Abstract
We introduce a quantum heat engine performing an Otto cycle by using the thermal properties of the quantum vacuum. Since Hawking and Unruh, it has been established that the vacuum space, either near a black hole or for an accelerated observer, behaves as a bath of thermal radiation. In this work, we present a fully quantum Otto cycle, which relies on the Unruh effect for a single quantum bit (qubit) in contact with quantum vacuum fluctuations. By using the notions of quantum thermodynamics and perturbation theory we obtain that the quantum vacuum can exchange heat and produce work on the qubit. Moreover, we obtain the efficiency and derive the conditions to have both a thermodynamic and a kinematic cycle in terms of the initial populations of the excited state, which define a range of allowed accelerations for the Unruh engine.
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References
J. Gemmer, M. Michel and G. Mahler, Quantum Thermodynamics: Emergence of Thermodynamic Behavior Within Composite Quantum Systems, Lect. Notes Phys. 657, Springer-Verlag, Berlin Heidelberg, Germany (2004).
J. Goold, M. Huber, A. Riera, L. del Rio and P. Skrzypczyk, The role of quantum information in thermodynamics — a topical review, J. Phys. A 49 (2016) 143001.
K. Maruyama, F. Nori and V. Vedral, Colloquium: The physics of Maxwell’s demon and information, Rev. Mod. Phys. 81 (2009) 1 [INSPIRE].
H.E.D. Scovil and E.O. Schulz-DuBois, Three-level masers as heat engines, Phys. Rev. Lett. 2 (1959) 262.
T.D. Kieu, The second law, Maxwell’s demons, and work derivable from quantum heat engines, Phys. Rev. Lett. 93 (2004) 140403.
T.D. Kieu, Quantum heat engines, the second law and Maxwell’s daemon, Eur. Phys. J. D 39 (2006) 115.
T. Zhang, W.-T. Liu, P.-X. Chen and C.-Z. Li, Four-level entangled quantum heat engines, Phys. Rev. A 75 (2007) 062102.
G.-F. Zhang, Entangled quantum heat engines based on two two-spin systems with Dzyaloshinski-Moriya anisotropic antisymmetric inteaction, Eur. Phys. J. D 49 (2008) 123.
H. Wang, S. Liu and J. He, Thermal entanglement in two-atom cavity QED and the entangled quantum Otto engine, Phys. Rev. E 79 (2009) 041113.
J.M. Bardeen, B. Carter and S.W. Hawking, The four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
S.W. Hawking, Black hole explosions, Nature 248 (1974) 30 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
S.W. Hawking, Black Holes and Thermodynamics, Phys. Rev. D 13 (1976) 191 [INSPIRE].
N.D. Birrell and P.C.W. Davis, Quantum Fields in Curved Space, Cambridge University Press, New York, U.S.A. (1982).
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
S. Felicetti, C. Sabín, I. Fuentes, L. Lamata, G. Romero and E. Solano, Relativistic Motion with Superconducting Qubits, Phys. Rev. B 92 (2015) 064501 [arXiv:1503.06653] [INSPIRE].
J. Rodríguez-Laguna, L. Tarruell, M. Lewenstein and A. Celi, Synthetic Unruh effect in cold atoms, Phys. Rev. A 95 (2017) 013627 [arXiv:1606.09505] [INSPIRE].
J. Wang, Z. Tian, J. Jing and H. Fan, Quantum metrology and estimation of Unruh effect, Sci. Rep. 4 (2014) 7195.
D.V. Ahluwalia, L. Labun and G. Torrieri, The Unruh effect and oscillating neutrinos, J. Phys. Conf. Ser. 706 (2016) 042006 [arXiv:1505.04082] [INSPIRE].
G. Cozzella, A.G.S. Landulfo, G.E.A. Matsas and D.A.T. Vanzella, Proposal for Observing the Unruh Effect using Classical Electrodynamics, Phys. Rev. Lett. 118 (2017) 161102 [arXiv:1701.03446] [INSPIRE].
L.C.B. Crispino, A. Higuchi and G.E.A. Matsas, The Unruh effect and its applications, Rev. Mod. Phys. 80 (2008) 787 [arXiv:0710.5373] [INSPIRE].
B.S. DeWitt, General relativity, an Einstein centenary survey, S.W. Hawking and W. Israel eds., Cambridge University Press, U.K. (1979).
B.F. Svaiter and N.F. Svaiter, Inertial and noninertial particle detectors and vacuum fluctuations, Phys. Rev. D 46 (1992) 5267 [INSPIRE].
A. Higuchi, G.E.A. Matsas and C.B. Peres, Uniformly accelerated finite time detectors, Phys. Rev. D 48 (1993) 3731 [INSPIRE].
M. Campisi, P. Hänggi and P. Talkner, Colloquium: Quantum fluctuations relations: Foundations and applications, Rev. Mod. Phys. 83 (2011) 771 [arXiv:1012.2268].
R.A. Horn and C.R. Johnson, Matrix Analysis, 2nd Edition, Cambridge University Press, New York, NY, U.S.A. (2013).
M. Born and V. Fock, Beweis des Adiabatensatzes, Z. Phys. 51 (1928) 165.
T. Kato, On the adiabatic theorem of quantum mechanics, J. Phys. Soc. Jap. 5 (1950) 435.
A. Messiah, Quantum mechanics, North-Holland, Amsterdam, The Netherlands (1962).
W. Niedenzu, V. Mukherjee, A. Ghosh, A.G. Kofman, G. Kurizki, Quantum engine efficiency bound beyond the second law of thermodynamics, Nature Commun. 9 (2018) 165 [arXiv:1703.02911].
J. Doukas, S.-Y. Lin, B.L. Hu and R.B. Mann, Unruh Effect under Non-equilibrium conditions: Oscillatory motion of an Unruh-DeWitt detector, JHEP 11 (2013) 119 [arXiv:1307.4360] [INSPIRE].
E.G. Brown and J. Louko, Smooth and sharp creation of a Dirichlet wall in 1+1 quantum field theory: how singular is the sharp creation limit?, JHEP 08 (2015) 061 [arXiv:1504.05269] [INSPIRE].
G. Salton, R.B. Mann and N.C. Menicucci, Acceleration-assisted entanglement harvesting and rangefinding, New. J. Phys. 17 (2015) 035001.
S. Deffner and E. Lutz, Nonequilibrium entropy productionfor open quantum systems, Phys. Rev. Lett. 107 (2011) 140404. Phys. Rev. Lett. 107 (2011) 140404 [arXiv:1103.4775].
S.D. Fisher, Complex Variables, second edition, Dover, U.S.A. (1999).
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Arias, E., de Oliveira, T.R. & Sarandy, M.S. The Unruh quantum Otto engine. J. High Energ. Phys. 2018, 168 (2018). https://doi.org/10.1007/JHEP02(2018)168
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DOI: https://doi.org/10.1007/JHEP02(2018)168