Fig. 2: Energy spectrum and dynamics for different values of atomic frequency detuning in the case of two lattice sites. | Communications Physics

Fig. 2: Energy spectrum and dynamics for different values of atomic frequency detuning in the case of two lattice sites.

From: Long-range quantum tunneling via matter waves

Fig. 2

a Energy spectrum and evolution of the absolute values of the probability amplitudes (b) ∣c1(t)∣ in the first site and (c) ∣c2(t)∣ in the second site for different values of atomic frequency detuning ω0. The red dot in a  marks the energy of the bound state in the continuum. T in b and c defined as \(2\pi /| {\varpi }_{1}^{{{{\rm{boc}}}}}-{\varpi }_{2}^{\,{{\rm{boc/bic}}}\,}|\) is the oscillation period in the steady state. Evolution of (d) ∣c1(t)∣ and (e) ∣c2(t)∣ when \({\omega }_{0}=-0.02\tilde{\omega }\) (blue dots), \(0.06\tilde{\omega }\) (orange squares), and \(0.18\tilde{\omega }\) (green rhombuses). Their long-time behaviors evaluated from Eq. (7) are shown by the solid lines in the same colors. We use \(d=5\bar{z}\), \(\Omega =0.13\tilde{\omega }\), \(\bar{z}=0.065\) nm, and \(\tilde{\omega }=2\pi \times 40\) kHz.

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