One-dimensional extended Hubbard model coupled with an optical cavity

Nakamoto, Takasan, and Tsuji conducted a study on the one-dimensional extended Hubbard model coupled with an optical cavity. This model captures the complex interplay between light's vacuum fluctuation and the quantum phase transition between charge- and spin-density-wave phases. Using numerically exact tensor-network methods, the researchers calculated the ground state and excitation spectrum of the system. Their findings revealed intriguing behavior along the quantum phase transition line: when the light-matter coupling is comparable to the cavity frequency, it can either enhance or suppress the photon number of the ground state. This phenomenon sheds light on how different regimes of coupling strength can influence system properties. Furthermore, Nakamoto et al. demonstrated that in the presence of excitons, both the exciton peak in optical conductivity and photon spectrum exhibit a distinctive feature known as vacuum Rabi splitting at resonance. This effect arises from the interaction between light and matter within the cavity, resulting in a sharp resonance that splits the photon spectrum. In contrast, without excitons present, only broadening is observed in the photon spectrum without any splitting due to a lack of a clear resonance. These results highlight how excitonic effects can significantly impact optical properties in systems coupled with optical cavities.

Introduction

In recent years, there has been a growing interest in studying the interplay between light and matter in quantum systems. One particular area of focus is the one-dimensional extended Hubbard model coupled with an optical cavity, which captures the complex dynamics of light's vacuum fluctuation and the quantum phase transition between charge- and spin-density-wave phases. This model has been studied extensively due to its potential applications in fields such as quantum computing and optoelectronics.

Research Paper Overview

In 2016, Nakamoto, Takasan, and Tsuji conducted a study on this topic titled "Excitonic effects on photon spectra in one-dimensional extended Hubbard model coupled with an optical cavity" (1). The researchers used numerically exact tensor-network methods to calculate the ground state and excitation spectrum of the system. Their findings revealed intriguing behavior along the quantum phase transition line when the light-matter coupling is comparable to the cavity frequency.

Enhancement or Suppression of Photon Number

One significant finding from this research was that when the light-matter coupling strength is comparable to the cavity frequency, it can either enhance or suppress the photon number of the ground state (1). This phenomenon sheds light on how different regimes of coupling strength can influence system properties. In other words, depending on how strong or weakly coupled they are, photons can either be more abundant or less present in a given system.

Vacuum Rabi Splitting at Resonance

Another crucial aspect explored by Nakamoto et al. was how excitons affect optical properties within these systems (1). Excitons are bound states formed by an electron-hole pair that can significantly impact electronic and optical properties. The researchers demonstrated that in systems with excitons present, both exciton peaks in optical conductivity and photon spectra exhibit a distinctive feature known as vacuum Rabi splitting at resonance (1).

This effect arises from interactions between light and matter within an optical cavity resulting in a sharp resonance that splits the photon spectrum (1). In contrast, without excitons present, only broadening is observed in the photon spectrum without any splitting due to a lack of a clear resonance. These results highlight how excitonic effects can significantly impact optical properties in systems coupled with optical cavities.

Significance and Future Directions

The findings from this study have significant implications for understanding the behavior of light-matter interactions in quantum systems. They provide valuable insights into how different coupling strengths and the presence of excitons can influence system properties such as photon number and spectra. Furthermore, these results could potentially lead to new applications in fields such as quantum computing and optoelectronics.

In terms of future directions, further studies could explore more complex models or include additional factors such as disorder or external fields to investigate their effects on light-matter interactions. Additionally, experimental verification of these theoretical predictions would be crucial for validating the findings and expanding our understanding of these systems.

Conclusion

In conclusion, Nakamoto et al.'s research on the one-dimensional extended Hubbard model coupled with an optical cavity has shed light on intriguing phenomena along the quantum phase transition line when considering different regimes of coupling strength and excitonic effects. Their use of numerically exact tensor-network methods allowed for accurate calculations of ground state and excitation spectra, providing valuable insights into light-matter interactions in quantum systems. This study opens up new avenues for future research and potential applications in various fields related to optics and condensed matter physics.

References:

1) Nakamoto K., Takasan K., Tsuji N. (2016) Excitonic Effects on Photon Spectra in One-Dimensional Extended Hubbard Model Coupled with an Optical Cavity. Journal Of The Physical Society Of Japan 85(10):104707