Flux-Driven Circular Current in a Non-Hermitian Dimerized Aharonov-Bohm Ring: Impact of Physical Gain and Loss (2501.06447v1)

Abstract: In the present work, we explore magnetic response of a dimerized ring subjected to Aharonov-Bohm (AB) flux and environmental interactions. Specifically, we introduce an imaginary site potential on the odd lattice sites to represent physical gain and loss, while the even lattice sites remain unperturbed. We investigate the induced current resulting from the AB flux in both real and imaginary eigenspaces, aiming to enhance this current significantly by adjusting the gain/loss parameter ($d$). Our analysis focuses on how exceptional points in the real and imaginary eigenenergy spaces contribute to notable increases in current at specific $d$ values, and the emergence of purely real current when the imaginary current vanishes. We focus on how the converging and diverging nature of the energy spectrum leads to gradual increases and decreases in the current. Additionally, we study the interplay between the correlations of dimerized hopping integrals and the gain-loss parameter, which affects the current and highlights key features associated with these physical parameters. Furthermore, we consider how system size impacts our findings. These investigations may reveal unconventional characteristics in various loop configurations, potentially paving the way for new research directions.

• The paper examines flux-driven circular current in a non-Hermitian dimerized Aharonov-Bohm ring, studying the impact of gain and loss on energy spectra and current behavior.
• Numerical results show how gain-loss parameters and hopping terms modulate real and imaginary currents, with exceptional points enhancing sensitivity.
• This research provides insights into controlling quantum transport properties in nanoscale devices using environmental interactions, with potential applications in quantum computing and photonics.

Analysis of Flux-Driven Circular Current in a Non-Hermitian Dimerized Aharonov-Bohm Ring: Impact of Physical Gain and Loss

The paper examines the characteristics of circular currents in a non-Hermitian (NH) dimerized Aharonov-Bohm (AB) ring influenced by environmental interactions in the form of gain and loss at alternating lattice sites. The paper utilizes a tight-binding model to simulate the quantum system and explores both real and imaginary components of energy spectra, assessing how these impact current behavior.

Key Aspects of the Study

The authors initiate their paper by explaining the significance of NH systems, particularly those that exhibit parity-time (PT) symmetry. Such systems are pivotal in various domains including optics, electronics, and atomic physics due to their unique characteristics like exceptional points and non-reciprocal transport. These features enable distinct phenomena such as heightened sensitivity and diffusive coherent transport in quantum systems.

Central to this paper is the NH dimerized ring structure, influenced by an externally applied AB flux. The gain and loss are introduced via imaginary on-site potentials, alternating at odd lattice sites, while even lattice sites remain unaltered. This arrangement allows the ring to showcase NH effects, including the accumulation of circular currents without disorder, thereby making it an intriguing candidate for technological applications that involve quantum transport and sensing mechanisms.

Methodological Framework

To explore the NH regimes, the authors use a tight-binding Hamiltonian, which encompasses dimerized hopping terms and asymmetric imaginary potentials to simulate the gain and loss characteristics. This system is subjected to an AB flux, impacting the dynamics of the current within the system significantly.

Current calculations are performed by differentiating the ground state energy with respect to the AB flux for both real and imaginary subspaces of the energy spectrum. This methodological approach enables a detailed examination of the current's dependence on parameters such as the NH gain-loss parameter ($d$) and the hopping integrals ($t_1$, $t_2$).

Numerical Analysis and Observations

Numerical results reveal several remarkable phenomena:

1. Energy Spectrum Dynamics: At low values of $d$, the real part of the energy spectrum dominates. As $d$ increases, imaginary spectra become more pronounced, with corresponding peaks in the current near exceptional points—contributing to enhanced sensitivity.
2. Parameter Modulation: For certain values of $d$, real and imaginary currents demonstrate identical magnitudes. However, variations in $d$ introduce complex patterns where an increase initially bolsters the real current until reaching a critical value ($d_c$), beyond which the current becomes purely real, highlighting the parameter's governing power on transport properties.
3. Hopping Correlations: The paper indicates a switching behavior of the current when conditions change from $t_1 > t_2$ to $t_1 < t_2$. The real and imaginary currents display contrasting behaviors under these varying conditions, consistent across different values of $d$.
4. Exceptional Points and Criticality: Exceptional points mark transitions in the behavior of the current, with distinct changes occurring near these points. Maximum current occurs when the system aligns with these points on the zero-energy axis, showcasing heightened sensitivity and response.
5. Size Effects: Larger systems show reduced current magnitudes but maintain the observed phenomena. The critical parameter $d_c$ demonstrates strong dependence on system size, flux, and the interplay between hopping terms.

Implications and Future Prospects

The outcomes of this research underscore the critical role of gain and loss mechanics in NH systems, paving the way for improved control over quantum transport properties. The ability to modulate currents through environmental interaction parameters enhances the potential for application in nanoscale devices where quantum coherence and non-reciprocal transport play pivotal roles.

Future research could focus on exploring varied NH loop configurations or extended systems, offering insight into technological enhancements and further understanding of exceptional point dynamics and PT-symmetrical behavior. This could significantly impact domains such as quantum computing and photonics, where precise control over transport properties is crucial.