Spinor Condensates Research Articles

Quantum dynamics of atomic coherence in a spin-1 condensate: Mean-field versus many-body simulation

We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a “ferromagnetic” state with all spins aligned along the y axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.

Spin-3 Chromium Bose-Einstein Condensates

We analyze the physics of spin-3 Bose-Einstein condensates, and, in particular, the new physics expected in ongoing experiments with condensates of chromium atoms. We first discuss the ground-state properties, which, depending on still unknown chromium parameters, and for low magnetic fields, can present various types of phases. We also discuss the spinor dynamics in chromium spinor condensates, which present significant qualitative differences when compared to other spinor condensates. In particular, dipole-induced spin relaxation may lead for low magnetic fields to transfer of spin into angular momentum similar to the well-known Einstein-de Haas effect. Additionally, a rapid large transference of population between distant magnetic states also becomes possible.

Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate

A central goal in condensed matter and modern atomic physics is the exploration of quantum phases of matter--in particular, how the universal characteristics of zero-temperature quantum phase transitions differ from those established for thermal phase transitions at non-zero temperature. Compared to conventional condensed matter systems, atomic gases provide a unique opportunity to explore quantum dynamics far from equilibrium. For example, gaseous spinor Bose-Einstein condensates (whose atoms have non-zero internal angular momentum) are quantum fluids that simultaneously realize superfluidity and magnetism, both of which are associated with symmetry breaking. Here we explore spontaneous symmetry breaking in 87Rb spinor condensates, rapidly quenched across a quantum phase transition to a ferromagnetic state. We observe the formation of spin textures, ferromagnetic domains and domain walls, and demonstrate phase-sensitive in situ detection of spin vortices. The latter are topological defects resulting from the symmetry breaking, containing non-zero spin current but no net mass current.

Magnetization, squeezing, and entanglement in dipolar spin-1 condensates

We study the static and dynamic responses of an $F=1$ dipolar spinor condensate with magnetic dipole moment under external magnetic fields, focusing on the effects induced by the magnetic dipolar interactions between atoms. A rich set of phenomena are investigated such as the ground state quantum phases, the magnetization steps, spin squeezing, and macroscopic entanglement generation.

Evolution of a spinor condensate: Coherent dynamics, dephasing, and revivals

We present measurements and a theoretical model for the interplay of spin dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features like quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a F=1 $^{87}$Rb Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to thermal equilibration.

Direct Nondestructive Imaging of Magnetization in a Spin-1 Bose-Einstein Gas

Polarization-dependent phase-contrast imaging is used to resolve the spatial magnetization profile of an optically trapped ultracold gas. This probe is applied to Larmor precession of degenerate and nondegenerate spin-1 87Rb gases. Transverse magnetization of the Bose-Einstein condensate persists for the condensate lifetime, with a spatial response to magnetic field inhomogeneities consistent with a mean-field model of interactions. In comparison, the magnetization of the non-condensed gas decoheres rapidly. Rotational symmetry implies that the Larmor frequency of a spinor condensate be density independent, and thus suitable for precise magnetometry with high spatial resolution.

Dynamics of dipolar spinor condensates

We study the semiclassical dynamics of a spinor condensate with the magnetic dipole–dipole interaction included. The time evolution of the population imbalance and the relative phase among different spin components depend greatly on the relative strength of interactions as well as on the initial conditions. The interplay of spin-exchange and dipole–dipole interaction makes it possible to manipulate the atomic population on different components, leading to the phenomena of spontaneous magnetization and macroscopic quantum self-trapping. A simple estimate demonstrates that these effects are accessible and controllable by modifying the geometry of the trapping potential.

Coherent spin mixing dynamics in a spin-1 atomic condensate

We study the coherent off-equilibrium spin mixing inside an atomic condensate. Using mean field theory and adopting the single spatial mode approximation (SMA), the condensate spin dynamics is found to be well described by that of a nonrigid pendulum, and displays a variety of periodic oscillations in an external magnetic field. Our results illuminate several recent experimental observations and provide critical insights into the observation of coherent interaction-driven oscillations in a spin-1 condensate.

Maximal entanglement of two spinor Bose-Einstein condensates

Starting with two weakly-coupled anti-ferromagnetic spinor condensates, we show that by changing the sign of the coefficient of the spin interaction, $U_{2}$, via an optically-induced Feshbach resonance one can create an entangled state consisting of two anti-correlated ferromagnetic condensates. This state is maximally entangled and a generalization of the Bell state from two anti-correlated spin-1/2 particles to two anti-correlated spin$-N/2$ atomic samples, where $N$ is the total number of atoms.

An effective quasi-one-dimensional description of a spin-1 atomic condensate

Within the mean field theory we extend the effective quasi-1D non-polynomial Schr\"{o}dinger equation (NPSE) approach to the description of a spin-1 atomic condensate in a tight radial confinement geometry for both weak and strong atom-atom interactions. Detailed comparisons with full time dependent 3D numerical simulations show excellent agreement as in the case of a single component scalar condensate, demonstrating our result as an efficient and effective tool for the understanding of spin-1 condensate dynamics observed in several recent experiments.

Non-Abelian Topological Excitations in Spinor Condensates

We investigate the topological defects in atomic spin-1 and spin-2Bose–Einstein condensates by applying the homotopy group theory. With thisrigorous approach we clarify the previously controversial identification ofsymmetry groups and order parameter spaces for the spin-1 case, and showthat the spin-2 case provides a rare example of a physical system withnon-Abelian line defects, and the possibility to have winding numbers of1/3 and its multiples.

Exact Analysis of Soliton Dynamics in Spinor Bose-Einstein Condensates

We propose an integrable model of a multicomponent spinor Bose-Einstein condensate in one dimension, which allows an exact description of the dynamics of bright solitons with spin degrees of freedom. We consider specifically an atomic condensate in the F=1 hyperfine state confined by an optical dipole trap. When the mean-field interaction is attractive (c(0)<0) and the spin-exchange interaction of a spinor condensate is ferromagnetic (c(2)<0), we prove that the system possesses a completely integrable point leading to the existence of multiple bright solitons. By applying results from the inverse scattering method, we analyze a collision law for two-soliton solutions and find that the dynamics can be explained in terms of the spin precession.

Bose-Einstein condensation at constant temperature

We present an experimental approach to Bose-Einstein condensation by increasing the particle number of the system at almost constant temperature. In particular, the emergence of a new condensate is observed in multicomponent $F=1$ spinor condensates of $^{87}\mathrm{Rb}$. Furthermore, we develop a simple rate-equation model for multicomponent Bose-Einstein condensate thermodynamics at finite temperature which well reproduces the measured effects.

Quantum phases of dipolar spinor condensates.

We study the zero-temperature ground state structure of a spin-1 condensate with magnetic dipole-dipole interactions. We show that the dipolar interactions break the rotational symmetry of the Hamiltonian and induce new quantum phases. Different phases can be reached by tuning the effective strength of the dipolar interactions via modifying the trapping geometry. The experimental feasibility of detecting these phases is investigated. The spin-mixing dynamics is also studied.

Observation of spinor dynamics in optically trapped 87Rb Bose-Einstein condensates.

We measure spin mixing of F=1 and F=2 spinor condensates of 87Rb atoms confined in an optical trap. We determine the spin mixing time to be typically less than 600 ms and observe spin population oscillations. The equilibrium spin configuration in the F=1 manifold is measured for different magnetic fields and found to show ferromagnetic behavior for low field gradients. An F=2 condensate is created by microwave excitation from the F=1 manifold, and this spin-2 condensate is observed to decay exponentially with time constant 250 ms. Despite the short lifetime in the F=2 manifold, spin mixing of the condensate is observed within 50 ms.

Imaging of spinor gases

We explore the dielectric properties of spinor condensates. Gases with vector (nematic) order, such as spin-1 condensates with ferromagnetic (antiferromagnetic) interactions, display optical activity (birefringence). This optical activity/birefringence is respectively seen for light detuned from resonance by a frequency which is not too large compared with the fine/hyperfine structure. Careful tuning of the light frequency can isolate either of these two effects. These features can be used to image spin textures in clouds of spin-1 bosons, and to discern states showing different types of spin order.

Quantum Zeno subspace and entangled Bose-Einstein condensates.

We discuss a proposal for the efficient generation of the maximally entangled atomic N-GHZ state in a spinor-1 condensate by driving internal state atomic Raman transitions using (classical) laser fields. We illustrate the dynamics in terms of a quantum Zeno subspace and identify the resultant atomic elastic collision in facilitating the deterministic entanglement creation. Our proposal can be readily implemented in several laboratories where ferromagnetic spinor condensates (of 87Rb atoms) are investigated.

Phenomenological theory of spinor Bose-Einstein condensates

A phenomenological model is proposed to describe the behavior of spinor Bose-Einstein condensates. In the absence of hyperfine spin-spin interactions, Bose-Einstein condensation leads to a spontaneous magnetization at the same transition temperature. This is the so-called Bose-Einstein ferromagnetism. Including the hyperfine spin interactions, the phase diagram of the spinor condensate in an optical trap is studied and the Gross-Pitaevskii equation is extended. The possibility of checking for the existence of the Bose-Einstein ferromagnetism experimentally is also discussed.

Dynamics of quantum phases in a spinor condensate

We discuss the quantum phases and their diffusion dynamics in a spinor-1 atomic Bose-Einstein condensate. For ferromagnetic interactions, we obtain the exact ground state distribution of the phases associated with the total atom number ($N$), the total magnetization (${\cal M}$), and the alignment (or hypercharge) ($Y$) of the system. The mean field ground state is stable against fluctuations of atom numbers in each of the spin components, and the phases associated with the order parameter for each spin components diffuse while dynamically recover the two broken continuous symmetries [U(1) and SO(2)] when $N$ and ${\cal M}$ are conserved as in current experiments. We discuss the implications to the quantum dynamics due to an external (homogeneous) magnetic field. We also comment on the case of a spinor-1 condensate with anti-ferromagnetic interactions.

Topological defects in spinor condensates

We investigate the structure of topological defects in the ground states of spinor Bose-Einstein condensates with spin F=1 or F=2. The type and number of defects are determined by calculating the first and second homotopy groups of the order-parameter space. The order-parameter space is identified with a set of degenerate ground state spinors. Because the structure of the ground state depends on whether or not there is an external magnetic field applied to the system, defects are sensitive to the magnetic field. We study both cases and find that the defects in zero and non-zero field are different.