Abstract
In this thesis we have studied equilibrium and nonequilibrium aspects of continuous phase transitions in distinct systems. We have made special emphasis on their nonequilibrium features, a much less understood topic than their static counterparts, aiming to elucidate questions such as to what extent the well-established universal static properties apply to the dynamics.
Keywords
- Nonequilibrium Aspects
- Continuous Phase Transition
- Nonequilibrium Features
- Lipkin Meshkov Glick Model
- Long-range Ising Model
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R. Puebla, R. Nigmatullin, T.E. Mehlstäubler, M.B. Plenio, Fokker-Planck formalism approach to Kibble-Zurek scaling laws and nonequilibrium dynamics. Phys. Rev. B 95, 134104 (2017a). https://doi.org/10.1103/PhysRevB.95.134104
M.-J. Hwang, R. Puebla, M.B. Plenio, Quantum phase transition and universal dynamics in the Rabi model. Phys. Rev. Lett. 115, 180404 (2015). https://doi.org/10.1103/PhysRevLett.115.180404
R. Puebla, M.-J. Hwang, M.B. Plenio, Excited-state quantum phase transition in the Rabi model. Phys. Rev. A 94, 023835 (2016a). https://doi.org/10.1103/PhysRevA.94.023835
R. Puebla, J. Casanova, M.B. Plenio, A robust scheme for the implementation of the quantum Rabi model in trapped ions. New J. Phys. 18, 113039 (2016b), http://stacks.iop.org/1367-2630/18/i=11/a=113039
R. Puebla, M.-J. Hwang, J. Casanova, M.B. Plenio, Probing the dynamics of a superradiant quantum phase transition with a single trapped ion. Phys. Rev. Lett. 118, 073001 (2017b). https://doi.org/10.1103/PhysRevLett.118.073001
L.D. Landau, E.M. Lifshitz, Statistical Physics, 3rd edn. (Butterworth-Heinemann, Oxford, 1980)
D.H.E. Dubin, T.M. O’Neil, Trapped nonneutral plasmas, liquids, and crystals (the thermal equilibrium states). Rev. Mod. Phys. 71, 87 (1999). https://doi.org/10.1103/RevModPhys.71.87
R.C. Thompson, Ion Coulomb crystals. Cont. Phys. 56, 63 (2015). https://doi.org/10.1080/00107514.2014.989715
P. Laguna, W.H. Zurek, Density of kinks after a quench: when symmetry breaks, how big are the pieces? Phys. Rev. Lett. 78, 2519 (1997). https://doi.org/10.1103/PhysRevLett.78.2519
P. Laguna, W.H. Zurek, Critical dynamics of symmetry breaking: quenches, dissipation, and cosmology. Phys. Rev. D 58, 085021 (1998). https://doi.org/10.1103/PhysRevD.58.085021
E. Moro, G. Lythe, Dynamics of defect formation. Phys. Rev. E 59, R1303(R) (1999). https://doi.org/10.1103/PhysRevE.59.R1303
G. De Chiara, A. del Campo, G. Morigi, M.B. Plenio, A. Retzker, Spontaneous nucleation of structural defects in inhomogeneous ion chains. New J. Phys. 12, 115003 (2010), http://stacks.iop.org/1367-2630/12/i=11/a=115003
A. del Campo, A. Retzker, M.B. Plenio, The inhomogeneous Kibble-Zurek mechanism: vortex nucleation during Bose-Einstein condensation. New J. Phys. 13, 083022 (2011), http://stacks.iop.org/1367-2630/13/i=8/a=083022
A. del Campo, G. De Chiara, G. Morigi, M.B. Plenio, A. Retzker, Structural defects in ion chains by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism. Phys. Rev. Lett. 105, 075701 (2010). https://doi.org/10.1103/PhysRevLett.105.075701
R. Nigmatullin, A. del Campo, G. De Chiara, G. Morigi, M.B. Plenio, A. Retzker, Formation of helical ion chains. Phys. Rev. B 93, 014106 (2016). https://doi.org/10.1103/PhysRevB.93.014106
K. Pyka, J. Keller, H.L. Partner, R. Nigmatullin, T. Burgermeister, D.M. Meier, K. Kuhlmann, A. Retzker, M.B. Plenio, W.H. Zurek, A. del Campo, T.E. Mehlstäubler, Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals. Nat. Commun. 4, 2291 (2013). https://doi.org/10.1038/ncomms3291
S. Ulm, J. Roßnagel, G. Jacob, C. Degünther, S.T. Dawkins, U.G. Poschinger, R. Nigmatullin, A. Retzker, M.B. Plenio, F. Schmidt-Kaler, K. Singer, Observation of the Kibble–Zurek scaling law for defect formation in ion crystals, Nat. Commun. 4, 2290 (2013). https://doi.org/10.1038/ncomms3290
C. Jarzynski, Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690 (1997). https://doi.org/10.1103/PhysRevLett.78.2690
G.E. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Phys. Rev. E 60, 2721 (1999). https://doi.org/10.1103/PhysRevE.60.2721
T.M. Hoang, H.M. Bharath, M.J. Boguslawski, M. Anquez, B.A. Robbins, M.S. Chapman, Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition. Proc. Natl. Acad. Sci. 113, 9475 (2016). https://doi.org/10.1073/pnas.1600267113
F. Cosco, M. Borrelli, P. Silvi, S. Maniscalco, G. De Chiara, Nonequilibrium quantum thermodynamics in Coulomb crystals. Phys. Rev. A 95, 063615 (2017). https://doi.org/10.1103/PhysRevA.95.063615
S. Deffner, Kibble-Zurek scaling of the irreversible entropy production. Phys. Rev. E 96, 052125 (2017). https://doi.org/10.1103/PhysRevE.96.052125
L.P. Kadanoff, More is the same; phase transitions and mean field theories. J. Stat. Phys. 137, 777 (2009). https://doi.org/10.1007/s10955-009-9814-1
M.O. Scully, M.S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997)
A.P. Hines, C.M. Dawson, R.H. McKenzie, G.J. Milburn, Entanglement and bifurcations in Jahn-Teller models. Phys. Rev. A 70, 022303 (2004). https://doi.org/10.1103/PhysRevA.70.022303
G. Levine, V.N. Muthukumar, Entanglement of a qubit with a single oscillator mode. Phys. Rev. B 69, 113203 (2004). https://doi.org/10.1103/PhysRevB.69.113203
S. Ashhab, F. Nori, Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states. Phys. Rev. A 81, 042311 (2010). https://doi.org/10.1103/PhysRevA.81.042311
L. Bakemeier, A. Alvermann, H. Fehske, Quantum phase transition in the Dicke model with critical and noncritical entanglement. Phys. Rev. A 85, 043821 (2012). https://doi.org/10.1103/PhysRevA.85.043821
S. Ashhab, Superradiance transition in a system with a single qubit and a single oscillator. Phys. Rev. A 87, 013826 (2013). https://doi.org/10.1103/PhysRevA.87.013826
R.H. Dicke, Coherence in spontaneous radiation processes. Phys. Rev. 93, 99 (1954). https://doi.org/10.1103/PhysRev.93.99
H. Lipkin, N. Meshkov, A. Glick, Validity of many-body approximation methods for a solvable model. Nucl. Phys. 62, 188 (1965). https://doi.org/10.1016/0029-5582(65)90862-X
C. Emary, T. Brandes, Quantum chaos triggered by precursors of a quantum phase transition: the Dicke model. Phys. Rev. Lett 90, 044101 (2003a). https://doi.org/10.1103/PhysRevLett.90.044101
C. Emary, T. Brandes, Chaos and the quantum phase transition in the Dicke model. Phys. Rev. E 67, 66203 (2003b). https://doi.org/10.1103/PhysRevE.67.066203
N. Lambert, C. Emary, T. Brandes, Entanglement and the phase transition in single-mode superradiance. Phys. Rev. Lett. 92, 073602 (2004). https://doi.org/10.1103/PhysRevLett.92.073602
N. Lambert, C. Emary, T. Brandes, Entanglement and entropy in a spin-boson quantum phase transition. Phys. Rev. A 71, 053804 (2005). https://doi.org/10.1103/PhysRevA.71.053804
P. Ribeiro, J. Vidal, R. Mosseri, Thermodynamical limit of the Lipkin-Meshkov-Glick model. Phys. Rev. Lett. 99, 050402 (2007). https://doi.org/10.1103/PhysRevLett.99.050402
P. Ribeiro, J. Vidal, R. Mosseri, Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections. Phys. Rev. E 78, 021106 (2008). https://doi.org/10.1103/PhysRevE.78.021106
P. Cejnar, M. Macek, S. Heinze, J. Jolie, J. Dobes, Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei. J. Phys. A Math. Theor. 39, L515 (2006), http://stacks.iop.org/0305-4470/39/i=31/a=L01
P. Cejnar, P. Stránský, Impact of quantum phase transitions on excited-level dynamics. Phys. Rev. E 78, 031130 (2008). https://doi.org/10.1103/PhysRevE.78.031130
M. Caprio, P. Cejnar, F. Iachello, Excited state quantum phase transitions in many-body systems. Ann. Phys. (N.Y.) 323, 1106 (2008). https://doi.org/10.1016/j.aop.2007.06.011
T. Caneva, R. Fazio, G.E. Santoro, Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model. Phys. Rev. B 78, 104426 (2008). https://doi.org/10.1103/PhysRevB.78.104426
O.L. Acevedo, L. Quiroga, F.J. Rodríguez, N.F. Johnson, New dynamical scaling universality for quantum networks across adiabatic quantum phase transitions. Phys. Rev. Lett. 112, 030403 (2014). https://doi.org/10.1103/PhysRevLett.112.030403
S. van Frank, M. Bonneau, J. Schmiedmayer, S. Hild, C. Gross, M. Cheneau, I. Bloch, T. Pichler, A. Negretti, T. Calarco, S. Montangero, Optimal control of complex atomic quantum systems. Sci. Rep. 6, 34187 (2016). https://doi.org/10.1038/srep34187
R. Barankov, A. Polkovnikov, Optimal nonlinear passage through a quantum critical point. Phys. Rev. Lett. 101, 076801 (2008). https://doi.org/10.1103/PhysRevLett.101.076801
E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, J.G. Muga, in Advances In Atomic, Molecular, and Optical Physics, vol. 62, ed. by E. Arimondo, P.R. Berman, C.C. Lin (Academic Press, 2013), pp. 117–169. https://doi.org/10.1016/B978-0-12-408090-4.00002-5
V.M. Bastidas, C. Emary, B. Regler, T. Brandes, Nonequilibrium quantum phase transitions in the Dicke model. Phys. Rev. Lett. 108, 043003 (2012). https://doi.org/10.1103/PhysRevLett.108.043003
M.-J. Hwang, P. Rabl, M.B. Plenio, Dissipative phase transition in the open quantum Rabi model. Phys. Rev. A 97, 013825 (2018). https://doi.org/10.1103/PhysRevA.97.013825
M.-J. Hwang, M.B. Plenio, Quantum phase transition in the finite Jaynes-Cummings lattice systems. Phys. Rev. Lett. 117, 123602 (2016). https://doi.org/10.1103/PhysRevLett.117.123602
M. Liu, S. Chesi, Z.-J. Ying, X. Chen, H.-G. Luo, H.-Q. Lin, Universal scaling and critical exponents of the anisotropic quantum Rabi model. Phys. Rev. Lett. 119, 220601 (2017). https://doi.org/10.1103/PhysRevLett.119.220601
D. Nagy, P. Domokos, Nonequilibrium quantum criticality and non-Markovian environment: critical exponent of a quantum phase transition. Phys. Rev. Lett. 115, 043601 (2015). https://doi.org/10.1103/PhysRevLett.115.043601
D. Nagy, P. Domokos, Critical exponent of quantum phase transitions driven by colored noise. Phys. Rev. A 94, 063862 (2016). https://doi.org/10.1103/PhysRevA.94.063862
D. Patanè, A. Silva, L. Amico, R. Fazio, G.E. Santoro, Adiabatic dynamics in open quantum critical many-body systems. Phys. Rev. Lett. 101, 175701 (2008). https://doi.org/10.1103/PhysRevLett.101.175701
D. Patanè, L. Amico, A. Silva, R. Fazio, G.E. Santoro, Adiabatic dynamics of a quantum critical system coupled to an environment: scaling and kinetic equation approaches. Phys. Rev. B 80, 024302 (2009). https://doi.org/10.1103/PhysRevB.80.024302
P. Nalbach, Adiabatic-Markovian bath dynamics at avoided crossings. Phys. Rev. A 90, 042112 (2014). https://doi.org/10.1103/PhysRevA.90.042112
P. Nalbach, S. Vishveshwara, A.A. Clerk, Quantum Kibble-Zurek physics in the presence of spatially correlated dissipation. Phys. Rev. B 92, 014306 (2015). https://doi.org/10.1103/PhysRevB.92.014306
N.K. Langford, R. Sagastizabal, M. Kounalakis, C. Dickel, A. Bruno, F. Luthi, D.J. Thoen, A. Endo, L. DiCarlo, Experimentally simulating the dynamics of quantum light and matter at deep-strong coupling. Nat. Comm. 8, 1715 (2017). https://doi.org/10.1038/s41467-017-01061-x
P. Schneeweis, A. Dareau, C. Sayrin, Cold-atom based implementation of the quantum Rabi model (2017). arXiv:1706.07781
M. Abdi, M.-J. Hwang, M. Aghtar, M.B. Plenio, Spin-mechanical scheme with color centers in hexagonal boron nitride membranes. Phys. Rev. Lett. 119, 233602 (2017). https://doi.org/10.1103/PhysRevLett.119.233602
B. Damski, The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective. Phys. Rev. Lett. 95, 035701 (2005). https://doi.org/10.1103/PhysRevLett.95.035701
W.H. Zurek, U. Dorner, P. Zoller, Dynamics of a quantum phase transition. Phys. Rev. Lett. 95, 105701 (2005). https://doi.org/10.1103/PhysRevLett.95.105701
J. Dziarmaga, Dynamics of a quantum phase transition: exact solution of the quantum Ising model. Phys. Rev. Lett. 95, 245701 (2005). https://doi.org/10.1103/PhysRevLett.95.245701
A. Polkovnikov, Universal adiabatic dynamics in the vicinity of a quantum critical point. Phys. Rev. B 72, 161201 (2005). https://doi.org/10.1103/PhysRevB.72.161201
L.W. Clark, L. Feng, C. Chin, Universal space-time scaling symmetry in the dynamics of bosons across a quantum phase transition. Science 354, 606 (2016). https://doi.org/10.1126/science.aaf9657
M. Anquez, B.A. Robbins, H.M. Bharath, M. Boguslawski, T.M. Hoang, M.S. Chapman, Quantum Kibble-Zurek mechanism in a spin-1 Bose-Einstein condensate. Phys. Rev. Lett. 116, 155301 (2016). https://doi.org/10.1103/PhysRevLett.116.155301
D. Leibfried, R. Blatt, C. Monroe, D. Wineland, Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281 (2003). https://doi.org/10.1103/RevModPhys.75.281
A. Friedenauer, H. Schmitz, J.T. Glueckert, D. Porras, T. Schaetz, Simulating a quantum magnet with trapped ions. Nat. Phys. 4, 757 (2008). https://doi.org/10.1038/nphys1032
K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E.E. Edwards, J.K. Freericks, G.-D. Lin, L.-M. Duan, C. Monroe, Quantum simulation of frustrated Ising spins with trapped ions. Nature 465, 590 (2010). https://doi.org/10.1038/nature09071
R. Islam, E.E. Edwards, K. Kim, S. Korenblit, C. Noh, H. Carmichael, G.-D. Lin, L.-M. Duan, C.-C. Joseph Wang, J.K. Freericks, C. Monroe, Onset of a quantum phase transition with a trapped ion quantum simulator. Nat. Commun. 2, 377 (2011). https://doi.org/10.1038/ncomms1374
R. Islam, C. Senko, W.C. Campbell, S. Korenblit, J. Smith, A. Lee, E.E. Edwards, C.-C.J. Wang, J.K. Freericks, C. Monroe, Emergence and frustration of magnetism with variable-range interactions in a quantum simulator. Science 340, 583 (2013). https://doi.org/10.1126/science.1232296
J. Zhang, P.W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I.-D. Potirniche, A.C. Potter, A. Vishwanath, N.Y. Yao, C. Monroe, Observation of a discrete time crystal. Nature 543, 217 (2017a). https://doi.org/10.1038/nature21413
P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B.P. Lanyon, M. Heyl, R. Blatt, C.F. Roos, Direct observation of dynamical quantum phase transitions in an interacting many-body system. Phys. Rev. Lett. 119, 080501 (2017). https://doi.org/10.1103/PhysRevLett.119.080501
J. Zhang, G. Pagano, P.W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A.V. Gorshkov, Z.-X. Gong, C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601 (2017b). https://doi.org/10.1038/nature24654
U. Schollwöck, The density-matrix renormalization group in the age of matrix product states. Ann. Phys. (N.Y.) 326, 96 (2011). https://doi.org/10.1016/j.aop.2010.09.012
D. Jaschke, K. Maeda, J.D. Whalen, M.L. Wall, L.D. Carr, Critical phenomena and Kibble-Zurek scaling in the long-range quantum Ising chain. New J. Phys. 19, 033032 (2017), http://stacks.iop.org/1367-2630/19/i=3/a=033032
T. Koffel, M. Lewenstein, L. Tagliacozzo, Entanglement entropy for the long-range Ising chain in a transverse field. Phys. Rev. Lett. 109, 267203 (2012). https://doi.org/10.1103/PhysRevLett.109.267203
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Puebla, R. (2018). Concluding Remarks and Outlook. In: Equilibrium and Nonequilibrium Aspects of Phase Transitions in Quantum Physics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-00653-2_7
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