[Paper Review] Mimicking black hole event horizons in atomic and solid-state systems

Marcel Franz, Moshe Rozali|arXiv (Cornell University)|Aug 1, 2018

Black Holes and Theoretical Physics77 references4 citations

TL;DR

This paper reviews theoretical proposals to experimentally realize the Sachdev-Ye-Kitaev (SYK) model—a solvable quantum mechanical system dual to a 1+1D quantum black hole—using atomic and solid-state systems such as quantum wires and Majorana-bound-state platforms in topological superconductors. The key contribution is identifying feasible routes to mimic black hole event horizons and study quantum gravity phenomena in tabletop experiments, despite significant experimental challenges in materials synthesis and control of many-body chaos.

ABSTRACT

Holographic quantum matter exhibits an intriguing connection between quantum black holes and more conventional (albeit strongly interacting) quantum many-body systems. This connection is manifested in the study of their thermodynamics,statistical mechanics and many-body quantum chaos. After explaining some of those connections and their significance, we focus on the most promising example to date of holographic quantum matter, the family of Sachdev-Ye-Kitaev (SYK) models. Those are simple quantum mechanical models that are thought to realize, holographically, quantum black holes. We review and assess various proposals for experimental realizations of the SYK models. Such experimental realization offers the exciting prospect of accessing black hole physics, and thus addressing many mysterious questions in quantum gravity, in tabletop experiments.

Motivation & Objective

• To identify and assess experimental platforms capable of realizing the Sachdev-Ye-Kitaev (SYK) model in atomic and solid-state systems.
• To establish a connection between strongly correlated quantum matter and holographic quantum gravity, particularly black hole thermodynamics and chaos.
• To evaluate the feasibility of observing emergent black hole-like properties such as out-of-time-ordered correlators and holographic scaling in condensed matter systems.
• To provide a roadmap for testing quantum gravity phenomena in experimentally accessible, non-gravitational many-body systems.

Proposed method

• Theoretical analysis of the SYK model as a holographic dual to a 1+1D quantum black hole in anti-de Sitter space.
• Use of effective field theories and symmetry protection to argue that Majorana zero modes in topological superconductors can host SYK-like interactions.
• Application of random matrix theory and disorder engineering to generate the required random four-fermion couplings $J_{ijkl}$ in the SYK Hamiltonian.
• Numerical and analytical studies of disordered quantum wires and irregularly shaped holes to induce random couplings and suppress bilinear terms.
• Identification of chemical potential tuning as a control knob to suppress non-SYK terms in the Fu-Kane superconductor platform.
• Proposal of spectroscopic and transport measurements to detect emergent black hole-like behavior, including holographic scaling and chaos indicators.

Experimental results

Research questions

• RQ1 Can the Sachdev-Ye-Kitaev (SYK) model be realized in solid-state or ultracold atomic systems to mimic quantum black hole physics?
• RQ2 What experimental platforms offer the best prospects for realizing the SYK model with minimal non-SYK terms and controllable interactions?
• RQ3 How can out-of-time-ordered correlators, a signature of quantum chaos, be measured in such systems to confirm black hole-like dynamics?
• RQ4 To what extent can topological protection and symmetry constraints in materials like the Fu-Kane superconductor stabilize the SYK Hamiltonian?
• RQ5 What measurable signatures in transport or spectroscopy can unambiguously identify emergent black hole behavior in non-gravitational quantum systems?

Key findings

• The SYK model can be realized in disordered quantum wires where random spatial structure of Majorana wavefunctions and screened Coulomb interactions generate the required random $J_{ijkl}$ couplings.
• In the Fu-Kane superconductor, tuning the chemical potential to the Dirac point suppresses bilinear terms, enabling a clean realization of the SYK Hamiltonian via topological protection.
• Numerical studies confirm that irregularly shaped holes in topological superconductors lead to random couplings and suppress non-SYK terms, supporting the feasibility of the proposal.
• Despite progress, reproducibility remains a challenge, as experimental observations of Majorana zero modes in this system have not yet been independently confirmed.
• Measuring out-of-time-ordered correlators remains a major unsolved challenge in both atomic and solid-state implementations.
• Theoretical frameworks now provide a clear roadmap to test quantum gravity phenomena in condensed matter systems, potentially enabling experimental access to black hole thermodynamics and chaos.