Abstract
We study the non-equilibrium dynamics of a one-dimensional system of hard core bosons (HCBs) in the presence of an onsite potential (with an alternating sign between the odd and even sites) which shows a quantum phase transition (QPT) from the superfluid (SF) phase to the so-called “Mott Insulator” (MI) phase. The ground state quantum fidelity shows a sharp dip at the quantum critical point (QCP) while the fidelity susceptibility shows a divergence right there with its scaling given in terms of the correlation length exponent of the QPT. We then study the evolution of this bosonic system following a quench in which the magnitude of the alternating potential is changed starting from zero (the SF phase) to a non-zero value (the MI phase) according to a half Rosen-Zener (HRZ) scheme or brought back to the initial value following a full Rosen-Zener (FRZ) scheme. The local von Neumann entropy density is calculated in the final MI phase (following the HRZ quench) and is found to be less than the equilibrium value (log 2) due to the defects generated in the final state as a result of the quenching starting from the QCP of the system. We also briefly dwell on the FRZ quenching scheme in which the system is finally in the SF phase through the intermediate MI phase and calculate the reduction in the supercurrent and the non-zero value of the residual local entropy density in the final state. Finally, the loss of coherence of a qubit (globally and weekly coupled to the HCB system) which is initially in a pure state is investigated by calculating the time-dependence of the decoherence factor when the HCB chain evolves under a HRZ scheme starting from the SF phase. This result is compared with that of the sudden quench limit of the half Rosen-Zener scheme where an exact analytical form of the decoherence factor can be derived.
Similar content being viewed by others
References
M. Greiner, I. Bloch, O.T.W. Mandel, T.W. Hänsch, T. Esslinger, Phys. Rev. Lett. 87, 160405 (2001)
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)
M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)
T. Stöferle, H. Moritz, C. Schori, M. Köhl, T. Esslinger, Phys. Rev. Lett. 92, 130403 (2004)
L.E. Sadler, J.M. Higbie, S.R. Leslie, M. Vengalattore, D.M. Stamper-Kurn, Nature 443, 312 (2006)
S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999)
B.K. Chakrabarti, A. Dutta, P. Sen, Quantum Ising Phases and transitions in transverse Ising Models, m41 (Springer, Heidelberg, 1996)
M.A. Continentino, Quantum Scaling in Many-Body Systems (World Scientific, Singapore, 2001)
S.L. Sondhi, S.M. Girvin, J.P. Carini, D. Shahar, Rev. Mod. Phys. 69, 315 (1997)
M. Vojta, Rep. Prog. Phys. 66, 2069 (2003)
H. Moritz, T. Stöferle, M. Köhl, T. Esslinger, Phys. Rev. Lett. 91, 250402 (2003)
L. Tonks, Phys. Rev. 50, 955 (1936)
M. Girardeu, J. Math. Phys. 1, 516 (1960)
A. Lenard, J. Math. Phys. 7, 1268 (1966)
B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G.V. Shlyapnikov, T.W. Hänsch, I. Bloch, Nature 429, 277 (2004)
T. Kinoshita, T. Wenger, D.S. Weiss, Science 305, 1125 (2004)
A. Polkovnikov, E. Altman, E. Demler, Proc. Natl. Acad. Sci. USA 103, 6125 (2006)
M.A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, M. Rigol, Rev. Mod. Phys. 83, 1405 (2011)
E. Altman, A. Auerbach, Phys. Rev. Lett. 89, 250404 (2002)
A. Polkovnikov, S. Sachdev, S.M. Girvin, Phys. Rev. A 66, 053607 (2002)
R. Schützhold, M. Uhlmann, Y. Zu, U.R. Fischer, Phys. Rev. Lett. 97, 200601 (2006)
K. Sengupta, S. Powell, S. Sachdev, Phys. Rev. A 69, 053616 (2004)
A.K. Tuchman, C. Orzel, A. Polkovnikov, M.A. Kasevich, Phys. Rev. A 74, 051601 (2006)
M. Rigol, A. Muramatsu, Phys. Rev. A 70, 031603(R) (2004)
M. Rigol, A. Muramatsu, Phys. Rev. A 72, 013604 (2005)
V.G. Rousseau, D.P. Arovas, M. Rigol, F. Hébert, G.G. Batrouni, R.T. Scalettar, Phys. Rev. B 73, 174516 (2006)
I. Klich, C. Lannert, G. Refael, Phys. Rev. Lett. 99, 205303 (2007)
A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 416, 608 (2002)
T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002)
L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)
P. Zanardi, N. Paunkovic, Phys. Rev. E 74, 031123 (2006)
S.J. Gu, Int. J. Mod. Phys. B 24, 4371 (2010)
L.C. Venuti, P. Zanardi, Phys. Rev. Lett. 99, 095701 (2007)
P. Zanardi, P. Giorda, M. Cozzini, Phys. Rev. Lett. 99, 100603 (2007)
W.-L. You, Y.-W. Li, S.-J. Gu, Phys. Rev. E 76, 022101 (2007)
S. Yang, S.-L. Gu, C.-P. Sun, H.-Q. Lin, Phys. Rev. A 78, 012304 (2008)
H.-Q. Zhou, R. Ors, G. Vidal, Phys. Rev. Lett. 100, 080601 (2008)
H. Zhou, J.P. Barjaktarevic, J. Phys. A 41, 412001 (2008)
H.-Q. Zhou, J.H. Zhao, B. Li, J. Phys. A 41, 492002 (2008)
J.-H. Zhao, H.-Q. Zhou, Phys. Rev. B 80, 014403 (2009)
V. Gritsev, A. Polkovnikov, in Understanding Quantum Phase Transitions, edited by L.D. Carr (Taylor and Francis, Boca Raton, 2010)
D. Schwandt, F. Alet, S. Capponi, Phys. Rev. Lett. 103, 170501 (2009)
A.F. Albuquerque, F. Alet, C. Sire, S. Capponi, Phys. Rev. B 81, 064418 (2010)
M.M. Rams, B. Damski, Phys. Rev. Lett. 106, 055701 (2011)
M.M. Rams, B. Damski, Phys. Rev. A 84, 032324 (2011)
R. Dillenschneider, Phys. Rev. B 78, 224413 (2008)
S. Luo, Phys. Rev. A 77, 042303 (2008)
M.S. Sarandy, Phys. Rev. A 80, 022108 (2009)
G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)
A. Kitaev, J. Preskill, Phys. Rev. Lett. 96, 110404 (2006)
W.H. Zurek, Rev. Mod. Phys. 75, 715 (2003)
E. Joos et al., Decoherence and Appearance of a Classical World in a Quantum Theory (Springer Press, Berlin, 2003)
B. Damski, T. Quan, H. Zurek, Phys. Rev. A 83, 062104 (2011)
T. Nag, U. Divakaran, A. Dutta, Phys. Rev. B 86, 020401(R) (2012)
V. Mukherjee, S. Sharma, A. Dutta, Phys. Rev. B 86, 020301 (R) (2012)
D. Rossini, T. Calarco, V. Giovannetti, S. Montangero, R. Fazio, Phys. Rev. A 75, 032333 (2007)
H.T. Quan, Z. Song, X.F. Liu, P. Zanardi, C.P. Sun, Phys. Rev. Lett. 96, 140604 (2006)
W.H. Zurek et al., Phys. Rev. Lett. 95, 105701 (2005)
A. Polkovnikov, Phys. Rev. B 72, 161201(R) (2005)
C. De Grandi, V. Gritsev, A. Polkovnikov, Phys. Rev. B 81, 012303 (2010)
C. De Grandi, V. Gritsev, A. Polkovnikov, Phys. Rev. B 81, 224301 (2010)
R.W. Cherng, L.S. Levitov, Phys. Rev. A 73, 043614 (2006)
V. Mukherjee, U. Divakaran, A. Dutta, D. Sen, Phys. Rev. B 76, 174303 (2007)
K. Sengupta, D. Sen, Phys. Rev. A 80, 032304 (2009)
T. Nag, A. Patra, A. Dutta, J. Stat. Mech. P08026 (2011)
A. Dutta, U. Divakaran, D. Sen, B.K. Chakrabarti, T.F. Rosenbaum, G. Aeppli, arXiv:1012.0653
A. Polkovnikov, K. Sengupta, A. Silva, M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011)
J. Dziarmaga, Adv. Phys. 59, 1063 (2010)
N. Rosen, C. Zener, Phys. Rev. 40, 502 (1932)
R.T. Robiscoe, Phys. Rev. A 17, 247 (1978)
C. Zener, Proc. Roy. Soc. London Ser. A 137, 696 (1932)
L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, 2nd edn. (Pergamon Press, Oxford, 1965)
E. Lieb, T. Schultz, D. Mattis, Ann. Phys. 16, 407 (1961)
A. Polkovnikov, Ann. Phys. 326, 486 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Roy, S., Nag, T. & Dutta, A. Fidelity, Rosen-Zener dynamics, entropy and decoherence in one dimensional hard-core bosonic systems. Eur. Phys. J. B 86, 204 (2013). https://doi.org/10.1140/epjb/e2013-40052-1
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2013-40052-1