Quantum Network of Atom Clocks: A Possible Implementation with Neutral Atoms

We propose a protocol for creating a fully entangled Greenberger-Horne-Zeilinger-type state of neutral atoms in spatially separated optical atomic clocks. In our scheme, local operations make use of the strong dipole-dipole interaction between Rydberg excitations, which give rise to fast and reliable quantum operations involving all atoms in the ensemble. The necessary entanglement between distant ensembles is mediated by single-photon quantum channels and collectively enhanced light-matter couplings. These techniques can be used to create the recently proposed quantum clock network based on neutral atom optical clocks. We specifically analyze a possible realization of this scheme using neutral Yb ensembles.

Figure 1

Schematic of the setup. $K$ clocks, each holding $M$ atomic ensembles of size $n$ are connected. Atoms within each ensemble get entangled using long-range interaction between Rydberg atoms; ensembles in the same clock are entangled either via Rydberg interactions or via the cavity mode, while neighboring clocks are entangled through single-photon quantum channels, enhanced by optical cavities. The resulting state is a global GHZ state, $|0{⟩}^{\otimes N}+|1{⟩}^{\otimes N}$ of all $N=KMn$ atoms in the network.

Figure 2

Steps to generate pairwise entanglement. (a) Pulse sequence used to initialize the spin waves $f$ and $s$ in an ensemble. (b) Pulse sequence inducing a conditional photon emission, the emitted photon becomes entangled with the spin state $s$. (c) In three steps, neighboring ensembles generate pairwise entanglement between their collective excitations. First, they induce $0+1$ superpositions of the two independent spin waves, $f^{†}$ and $s^{†}$. Then, applying the conditional photon emission sequence four times, they emit four pulses, containing two photons total. Each pair of photons is correlated with a unique spin state. Finally, photons are measured with a linear optics setup, and 2-photon coincidences indicate the creation of entanglement between neighboring ensembles. (Blue and red shadings indicate positive and negative correlation between qubits, respectively).

Figure 3

Connecting links into nonlocal GHZ state. (a) cnot gate between the two excitations $f$ and $s$: If level $s$ is occupied, then the coherent (de)excitation of the $f$ level is blocked by the Rydberg blockade between the $r_1$ and $r_2$ intermediate levels, otherwise it succeeds. (b) Connecting two entanglement links. The local cnot and measurement operations on ensemble $k$ entangle the two, initially independent, parts of the system: $s_{k-1},f_k$ and $s_k,f_{k+1}$. Depending on the outcome of the measurement, either only $f_k$, or the entire right-hand side needs to be flipped in order to arrive to the proper GHZ state.

Figure 4

Local GHZ creation. (a) Conditional, local GHZ state generation: Any excitation in level $s$ prevents the transfer from $g$ to $f$. (b) The local entangling operation extends the GHZ state from the $f$ spin wave to all atoms. As a result, every atom in the network gets entangled.

Figure 5

Implementation of our protocol in the lower level of neutral Yb. We assign the roles of $g$ and $f$ to the clock levels, the role of $s$ to the metastable $J=2$ level of $6s6p$, and the role of $e$ to the ${{}^{1}P}_1$ excited state, which spontaneously decays to the ground state.