Abstract
We propose a method to experimentally measure the internal energy of a system of ultracold atoms trapped in optical lattices by coupling them to the fields of two optical cavities. We show that the tunnelling and self-interaction terms of the one-dimensional Bose-Hubbard Hamiltonian can be mapped to the field and photon number of each cavity, respectively. We compare the energy estimated using this method with numerical results obtained using the density matrix renormalisation group algorithm. Our method can be employed for the assessment of power and efficiency of thermal machines whose working substance is a strongly correlated many-body system.
Highlights
The precise measurement of energy of a physical system during a thermodynamic process is necessary for assessing the power and efficiency of thermal engines and refrigerators
For classical systems undergoing a transformation under the influence of an external force and in contact to an external reservoir the first law of thermodynamics establishes the balance of the internal energy ∆Uint, the work W done or extracted from the system and the heat Q exchanged with the reservoir:
For quantum systems a similar relation holds provided that we identify the internal energy of the system with the mean value of the Hamiltonian HS governing its dynamics: Uint = Tr(ρHS) where ρ is the density matrix of the system
Summary
The precise measurement of energy of a physical system during a thermodynamic process is necessary for assessing the power and efficiency of thermal engines and refrigerators. Its realisation in a nuclear magnetic resonant experiment allowed for the first experimental verification of the Jarzynski equality [21] in a quantum setting [22] Another scheme has been proposed which would be suitable for atomic ensembles and dimers in optical lattices and it involves coupling the atoms to the polarisation of a light mode [23]. We review the concepts of heat and work in quantum systems
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