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Detecting Out-of-Time-Order Correlations via Quasiadiabatic Echoes as a Tool to Reveal Quantum Coherence in Equilibrium Quantum Phase Transitions

R. J. Lewis-Swan, S. R. Muleady, and A. M. Rey
Phys. Rev. Lett. 125, 240605 – Published 10 December 2020
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Abstract
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Article Text
  • Introduction.—
  • Quantifying quantum coherence.—
  • Signals of a QPT in MQCs.—
  • Demonstrative examples.—
  • Obtaining FOTOCs without time reversal.—
  • Numerical study of quasi-adiabatic…
  • Experimental implementation.—
  • Conclusion.—
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    We propose a new dynamical method to connect equilibrium quantum phase transitions and quantum coherence using out-of-time-order correlations (OTOCs). Adopting the iconic Lipkin-Meshkov-Glick and transverse-field Ising models as illustrative examples, we show that an abrupt change in coherence and entanglement of the ground state across a quantum phase transition is observable in the spectrum of multiple quantum coherence intensities, which are a special type of OTOC. We also develop a robust protocol to obtain the relevant OTOCs using quasi-adiabatic quenches through the ground state phase diagram. Our scheme allows for the detection of OTOCs without time reversal of coherent dynamics, making it applicable and important for a broad range of current experiments where time reversal cannot be achieved by inverting the sign of the underlying Hamiltonian.

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    • Received 11 June 2020
    • Revised 9 September 2020
    • Accepted 26 October 2020

    DOI:https://doi.org/10.1103/PhysRevLett.125.240605

    © 2020 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Long-range interactionsQuantum coherence & coherence measuresQuantum phase transitionsQuantum simulation
    1. Physical Systems
    Quantum spin models
    1. Techniques
    Nuclear magnetic resonance
    Atomic, Molecular & OpticalGeneral PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsGravitation, Cosmology & AstrophysicsNuclear Physics

    Authors & Affiliations

    R. J. Lewis-Swan1,2,3, S. R. Muleady2,3, and A. M. Rey2,3

    • 1Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019, USA
    • 2JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
    • 3Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA

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    Vol. 125, Iss. 24 — 11 December 2020

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    Images

    • Figure 1
      Figure 1

      Characteristic MQC spectra ImS^x(ρ^GS) of the numerically computed ground state for the LMG (N=250) and the analytically computed ground state for the TFI (N=20) models as a function of Ω/χ. The phase boundary near Ω/χ≈1 in both models is signified by an abrupt change in the spectrum width σMQC (blue line, lower panels), which we also compare to the order parameter ⟨|S^z|⟩ (black, lower panels).

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    • Figure 2
      Figure 2

      Signatures of a QPT in the MQC intensities ImS^x. (a) The LMG model in the N→∞ limit (faded lines) has abruptly vanishing intensities I0S^x (blue) and I2S^x (red) at the critical point, (Ω/χ)c=1. Dark lines indicate a numerical comparison for N=250. (b) The TFI model displays a sharp kink in the I0S^x and I2S^x components at the critical point (Ω/χ)c=1. We plot results for the analytically computed ground state using N=250 to facilitate comparison with the LMG results. Insets for Figs. 2 and 2 highlight the divergence in d2I0S^x/dΩ2 at the QPT for N=250.

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    • Figure 3
      Figure 3

      (a) Schematic of many-body echo to obtain the MQC spectrum. The system is initialized in ρ^0, corresponding to the ground state at Ω(0)/χ, before the field is slowly ramped to Ω(τ), described by unitary U^(τ). A global rotation is imprinted on the state before the dynamics are reversed via (i) a many-body echo U^†(t) or (ii) a pseudoecho U^PE(τ). In the former, the sign of the Hamiltonian is also flipped; whereas in the latter, it is not. (b)–(c) Benchmark of dynamical protocol. The MQC components predicted from the exact ground state (faded blue lines) compared to those obtained from a pseudoecho ramping sequence of durations χτ=10 (black) and χτ=100 (red). All data are from numerical simulations using N=50 and N=20 for the LMG and TFI models, respectively (see Ref. [50] for details of ramps).

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