Self-Trapping, Multistability, and Chaos in an Open Anisotropic Dicke Dimer: A Semiclassical Study

Основные понятия

This study reveals the emergence of self-trapping phenomena, multistability of dynamical states, and dissipative chaos in a coupled atom-photon system described by an open anisotropic Dicke dimer model.

Аннотация

Vivek, G., Mondal, D., Chakraborty, S., & Sinha, S. (2024). Self-trapping phenomenon, multistability and chaos in open anisotropic Dicke dimer. arXiv preprint arXiv:2405.13809.

This study investigates the semiclassical dynamics of a coupled atom-photon system, specifically an anisotropic Dicke dimer model in the presence of photon loss, to explore the emergence of non-linear dynamical phenomena.

Ключевые выводы из

Self-trapping phenomenon, multistability and chaos in open anisotropic Dicke dimer

by G. Vivek, De... в arxiv.org 11-19-2024

https://arxiv.org/pdf/2405.13809.pdf

Дополнительные вопросы

How would the introduction of controlled dissipation or decoherence mechanisms affect the observed self-trapping and chaotic dynamics in the system?

Introducing controlled dissipation or decoherence mechanisms into the anisotropic Dicke dimer (ADD) system would offer a fascinating avenue to manipulate and control the self-trapping and chaotic dynamics. Here's a breakdown of the potential effects:
Impact on Self-Trapping:

Enhancement of Self-Trapping: Carefully engineered dissipation, such as selectively coupling one cavity to a lossy environment, could enhance the self-trapping phenomenon. This selective dissipation could act as an effective potential barrier, further localizing photons in one cavity and reinforcing the population imbalance.
Suppression of Self-Trapping: Conversely, introducing dissipation that promotes photon exchange between the cavities could disrupt the delicate balance required for self-trapping. This could lead to a suppression of the self-trapped state and drive the system towards a more symmetric photon distribution.
Shifting Stability Regions: Controlled dissipation can shift the stability regions of different dynamical phases in the parameter space. This opens up possibilities for dynamically tuning the system into or out of regimes where self-trapping is favored.
Impact on Chaotic Dynamics:

Taming Chaos: Dissipation can sometimes act as a stabilizing force. By carefully introducing dissipation, it might be possible to suppress the chaotic behavior and drive the system towards more predictable limit cycles or steady states.
Enhancing Chaos: In contrast, certain types of dissipation or decoherence can amplify chaotic behavior. If the dissipation introduces noise or fluctuations that resonate with the system's natural frequencies, it could push the system further into the chaotic regime.
Controlling Chaotic Attractors: Controlled dissipation might allow for manipulating the shape and size of chaotic attractors in phase space. This could have implications for the system's sensitivity to initial conditions and its long-time dynamics.
Experimental Realizations:
Experimentally realizing controlled dissipation could involve techniques such as:

Coupling to Auxiliary Cavities: Coupling the ADD system to auxiliary cavities with tunable loss rates would provide a handle to engineer desired dissipation profiles.
Engineering Atom-Photon Interactions: By tailoring the atom-photon interaction strengths or introducing additional atomic levels, one could effectively modify the system's dissipative properties.
In summary, controlled dissipation offers a powerful tool to shape the landscape of dynamical phases in the ADD system. It provides a means to not only understand the interplay between dissipation, self-trapping, and chaos but also to potentially harness these phenomena for quantum control and information processing applications.

Could the multistability observed in this system be harnessed for quantum information processing tasks, such as qubit encoding or quantum state preparation?

The multistability exhibited by the anisotropic Dicke dimer (ADD) system, particularly the coexistence of distinct superradiant phases and self-trapped states, holds intriguing potential for quantum information processing tasks. Here's how this multistability could be harnessed:
Qubit Encoding:

Encoding in Superradiant States: The distinct symmetric (SSR) and anti-symmetric (SSR) superradiant phases could serve as the basis states for a qubit—a quantum bit of information. These states are naturally robust due to their collective nature, potentially offering protection against certain types of noise.
Encoding in Self-Trapped States: The two possible self-trapped states, characterized by photon localization in either the left or right cavity, could also represent the logical '0' and '1' states of a qubit. This encoding would rely on the system's ability to maintain a distinct photon number imbalance.
Quantum State Preparation:

Initializing into Desired States: By carefully choosing the initial conditions, such as the initial spin polarization or photon number, one could guide the system to settle into a specific desired state. The non-overlapping basins of attraction of the different stable states would be crucial for reliable state preparation.
Adiabatic Passage: Techniques like adiabatic rapid passage could be employed to transfer the system from one stable state to another in a controlled manner. This would be essential for implementing quantum gates and manipulating the encoded information.
Challenges and Considerations:

Scalability: Scaling up the ADD system to a larger number of qubits while maintaining control and coherence poses a significant challenge.
Decoherence: Interactions with the environment can lead to decoherence, which degrades the quantum information. Strategies for mitigating decoherence, such as using error correction codes or working at ultra-low temperatures, would be essential.
Readout: Developing efficient and reliable methods for reading out the state of the encoded qubit is crucial. This might involve measuring photon leakage from the cavities or probing the collective spin state of the atoms.
Outlook:
While challenges remain, the multistability inherent in the ADD system offers a promising platform for exploring novel quantum information processing schemes. Further theoretical and experimental investigations are needed to fully assess the potential and limitations of this approach.

What are the potential implications of the coexistence of self-trapped states and chaotic attractors for the system's long-time evolution and its sensitivity to initial conditions?

The coexistence of self-trapped states and chaotic attractors in the anisotropic Dicke dimer (ADD) system creates a complex and fascinating dynamical landscape with significant implications for its long-time evolution and sensitivity to initial conditions:
Long-Time Evolution:

Competition Between Order and Chaos: The system's long-time behavior would be governed by the interplay between the stable self-trapped states, representing a form of order, and the chaotic attractor, representing disorder. This competition could lead to a rich variety of dynamical regimes.
Intermittent Dynamics: The system might exhibit intermittent switching between periods of relatively stable self-trapping and bursts of chaotic behavior. This intermittency could arise from noise or fluctuations that drive the system back and forth across the boundaries separating these dynamical regimes.
Sensitivity to System Parameters: Small changes in system parameters, such as the atom-photon coupling strengths or the dissipation rate, could dramatically alter the balance between self-trapping and chaos, leading to qualitatively different long-time dynamics.
Sensitivity to Initial Conditions:

Fractal Basin Boundaries: The coexistence of stable states and chaotic attractors often leads to fractal basin boundaries in phase space. This means that even infinitesimally close initial conditions can result in drastically different long-term outcomes—the system might settle into a self-trapped state or get caught in the chaotic attractor.
Unpredictability: The chaotic nature of one of the attractors introduces an inherent element of unpredictability into the system's evolution. Even with precise knowledge of the initial conditions, it becomes challenging to predict the system's state with certainty after a sufficiently long time.
Quantum Manifestations: In the quantum regime, the coexistence of self-trapping and chaos could have intriguing consequences for phenomena like chaos-assisted tunneling. The chaotic dynamics might enhance or suppress tunneling between different self-trapped states, offering a novel avenue for quantum control.
Implications:

Fundamental Understanding: Studying the ADD system provides valuable insights into the broader interplay between order, chaos, and dissipation in open quantum systems.
Quantum Control: Understanding and potentially controlling the sensitivity to initial conditions in this system could be harnessed for quantum state preparation or switching between different dynamical regimes.
Exploring Quantum Chaos: The ADD system offers a platform to investigate the quantum manifestations of classical chaos, such as the potential for quantum scarring or the emergence of universal statistical properties in the system's spectrum.
In conclusion, the coexistence of self-trapped states and chaotic attractors in the ADD system highlights the intricate and often counterintuitive behavior of driven-dissipative quantum systems. It underscores the importance of considering both order and chaos when analyzing the long-time dynamics and sensitivity to initial conditions in such systems.