Generation of Maximally Entangled Long-Lived States with Giant Atoms in a Waveguide

In this Letter, we show how to efficiently generate entanglement between two artificial giant atoms with photon-mediated interactions in a waveguide. Taking advantage of the adjustable decay processes of giant atoms into the waveguide and of the interference processes, spontaneous sudden birth of entanglement can be strongly enhanced with giant atoms. Highly entangled states can also be generated in the steady-state regime when the system is driven by a resonant classical field. We show that the statistics of the light emitted by the system can be used as a witness of the presence of entanglement in the system, since giant photon bunching is observed close to the regime of maximal entanglement. Given the degree of quantum correlations incoherently generated in this system, our results open a broad avenue for the generation of quantum correlations and manipulation of photon statistics in systems of giant atoms.

Figure 1

(a) Two giant atoms in the “nested” configuration considered in the present Letter. (b) Energy diagram showing collective states of the system and the decay rates between them. (c) Population dynamics of the ground state $|gg⟩$ and the Bell state $|\beta ⟩=(|ge⟩-|eg⟩)/\sqrt{2}$, for the nested giant atoms with $\kappa \mathrm{\Delta }x/\pi =0.01$ and Rabi frequency of the external field ${\mathrm{\Omega }}_0=1.5{\gamma }_0$. (d) State tomography of the steady-state density matrix ${\rho }_{\mathrm{SS}}\approx |\beta ⟩⟨\beta |$ for the dynamics considered in (c).

Figure 2

Collective decay rates, as a function of $\kappa \mathrm{\Delta }x$, for (a) two nested giant atoms and (b) two small atoms. For small atoms, one has ${\mathrm{\Gamma }}_{e+}={\mathrm{\Gamma }}_{+g}$ and ${\mathrm{\Gamma }}_{e-}={\mathrm{\Gamma }}_{-g}$ for any $\kappa \mathrm{\Delta }x$.

Figure 3

(a) Effective coupling as function of the relative energy shift ${\delta }_{\mathrm{rel}}$ for nested giant atoms, written as a multiple of $\sqrt{2}{\mathrm{\Omega }}_0$. (b) Steady-state entanglement obtained through local (resonant) fields driving two nested giant atoms, for $\kappa \mathrm{\Delta }x=0.01\pi$.

Figure 4

(a) Maximum amount of entanglement generated through sudden birth for small and giant nested atoms as a function of $\kappa \mathrm{\Delta }x$. (b) Dynamics of the optimal sudden birth of entanglement for small and giant nested atoms as a function of ${\gamma }_{0}t$. Here $\kappa \mathrm{\Delta }x\approx 0.19\pi$ for small atoms and $\kappa \mathrm{\Delta }x=0.99\pi$ for giant nested atoms.

Figure 5

(a) Function $g_{\alpha }^{(2)}(0)$ and (b) Mandel parameter for the emitted light by small and giant atoms, as a function of the pumping detuning ${\mathrm{\Delta }}_p$. (c) Population in the state $|\beta ⟩$ and (d) the corresponding concurrence. Here ${\mathrm{\Omega }}_0=1.5{\gamma }_0$ and $\kappa \mathrm{\Delta }x=0.01\pi$.