Floquet Engineering of Many-Body Systems: Enhancing Interactions and Dynamics Control

Alapfogalmak

This thesis explores Floquet engineering as a powerful tool to manipulate and enhance interactions in driven many-body systems, particularly focusing on the role of correlations and the development of advanced Floquet methods for accurate prediction and control of system dynamics.

Kivonat

• Bibliographic Information: Wang, X. (2024). Floquet-induced interactions in many-body systems [Doctoral dissertation, University of Oxford]. arXiv:2410.22834v1

• Research Objective: This thesis investigates the enhancement of Floquet-induced interactions by many-body correlations and develops advanced Floquet methods to understand and predict these interactions in driven many-body systems, particularly in the context of quantum devices.

• Methodology: The research employs theoretical and computational approaches within the framework of Floquet theory. It utilizes techniques like Sambe space matrix diagonalization, Gaussian elimination, projector techniques, and a novel Floquet Schrieffer-Wolff transform (FSWT) to derive effective Floquet Hamiltonians and analyze system dynamics.

• Key Findings:

  • Many-body correlations significantly enhance Floquet-induced interactions, as demonstrated by the excitonic enhancement of cavity-mediated interactions in a two-band Hubbard model.
  • The developed FSWT method enables accurate prediction of Floquet-induced interactions beyond mean-field approximations, offering improved accuracy compared to traditional high-frequency expansion methods.
  • FSWT proves effective in analyzing complex driven systems, including multi-orbital systems with long-range interactions and cavity-semiconductor setups, revealing the interplay between cavity-mediated and cavity-independent Floquet-induced interactions.

• Main Conclusions:

  • Understanding and harnessing Floquet-induced interactions is crucial for controlling and manipulating driven many-body systems.
  • The thesis provides a comprehensive framework and advanced tools for analyzing and predicting these interactions, paving the way for novel applications in quantum simulation, quantum computing, and the exploration of exotic quantum phases.

• Significance: This research significantly contributes to the field of Floquet engineering by providing a deeper understanding of the role of correlations in driven systems and developing advanced theoretical methods for accurate prediction and control of their dynamics.

• Limitations and Future Research: The thesis primarily focuses on theoretical modeling and analysis. Future research could explore experimental realizations of the proposed schemes and investigate the impact of decoherence and dissipation on Floquet-engineered systems. Further development of FSWT for more complex systems and driving regimes is also promising.

Statisztikák

Idézetek

Főbb Kivonatok

Floquet-induced interactions in many-body systems

by Xiao Wang : arxiv.org 10-31-2024

https://arxiv.org/pdf/2410.22834.pdf

Mélyebb kérdések

How can the insights from this research be applied to develop robust and scalable quantum technologies based on Floquet engineering?

This research significantly contributes to developing robust and scalable quantum technologies based on Floquet engineering in several ways:

Enhanced Control Over Interactions: By understanding and predicting Floquet-induced interactions, especially their enhancement by many-body correlations, we gain finer control over the effective interactions in quantum systems. This is crucial for engineering desired quantum states and dynamics. For instance, the excitonic enhancement of cavity-mediated interactions demonstrated in the thesis can be leveraged to design stronger and more controllable long-range interactions, which are essential for applications like quantum simulation of complex materials and the realization of exotic quantum phases.

Beyond High-Frequency Limitations: The development of the Floquet Schrieffer-Wolff transform (FSWT) overcomes the limitations of traditional high-frequency expansion (HFE) methods. This is significant because it allows for the exploration of Floquet engineering in regimes where the driving frequency is comparable to or even smaller than the intrinsic energy scales of the system. This opens up new possibilities for controlling systems with stronger interactions and exploring novel Floquet phenomena inaccessible by HFE.

Predictive Power for Driven Cavity-QED Systems: The application of FSWT to driven cavity-QED setups provides a systematic way to predict driving-induced phase transitions and other non-equilibrium phenomena in these systems. This is particularly relevant for developing quantum technologies based on light-matter interactions, such as quantum information processing with superconducting circuits or simulating strongly correlated systems with trapped ions coupled to cavities.

Mitigating Errors and Decoherence: A deep understanding of Floquet-induced interactions is essential for mitigating errors and decoherence in Floquet-engineered quantum systems. By carefully choosing driving parameters and exploiting the interplay between different types of interactions, we can suppress unwanted transitions and stabilize desired quantum states, paving the way for more robust and fault-tolerant quantum devices.

Scalability through Effective Hamiltonians: The use of effective Floquet Hamiltonians, derived from methods like Gaussian elimination or FSWT, simplifies the theoretical description of driven many-body systems. This simplification is crucial for simulating and understanding the behavior of larger systems, ultimately aiding in the development of scalable quantum technologies.

In summary, this research provides a powerful toolkit for understanding and harnessing Floquet-induced interactions in many-body systems. By leveraging these insights, we can design more robust, controllable, and scalable quantum technologies based on Floquet engineering, pushing the boundaries of quantum control and its applications.

Could the presence of strong dissipation or disorder fundamentally alter the effectiveness of Floquet engineering in controlling many-body interactions?

Yes, the presence of strong dissipation or disorder can significantly alter the effectiveness of Floquet engineering in controlling many-body interactions.
Dissipation:

Heating and Decoherence: Dissipation, arising from coupling to an external environment, introduces energy into the system and leads to decoherence. This can be detrimental to Floquet engineering, which relies on coherent manipulation of quantum states. Strong dissipation can wash out the delicate Floquet-induced interactions and drive the system towards a featureless thermal state, hindering the desired control.
Modification of Effective Interactions: Dissipation can modify the effective interactions in a driven system. For instance, it can introduce non-local dissipation channels that compete with the engineered Floquet-induced interactions, altering the system's dynamics and potentially suppressing desired phases.
Engineering with Dissipation: While often detrimental, dissipation can also be harnessed as a resource for Floquet engineering. By carefully designing the system-environment coupling, one can induce desired dissipative processes that stabilize specific quantum states or drive the system towards novel non-equilibrium phases. This approach, known as dissipative Floquet engineering, is an active area of research.
Disorder:

Localization and Suppression of Transport: Disorder can lead to localization phenomena, where particles become trapped in localized regions of space, inhibiting transport and hindering the establishment of long-range order. This can significantly impact the effectiveness of Floquet engineering, especially in systems where long-range interactions are crucial for the desired effects.
Modification of Resonance Conditions: Disorder can modify the energy spectrum and resonance conditions of the system, making it challenging to achieve the desired Floquet engineering effects. The presence of disorder can broaden or shift the energy levels, requiring careful tuning of the driving parameters to compensate for these effects.
Many-Body Localization and Novel Phases: Interestingly, the interplay of disorder and driving can lead to novel phenomena like many-body localization (MBL). In MBL phases, strong disorder prevents the system from thermalizing, even in the presence of interactions. This opens up possibilities for exploring exotic non-equilibrium phases and realizing robust quantum memories.
In conclusion, strong dissipation and disorder present significant challenges for Floquet engineering, potentially hindering its effectiveness in controlling many-body interactions. However, they also offer exciting opportunities for exploring novel non-equilibrium phenomena and developing new strategies for quantum control. Understanding the interplay of driving, dissipation, and disorder is crucial for harnessing the full potential of Floquet engineering in realistic settings.

What are the potential implications of this research for understanding and manipulating complex systems beyond the realm of condensed matter physics, such as biological systems or financial markets?

While this research primarily focuses on condensed matter physics, the concepts and techniques developed hold intriguing potential implications for understanding and manipulating complex systems beyond this realm, such as biological systems or financial markets.
Biological Systems:

Light-Harvesting Complexes: The study of Floquet-induced interactions and cavity-mediated interactions could provide insights into energy transfer processes in light-harvesting complexes found in plants and bacteria. These systems often involve strong light-matter coupling and coherent energy transfer, making them amenable to analysis using Floquet theory.
Neural Networks: The brain exhibits complex dynamics and emergent behavior arising from the interactions of a vast network of neurons. While highly speculative, exploring concepts like Floquet engineering and driven many-body systems could offer new perspectives on understanding and potentially manipulating neural activity, particularly in the context of external stimuli like light or magnetic fields.
Molecular Dynamics: The techniques developed for studying driven many-body systems could be adapted to investigate the dynamics of complex molecules under external driving forces, such as laser pulses used in ultrafast spectroscopy. This could lead to a better understanding of chemical reactions, molecular self-assembly, and other biomolecular processes.
Financial Markets:

Agent-Based Models: Financial markets can be viewed as complex systems composed of interacting agents (traders, investors) whose collective behavior determines market dynamics. Concepts from driven many-body systems and non-equilibrium statistical mechanics could provide new tools for modeling and analyzing market behavior, particularly in the presence of external shocks or policy interventions.
Predicting Market Fluctuations: While highly challenging, exploring the role of Floquet-induced interactions and resonance phenomena in financial systems could potentially offer insights into the emergence of market bubbles, crashes, and other extreme events. However, applying these concepts to financial markets requires careful consideration of the underlying assumptions and limitations.
Optimal Control Strategies: Techniques from Floquet engineering and coherent control, adapted to the context of financial markets, could potentially inspire new strategies for portfolio optimization, risk management, and market intervention. However, the ethical and practical implications of such approaches require careful consideration.
Challenges and Considerations:
It's important to acknowledge the significant challenges in applying these concepts to complex systems like biological and financial systems. These systems often exhibit:

High Dimensionality and Complexity: Biological and financial systems involve a vast number of interacting components, making them computationally challenging to model and analyze.
Non-Equilibrium Dynamics: These systems are inherently out of equilibrium, driven by complex feedback loops and external influences.
Stochasticity and Noise: Biological and financial systems are subject to significant noise and randomness, making it difficult to isolate and control specific interactions.
Despite these challenges, the potential rewards of applying insights from driven many-body systems and Floquet engineering to these fields are significant. Further research is needed to bridge the gap between these disciplines and develop tailored theoretical and computational tools for tackling the unique complexities of biological and financial systems.