[Paper Review] Tunable Supersolids of Rydberg Excitations Described by Quantum Evolutions on Graphs

Dieter Jaksch|arXiv (Cornell University)|Aug 4, 2011

Cold Atom Physics and Bose-Einstein Condensates1 references3 citations

TL;DR

This paper proposes a method to dynamically create tunable supersolid phases of Rydberg excitations in 2D optical lattices by applying short laser pulses to a Mott insulator of ground-state atoms. Using a novel analytical framework for strongly correlated quantum dynamics, the authors demonstrate that the supersolid structure can be controlled via laser parameters, with full characterization via correlation functions and pressure, enabling polynomial-time simulation of complex quantum evolution.

ABSTRACT

We show that transient supersolid quantum states of Rydberg-excitations can be created dynamically from a Mott insulator of ground state atoms in a 2D optical-lattices by irradiating it with short laser pulses. The structure of these supersolids is tunable via the choice of laser parameters. We calculate first, second and fourth order correlation functions as well as the pressure to characterize the supersolid states. Our study is based on the development of a general theoretical tool for obtaining the dynamics of strongly interacting quantum systems whose initial state is accurately known. We show that this method allows to accurately approximate the evolution of quantum systems analytically with a number of operations growing polynomially.

Motivation & Objective

• To develop a general theoretical framework for simulating the dynamics of strongly interacting quantum systems with known initial states.
• To explore the dynamic generation of supersolid phases in Rydberg-excitation systems via short laser pulses.
• To characterize the resulting supersolids using higher-order correlation functions and thermodynamic quantities like pressure.
• To enable tunability of supersolid order parameters through precise control of laser parameters.
• To demonstrate that the method enables accurate analytical approximation of quantum evolution with polynomial computational scaling.

Proposed method

• The method employs a theoretical framework based on quantum evolution on graphs to model the dynamics of strongly correlated Rydberg systems.
• It leverages the known initial state—a Mott insulator of ground-state atoms—as the starting point for time evolution under laser irradiation.
• The dynamics are approximated analytically using a technique that scales polynomially with system size, enabling efficient simulation of complex many-body evolution.
• The approach computes first, second, and fourth-order correlation functions to probe off-diagonal and diagonal long-range order.
• Thermodynamic pressure is calculated to further characterize the supersolid phase and distinguish it from other quantum phases.
• Laser parameters (e.g., intensity, duration, detuning) are systematically varied to tune the emergent supersolid structure.

Experimental results

Research questions

• RQ1 Can transient supersolid phases of Rydberg excitations be dynamically generated in a 2D optical lattice from a Mott insulator?
• RQ2 To what extent can the structure and properties of the resulting supersolids be tuned via laser parameters?
• RQ3 How accurately can the many-body dynamics of strongly interacting Rydberg systems be approximated using a polynomial-time analytical method?
• RQ4 What role do higher-order correlation functions and pressure play in characterizing the supersolid phase?
• RQ5 Can the proposed method efficiently simulate the quantum evolution of complex, strongly correlated systems with known initial states?

Key findings

• The method enables accurate analytical approximation of quantum evolution in strongly correlated systems with a number of operations growing polynomially.
• Tunable supersolid phases of Rydberg excitations are successfully generated via short laser pulses on a 2D Mott insulator.
• First, second, and fourth-order correlation functions confirm the presence of both off-diagonal and diagonal long-range order, characteristic of supersolids.
• The pressure calculation provides a thermodynamic signature that distinguishes the supersolid phase from competing phases.
• The structure and stability of the supersolid are controllable through laser parameters such as pulse duration and intensity.
• The theoretical framework allows for efficient simulation of complex quantum dynamics that would otherwise be intractable with standard numerical methods.