Directional Quantum Walks of Two Bosons Demonstrate Asymmetric Density Cones and Bloch Oscillations on Hatano-Nelson Lattices

The behaviour of particles in non-Hermitian systems, where fundamental rules of symmetry are broken, presents a fascinating challenge to physicists, and recent work by Sk Anisur, Kartik Singh from the Indian Institute of Science Education and Research, Pune, and Sayan Choudhury explores this in the context of interacting particles moving on a specially designed lattice. Their research investigates how two particles, known as bosons, behave when subjected to asymmetric forces on this lattice, revealing a surprising link between asymmetry and particle movement. The team demonstrates that this asymmetry leads to unusual patterns in particle distribution, including the formation of cone-shaped densities and asymmetric oscillations, and importantly, they establish that this system enhances the detection of weak forces, potentially offering new avenues for sensitive measurement technologies. This achievement represents a significant step forward in understanding non-Hermitian physics and its potential applications in quantum technologies.

The study investigates how interactions between the bosons and this non-reciprocity affect the quantum walk, a fundamental process in quantum mechanics, and how it differs from conventional quantum walks. The team demonstrates that non-reciprocal hopping introduces a directional bias, causing the bosons to propagate asymmetrically. Interactions can either strengthen or weaken this bias, leading to complex and controllable dynamics. These findings deepen our understanding of open quantum systems and offer insights into controlling quantum transport in non-Hermitian environments.

The system exhibits non-reciprocity, resulting in an asymmetric distribution of particles as time progresses. The degree of this asymmetry can be tuned by adjusting the strength of the non-reciprocity. When an external force is applied, the system displays asymmetric Bloch oscillations, a rhythmic motion influenced by the non-Hermitian nature of the lattice. Interestingly, strong interactions create an inner density structure resembling an hourglass, which also becomes asymmetric in the presence of non-reciprocity. Further analysis reveals detailed spatial correlations between the particles.

Non-Hermitian Topology and Quantum Sensing Research

This body of work encompasses a broad range of research papers exploring the frontiers of condensed matter physics, quantum optics, and quantum simulation. A central theme is non-Hermitian physics, investigating systems where the usual rules of quantum mechanics are modified, alongside topological phenomena and their potential for quantum sensing. The research covers foundational work on non-Hermitian models and recent explorations of disorder, quasiperiodicity, and interactions within these systems. It also includes studies of topological insulators, topological phases of matter, and the realization of topological phenomena in ultracold gases.

A significant portion of the research focuses on using ultracold atoms, such as Bose-Einstein condensates and Fermi gases, to simulate complex condensed matter systems. This allows scientists to explore novel quantum phenomena and realize topological phases. The research also investigates the use of quantum systems for precision measurements and sensing, employing concepts like the quantum Fisher information to optimize sensing protocols. Studies of Bloch oscillations and Wannier-Stark localization, often in the context of ultracold gases, are also prominent. The interplay between disorder and localization, particularly in non-Hermitian systems, receives considerable attention. This interdisciplinary work connects condensed matter physics with quantum optics, quantum information, and materials science.

Non-Reciprocal Boson Dynamics and Density Control

This research investigates how interacting bosons behave on a one-dimensional lattice designed to exhibit non-reciprocal tunneling, where particle movement is not symmetrical in both directions. The team discovered that this non-reciprocity fundamentally alters the system’s evolution, causing an asymmetry to develop in the distribution of particles over time. The extent of this asymmetry is directly controllable by adjusting the degree of non-reciprocity. Applying an external force induces asymmetric Bloch oscillations, demonstrating the interplay between non-Hermiticity and external forces.

Strong interactions between the bosons lead to the formation of an inner density structure, which also exhibits asymmetry when the system is non-reciprocal. The researchers also characterized the spatial correlations between particles, finding that weak interactions promote bunching, while strong interactions lead to anti-bunching, effectively mimicking the behaviour of fermions. A key achievement of this work is the demonstration that the system’s sensitivity to external forces can be significantly enhanced by measuring the growth of a quantity called the Fisher Information, suggesting potential applications in precision sensing. Future research could explore the effects of disorder and investigate the potential for extending these findings to higher dimensions.