Quantum many-body models with cold atoms coupled to photonic crystals (1312.2435v3)

Abstract: Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, as atoms are nominally neutral point particles, this limits the types of interactions that can be produced. We propose to use the powerful new platform of cold atoms trapped near nanophotonic systems to extend these limits, enabling a novel quantum material in which atomic spin degrees of freedom, motion, and photons strongly couple over long distances. In this system, an atom trapped near a photonic crystal seeds a localized, tunable cavity mode around the atomic position. We find that this effective cavity facilitates interactions with other atoms within the cavity length, in a way that can be made robust against realistic imperfections. Finally, we show that such phenomena should be accessible using one-dimensional photonic crystal waveguides in which coupling to atoms has already been experimentally demonstrated.

• The paper demonstrates that cold atoms near photonic crystals induce localized cavity modes, enabling strong and tunable long-range interactions.
• It derives a detailed mapping to cavity QED systems, supported by numerical simulations using finite-difference time-domain methods.
• The study sets the stage for experimental quantum simulators and advanced quantum computation through engineered atom-atom couplings.

Quantum Many-Body Models with Cold Atoms Coupled to Photonic Crystals

The paper presented in the paper titled "Quantum many-body models with cold atoms coupled to photonic crystals" explores a sophisticated avenue for exploring quantum many-body physics by leveraging the interaction between cold atoms and photonic crystal structures. This paper proposes a theoretical framework wherein cold atoms, when placed in proximity to photonic crystals, can serve as dynamic elements that induce localized cavity modes capable of mediating strong, tunable, long-range interactions. This approach seeks to overcome some limitations inherent in conventional ultracold atomic systems, such as the typically short-range nature of interactions that can be manipulated using methods like Feshbach resonance.

Core Contributions

The authors focus on how cold atoms positioned near one-dimensional photonic crystal waveguides can seed effective cavity modes, facilitating interactions across extended distances. At a fundamental level, the paper derives how an atom, when trapped near a photonic crystal, instigates a localized, tunable photonic cavity mode akin to traditional cavity quantum electrodynamics (QED) systems. The inherent structure of photonic crystals creates frequency bands and gaps, within which localized states can reside, offering a unique mechanism for promoting coherent atom-atom interactions.

Results and Validation

Conclusion stems from an in-depth mathematical formalism mapping the physics of atom-induced localized modes to established cavity QED paradigms. Such mapping identifies key quantities like effective atom-cavity coupling strengths and engineered atom-cavity detunings. The theoretical model predicted that atom-atom interactions facilitated by atom-induced cavity modes decay exponentially over distances comparable to hundreds of optical wavelengths, showing notable versatility regarding spatial interaction tunability via detuning adjustments and band curvature. Furthermore, the model's fidelity is supported by comprehensive numerical simulations using finite-difference time-domain methods, matching the proposed model against realistic conditions in advanced photonic crystal designs—specifically, the "alligator" photonic crystal waveguide.

Practical and Theoretical Implications

The implications of realizing long-range atom-atom interactions using photonic crystals are manifold. Practically, this model advances the feasibility of constructing robust, miniaturized quantum simulators capable of exploring dynamic quantum phases and complex entanglement phenomena. Theoretically, it paves a pathway towards exploring non-trivial non-equilibrium physics due to the interplay of spin, phononic, and photonic degrees of freedom within a coherent framework.

Future Prospects

The work invites expansive research into more intricate models and higher-dimensional structures, such as two-dimensional photonic crystals, to extend the results presented herein. Additionally, the introduction of atomic level schemes with Λ-type configurations reveals pathways to continuously tune interaction potentials and lengths, achieving behaviors long-sought in quantum operations such as spin-squeezing and fault-tolerant quantum computation. The authors highlight the need for further investigation into disorder effects and the integration of active control fields for dynamic settings, opening broader vistas for realizing exotic quantum states.

In summation, this paper contributes a bold foray into leveraging photonic architecture for realizing long-range quantum interactions, setting a cornerstone for future experimental endeavors in quantum simulations and information processing.