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Register a new userHall response of interacting bosonic atoms in strong gauge fields: from condensed to FQH states
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Interacting bosonic atoms under strong gauge fields undergo a series of phase transitions that take the cloud from a simple Bose-Einstein condensate all the way to a family of fractional-quantum-Hall-type states [M. Popp, B. Paredes, and J. I. Cirac, Phys. Rev. A 70, 053612 (2004)]. In this work we demonstrate that the Hall response of the atoms can be used to locate the phase transitions and characterize the ground state of the many-body state. Moreover, the same response function reveals within some regions of the parameter space, the structure of the spectrum and the allowed transitions to excited states. We verify numerically these ideas using exact diagonalization for a small number of atoms, and provide an experimental protocol to implement the gauge fields and probe the linear response using a periodically driven optical lattice. Finally, we discuss our theoretical results in relation to recent experiments with condensates in artificial magnetic fields [ L. J. LeBlanc, K. Jimenez-Garcia, R. A. Williams, M. C. Beeler, A. R. Perry, W. D. Phillips, and I. B. Spielman, Proc. Natl. Acad. Sci. USA 109, 10811 (2012)] and we analyze the role played by vortex states in the Hall response.
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We employ the exact diagonalization method to analyze the possibility of generating strongly correlated states in two-dimensional clouds of ultracold bosonic atoms which are subjected to a geometric gauge field created by coupling two internal atomic states to a laser beam. Tuning the gauge field strength, the system undergoes stepwise transitions between different ground states, which we describe by analytical trial wave functions, amongst them the Pfaffian, the Laughlin, and a Laughlin quasiparticle many-body state. The adiabatic following of the center of mass movement by the lowest energy dressed internal state, is lost by the mixing of the second internal state. This mixture can be controlled by the intensity of the laser field. The non-adiabaticity is inherent to the considered setup, and is shown to play the role of circular asymmetry. We study its influence on the properties of the ground state of the system. Its main effect is to reduce the overlap of the numerical solutions with the analytical trial expressions by occupying states with higher angular momentum. Thus, we propose generalized wave functions arising from the Laughlin and Pfaffian wave function by including components, where extra Jastrow factors appear, while preserving important features of these states. We analyze quasihole excitations over the Laughlin and generalized Laughlin states, and show that they possess effective fractional charge and obey anyonic statistics. Finally, we study the energy gap over the Laughlin state as the number of particles is increased keeping the chemical potential fixed. The gap is found to decrease as the number of particles is increased, indicating that the observability of the Laughlin state is restricted to a small number of particles.
The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases. Here, we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate in and near the lowest Landau level (LLL). We observe a spontaneous crystallization driven by condensation of magneto-rotons, excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin-Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets, separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.
We consider a system of weakly interacting bosons confined on a planar double ring lattice subjected to two artificial gauge fields. We determine its ground state by solving coupled discrete non-linear Schrodinger equations at mean field level. At varying inter-ring tunnel coupling, flux and interactions we identify the vortex, Meissner and biased-ladder phases also predicted for a bosonic linear ladder by a variational Ansatz. We also find peculiar features associated to the ring geometry, in particular parity effects in the number of vortices, and the appearance of a single vortex in the Meissner phase. We show that the persistent currents on the rings carry precise information on the various phases. Finally, we propose a way of observing the Meissner and vortex phases via spiral interferogram techniques.
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.
The use of coherent optical dressing of atomic levels allows the coupling of ultracold atoms to effective gauge fields. These can be used to generate effective magnetic fields, and have the potential to generate non-Abelian gauge fields. We consider a model of a gas of bosonic atoms coupled to a gauge field with U(2) symmetry, and with constant effective magnetic field. We include the effects of weak contact interactions by applying Gross-Pitaevskii mean-field theory. We study the effects of a U(2) non-Abelian gauge field on the vortex lattice phase induced by a uniform effective magnetic field, generated by an Abelian gauge field or, equivalently, by rotation of the gas. We show that, with increasing non-Abelian gauge field, the nature of the groundstate changes dramatically, with structural changes of the vortex lattice. We show that the effect of the non-Abelian gauge field is equivalent to the introduction of effective interactions with non-zero range. We also comment on the consequences of the non-Abelian gauge field for strongly correlated fractional quantum Hall states.
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