Measurement of linear response functions in Nuclear Magnetic Resonance

Area of Science:

• Quantum Information Science
• Magnetic Resonance Spectroscopy
• Quantum Computing

Background:

• Linear response functions are crucial for characterizing system dynamics and calculating physical quantities like magnetic susceptibility.
• Quantum systems, particularly two-level systems, are fundamental building blocks in quantum information processing and condensed matter physics.
• Measuring multi-time correlation functions provides deeper insights into quantum dynamics beyond traditional methods.

Purpose of the Study:

• To measure multi-time correlation functions of Pauli operators on a two-level system.
• To demonstrate the retrieval of linear response functions from these correlations.
• To explore the computation of higher-order time correlation functions using quantum information techniques.

Main Methods:

• Utilized a two-level system constructed from nuclear spins (¹H and ¹³C) in chloroform.
• Employed techniques from quantum information, including an ancillary qubit and controlled operations.
• Measured multi-time correlation functions, including three-time correlations and fixed-time correlations up to tenth order.

Main Results:

• Successfully measured multi-time correlation functions on the defined two-level system.
• Demonstrated the capability to compute linear response functions from the measured correlations.
• Showcased the quantum platform's ability to calculate arbitrary-order time correlation functions.

Conclusions:

• The developed quantum information approach effectively measures multi-time correlation functions for linear response analysis.
• This method provides a pathway for computing higher-order correlations, relevant for advanced perturbative theories.
• The study highlights the potential of quantum platforms for sophisticated calculations in quantum dynamics.