Cavity assisted measurements of heat and work in optical lattices

Louis Villa1,2 and Gabriele De Chiara2

1Univ Lyon, Ens de Lyon, Univ Claude Bernard,F-69342 Lyon, France
2Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University, Belfast BT7 1NN, United Kingdom

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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.

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 strongly-interacting quantum systems, measuring the total energy is however challenging. In this paper, we show how to estimate the total internal energy of atoms in optical lattices by coupling the atoms to two optical cavities. Our result can be used for the monitoring of internal energy, work extracted and heat currents in optical lattice gases employed as working fluids for quantum thermal machines.

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