Phase separation and pattern formation in a binary Bose-Einstein
  condensate

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Abstract

The miscibility-immiscibility phase transition in binary Bose-Einstein condensates (BECs) can be controlled by a coupling between the two components. Here we propose a new scheme that uses coupling-induced pattern formation to test the Kibble-Zurek mechanism (KZM) of topological-defect formation in a quantum phase transition. For a binary BEC in a ring trap we find that the number of domains forming the pattern scales with the coupling quench rate with an exponent as predicted by the KZM. For a binary BEC in an elongated harmonic trap we find a different scaling law due to the transition being spatially inhomogeneous. We perform a "simulation" of the harmonically trapped system in a ring trap to verify the scaling exponent.

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A spin-orbit coupled Bose-Einstein condensate

I. B. Spielman, K Jiménez-García, Y. Lin (2011)

Spin-orbit (SO) coupling -- the interaction between a quantum particle's spin and its momentum -- is ubiquitous in nature, from atoms to solids. In condensed matter systems, SO coupling is crucial for the spin-Hall effect and topological insulators, which are of extensive interest; it contributes to the electronic properties of materials such as GaAs, and is important for spintronic devices. Ultracold atoms, quantum many-body systems under precise experimental control, would seem to be an ideal platform to study these fascinating SO coupled systems. While an atom's intrinsic SO coupling affects its electronic structure, it does not lead to coupling between the spin and the center-of-mass motion of the atom. Here, we engineer SO coupling (with equal Rashba and Dresselhaus strengths) in a neutral atomic Bose-Einstein condensate by dressing two atomic spin states with a pair of lasers. Not only is this the first SO coupling realized in ultracold atomic gases, it is also the first ever for bosons. Furthermore, in the presence of the laser coupling, the interactions between the two dressed atomic spin states are modified, driving a quantum phase transition from a spatially spin-mixed state (lasers off) to a phase separated state (above a critical laser intensity). The location of this transition is in quantitative agreement with our theory. This SO coupling -- equally applicable for bosons and fermions -- sets the stage to realize topological insulators in fermionic neutral atom systems.

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Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate

M Vengalattore, L. Sadler, J. Higbie … (2006)

A central goal in condensed matter and modern atomic physics is the exploration of many-body quantum phases and the universal characteristics of quantum phase transitions in so far as they differ from those established for thermal phase transitions. Compared with condensed-matter systems, atomic gases are more precisely constructed and also provide the unique opportunity to explore quantum dynamics far from equilibrium. Here we identify a second-order quantum phase transition in a gaseous spinor Bose-Einstein condensate, a quantum fluid in which superfluidity and magnetism, both associated with symmetry breaking, are simultaneously realized. \(^{87}\)Rb spinor condensates were rapidly quenched across this transition to a ferromagnetic state and probed using in-situ magnetization imaging to observe spontaneous symmetry breaking through the formation of spin textures, ferromagnetic domains and domain walls. The observation of topological defects produced by this symmetry breaking, identified as polar-core spin-vortices containing non-zero spin current but no net mass current, represents the first phase-sensitive in-situ detection of vortices in a gaseous superfluid.

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Cosmology in the laboratory: defect dynamics in liquid crystals.

I Chuang, R Durrer, N Turok … (1991)

Liquid crystals are remarkably useful for laboratory exploration of the dynamics of cosmologically relevant defects. They are convenient to work with, they allow the direct study of the "scaling solution" for a network of strings, and they provide a model for the evolution of monopoles and texture. Experiments described here support the simple "one-scale" model for cosmic string evolution, as well as some qualitative predictions of string statistical mechanics. The structure of monopoles and their apparent cylindrical but not spherical symmetry is discussed. A particular kind of defect known as texture is described and is shown to have a dynamical instability-it can decay into a monopole-antimonopole pair. This decay process has been observed occurring in the liquid crystal, and studied with numerical simulations.