Stabilizing the Laughlin state of light: dynamics of hole fractionalization

Abstract

Particle loss is the ultimate challenge for preparation of strongly correlated many-body states of photons. An established way to overcome the loss is to employ a stabilization setup that autonomously injects new photons in place of the lost ones. However, as we show, the effectiveness of such a stabilization setup is compromised for fractional quantum Hall states. There, a hole formed by a lost photon can separate into several remote quasiholes none of which can be refilled by injecting a photon locally. By deriving an exact expression for the steady-state density matrix, we demonstrate that isolated quasiholes proliferate in the steady state which damages the quality of the state preparation. The motion of quasiholes leading to their separation is allowed by a repeated process in which a photon is first lost and then quickly refilled in the vicinity of the quasihole. We develop the theory of this dissipative quasihole dynamics and show that it has diffusive character. Our results demonstrate that fractionalization might present an obstacle for both creation and stabilization of strongly-correlated states with photons.

36 pages, 6 figures. SciPost resubmission

References in corpus (19)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Non-Abelian Anyons and Topological Quantum Computation
• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Time-reversal symmetry breaking in circuit-QED based photon lattices
• Topological properties of linear circuit lattices
• Fractional Quantum Hall States and Jack Polynomials
• Topologically Robust Transport of Photons in a Synthetic Gauge Field
• Fractional Quantum Hall Effect in Optical Lattices
• Cooling and squeezing via quadratic optomechanical coupling
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Fractional Quantum Hall State in Coupled Cavities
• Induced self-stabilization in fractional quantum Hall states of light
• Quarter-Flux Hofstadter Lattice in Qubit-Compatible Microwave Cavity Array
• Signatures of Fractional Exclusion Statistics in the Spectroscopy of Quantum Hall Droplets
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Universal two-qubit interactions, measurement and cooling for quantum simulation and computing
• Generation and spectroscopic signatures of a fractional quantum Hall liquid of photons in an incoherently pumped optical cavity
• Diffusive spin transport

Cited by in corpus (6)

• Many-Body Open Quantum Systems
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Reaction-diffusive dynamics of number-conserving dissipative quantum state preparation
• Growing Extended Laughlin States in a Quantum Gas Microscope: A Patchwork Construction
• How to exploit driving and dissipation to stabilize and manipulate quantum many-body states
• Reservoir Engineering for Classical Nonlinear Fields