Macroscopic Particle Transport in Dissipative Long-Range Bosonic Systems (2503.13731v1)

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

The paper under discussion investigates the dynamics of particle transport in dissipative bosonic systems characterized by long-range hopping and interactions. The framework developed in this paper is crucial for understanding transport in open quantum systems, particularly under the influence of particle dissipation mechanisms like one-body and multi-body losses, as well as scenarios where both particle gain and loss occur. Such models are relevant in quantum many-body systems, where dissipation is unavoidable due to interactions with the environment or intrinsic particle collisions.

Key Contributions and Results

The authors introduce a generalized optimal transport theory tailored for open quantum systems, providing a rigorous framework for analyzing the maximal speed and efficiency of particle transport in these systems. A few notable results from their work include:

1. Maximal Transport Speed with One-body Loss: For systems experiencing one-body loss, characterized by Lindblad operators corresponding to bosonic annihilation, the research identifies a reduced transport speed due to the exponential decay of particle numbers. The minimum time required for a given fraction of particles to reach a target region scales with the distance as $\tau \exp(-\gamma \tau) \geq \kappa d^\alpha$, where $\gamma$ is the loss rate. This result highlights the impact of dissipation, diminishing the transport speed compared to closed systems.
2. Multi-body Loss Dynamics: In cases of multi-body loss, where the Lindblad operator takes the form of higher-order products of the annihilation operator, the authors demonstrate that transport time is no longer limited by an exponential decay factor, aligning with expectations in closed-system analysis. This is attributed to the presence of decoherence-free subspaces in multi-body systems, which sustain transport efficiencies akin to closed systems.
3. Combined Loss and Gain Influence: The research further explores systems with both particle gain and loss. Interestingly, the inclusion of a gain mechanism significantly alters transport dynamics, allowing for the extension of transport distance, particularly in dilute systems. Under specific conditions, even negligible particle gain rates can render long-distance transport feasible, due to the stabilizing effects of gain-riddled decoherence-free subspaces.
4. Transport Probability Bounds: The paper also derives bounds on the probability of successful particle transport over a fixed time period, remaining consistent with closed system predictions. This indicates that certain fundamental transport characteristics persist despite dissipative effects.

Theoretical Implications and Future Directions

The implications of these findings are twofold. Practically, they offer a quantitative toolset for assessing transport dynamics in experimental setups involving ultracold gases, optical lattices, and systems with engineered loss-gain balance. Theoretically, they open pathways to explore dissipation-driven quantum phenomena beyond the scope of closed systems, granting insights into how decoherence-free subspaces can be harnessed to control quantum transport.

The paper prompts several avenues for future research. Extending the analysis to more general nonlocal dissipation mechanisms, as well as delving deeper into the implications of decoherence-free subspaces in fermionic systems, represents worthwhile pursuits. Moreover, leveraging these insights for experimental protocols could lead to novel quantum technologies.

In summary, this work provides a comprehensive examination of particle transport in dissipative long-range bosonic systems, offering valuable theoretical insights and practical guidelines for future experimental investigation and technological application in the field of quantum many-body physics.