研究目的
To investigate the Jarzynski equality in the superconducting cavity context and find a relation between fringes visibility and free energy variation, providing an alternative path to determine Helmholtz free energy.
研究成果
The Jarzynski equality can be tested experimentally in superconducting cavities, with a direct relationship found between visibility and free energy variation. Visibility measurements can determine the work done on the cavity, offering an efficient alternative to usual state measurements. Future work could address dissipation and explore different quantum work definitions.
研究不足
The calculations are carried out without considering dissipation, so the protocol time must be small compared to the lifetime of the field in the cavity. The quantum work definition is still an open question, and the model assumes no system-environment coupling during the protocol.
1：Experimental Design and Method Selection:
The study uses a quantum harmonic oscillator model coupled to a thermal bath, implemented with cavity quantum electrodynamics (CQED). The protocol involves injecting a coherent field into the cavity, and the work is defined as the difference in the cavity's Hamiltonian at initial and final times. The Jarzynski equality is applied to relate free energy variation to work.
2：Sample Selection and Data Sources:
The system consists of N non-interacting harmonic oscillators initially in thermal equilibrium at temperature T. A superconducting microwave cavity is used, with the field state monitored via interaction with Rydberg atoms.
3：List of Experimental Equipment and Materials:
A high-Q superconducting cavity, Rydberg atoms (e.g., alkali elements), Ramsey interferometry apparatus with two Ramsey zones (R1 and R2), a detector (D), and equipment for preparing and measuring atomic states.
4：Experimental Procedures and Operational Workflow:
A Rydberg atom is prepared in a highly excited state and sent through the apparatus. It passes through Ramsey zones to prepare a superposition state, interacts dispersively with the cavity field, and is measured to obtain interference fringes visibility. The protocol time is chosen to be small compared to the cavity field lifetime to avoid dissipation.
5：Data Analysis Methods:
Mathematical derivations are used to relate visibility to free energy variation and work. Equations are solved analytically, and limiting cases (e.g., low and high temperature) are considered.
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