Session G4: Spinor Condensates and Dynamics

Reversal of spin dynamics in an antiferromagnetic F=1 spinor Bose-Einstein condensate

The antiferromagnetic F=1 sodium spinor Bose-Einstein condensate (BEC) exhibits coherent population oscillations of the magnetic sublevels that are internally driven by spin-exchange collisions. Here, we experimentally demonstrate reversals of the collisional dynamics. The reversals are controlled with microwave pulses. We observe nearly complete reversals even after a significant amount of population oscillation has already occurred. In addition, and somewhat surprisingly, we can generate partial reversals in the cold, non-condensed normal gas. We explain our results with numerical calculations based on the truncated Wigner approximation and an analytical theory based on the Bogoliubov approximation. In the future, this type of microwave control of collisional dynamics will allow us to implement matter-wave analogs of devices known from quantum optics with photons, such as a phase-sensitive matter-wave amplifier.   

Relaxation dynamics of a fermionic quantum gas with high spin

The relaxation of a closed quantum system constitutes a fundamental question in many-body physics. We present a detailed study of relaxation dynamics in a fermionic quantum gas of 40K atoms with high spin. The fermions are initially prepared far from equilibrium occupying only a few spin states. This induces a complex relaxation dynamics towards an equal spin population; meanwhile the whole spin system provides a bath for the thermalization for its individual spin subsystems. Our experimental results yield a good agreement with a kinetic Boltzmann equation, derived from a microscopic approach without free parameters. We identify several collisional processes governing the dynamics on fully different time scales and demonstrate the high experimental control by tuning the crucial parameters of the system, e.g. density and magnetic field. Our results open the path to engineering an open system with controllable dissipation into empty subsystems.   

Coherent spinor dynamics in a spin-2 thermal gas

Spinor dynamics has been explored extensively in spin-1 and spin-2 Bose Einstein condensates both theoretically and experimentally. However, few experiments have been done in normal spinor gases, especially spin-2 case. Here, we report an experimental study on coherent spin-population oscillations in an ultracold, thermal spin-2 $^{87}Rb$ gas. By tuning the magnetic field we observe a dynamics resonance corresponding to the maximum values of both the oscillation period and oscillation amplitude. We also identify the interaction dominated regime and the quadratic Zeeman dominated regime. A spin-2 kinetic theory is developed and its numerical solution shows reasonable agreement with our observation.   

Coherent spin dynamics under single mode approximation in a dipolar spin-1 Bose-Einstein condensate

Spin interactions, including the spin exchange and the magnetic dipolar interaction between ultracold atoms, are of key importance for high precision measurements utilizing dipolar spinor Bose condensates. Under the single spatial mode approximation in the framework of the mean field theory, we investigate analytically the spin mixing dynamics in a dipolar spin-1 Bose condensate ($^{87}$Rb or $^{23}$Na) with both the spin exchange interaction and the magnetic dipolar interaction. We discuss the evolutions of the fractions of the three components, the spin, and the energy transfer between the spin exchange interaction and the magnetic dipolar interaction. The effects of the magnetic dipolar interaction on the coherent spin dynamics are explored in a systematic way. Preliminary numerical results on the validity of the single mode approximation are also presented.   

Dynamics of spinor condensates in a microwave dressing field

We experimentally study dynamics in a sodium antiferromagnetic spinor condensate as a result of spin-dependent interactions $c$ and microwave dressing field interactions characterized by the net quadratic Zeeman effect $q_{\rm net}$. In contrast to magnetic fields, microwave dressing fields enable us to access both negative and positive values of $q_{\rm net}$. We find an experimental signature to determine the sign of $q_{\rm net}$, and observe harmonic spin population oscillations at every $q_{\rm net}$ except near each separatrix in phase space where spin oscillation period diverges. Our data in the negative $q_{\rm net}$ region exactly resembles what is predicted to occur in a ferromagnetic spinor condensate in the positive $q_{\rm net}$ region. This observation agrees with an important prediction derived from the mean-field theory: spin dynamics in spin-1 condensates substantially depends on the sign of $q_{\rm net}/c$. This work may be the first to use only one atomic species to reveal mean-field spin dynamics, especially the remarkably different relationship between each separatrix and the magnetization, of spin-1 antiferromagnetic and ferromagnetic spinor condensates.   

Heteronuclear coherent spinor dynamics in an ultracold spin-1 mixture

Coherent spin mixing dynamics in ultracold spinor gases is a signature of macroscopic quantum coherence. It has been studied intensively in both thermal and degenerate single species atomic gases. In this talk, we present the first observation of such dynamics in a heteronuclear spinor system. Our experiment is carried out with an ultracold spinor mixture of $^{87}$Rb and $^{23}$Na atoms in their F = 1 hyperfine states. Heteronuclear spinor dynamics induced by interspecies spin-spin interactions manifests as coherent oscillations in both the spin state populations and magnetization of each species with the system's total magnetization conserved. We have also observed clear dependence of these dynamics on external magnetic fields and atomic sample parameters. Theoretical modeling of our observations is underway.   

The truncated Wigner approximation for spin dynamics in systems of trapped ions, atoms \& molecules

Trapped ions and systems of cold atoms or molecules in optical lattices offer controlled environments to experimentally study non-equilibrium dynamics of many-body quantum spin-models with interactions of varying range. Theoretically calculating dynamics of observables for these experiments is a major challenge both analytically and numerically. While in one dimension, time-dependent density matrix renormalization group techniques (t-DMRG) allow for an efficient simulation of the dynamics as long as the time-dependent bi-partite entanglement growth remains moderate, a simulation for systems in two or three dimensions is more demanding. Here we present a numerical technique, which employs the truncated Wigner approximation (TWA) and which can be used to simulate Ramsey-dynamics for current experiments with trapped ions, alkaline earth atoms, polar molecules in optical lattices, or for systems with Rydberg atoms.   

Many-body Quantum Control of a Spin-1 BEC

Spin-1 condensates provide a useful platform for investigations of atom squeezing,\footnote{C.D. Hamley, \emph{et al.}, Nat. Phys. 8, 305 (2012)} generation of non-Gaussian states,\footnote{C.S. Gerving, \emph{et al.}, Nat. Commun. 3, 1169 (2012)} and dynamical control.\footnote{T.M. Hoang, \emph{et al.}, Phys. Rev. Lett. 111, 090403 (2013)} We demonstrate dynamic control of a quantum many-body spin-1 system that is enabled by strong collisional interactions. In contrast to the usual single-particle quantum control techniques, the method demonstrated here is intrinsically many-body, exploiting the strong collisional interactions. The experiment uses a spin-1 $^{87}$Rb condensate initialized in the $|F=1,m_F=0\rangle$ polar state at a high magnetic field above the quantum phase transition, and then prepared in a coherent state using a rf rotation. The many-body control is implemented by time-varying the relative strength of the Zeeman and spin interaction energies of the condensate at multiples of the natural coherent oscillation frequency of the system. This is a parametric excitation method relying on time varying changes to the Hamiltonian. We will present our experimental results, which compare well to theory, and will discuss future directions and applications.   

Permutation-symmetry related selection rules in spinor quantum gases

Selection rules constraining possible transitions between states of quantum systems can be derived from the system symmetry. Invariance over permutations of indistinguishable particles, contained in each physical system, is one of the basic symmetries. Consider a many-body system with separable spin and spatial degrees of freedom of particles with arbitrary spins $s$. Eigenfunctions of such systems can be expressed as a sum of products of spin and spatial functions, which form irreducible representations (irreps) of the symmetric group. The quantum numbers are the Young diagrams $\lambda=[\lambda_1,\ldots,\lambda_{2s+1}]$. The selection rules for a general $k$-body interactions allow transitions between the states $\lambda$ and $\lambda'$ only if $ \sum_{m=1}^{2s+1} |\lambda_m-\lambda'_m|\leq 2k$. For $s=1/2$, the Young diagrams are unambiguously related to the total spin, and if $k=1$, we get the conventional selection rule for dipole transitions. However, if $s>1/2$, the rules cannot be expressed in terms of spins. The selection rules provide a way of control over the formation of many-body entangled states, belonging to multidimensional, non-Abelian irreps of the symmetric group. The effects can be observed with spinor atoms in an optical lattice in the Mott-insulator regime.   

Phase diagram and quantum phase transitions in sodium spinor condensates

We observe two quantum phase transitions in sodium spinor condensates driven by a microwave dressing field and antiferromagnetic s-wave interactions. We find that the ground states of the antiferromagnetic spinor condensates can be created by adiabatically tuning the microwave field across one of the two quantum phase transitions. This method avoids significant atom losses in large microwave fields, and thus allows us to explore the phase diagram of antiferromagnetic spinor condensates in both negative and positive quadratic Zeeman energy regions. We also find a good agreement between our data and the mean-field theory for spinor Bose gases.