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We explore the potential of a spin-orbit coupled Bose-Einstein condensate for thermodynamic cycles. For this purpose we propose a quantum heat engine based on a condensate with spin-orbit and Zeeman coupling as a working medium. The cooling and heating are simulated by contacts of the condensate with an external magnetized media and demagnetized media. We examine the condensate ground state energy and its dependence on the strength of the synthetic spin-orbit and Zeeman couplings and interatomic interaction. Then we study the efficiency of the proposed engine. The cycle has a critical value of spin-orbit coupling related to the engine maximum efficiency.

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