Ozawa and Colleagues Models Non-Hermitian Framework for Wave-Packet Dynamics

Non-Hermitian Bloch oscillations, the periodic motion of quantum particles in lattices with a driving force, are now understood through a new framework developed by Yanyan He and Tomoki Ozawa at Tohoku University. This framework reveals nonreciprocal non-smooth Bloch oscillations characterised by periodic jumps in group velocity. Wave-packet momentum drifts at a rate of -F/2, uncovering periodic temporal shifts and unusual wave propagation in lattices with unidirectional hopping.

The behaviour of waves in specifically designed, non-Hermitian systems revealed unusual oscillatory patterns absent in conventional wave physics. The team detailed ‘non-smooth Bloch oscillations’, where wave movement isn’t continuous but jumps abruptly in speed when a force applies. This establishes a general framework detailing how wave-packet momentum drifts, leading to periodic shifts and unusual propagation within these complex lattices.

Yanyan He and Tomoki Ozawa at Tohoku University have established a thorough framework for understanding non-Hermitian Bloch oscillations, a phenomenon describing the repetitive motion of quantum particles within a lattice subjected to a driving force. These non-Hermitian systems behave differently from conventional ones, resembling a battery that gradually loses charge rather than perfectly retaining it, representing a departure from energy conservation. The team detailed ‘non-smooth Bloch oscillations’, where wave movement isn’t continuous but jumps abruptly in speed when a force applies, a behaviour not seen in standard wave physics. They discovered that these jumps, termed nonreciprocal non-smooth Bloch oscillations, arise from periodic shifts in the wave packet’s momentum, and further uncovered periodic temporal Goos, Hänchen shifts, a small sideways displacement of a wave as it reflects, similar to nudging a bowling ball as it bounces off the gutter.

Non-Hermitian lattices induce anomalous wave-packet drift and non-reciprocal oscillations

Wave-packet momentum drifts at a rate of -F/2, a sharp departure from the -F drift observed in conventional Bloch oscillations, and previously unattainable in Hermitian systems. Detailed mapping of wave-packet dynamics revealed this anomalous drift, which arises within non-Hermitian lattices, specifically, one-dimensional structures subjected to a constant force, and fundamentally alters wave behaviour. Alongside unusual wave propagation patterns in lattices designed with unidirectional hopping under open boundary conditions, periodic temporal Goos-Hänchen shifts, a sideways displacement of waves upon reflection, uncovered.

These findings establish a general framework for understanding non-Hermitian Bloch oscillations, revealing nonreciprocal non-smooth oscillations characterised by periodic, abrupt jumps in group velocity, a behaviour absent in standard wave physics. Analysis of wave-packet behaviour initiated from both broad and single-site excitations confirmed that the maximum momentum of a wave packet drifts at a rate of -F/2, differing from the -F drift seen in standard Bloch oscillations. The anomalous drift persists even with a single initial excitation, revealing periodic jumps in group velocity and cusps in real-space dynamics under certain conditions, while symmetric breathing modes emerge under others. Further calculations demonstrate that the anomalous group velocity precisely cancels the Hermitian counterpart, leading to a vanishing net group velocity in specific scenarios, and these analytical predictions for the centre of mass and group velocity align with numerical simulations. Currently, these results limit themselves to one-dimensional lattices and do not yet demonstrate how these non-Hermitian effects might be used for practical applications in photonic or electronic devices.

Non-Hermitian lattice behaviour necessitates high-precision computational modelling techniques

Tohoku University researchers have established a framework for understanding how waves behave in specifically designed, non-Hermitian lattices, revealing unusual oscillatory patterns not seen in conventional physics. The team relied on an arbitrary precision library within Matlab to improve accuracy, suggesting inherent difficulties in modelling these complex systems without sophisticated computational tools, and this highlights a tension between analytical predictions and numerical simulations. Nevertheless, the discrepancies between theoretical predictions and simulations do not diminish the importance of this work.

Identifying anomalous group velocity and non-smooth Bloch oscillations, where waves jump rather than flow smoothly, opens new avenues for manipulating wave propagation. A general understanding of wave behaviour within non-Hermitian lattices has been established by the team at Tohoku University, moving beyond standard oscillatory patterns to characterise more complex dynamics. This framework details how wave-packet momentum drifts at a rate differing from conventional systems, leading to periodic, non-smooth Bloch oscillations where wave movement isn’t continuous but jumps abruptly. Specifically, these jumps, coupled with periodic temporal Goos-Hänchen shifts, a sideways displacement of waves upon reflection, arise within lattices designed with unidirectional hopping.

The researchers demonstrated non-reciprocal, non-smooth Bloch oscillations within one-dimensional non-Hermitian lattices, revealing periodic jumps in wave velocity. This is significant because it establishes a new understanding of wave behaviour in systems where conventional physics principles do not fully apply. The study identified an anomalous group velocity that cancels Hermitian velocity in certain instances, aligning with numerical simulations. The authors suggest further work is needed to extend these findings beyond one-dimensional lattices and explore potential applications.