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Quantum thermodynamics [1] is a fast emergent new field which studies the statistical mechanical and thermodynamic properties of quantum systems, especially small systems. It goes beyond traditional textbook quantum statistical mechanics in that the quantum features pertaining to the quantum correlation, coherence, fluctuations and entanglement of a system are now of primary concern, not just the spinstatistics aspects, and the nonequilibrium dynamics of such systems occupies the center stage. It is of theoretical interest because it addresses issues at the interface of quantumclassical and micromacro domains, where traditional laws and concepts of thermodynamics are fundamentally challenged. It is of practical interest in the qubit scaleup design of quantum computers, in understanding the quantum properties of mesosystems, in the fabrication of nanomaterials, and the electromechanical properties of chemicalbiological systems such as molecular motors and engines. One exemplary investigation we carried out recently in this field is whether quantum entanglement can be maintained up to some high temperatures. This is of special interest because if it does the stringent conditions for quantum information processing can be relaxed [2]. Galve et al [3] showed that entanglement can be kept to a high temperature if the intrasystem coupling is parametrically driven. To address this issue we compare the case of a model system S of two coupled oscillators interacting with a common thermal bath [46,7] with the case when each oscillator is coupled to its own bath, kept at different temperatures [8]. After S is fully relaxed, assuming weak coupling with the bath(s), the quantum system in the former case approaches thermal equilibrium, the latter case approaches a nonequilibrium steady state (NESS). Our present study of quantum systems with bilinear and timeindependent coupling 1) proves the existence of a NESS by considering the heat transfer in the total systemenvironment complex [9] and 2) compares the entanglement at high temperatures between a system a) in equilibrium, and b) under the NESS condition. These studies serve to discern the true physical causes of a system’s ability to sustain quantum entanglement at high temperatures, if at all. * Based on J. T. Hsiang and B. L. Hu, “Quantum Entanglement at High Temperatures? I. Bosonic Systems in Nonequilibrium Steady State” (in preparation) [1] See, e.g., Gemmer, J., Michel, M., Mahler, G.: Quantum Thermodynamics. Springer, Berlin (2004) [2] V. Vedral, “Quantum Physics: Hot Entanglement” Nature 468, 769 (2010). [3] F. Galve, L.A. Pachon and D. Zueco, "Bringing entanglement to the high temperature limit", Phys. Rev. Lett. 105, 180501 (2010). [4] J. P. Paz and A. J. Roncaglia, Phys. Rev. Lett. 100, 220401 (2008) [5] S. Y. Lin and B. L. Hu, Phys. Rev. D79, 085020 (2009) [6] T. Zell, F. Queisser, and R. Klesse, Phys. Rev. Lett. 102, 160501 (2009) [7] J. Anders and A. Winter, Quantum Information and Computation, Vol. 8, No. 3&4 (2008) 0245–0262 [8] A. Ghesquiere, I. Sinayskiy and F. Petruccione, Phys. Lett. A 377, 1682 (2013). [9] J. T. Hsiang and B. L. Hu, “Nonequilibrium Steady State in Open Quantum Systems” [arXiv:1405.7642] Host: Sebastian Deffner 