchange between heteronuclear atoms assisted by periodic driving

Spin exchange (SE) is one of the most fundamental two-body interactions. It is essential to fascinating properties such as magnetic ordered states and collective spin excitations, {\it etc}., in quantum many body systems. However, SE between heteronuclear atoms is typically small, suppressed by their large Zeeman energy difference in an external magnetic field. This work proposes a general scheme for inducing resonant exchange between spins or pseudo-spins of unmatched levels via periodic driving. The basic idea is illustrated with two heteronuclear atoms, for which analytical results describing their effective SE interaction strength are derived. It is then applied to the mixture of ground state ($F=1$) $^{23}$Na and $^{87}$Rb atoms with a radio-frequency (rf) or microwave field near-resonant to the mismatched Zeeman level spacings. SE interaction engineered this way is applicable to ultracold quantum gas mixtures involving spinor Bose-Bose, Bose-Fermi, and Fermi-Fermi atoms.   

Singular loops and their non-Abelian geometric phases in ultracold spin-1 atoms

Non-Abelian and non-adiabatic variants of Berry's phase have been pivotal in the recent advances in holonomic quantum gates, while Berry's phase itself is at the heart of the study of topological phases of matter. Here we use ultracold atoms to study the unique properties of spin-1 geometric phase [1]. The spin vector of a spin-1 system, unlike that of a spin-1/2 system, can lie anywhere on or inside the Bloch sphere representing the phase space. This suggests a generalization of Berry's phase to include closed paths that go inside the Bloch sphere. In [2], this generalized geometric phase was formulated as an SO(3) operator carried by the spin fluctuation tensor. Under this generalization, the special class of loops that pass through the center, which we refer to as singular loops, are significant because their geometrical properties are qualitatively different from the nearby non-singular loops, making them akin to critical points of a quantum phase transition. Here we use coherent control of ultracold 87Rb atoms in an optical trap to experimentally explore the geometric phase of singular loops in a spin-1 quantum system [1]. [1] H. M. Bharath, M. Boguslawski, M. Barrios, Lin Xin and M. S. Chapman, arXiv:1801.00586 [2] H. M. Bharath, arXiv:1702.08564   

Alice Ring in a Bose-Einstein Condensate

Topological excitations analogous to 't Hooft-Polyakov magnetic monopoles have recently been observed in spinor Bose-Einstein condensates. While the singular point defect is topologically stable, it can undergo a continuous transition to a more energetically favorable but topologically equivalent structure consisting of a half-quantum vortex ring with a ferromagnetic core. This nonsingular excitation is known as an Alice ring. We observe the transition from monopole to Alice ring experimentally in a spin-1 Bose-Einstein condensate in its polar phase, with numerical simulations matching our experimental results. We further characterize the Alice ring and observe its oscillations in the harmonically trapped condensate.   

Critical spin superflow in a spinor Bose-Einstein condensate

The hallmark of superfluid is the existence of critical velocity. In a spinor Bose-Einstein condensate (BEC), the stability of superflow is intertwined with internal spin degrees of freedom, which interestingly induces a new kind of critical behaviors. Here, we report our investigation on the critical dynamics of spin superflow in a spin-1 antiferromagnetic spinor BEC. A pure spin superflow is obtained in a trapped condensate by transmuting an easy-axis polar state into an easy-plane polar state under a magnetic field gradient. We observe that with the field gradient exceeding a certain critical value, the dissipation rate of spin superflow rapidly grows. The onset of dissipation is found to be related to the modulation instability of the two counterflowing spin components, which generates the dark-bright solitons. The solitons are split into vortices via snake instability, leading to the formation of spin turbulence. We also observe the generation of transient axial polar spin domains due to the dynamical excitation of transverse magnon mode via spin-exchange collisions, which develops the second critical point for spin superflow. Our work provides a comprehensive picture of spin superfluidity and its dissipation mechanisms in a spin-1 antiferromagnetic condensate system.   

Collisional narrowing in a one-dimensional gas of spinor Bose atoms

Interatomic interactions can lead to the Dicke narrowing [1] and prolong the coherence time in a dense cold-atom 3D gas as observed [2] for the spin-relaxation of Bose atoms with two internal (spin) states. Here this effect is analyzed in the 1D geometry. Many-body eigenstates of this system have a defined total spin $S$ and the eigenenergies become separated due to the two-body interactions. The energy gap is proportional to $S$ and to the interaction strength [3]. As we show here, when the interactions is strong enough, $S$ is conserved and the spin-dynamics become insensitive to the difference of the trap potentials for the two internal states. In this case, the decoherence is caused by the spin-dependence of the interactions. This dependence can be minimized using a Feshbach resonance. The coherence time can exceed several seconds at microkelvin temperatures. A similar effect of self-rephasing, observed in 3D geometry [4], requires nanokelvin temperatures. [1] R. H. Dicke, Phys. Rev. {\bf 89}, 472 (1953). [2] Y. Sagi, I. Almog, and N. Davidson, Phys. Rev. Lett. {\bf 105}, 093001 (2010). [3] V. A. Yurovsky, Phys. Rev. A {\bf 91}, 053601 (2015). [4] C. Deutsch {\it et al.}, Phys. Rev. Lett. {\bf 105}, 020401 (2010).   

Orbital Quantum Magnetism of Lanthanide Dimers in an Optical Lattice

Lanthanide atoms with their open 4f-shell are ideal candidates with which to study strong and unconventional quantum magnetism. Here, we use state-of-the-art closed-coupling simulations to model quantum magnetism for pairs of ultracold spin-6 erbium lanthanide atoms placed in sites of a deep optical lattice. In spite of the successes of previous analyses of quantum simulations with ultracold atoms in optical lattices, simplified representations with atoms as point particles and point dipoles can not always be applied to magnetic lanthanide atoms. Important information about the electron orbital structure within the constituent atoms is lost. In contrast to the widely used single-channel Hubbard model description of atoms and molecules in an optical lattice, we focus on the single-site multi-channel spin evolution due to spin-dependent contact, anisotropic van der Waals, and dipolar forces. This allowed us to identify orbital anisotropy as the leading mechanism governing molecular spin dynamics.