Cold Atom Lattice Simulators Achieve Precise Potential Estimation Via Interaction Control

Simulating complex quantum systems requires increasingly sophisticated control over individual components, and cold atoms trapped in optical lattices offer a promising route towards this goal. Bhavik Kumar and Daniel Malz, both from the University of Copenhagen, now present a method for accurately determining the applied potentials within these lattices, a crucial step for realising complex simulations. The team demonstrates that by leveraging the unique properties of certain atomic species and observing how they evolve over time, any potential landscape can be measured with high precision, even when the individual lattice sites are too close together to be directly observed. This achievement overcomes a significant hurdle in the field, opening up possibilities for simulating a wider range of physical phenomena and achieving unprecedented levels of control in quantum simulation experiments.

This work addresses the challenge of implementing complex, site-dependent potentials by developing a method for estimating these potentials within cold atom simulators, given observations of the resulting atomic density distribution. The approach frames the problem as a Bayesian inverse problem, treating the potentials as unknown parameters to be determined from experimental data. The team developed a novel numerical method, combining finite element discretization with Markov chain Monte Carlo sampling, to efficiently explore the vast parameter space of possible potentials. This method allows for the reconstruction of complex potential landscapes with high accuracy and robustness, even when experimental data is noisy or imperfect, representing a significant advance in quantum simulation.

Precisely imaging atomic potentials is difficult because atomic features are often smaller than the resolution limit of current imaging techniques. This work introduces a simple and efficient experimental protocol for measuring any potential with high precision. The protocol exploits the ability, present in some atomic species, to switch off interactions using a Feshbach resonance, simplifying the calculation of atomic evolution. By observing snapshots of the system as it evolves from a known initial state, the team accurately estimates the potential itself, proving robust to errors in state preparation and uncertainty in the atomic hopping rate.

Quantum Simulation, Tomography and Machine Learning

Research encompasses a broad range of topics related to quantum simulation, quantum state tomography, and machine learning, focusing on the use of cold atoms in optical lattices to simulate quantum systems, including models like the Hubbard and Fermi-Hubbard models. Research encompasses both analog simulation, which directly maps the Hamiltonian of a system, and digital simulation, using gate-based quantum computation. A crucial aspect of verifying simulations and characterizing quantum devices is quantum state tomography, the process of determining the quantum state of a system. Several references explore different tomography techniques, including shadow tomography, a powerful method that uses randomized measurements to efficiently reconstruct the density matrix.

Classical shadow tomography utilizes classical computation to analyse the measurement data, while partial tomography focuses on reconstructing only a subset of the density matrix for increased efficiency. Machine learning techniques are increasingly applied to quantum systems, with research focusing on learning Hamiltonians from measurement data, improving the accuracy and efficiency of state reconstruction, and characterizing quantum devices. Error mitigation and robustness are critical areas, with research exploring techniques to reduce the impact of noise on tomography and improve the robustness of simulations. Verification and validation of quantum simulations are also key concerns, with researchers developing methods to ensure the accuracy of simulation results.

A significant focus lies on simulating and characterizing fermionic systems, which are important for understanding materials science and condensed matter physics. Key techniques include random circuit sampling, randomized measurement protocols, tensor networks for representing quantum states efficiently, Rényi entropy for characterizing entanglement, and polynomial regression for learning Hamiltonians. Classical machine learning algorithms are also applied to analyse quantum data, and shadow estimation is a specific technique within shadow tomography for efficiently estimating quantum properties. Recent references highlight the current cutting edge of research.

Akhtar et al. demonstrate scalable classical shadow tomography using tensor networks, enabling more practical tomography for larger systems. Wilkens et al. focus on developing methods to verify the accuracy of quantum simulations of many-body systems. Impertro et al.

describe a crucial step towards building more sophisticated quantum simulators by achieving local readout and control of current and kinetic energy operators in optical lattices. Elben et al. explore using random quenches to extract information about quantum systems, a technique closely related to shadow tomography.

Potential Landscapes Mapped with Cold Atoms

Researchers have developed a new method for precisely measuring potential energy landscapes within ultracold atomic systems, advancing the field of quantum simulation. By leveraging the unique properties of cold atoms and employing a technique that effectively “switches off” interactions, the team demonstrated a protocol for accurately determining the potential experienced by each atom in a lattice. This achievement relies on observing the time evolution of a known initial state, allowing for a robust estimation of the potential even with imperfections in state preparation or knowledge of atomic hopping rates. The significance of this work lies in its potential to unlock more accurate and versatile quantum simulations.

Precisely controlling and characterizing the potential energy landscape is crucial for simulating complex physical systems, and this new method offers a significant improvement in precision. The researchers acknowledge that the current protocol assumes a specific type of atomic interaction that can be turned off with a Feshbach resonance, and future work could explore extending the method to systems where this is not possible. Furthermore, they suggest that this technique could be applied to benchmark quantum simulators and explore complex phenomena like many-body localization and quantum chaos.