This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.

https://iopscience.iop.org/article/10.1088/0034-4885/77/12/126401/pdf

Light-induced gauge fields for ultracold atoms

After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, the effect of interactions on the formation of a Bose-Einstein condensate are discussed, along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity $\ensuremath{\Omega}$, one or several vortices nucleate, leading to many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For $\ensuremath{\Omega}$ near the radial trap frequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}$, the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as $\ensuremath{\Omega}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{\ensuremath{\perp}}$, the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.

Rotating trapped Bose-Einstein condensates

Spinor Bose–Einstein condensates

Spinor Bose gases form a family of quantum fluids manifesting both magnetic order and superfluidity. This article reviews experimental and theoretical progress in understanding the static and dynamic properties of these fluids. The connection between system properties and the rotational symmetry properties of the atomic states and their interactions are investigated. Following a review of the experimental techniques used for characterizing spinor gases, their mean-field and many-body ground states, both in isolation and under the application of symmetry-breaking external fields, are discussed. These states serve as the starting point for understanding low-energy dynamics, spin textures and topological defects, effects of magnetic dipole interactions, and various non-equilibrium collective spin-mixing phenomena. The paper aims to form connections and establish coherence among the vast range of works on spinor Bose gases, so as to point to open questions and future research opportunities.

Spinor Bose gases: Symmetries, magnetism, and quantum dynamics

We study the dynamics of vortex lattice formation of a rotating trapped Bose-Einstein condensate by numerically solving the two-dimensional Gross-Pitaevskii equation, and find that the condensate undergoes elliptic deformation, followed by unstable surface-mode excitations before forming a quantized vortex lattice. The origin of the peculiar surface-mode excitations is identified to be phase fluctuations at the low-density surface regime. The obtained dependence of a distortion parameter on time and that on the driving frequency agree with the recent experiments by Madison et al. [Phys. Rev. Lett. 86, 4443 (2001)].

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Vortex lattice formation in a rotating Bose-Einstein condensate

We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotatio...

Vortices in multicomponent bose–einstein condensates

We review the topic of quantized vortices in multicomponent Bose-Einstein condensates of dilute atomic gases, with an emphasis on that in two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross-Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose-Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose-Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.

https://arxiv.org/pdf/cond-mat/0505546.pdf

Vortices in multicomponent Bose-Einstein condensates

We investigate the structure of vortex states in rotating two-component Bose-Einstein condensates with equal intracomponent but varying intercomponent-coupling constants. A phase diagram in the intercomponent-coupling versus rotation-frequency plane reveals rich equilibrium structures of vortex states. As the ratio of intercomponent to intracomponent couplings increases, the interlocked vortex lattices undergo phase transitions from triangular to square, to double-core lattices, and eventually develop interwoven "serpentine" vortex sheets with each component made up of chains of singly quantized vortices.

http://cat.phys.s.u-tokyo.ac.jp/~ueda/KasamatsuPRL91.pdf

Vortex Phase Diagram in Rotating Two-Component Bose-Einstein Condensates

We study the response of a trapped Bose-Einstein condensate to a sudden turn on of a rotating drive by numerically solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by a quasiparticle projection method. In a quadrupolar resonant regime, which depends on the trap anisotropy, simple periodic oscillations in surface-mode populations disappear and the system exhibits stochastic dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.

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Kenichi Kasamatsu

Papers

Vortex lattice formation in a rotating Bose-Einstein condensate

Vortices in multicomponent bose–einstein condensates

Vortices in multicomponent Bose-Einstein condensates

Vortex Phase Diagram in Rotating Two-Component Bose-Einstein Condensates

Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate