Finding Critical States of Enhanced Memory Capacity in Attractive Cold Bosons

Abstract

We discuss a class of quantum theories which exhibit a sharply increased memory storage capacity due to emergent gapless degrees of freedom. Their realization, both theoretical and experimental, is of great interest. On the one hand, such systems are motivated from a quantum information point of view. On the other hand, they can provide a framework for simulating systems with enhanced capacity of pattern storage, such as black holes and neural networks. In this paper, we develop an analytic method that enables us to find critical states with increased storage capabilities in a generic system of cold bosons with weak attractive interactions. The enhancement of memory capacity arises when the occupation number $N$ of certain modes reaches a critical level. Such modes, via negative energy couplings, assist others in becoming effectively gapless. This leads to degenerate microstates labeled by the occupation numbers of the nearly-gapless modes. In the limit of large $N$, they become exactly gapless and their decoherence time diverges. In this way, a system becomes an ideal storer of quantum information. We demonstrate our method on a prototype model of $N$ attractive cold bosons contained in a one-dimensional box with Dirichlet boundary conditions. Although we limit ourselves to a truncated system, we observe a rich structure of quantum phases with a critical point of enhanced memory capacity.

arXiv comment42 pages, 11 figures, 2 appendices; v2: matches published version

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• The World as a Hologram
• The Holographic Bound in Anti-de Sitter Space
• Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions
• Scrambling in the Black Hole Portrait
• Black Holes and Quantumness on Macroscopic Scales
• Nambu-Goldstone Effective Theory of Information at Quantum Criticality
• Black Holes as Brains: Neural Networks with Area Law Entropy
• Area Law Micro-State Entropy from Criticality and Spherical Symmetry
• Black Hole Type Quantum Computing in Critical Bose-Einstein Systems
• Black Hole Based Quantum Computing in Labs and in the Sky
• Critically excited states with enhanced memory and pattern recognition capacities in quantum brain networks: Lesson from black holes
• Classicalization Clearly: Quantum Transition into States of Maximal Memory Storage Capacity
• The Lieb-Liniger model at the critical point as toy model for Black Holes

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