Mitigating Heating to Higher Energy Bands in Floquet-Hubbard Lattices Using Two-Tone Driving: An Experimental and Theoretical Study

Основні поняття

Two-tone driving can effectively mitigate heating to higher energy bands in strongly driven, strongly interacting Fermi-Hubbard systems, offering a promising approach for improving ground-state coherence in Floquet engineering.

Анотація

Bibliographic Information:

Chen, Y., Zhu, Z., & Viebahn, K. (2024). Mitigating higher-band heating in Floquet-Hubbard lattices via two-tone driving. arXiv preprint arXiv:2410.12308.

Research Objective:

This research paper investigates the effectiveness of a two-tone driving method for mitigating heating to higher energy bands in strongly driven, strongly interacting Fermi-Hubbard systems. The authors aim to determine if this technique, previously demonstrated in non-interacting or weakly driven systems, can improve ground-state coherence in the presence of strong interactions.

Methodology:

The researchers conducted experiments using ultracold potassium-40 atoms loaded into a three-dimensional optical lattice. They implemented a two-frequency driving scheme, with a strong primary drive at frequency ω and a weaker "cancelling" drive at 3ω. By varying the strength of the cancelling drive and the interaction strength between atoms (Hubbard U), they measured the resulting population of atoms excited to the higher energy p-band. The experimental findings were compared with theoretical simulations using exact diagonalization of a two-band Fermi-Hubbard model.

Key Findings:

• The two-tone driving method successfully reduced heating to the p-band for all tested interaction strengths, including both attractive and repulsive interactions.
• The effectiveness of the cancelling effect decreased with increasing interaction strength, suggesting a limit to the technique's applicability in highly correlated systems.
• The optimal strength of the cancelling drive exhibited a clear dependence on the interaction strength, a finding not predicted by existing analytical models for non-interacting systems.

Main Conclusions:

The study demonstrates the potential of two-tone driving for mitigating heating in strongly driven, strongly interacting quantum systems, a crucial step towards realizing robust Floquet engineering protocols. The observed dependence of the optimal cancelling parameters on interaction strength highlights the need for new theoretical approaches to fully capture the physics of these complex systems.

Significance:

This research contributes to the field of Floquet engineering by providing experimental evidence for a technique to mitigate a major obstacle - heating - in the quest to engineer novel quantum states of matter. The findings have implications for various platforms beyond cold atoms, including condensed matter and quantum optics, where periodic driving is employed.

Limitations and Future Research:

The theoretical model used in the study simplifies the experimental system by neglecting certain factors like band-dependent interactions and higher-order tunneling terms. Future research could explore these aspects in more detail. Additionally, investigating the performance of the two-tone method with more complex driving waveforms and in higher dimensional systems could further advance the field.

Статистика

The lattice depths are [VX, VY, VZ] = [5.99(2), 14.95(3), 14.97(5)] Erec.
The s band tunnelling amplitudes are [224(1), 29.0(1), 28.9(3)] Hz.
The shaking duration is 30 ms (≃42 tunnelling times).
The fundamental drive frequency (ω1) is 5300 Hz × 2π.
The cancelling drive frequency (ω3) is 15 900 Hz × 2π.
The 1ω driving strength (K1) is fixed at 1.4.
The minimal detectable p band fraction is 0.028(4).
Without the cancelling drive, the p band fraction increases from 0.028 to 0.24 within 30 ms.
With the cancelling drive, the p band fraction drops to Pmin = 0.066(5).
The optimal cancelling strength K3 for U = 0 is 0.0741(4).

Цитати

"Multi-photon resonances to high-lying energy levels represent an unavoidable source of Floquet heating in strongly driven quantum systems."
"The key idea behind two-tone cancelling is destructive quantum interference."
"Our results call for novel analytical approaches to capture the physics of strongly-driven-strongly-interacting many-body systems."

Ключові висновки, отримані з

Mitigating higher-band heating in Floquet-Hubbard lattices via two-tone driving

by Yuanning Che... о arxiv.org 10-17-2024

https://arxiv.org/pdf/2410.12308.pdf

Глибші Запити

How might the two-tone driving method be adapted for more complex lattice geometries and higher dimensional systems?

Adapting the two-tone driving method for more complex scenarios presents both opportunities and challenges:
Complex Lattice Geometries:

Identifying Resonances: The first hurdle is identifying the dominant multi-photon resonances that contribute to higher-band heating. This becomes more complex as the lattice geometry dictates the band structure and possible excitation pathways. Numerical simulations become crucial for predicting these resonances.
Symmetry Considerations: Different lattice geometries possess distinct symmetries. The two-tone drive must be tailored to respect or exploit these symmetries for effective cancellation. For example, the choice of even or odd harmonics for cancellation depends on the spatial symmetry of the drive.
Mode Coupling: Complex lattices can lead to coupling between different orbital modes (e.g., s, p, d orbitals). The two-tone drive needs to account for these couplings to avoid unintended excitations.
Higher Dimensional Systems:

Increased Resonances: Higher dimensions introduce a larger density of states and, consequently, more potential multi-photon resonance channels. This necessitates careful selection of driving frequencies and amplitudes.
Drive Polarization: In two or three dimensions, the polarization of the driving fields becomes crucial. Different polarizations can selectively address specific transitions, offering an additional control knob for the two-tone cancellation.
Computational Complexity: Simulating higher-dimensional, strongly-interacting systems under two-tone driving is computationally demanding. Efficient numerical methods and approximations are needed to guide experimental implementations.
Overall, extending the two-tone method involves:

Characterizing the System: Thorough theoretical and numerical analysis of the specific lattice geometry and dimensionality to identify relevant heating channels.
Tailoring the Drive: Designing the two-tone drive (frequencies, amplitudes, polarizations) to exploit system symmetries and selectively suppress the identified resonances.
Experimental Optimization: Fine-tuning the drive parameters experimentally to account for imperfections and optimize for the desired Floquet state.

Could the inclusion of interactions in analytical models like the Floquet-Fermi-Golden rule lead to more accurate predictions of optimal cancelling parameters?

Yes, incorporating interactions into analytical models like the Floquet-Fermi-Golden rule holds the potential to significantly improve the prediction accuracy of optimal cancelling parameters. Here's why:

Capturing Interaction Effects: The standard Floquet-Fermi-Golden rule typically treats interactions perturbatively or neglects them entirely. However, as demonstrated in the paper, interactions can significantly shift the optimal cancelling drive strength (K3). Including interactions more rigorously in the model would capture these shifts.
Beyond Single-Particle Picture: Interactions introduce correlations and many-body effects that are not present in single-particle descriptions. An interaction-inclusive Floquet-Fermi-Golden rule could account for these correlations, leading to more realistic predictions of excitation pathways and heating rates.
Predictive Power for Strongly Correlated Systems: For strongly correlated systems, where interactions dominate, incorporating them into analytical models is essential. This would enable the prediction of optimal cancelling parameters even in regimes where perturbative approaches fail.
Challenges and Approaches:

Theoretical Complexity: Incorporating interactions into the Floquet-Fermi-Golden rule significantly increases the theoretical complexity. New techniques and approximations might be needed to make calculations tractable.
Effective Interaction Parameters: Determining the effective interaction parameters to use in the analytical model can be challenging, especially in strongly correlated regimes.
Experimental Validation: Rigorous experimental validation would be crucial to assess the accuracy and limitations of the interaction-inclusive Floquet-Fermi-Golden rule.

What are the potential implications of achieving robust Floquet engineering in strongly correlated systems for developing new quantum technologies?

Robust Floquet engineering in strongly correlated systems opens up exciting possibilities for quantum technologies:

Designer Quantum Materials: It paves the way for creating exotic quantum phases of matter that do not exist naturally. By controlling the interplay of driving and interactions, we could realize novel superconducting states, topological phases with enhanced robustness, and fractional quantum Hall-like systems.
Quantum Simulation: Strongly correlated systems are notoriously difficult to simulate classically. Robust Floquet engineering would provide a powerful platform for simulating complex condensed matter phenomena, such as high-temperature superconductivity, and for benchmarking theoretical models.
Quantum Information Processing: Floquet systems offer intriguing possibilities for quantum information processing. For example, they could be used to engineer robust qubits, implement fast and controllable quantum gates, and protect quantum information from decoherence.
Ultrafast Optoelectronics: The ability to manipulate electronic properties at ultrafast timescales using light could lead to breakthroughs in optoelectronics. Imagine devices that operate at petahertz frequencies, enabling ultrafast switching and information processing.
Novel Sensors: Floquet-engineered materials could exhibit enhanced sensitivity to external stimuli, leading to the development of highly sensitive sensors for magnetic fields, electric fields, and other physical quantities.
Realizing these implications requires overcoming challenges such as:

Heating and Dissipation: Minimizing unwanted heating effects remains crucial for maintaining long coherence times, which are essential for many quantum technologies.
Scalability: Scaling up Floquet engineering to larger systems with many particles is necessary for practical applications.
Control and Measurement: Precise control over the driving fields and the development of advanced measurement techniques are essential for characterizing and manipulating Floquet-engineered states.