Enhance the coherence of open two-level system through the superposition of environments

Authors

  • Jin-Chuan Sun Wuhan University

DOI:

https://doi.org/10.31349/RevMexFis.70.020401

Keywords:

Spin-boson model; superposition of environments; initial system-environment correlations; decoherence.

Abstract

Dynamics of a two-level system in the superposition of two dephasing environments with Ohmic-like spectral density is studied when considering initial system-environment correlations. The quantum system and one environment are treated as whole thermal equilibrium state, while the other environment is at thermal equilibrium state alone. Which environment the system interacts with is determined by an ancillary two-level system. When the system interacts with mixture of two sub-Ohmic environments, initial correlations can make the mixed dynamics non-Markovian. For two identical sub-Ohmic environments, if performing the projective measurement on the ancillary two-level system at the special time points, whatever the initial state of the system is, the coherence can be enhanced. For two different environments with βħω0/2>>, we get the approximate expression about the coherence of the system when measuring the ancillary two-level system.

References

A. Streltsov, G. Adesso and M. B. Plenio, Colloquium: Quantum coherence as a resource, Rev. Mod. Phys. 89 (2017) 041003. https://doi.org/10.1103/RevModPhys.89.041003

U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 2008)

H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, United States, 2002)

P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A. 52 (1995) R2493(R). https://doi.org/10.1103/PhysRevA.52.R2493

A. M. Steane, Error Correcting Codes in Quantum Theory, Phys. Rev. Lett. 77 (1996) 793. https://doi.org/10.1103/PhysRevLett.77.793

D. Gottesman, Class of quantum error-correcting codes saturating the quantum Hamming bound, Phys. Rev. A. 54 (1996) 1862. https://doi.org/10.1103/PhysRevA.54.1862

L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A. 58 (1998) 2733. https://doi.org/10.1103/PhysRevA.58.2733

L. Viola, E. Knill, and S. Lloyd, Dynamical Decoupling of Open Quantum Systems, Phys. Rev. Lett. 82 (1999) 2417. https://doi.org/10.1103/PhysRevLett.82.2417

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, Experimental Investigation of a TwoQubit Decoherence-Free Subspace, Phys. Rev. Lett. 92 (2004) 147901. https://doi.org/10.1103/PhysRevLett.92.147901

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, Experimental Verification of Decoherence-Free Subspaces, Science 290 (2000) 498-501. https://doi.org/10.1126/science.290.5491.498

R. I. Karasik, K-P. Marzlin, B. C. Sanders, and K. B. Whaley, Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences, Phys. Rev. A. 77 (2008) 052301. https://doi.org/10.1103/PhysRevA.77.052301

G. J. Milburn, Intrinsic decoherence in quantum mechanics, Phys. Rev. A. 44 (1991) 5401. https://doi.org/10.1103/PhysRevA.44.5401

A. Vidiella-Barranco and H. Moya-Cessa, Nonextensive approach to decoherence in quantum mechanics, Physics Letters A 279 (2001) 56. https://doi.org/10.1016/S0375-9601(00)00820-3

M. M. Wilde, Quantum Information Theory (Cambridge University Press, 2013), pp. 26-50

G. Chiribella and H. Kristj´ansson, Quantum Shannon theory with superpositions of trajectories, Proc. R. Soc. A. 475 (2019) 20180903. https://doi.org/10.1098/rspa.2018.0903

F. A. Jenkins and H. E. White, Fundamentals of optics (McGraw-Hill, 2001), pp. 261-263

Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman, Superpositions of Time Evolutions of a Quantum System and a Quantum Time-Translation Machine, Phys. Rev. Lett. 64 (1990) 2965. https://doi.org/10.1103/PhysRevLett.64.2965

D. K. L. Oi, Interference of Quantum Channels, Phys. Rev. Lett. 91 (2003) 067902. https://doi.org/10.1103/PhysRevLett.91.067902

G. Chiribella, Perfect discrimination of no-signalling channels via quantum superposition of causal structures, Phys. Rev. A. 86 (2012) 040301. https://doi.org/10.1103/PhysRevA.86.040301

G. Rubino, L. A. Rozema, D. Ebler et al., Experimental quantum communication enhancement by superposing trajectories, Phys. Rev. Research 3 (2021) 013093. https://doi.org/10.1103/PhysRevResearch.3.013093

G. Chiribella, G. M. D’Ariano, P. Perinotti, and B. Valiron, Quantum computations without definite causal structure, Phys. Rev. A 88 (2013) 022318. https://doi.org/10.1103/PhysRevA.88.022318

M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge University Press, 1997), pp. 494-496

N. Meher, S. Sivakumar, and P. K. Panigrahi, Duality and quantum state engineering in cavity arrays, Sci Rep 7 (2017) 9251. https://doi.org/10.1038/s41598-017-08569-8

A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Dynamics of the dissipative two-state system, Rev. Mod. Phys. 59 (1987) 1. https://doi.org/10.1103/RevModPhys.59.1

D. W. S. Carvalho, A. Foerster, and M. A. Gusmão, Coupled dynamics of interacting spin-1 bosons in a double-well potential, Phys. Rev. A 97 (2018) 033615. https://doi.org/10.1103/PhysRevA.97.033615

P. Pechukas, Reduced Dynamics Need Not Be Completely Positive, Phys. Rev. Lett. 73 (1994) 1060. https://doi.org/10.1103/PhysRevLett.73.1060

M. Ban, Decoherence of a two-level system in a coherent superposition of two dephasing environments, Quantum Inf Process 19 (2020) 409. https://doi.org/10.1007/s11128-020-02903-2

J. Luczka, Spin in contact with thermostat: exact reduced dynamics, Physica A: Statistical Mechanics and its Applications 167 (1990) 919. https://doi.org/10.1016/0378-4371(90)90299-8

V. G. Morozov, S. Mathey, and G. R¨opke, Decoherence in an exactly solvable qubit model with initial qubit-environment correlations, Phys. Rev. A 85 (2012) 022101. https://doi.org/10.1103/PhysRevA.85.022101

H.-P. Breuer, G. Amato, and B. Vacchini, Mixing-induced quantum non-Markovianity and information flow, New J. Phys. 20 (2018) 043007. https://doi.org/10.1088/1367-2630/aab2f9

T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying Coherence, Phys. Rev. Lett. 113 (2014) 140401. https://doi.org/10.1103/PhysRevLett.113.140401

Downloads

Published

2024-03-01

How to Cite

[1]
J.-C. Sun, “Enhance the coherence of open two-level system through the superposition of environments”, Rev. Mex. Fís., vol. 70, no. 2 Mar-Apr, pp. 020401 1–, Mar. 2024.

Issue

Section

04 Atomic and Molecular Physics