Papers
Topics
Authors
Recent
2000 character limit reached

Spectral continuum in the Rabi-Stark model

Published 25 Mar 2024 in quant-ph, cond-mat.quant-gas, math-ph, and math.MP | (2403.16758v2)

Abstract: The Rabi-Stark model is a non-linear generalization of the quantum Rabi model including the dynamical Stark shift as a tunable term, which can be realized via quantum simulation on a cavity QED platform. When the Stark coupling becomes equal to the mode frequency, the spectrum changes drastically, a transition usually termed "spectral collapse" because numerical studies indicate an infinitely degenerate ground state. We show that the spectrum extends continuously from a threshold value up to infinity. A set of normalizable states are embedded in the continuum which furnishes an unexpected analogy to the atomic Stark effect. Bound states and continuum can be obtained analytically through two equally justified, but different confluence processes of the associated differential equation in Bargmann space. Moreover, these results are obtained independently using a method based on adiabatic elimination of the spin degree of freedom and corroborated through large-scale numerical checks.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (69)
  1. Isidor I. Rabi. On the process of space quantization. Phys. Rev., 49:324, 1936.
  2. Comparison of quantum and semiclassical radiation theories with applications to the beam maser. Proc. IEEE, 51:89, 1963.
  3. E. K. Twyeffort Irish. Generalized Rotating-Wave Approximation for Arbitrarily Large Coupling. Phys. Rev. Lett., 99(17):173601, October 2007.
  4. Daniel Braak. Integrability of the Rabi Model. Phys. Rev. Lett., 107(10):100401, August 2011.
  5. Exact solvability of the quantum Rabi model using bogoliubov operators. Phys. Rev. A, 86:023822, 2012.
  6. Circuit quantum electrodynamics in the ultrastron-coupling regime. Nature Physics, 6:772, 2010.
  7. Deep strong coupling regime of the Jaynes-Cummings model. Phys. Rev. Lett., 195:263603, 2010.
  8. Exploring the Quantum: Atoms, Cavities, and Photons. Oxford University Press, 2008.
  9. Quantum information processing and quantum optics with circuit quantum electrodynamic. Nature Physics, 16:247, 2020.
  10. Circuit quantum electrodynamics. Rev. Mod. Phys., 93:025005, 2021.
  11. Quantum Phase Transition and Universal Dynamics in the Rabi Model. Phys. Rev. Lett., 115:180404, 2015.
  12. Subir Sachdev. Quantum Phase Transitions. Cambridge University Press, 2 edition, 2011.
  13. J. Larson and E. K. Irish. Some remarks on ’superradiant’ phase transitions in light-matter systems. J. Phys. A: Math. Gen., 50:17002, April 2017.
  14. Integrability and solvability of the simplified two-qubit Rabi model. J. Phys. A: Math. Theor., 45(36):365302, August 2012.
  15. Application of the polaron method in the two-qubit quantum Rabi model. Phys. Rev. A, 101:063832, 2020.
  16. Two-photon Rabi model: Analytic solutions and spectral collapse. Journal of Physics A: Mathematical and Theoretical, 49(46):464002, November 2016.
  17. Daniel Braak. Spectral Determinant of the Two-Photon Quantum Rabi Model. Annalen der Physik, 535(3):2200519, 2023.
  18. Sahel Ashhab. Attempt to find the hidden symmetry in the asymmetric quantum Rabi model. Phys. Rev. A, 101:023808, 2020.
  19. The hidden symmetry of the asymmetric quantum Rabi model. J. Phys. A: Math. Theor., 54:12LT01, 2021.
  20. Hidden symmetry and tunneling dynamics in the asymmetric quantum Rabi model. Phys. Rev. A, 103:023719, 2021.
  21. Determinant expression of constraint polynomials and the spectrum of the asymmetric quantum Rabi model. Int. Math. Res. Not., 2021:9458, 2021.
  22. Remarks on the hidden symmetry of the asymmetric quantum Rabi model. J. Phys. A: Math. Theor., 54:285202, 2021.
  23. Generalized adiabatic approximation to the asymmetric quantum Rabi model: conical intersections andgeometric phases. J. Phys. A: Math. Theor., 54:405201, 2021.
  24. Double degeneracy associated with hidden symmetries in the asymmetric two-photon Rabi model. Phys. Rev. Research, 3:033057, 2021.
  25. Quantum entanglement resonance in the asymmetric quantum Rabi model. Phys. Rev. A, 105:0624450, 2022.
  26. The quantum Rabi model: solution and dynamics. J. Phys. A: Math. Theor., page 113001, 2017.
  27. Alexandre Le Boité. Theortical Methods for Ultrastrong Light-Matter Interactions. Adv. Quantum Technol., 3:1900140, 2020.
  28. The Jaynes–Cummings Model and Its Descendants. IOP Publishing Ltd, 2021.
  29. Hans-Peter Eckle. Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz. Oxford University Press, 2019.
  30. Cavity-QED simulation of qubit-oscillator dynamics in the ultrastrong-coupling regime. Phys. Rev. A, 87(3):033814, March 2013.
  31. A Group-Theoretical Approach to Quantum Optics. Wiley-VCH, 2009.
  32. Selective interactions in the quantum Rabi model. Phys. Rev. A, 108:023720, 2023.
  33. Open Rabi model with ultrastrong coupling plus large dispersive-type nonlinearity: Nonclassical light via a tailored degeneracy. Phys. Rev. A, 89(3):033802, March 2014.
  34. Analytical method of spectra calculations in the Bargmann representation. Physics Letters A, 378(46):3445–3451, October 2014.
  35. An exactly solvable system from quantum optics. Physics Letters A, 379(24):1503–1509, July 2015.
  36. A generalization of the quantum Rabi model: Exact solution and spectral structure. J. Phys. A: Math. Theor., 50(29):294004, June 2017.
  37. Corrigendum: A generalization of the quantum Rabi model: Exact solution and spectral structure (2017 J. Phys. A: Math Theor. 50:294004). J. Phys. A: Math. Theor., 56(34):345302, August 2023.
  38. Quantum Rabi–Stark model: Solutions and exotic energy spectra. J. Phys. A: Math. Theor., 52(24):245304, May 2019.
  39. Multiple ground-state instabilities in the anisotropic quantum Rabi model. Phys. Rev. A, 103(4):043708, April 2021.
  40. Exact eigenstates of the two-photon Jaynes-Cummings model with the counter-rotating term. Eur. Phys. J D, 6:119, 1999.
  41. Spectral collapse via two-phonon interactions in trapped ions. Phys. Rev. A, 92(3):033817, September 2015.
  42. Bound states in the continuum. Nature Reviews Materials, 1:16048, 2016.
  43. Quantum criticality of the Rabi-Stark model at finite frequency ratios. Phys. Rev. A, 102:063721, 2020.
  44. Bound states in the continuum in photonic structures. Physics-Uspekhi, 66:494, April 2021.
  45. A. F. Sadreev. Interference traps waves in an open system: bound states in the continuum. Rep. Prog. Phys., 84:055901, April 2021.
  46. Lasing action from photonic bound states in continuum. Nature, 541:196, April 2017.
  47. S. Longhi. Dispersive bands of bound states in the continuum. Nanophotonics, 10:4241, April 2021.
  48. Exceptional points at bound states in the continuum in photonic integrated circuits. Nanophotonics, 11:4909, April 2022.
  49. Applications of bound states in the continuum in photonics. Nat. Rev. Phys., 5:659, April 2023.
  50. John von Neumann and Eugene Wigner. Über merkwürdige diskrete Eigenwerte. Phys. Z., 30:465, 1929.
  51. Experimental observation of optical bound states in the continuum. Phys. Rev. Lett., 107:183901, 2011.
  52. Bound states in the continuum realized in the one-dimensional two-particle Hubbard model with an impurity. Phys. Rev. Lett., 109:116405, 2012.
  53. Bound states in the continuum for separable nonlocal potentials. Phys. Rev. A, 12:2237, 1975.
  54. M. J. Robnik. A simple separable Hamiltonian having bound states in the continuum. J. Phys. A, 19:3845, 1986.
  55. Observation of trapped light within the radiation continuum. Nature, 499:188, 2013.
  56. Valentine Bargmann. On a Hilbert space of analytic functions and an associated integral transform part I. Communications on Pure and Applied Mathematics, 14(3):187–214, 1961.
  57. Spacing distribution for quantum Rabi models. arXiv:2310.09811, 2024.
  58. Zeév Rudnick. The Quantum Rabi model: Towards Braak’s conjecture. arXiv:2311.12622, 2023.
  59. Special Functions: A Unified Theory Based on Singularities. Oxford University Press, 2000.
  60. A. Vourdas. Analytic representations in quantum mechanics. J. Phys. A: Math. Gen., 39(7):R65–R141, February 2006.
  61. Methods of Modern Mathematical Physics I: Functional Analysis. Academic Press, February 1981.
  62. Mathematical problems of relativistic physics. American Mathematical Society, 1970.
  63. Excited-state quantum phase transitions. J. Phys. A: Math. Theor., 54(13):133001, March 2021.
  64. R. Graham and M. Höhnerbach. Two-state system coupled to a boson mode: Quantum dynamics and classical approximations. Z. Phys. B, 57:233–248, 1984.
  65. E. K. Irish. The Theory of Quantum Electromechanics: A Solid-State Analog of Quantum Optics. PhD thesis, University of Rochester, 2006.
  66. Solving and completing the Rabi-Stark model in the ultrastrong-coupling regime. Phys. Rev. A, 108(2):023720, August 2023.
  67. Weyl’s theory applied to the Stark effect in the hydrogen atom. Phys. Rev. A, 10(5):1494–1506, November 1974.
  68. Complex coordinates and the Stark effect. International Journal of Quantum Chemistry, 14(4):393–418, 1978.
  69. DC strong-field Stark effect: Consistent quantum-mechanical approach. J. Phys. B: At. Mol. Opt. Phys., 26(14):L379–L385, July 1993.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now

Whiteboard

Paper to Video (Beta)

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Tweets

Sign up for free to view the 1 tweet with 1 like about this paper.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up for Free