Research ArticleCONDENSED MATTER PHYSICS

Initialization of quantum simulators by sympathetic cooling

See allHide authors and affiliations

Science Advances  06 Mar 2020:
Vol. 6, no. 10, eaaw9268
DOI: 10.1126/sciadv.aaw9268
  • Fig. 1 Sympathetic cooling of a quantum simulator.

    (A) A system of N spins performing the quantum simulation is interacting with an additional bath spin that is dissipatively driven. (B) Sketch of the energy level structure showing resonant energy transport between the system and the bath, after which the bath spin is dissipatively pumped into its ground state. (C) Level scheme for the implementation with trapped 40Ca+ ions.

  • Fig. 2 Sympathetic cooling of the transverse field Ising model in the ferromagnetic phase (J/g = 5, N = 5, fx, y, z = {1,1.1,0.9}).

    The speed of the cooling dynamics and the final energy of the system depend on the system-bath coupling gsb for γ/g = 1.9 (A) and the dissipation rate γ for gsb/g = 1.15 (B). The ground-state energy is indicated by the dashed line. The insets show that the ground state can be prepared with greater than 90% fidelity.

  • Fig. 3 Sympathetic cooling of the antiferromagnetic Heisenberg model (N = 4, gsb/J = 0.2, γ/J = 0.6, fx,y,z = {0.4,2.3,0.3}).

    (A) The efficiency of the cooling procedure depends on the choice of the bath spin splitting Δ. (B) The optimal cooling leading to the lowest system energy 〈Hsys〉 corresponds to setting Δ to the many-body gap ΔE (vertical dashed line). The same minimum is observed when measuring the energy Edis that is being dissipated during the cooling process. The ground-state energy is indicated by the horizontal dashed line.

  • Fig. 4 Scalability of the cooling protocol.

    The preparation time tp to reach a final dimensionless energy of ε = 0.2 grows linearly on a log-log scale, i.e., tpNα. The solid line is a fit to the data according to α = 3.1 ± 0.1.

  • Fig. 5 Cooling performance in the presence of decoherence in the quantum simulator for the transverse field Ising chain (J/g = 5, N = 4).

    The inset shows the dimensionless energy ε as a function of the product κtp, where tp was taken from the dynamics without decoherence corresponding to a ground-state preparation fidelity of f = 0.9 (dashed line).

  • Fig. 6 Cooling performance of an Ising-like chain of 5 + 1 ions of tp = 80ℏ/g = 24s.

    The blue line shows the dynamics in the decoherence-free case resulting in a fidelity of f = 0.92, while the orange line indicates the dynamics under a collective decoherence mechanism with rate κc = 3.3Hz, resulting in f = 0.89. The dashed line indicates the ground-state energy of the system.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/10/eaaw9268/DC1

    Section S1. Energy-level representation of the cooling protocol

    Section S2. Cooling in the paramagnetic and the critical regime of the Ising model

    Section S3. Dependence of the cooling performance on the initial state

    Section S4. Efficiency of the cooling protocol for the Heisenberg model

    Section S5. Entanglement measure for the ground-state cooling of the Heisenberg model

    Fig. S1. Possible paths via which an excitation can be cooled down to the ground state.

    Fig. S2. Cooling dynamics in different regimes.

    Fig. S3. Cooling performance of the transverse field Ising model in the ferromagnetic phase for various initial states.

    Fig. S4. Scalability of the protocol for the antiferromagnetic Heisenberg model.

    Fig. S5. Negativity as a measure of entanglement of the prepared states in time for a system of N = 6 spins.

    References (4952)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Energy-level representation of the cooling protocol
    • Section S2. Cooling in the paramagnetic and the critical regime of the Ising model
    • Section S3. Dependence of the cooling performance on the initial state
    • Section S4. Efficiency of the cooling protocol for the Heisenberg model
    • Section S5. Entanglement measure for the ground-state cooling of the Heisenberg model
    • Fig. S1. Possible paths via which an excitation can be cooled down to the ground state.
    • Fig. S2. Cooling dynamics in different regimes.
    • Fig. S3. Cooling performance of the transverse field Ising model in the ferromagnetic phase for various initial states.
    • Fig. S4. Scalability of the protocol for the antiferromagnetic Heisenberg model.
    • Fig. S5. Negativity as a measure of entanglement of the prepared states in time for a system of N = 6 spins.
    • References (4952)

    Download PDF

    Files in this Data Supplement:

Stay Connected to Science Advances

Navigate This Article