Crystallization of strongly interacting photons in a nonlinear optical fiber (0712.1817v1)

Abstract: Understanding strongly correlated quantum systems is a central problem in many areas of physics. The collective behavior of interacting particles gives rise to diverse fundamental phenomena such as confinement in quantum chromodynamics, phase transitions, and electron fractionalization in the quantum Hall regime. While such systems typically involve massive particles, optical photons can also interact with each other in a nonlinear medium. In practice, however, such interactions are often very weak. Here we describe a novel technique that allows the creation of a strongly correlated quantum gas of photons using one-dimensional optical systems with tight field confinement and coherent photon trapping techniques. The confinement enables the generation of large, tunable optical nonlinearities via the interaction of photons with a nearby cold atomic gas. In its extreme, we show that a quantum light field can undergo fermionization in such one-dimensional media, which can be probed via standard photon correlation measurements.

Crystallization of Strongly Interacting Photons in a Nonlinear Optical Fiber

The paper "Crystallization of strongly interacting photons in a nonlinear optical fiber" investigates a novel approach to manipulating photon interactions in one-dimensional optical systems. This research addresses the widely recognized challenge of achieving strong correlations in quantum systems composed of photons, which traditionally exhibit weak interactions. By leveraging confined optical fields and coherent photon trapping techniques, the authors present a methodology for inducing significant nonlinearities through photon-gas interactions with nearby cold atoms. This approach facilitates the transition of photons into a fermionized regime, akin to the Tonks-Girardeau gas, which can be experimentally probed using photon correlation measurements.

Theoretical Background and System Fabrication

The concept of nonlinear effects to generate optical systems with unique properties has been explored over several decades. Historically, such investigations focused predominantly on small photon populations, whereas robust many-body correlations can lead to new states of matter. This work examines an innovative method to establish a Tonks-Girardeau-like photon system, marking an extreme of nonlinear quantum optics where individual photons manifest as impenetrable particles capable of forming a "crystal of photons."

In this framework, one-dimensional structures like tapered optical fibers, hollow-core photonic crystal fibers, or surface plasmons on nanowires are pivotal for achieving tight transverse confinement necessary for significant photon-atom interaction strength. The scheme employs techniques like Electromagnetically Induced Transparency (EIT) to facilitate resonantly enhanced optical nonlinearities, allowing light pulses to be stationary within the medium. Such interaction is quantifiable through the nonlinear Schrödinger Equation (NLSE), with tunable parameters that enable the exploration of the Tonks-Girardeau regime.

Model and Implications

The dynamics of the proposed system correlate with the Lieb-Liniger model, traditionally used for interacting massive particles. The authors highlight the importance of considering repulsive interactions for achieving quantum mechanical behavior in the photon system. The strongly interacting regime presents opportunities for forming a TG gas of photons, driven by altering photon fields and atomic states.

Crucially, the paper outlines methods for loading, evolving, and detecting photon states. By modulating atomic parameters and controlling spin-wave excitations, the characteristics of a strongly interacting photon gas can be prepared and monitored via standard quantum optical techniques. The signature of such states, Friedel oscillations, denotes significant fermionization, where photon positions are discerned in a crystal-like arrangement.

Practical and Theoretical Implications

The ability to control and probe these strongly correlated photonic states possesses several implications and potential applications. The resulting photon "crystal" could be instrumental in quantum metrology, sub-shot noise interferometers, quantum computing, and quantum cryptography due to its suppressed photon number fluctuations. Additionally, by expanding the system to include multiple polarization states, it is feasible to simulate complex matter Hamiltonians, thus providing a versatile platform for exploring spin systems and non-Abelian symmetry scenarios.

Furthermore, leveraging light as a medium to simulate matter systems could offer fresh insights into phenomena like spin-charge separation or multi-channel Kondo effects. Such endeavors underline light's capacity to emulate matter-like properties, advancing our understanding of quantum systems.

Conclusion

This paper represents a significant advancement in the field of nonlinear quantum optics, proposing feasible experimental techniques with existing technologies to realize strongly interacting photons. These theoretical and practical contributions pave the way for a variety of applications in understanding complex quantum systems, and hold promise for future explorations in simulations of unconventional matter behavior using controlled photon interactions.