Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System (1409.4485v2)

Abstract: The past two decades witnessed important developments in the field of non-equilibrium statistical mechanics. Among these developments, the Jarzynski equality, being a milestone following the landmark work of Clausius and Kelvin, stands out. The Jarzynski equality relates the free energy difference between two equilibrium states and the work done on the system through far from equilibrium processes. While experimental tests of the equality have been performed in classical regime, the verification of the quantum Jarzynski equality has not yet been fully demonstrated due to experimental challenges. Here, we report an experimental test of the quantum Jarzynski equality with a single \Yb ion trapped in a harmonic potential. We perform projective measurements to obtain phonon distributions of the initial thermal state. Following that we apply the laser induced force on the projected energy eigenstate, and find transition probabilities to final energy eigenstates after the work is done. By varying the speed of applying the force from equilibrium to far-from equilibrium regime, we verified the quantum Jarzynski equality in an isolated system.

• The paper experimentally validates the quantum Jarzynski equality using projective measurements on a single 171Yb ion.
• It employs laser-induced forces to drive the ion from equilibrium to far-from-equilibrium states, enabling accurate work and free energy measurements.
• Results confirm the equality’s robustness across regimes, highlighting its importance for advancing quantum thermodynamics and engine design.

Experimental Verification of Quantum Jarzynski Equality Using Trapped Ions

The paper "Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System" presents an empirical evaluation of the quantum Jarzynski equality using a ^{171}Yb ion confined in a harmonic potential. This paper addresses one of the fundamental challenges in quantum thermodynamics: the experimental validation of non-equilibrium statistical mechanics principles in the quantum domain.

Summary and Methodology

The Jarzynski equality offers a profound relation connecting the free energy difference between two equilibrium states with the work done during a non-equilibrium process. While its verification is extensively demonstrated in classical systems, establishing its validity in quantum systems poses significant experimental obstacles, primarily due to quantum measurement constraints imposed by Heisenberg's uncertainty principle.

In this work, the authors overcome these challenges by utilizing projective measurements on a single trapped ion, which allows them to capture the transitions between energy eigenstates. They employ laser-induced forces to manipulate the ion from equilibrium to far-from-equilibrium conditions, thereby enabling the testing of the Jarzynski equality in isolated quantum systems.

The experiment comprises four key stages:

1. Preparation of the trapped ion in a thermal state.
2. Projection of this state onto an energy eigenstate using projective measurements.
3. Application of work by exerting a laser-induced force.
4. Measurement of the final phonon distribution to determine the work distribution.

Through these stages, the authors verify the quantum Jarzynski equality by calculating the exponentiated average of the work done on the system and comparing it to the free energy difference, demonstrating consistency across various conditions.

Numerical Results and Implications

The paper presents a rigorous comparison between the Jarzynski equality and other thermodynamic identities, such as the Fluctuation-Dissipation theorem, across different experiment scenarios including temperatures and work application speeds. Remarkably, the results substantiate the Jarzynski equality over broader regimes, even in far-from-equilibrium processes where traditional approaches like average work fail to accurately estimate free energy differences.

The experimental setup achieves high precision in controlling quantum states through projective phonon measurements, ultimately delivering accurate work distribution profiles. The distribution reflects non-Gaussian characteristics attributed to quantum mechanical nature, particularly at low initial temperatures.

Practical and Theoretical Implications

The implications of this research are multifaceted:

• Empirical Validation: It provides a firm experimental basis for the quantum Jarzynski equality, enhancing our understanding of quantum thermodynamics.
• Technological Advancements: The methodology paves the way for further exploration of quantum fluctuation theorems and related principles.
• Quantum Heat Engines: Insights from this paper could be imperative in designing efficient quantum engines, maximizing work extraction from quantum systems.

Speculation on Future Developments

Given the burgeoning interest in quantum computation and information theory, advancements in this line of research may lead to substantial progress in simulating and understanding complex quantum systems under non-equilibrium conditions. Future endeavors will likely involve expanding such experimental validations to open quantum systems where environmental interactions play a crucial role, thereby bridging the gap between theory and application in quantum thermodynamic cycles.

In summary, this paper's rigorous experimental validation of the quantum Jarzynski equality not only strengthens the theoretical landscape of quantum thermodynamics but also catalyzes potential applications in quantum technologies, presenting a significant stride forward in the practical exploration of quantum statistical mechanics.