Dynamical Casimir Effect Entangles Artificial Atoms

We show that the physics underlying the dynamical Casimir effect may generate multipartite quantum correlations. To achieve it, we propose a circuit quantum electrodynamics scenario involving superconducting quantum interference devices, cavities, and superconducting qubits, also called artificial atoms. Our results predict the generation of highly entangled states for two and three superconducting qubits in different geometric configurations with realistic parameters. This proposal paves the way for a scalable method of multipartite entanglement generation in cavity networks through dynamical Casimir physics.

Figure 1

Quantum optical implementation of the model of Eq. (1): two cavities with a common partially reflecting mirror, each one containing a two-level artificial atom in the strong-coupling regime. If the position and/or transmission coefficient of the central mirror is time modulated, correlated photon pairs are generated and entanglement is transferred to qubits via the Jaynes-Cummings interaction.

Figure 2

(a) The model of Fig. 1 can be implemented by means of two coplanar waveguides, grounded through a SQUID, containing two superconducting qubits. The blue lines represent two parallel strip lines of isolating material, where the superconducting region between them constitutes the coplanar waveguide. Each cavity interacts with a transmon qubit that is denoted by a red dot. Different resonator lengths result in distinct resonator frequencies. (b) Circuit diagram for the previous scheme, where the cavities are effectively represented by $LC$ resonators. We assume two identical Josephson junctions of the SQUID, while transmon qubits are constituted by two Josephson junctions shunted by a large capacitance.

Figure 3

(a) Concurrence and mean photon number as a function of time in units of the cavity frequency ${\omega }_1$. Here, the chosen parameters are ${\omega }_1/2\pi =4\mathrm{GHz}$, ${\omega }_2/2\pi =5\mathrm{GHz}$, the impedance for both cavities is $Z_0=50\mathrm{\Omega }$, and the critical current of the SQUID junctions is $I_C=1.1\mu \mathrm{A}$. Such parameters result in a squeezing parameter ${\alpha }_0={\omega }_1\times 10^{-3}$. Each qubit is resonant with its corresponding cavity and they are coupled with the same interaction strength $g=0.04{\omega }_2$. (b) Real and imaginary parts of the density matrix $\rho$ associated with the two-qubit system.

Figure 4

Three coplanar waveguide resonators are connected to the ground through a SQUID. Each resonator is coupled with a resonant transmon qubit. This scheme allows generation of GHZ-like entangled states, through a first-order process. By using this circuit design as a building block, it is possible to explore more complex configurations and to build scalable cavity networks [21].

Figure 5

(a) Negativity of the bipartite system obtained isolating one qubit from the set of the other two, as a function of time. Here, we considered resonator frequencies of ${\omega }_1/2\pi =3.8\mathrm{GHz}$, ${\omega }_2/2\pi =5.1\mathrm{GHz}$, and ${\omega }_3/2\pi =7.5\mathrm{GHz}$. The SQUID is identical to the bipartite case and we use resonant qubits. The coupling parameters are homogeneous and their bare value is given by ${\alpha }_0=5{\omega }_1\times 10^{-3}$. (b) Average photon number in each cavity as a function of time. Because of the symmetric configuration the photon distribution is the same for the three cavities.