Skip to main content
Log in

Simulation of the spin-boson model with superconducting phase qubit coupled to a transmission line

  • Article
  • Progress of Projects Supported by NSFC
  • Published:
Science China Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

Based on the rapid experimental developments of circuit QED, we propose a feasible scheme to simulate the spin-boson model with superconducting circuits, which can be used to detect quantum Kosterlitz-Thouless (KT) phase transition. We design the spinboson model by using a superconducting phase qubit coupled to a semi-infinite transmission line, which is regarded as a bosonic reservoir with a continuum spectrum. By tuning the bias current or the coupling capacitance, the quantum KT transition can be directly detected through tomography measurement on the states of the phase qubit. We also estimate the experimental parameters using the numerical renormalization group method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Feynman R P. Simulating physics with computers. Int J Theor Phys, 1982, 21 (6-7): 467–488

    Article  MathSciNet  Google Scholar 

  2. Sachdev S. Quantum Phase Transitions. Cambridge: Cambridge University Press, 1999

    Google Scholar 

  3. Leggett A J, Chakravarty S, Dorsey A T, et al. Dynamics of the dissipative two-state system. Rev Mod Phys, 1987, 59 (1): 1–85

    Article  ADS  Google Scholar 

  4. Weiss U. Quantum Dissipative Systems. 2nd ed. Singapore: World Scientific, 1999

    Book  MATH  Google Scholar 

  5. Bulla R, Costi T A, Pruschke T. Numerical renormalization group method for quantum impurity systems. Rev Mod Phys, 2008, 80 (2): 395–450

    Article  ADS  Google Scholar 

  6. Bulla R, Lee H J, Tong N H, et al. Numerical renormalization group for quantum impurities in a bosonic bath. Phys Rev B, 2005, 71(4): 045122

    Article  ADS  Google Scholar 

  7. Tong N H, Vojta M. Signatures of a noise-induced quantum phase transition in a mesoscopic metal ring. Phys Rev Lett, 2006, 97 (1): 016802

    Article  ADS  Google Scholar 

  8. Hur K L. Coulomb blockade of a noisy metallic box: A realization of Bose-Fermi kondo models. Phys Rev Lett, 2004, 92 (19): 196804

    Article  Google Scholar 

  9. Furusaki A, Matveev K A. Occupation of a resonant level coupled to a chiral luttinger liquid. Phys Rev Lett, 2002, 88 (22): 226404

    Article  ADS  Google Scholar 

  10. Orth P P, Stanic I, Hur K L. Dissipative quantum Ising model in a coldatom spin-boson mixture. Phys Rev A, 2008, 77 (5): 051601

    Article  ADS  Google Scholar 

  11. Kopp A, Hur K L. Universal and measurable entanglement entropy in the spin-boson model. Phys Rev Lett, 2007, 98(22): 220401; Hur K L, Doucet-Beaupré P, Hofstetter W. Entanglement and criticality in quantum impurity systems. Phys Rev Lett, 2007, 99 (12): 126801

    Article  ADS  Google Scholar 

  12. Makhlin Y, Schön G, Shnirman A. Quantum-state engineering with Josephson-junction devices. Rev Mod Phys, 2001, 73 (2): 357–400

    Article  ADS  Google Scholar 

  13. You J Q, Nori F. Superconducting circuits and quantum information. Phys Tod, 2005, 58 (11): 42–47

    Article  Google Scholar 

  14. Yu Y, Han S Y, Chu X, et al. Coherent temporal oscillations of macroscopic quantum states in a Josephson junction. Science, 2002, 296: 889–892; Yu Y, Zhu S L, Sun G, et al. Quantum jumps between macroscopic quantum states of a superconducting qubit coupled to a microscopic two-level system. Phys Rev Lett, 2008, 101 (15): 157001

    Article  ADS  Google Scholar 

  15. Blais A, Huang R S, Wallraff A, et al. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation. Phys Rev A, 2004, 69 (6): 062320

    Article  ADS  Google Scholar 

  16. Wallraff A, Schuster D I, Blais A, et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature, 2004, 431: 162–167; Blais A, Gambetta J, Wallraff A, et al. Quantum-information processing with circuit quantum electrodynamics. Phys Rev A, 2007, 75(3): 032329; Hu Y, Xiao Y F, Zhou ZW, et al. Controllable coupling of superconducting transmission-line resonators. Phys Rev A, 2007, 75 (1): 012314

    Article  ADS  Google Scholar 

  17. Hofheinz M, Weig E M, Ansmann M, et al. Generation of Fock states in a superconducting quantum circuit. Nature, 2008, 454: 310–314; Hofheinz M, Wang H, Ansmann M, et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature, 2009, 459: 546–549

    Article  ADS  Google Scholar 

  18. Zhou L, Gong Z R, Liu Y X, et al. Controllable scattering of a single photon inside a one-dimensional resonator waveguide. Phys Rev Lett, 2008, 101(10): 100501

    Article  ADS  Google Scholar 

  19. Martinis J M, Nam S, Aumentado J, et al. Decoherence of a superconducting qubit due to bias noise. Phys Rev B, 2003, 67 (9): 094510

    Article  ADS  Google Scholar 

  20. Steffen M, Ansmann M, McDermott R, et al. State tomography of capacitively shunted phase qubits with high fidelity. Phys Rev Lett, 2006, 97 (5): 050502

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to ShiLiang Zhu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yu, L., Tong, N., Xue, Z. et al. Simulation of the spin-boson model with superconducting phase qubit coupled to a transmission line. Sci. China Phys. Mech. Astron. 55, 1557–1561 (2012). https://doi.org/10.1007/s11433-012-4863-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-012-4863-x

Keywprds

Navigation