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Register a new userCrystallization of Bosonic Quantum Hall States
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Added by
Biswaroop Mukherjee
Publication date
2021
fields
Physics
and research's language is
English
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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.
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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.
We study an interacting two-component hard-core bosons on square lattice for which, in the presence of staggered magnetic flux, the ground state is a bosonic integer quantum Hall (BIQH) state. Using a coupled-wire bosonization approach, we analytically show this model exhibits a BIQH state at total charge half filling associated with a symmetry-protected topological phase under $U(1)$ charge conservation. These theoretical expectations are verified, using the infinite density matrix renormalization group method, by providing numerical evidences for: (i) a quantized Hall conductance $sigma_{xy}=pm2$, and (ii) two counter-propagating gapless edge modes. Our model is a bosonic cousin of the fermionic Haldane model and serves as an additional case of analogy between bosonic and fermionic quantum Hall states.
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We report a new many body phenomena called Nearly order from quantum disorder phenomena (NOFQD). We demonstrate the NOFQD in the experimentally realized weakly interacting Quantum Anomalous Hall system of spinor bosons in an optical lattice. We establish intrinsic connections between the phenomenological GL theory and the microscopic calculations on the effective potential. Connections with the bilayer quantum Hall system with a total filling factor $ u_T=1 $ are made. Some insightful analogy with $ NAdS_2/NCFT_1 $ ( where $ N $ also means nearly ) correspondence in the context of Sachdev-Ye-Kitaev models are hinted. Two types of OFQDs are classified, one response trivially, another non-trivially to a small deformation to the Hamiltonian leading to NOFQD. The NOFQD can be detected in the current cold atom bosonic quantum anomalous Hall experiments and may also appear in many other frustrated systems.
The combination of interactions and static gauge fields plays a pivotal role in our understanding of strongly-correlated quantum matter. Cold atomic gases endowed with a synthetic dimension are emerging as an ideal platform to experimentally address this interplay in quasi-one-dimensional systems. A fundamental question is whether these setups can give access to pristine two-dimensional phenomena, such as the fractional quantum Hall effect, and how. We show that unambiguous signatures of bosonic and fermionic Laughlin-like states can be observed and characterized in synthetic ladders. We theoretically diagnose these Laughlin-like states focusing on the chiral current flowing in the ladder, on the central charge of the low-energy theory, and on the properties of the entanglement entropy. Remarkably, Laughlin-like states are separated from conventional liquids by Lifschitz-type transitions, characterized by sharp discontinuities in the current profiles, which we address using extensive simulations based on matrix-product states. Our work provides a qualitative and quantitative guideline towards the observability and understanding of strongly-correlated states of matter in synthetic ladders. In particular, we unveil how state-of-the-art experimental settings constitute an ideal starting point to progressively tackle two-dimensional strongly interacting systems from a ladder viewpoint, opening a new perspective for the observation of non-Abelian states of matter.
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