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Macroscopic Particle Transport in Dissipative Long-Range Bosonic Systems

Hongchao Li, Cheng Shang, Tomotaka Kuwahara, Tan Van Vu

TL;DR

This work establishes a macroscopic theory of particle transport for dissipative bosonic systems with long-range hopping and interactions by extending optimal transport to open quantum dynamics. It derives lower bounds on transport time and maximal transport distance under one-body loss, multi-body loss, and gain, highlighting how decoherence-free subspaces enable long-distance and even perfect transport, especially in dilute lattices with gain. A generalized Wasserstein distance is introduced to handle particle loss, and the framework yields a probabilistic bound on transported particles that matches closed-system results, reflecting robust transport against dissipation in certain regimes. The findings point to experimental platforms such as ultracold atoms, Rydberg ensembles, and polar molecules, and suggest protocols to observe the predicted transport bounds and decoherence-free-subspace effects.

Abstract

The inevitable loss of particles in quantum many-body systems provides a more general and experimentally realistic perspective on particle transport. In this work, we determine the maximal speed of macroscopic particle transport in dissipative bosonic systems featuring both long-range hopping and long-range interactions. By developing a generalized optimal transport theory for open quantum systems, we rigorously establish the relationship between the minimum transport time and the source-target distance, and investigate the maximal transportable distance of bosons. We demonstrate that optimal transport exhibits a fundamental distinction depending on whether the system experiences one-body loss or multi-body loss. Furthermore, we present the minimal transport time and the maximal transport distance for systems with both gain and loss. We observe that even an arbitrarily small gain rate enables transport over long distances if the lattice gas is dilute. Moreover, we generally reveal that the emergence of decoherence-free subspaces facilitates the long-distance and perfect transport process. We also derive an upper bound for the probability of transporting a given number of particles during a fixed period with one-body loss. Possible experimental protocols for observing our theoretical predictions are discussed.

Macroscopic Particle Transport in Dissipative Long-Range Bosonic Systems

TL;DR

This work establishes a macroscopic theory of particle transport for dissipative bosonic systems with long-range hopping and interactions by extending optimal transport to open quantum dynamics. It derives lower bounds on transport time and maximal transport distance under one-body loss, multi-body loss, and gain, highlighting how decoherence-free subspaces enable long-distance and even perfect transport, especially in dilute lattices with gain. A generalized Wasserstein distance is introduced to handle particle loss, and the framework yields a probabilistic bound on transported particles that matches closed-system results, reflecting robust transport against dissipation in certain regimes. The findings point to experimental platforms such as ultracold atoms, Rydberg ensembles, and polar molecules, and suggest protocols to observe the predicted transport bounds and decoherence-free-subspace effects.

Abstract

The inevitable loss of particles in quantum many-body systems provides a more general and experimentally realistic perspective on particle transport. In this work, we determine the maximal speed of macroscopic particle transport in dissipative bosonic systems featuring both long-range hopping and long-range interactions. By developing a generalized optimal transport theory for open quantum systems, we rigorously establish the relationship between the minimum transport time and the source-target distance, and investigate the maximal transportable distance of bosons. We demonstrate that optimal transport exhibits a fundamental distinction depending on whether the system experiences one-body loss or multi-body loss. Furthermore, we present the minimal transport time and the maximal transport distance for systems with both gain and loss. We observe that even an arbitrarily small gain rate enables transport over long distances if the lattice gas is dilute. Moreover, we generally reveal that the emergence of decoherence-free subspaces facilitates the long-distance and perfect transport process. We also derive an upper bound for the probability of transporting a given number of particles during a fixed period with one-body loss. Possible experimental protocols for observing our theoretical predictions are discussed.

Paper Structure

This paper contains 14 sections, 85 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Main Results
  3. Local particle loss
  4. Local particle loss and gain
  5. Probability Transport
  6. Discussion
  7. Method
  8. Outline of the proof for Result 1
  9. Outline of the proof for Result 2
  10. Outline of the proof for Result 3
  11. Outline of the proof for Result 4
  12. Acknowledgment
  13. Macroscopic particle transport theory in closed quantum systems
  14. Triangle inequality of the generalized Wasserstein distance

Figures (1)

  • Figure 1: Schematic of particle transport in long-range bosonic open systems, wherein bosons are transported from region $X$ to a separate region $Y$ over a distance ${d_{XY}}$. $(\rm{a})$ The scenario with local particle loss includes Result 1 and Result 2. (b) The scenario corresponds to Result 3, where local particle loss (${\gamma _1}$) and gain (${\gamma _2}$) coexist. Particle gain counteracts loss, extending the maximal transport distance.