Photon Generation from Quantum Vacuum Using a Josephson Metamaterial

Abstract

When one of the parameters in the Euler-Lagrange equations of motion of a sys- tem is modulated, particles can be generated out of the quantum vacuum. This phenomenon is known as the dynamical Casimir efiect, and it was recently realized experimentally in systems of superconducting circuits, for example by using modulated resonators made of coplanar waveg- uides, or arrays of superconducting quantum intereference devices (SQUIDs) forming a Josephson metamaterial. In this paper, we consider a simple electrical circuit model for dynamical Casimir efiects, consisting of an LC resonator, with the inductor modulated externally at 10.8GHz and with the resonant frequency tunable over a range of §400MHz around 5.4GHz. The circuit is analyzed classically using a circuit simulator (APLAC). We demonstrate that if an additional source of classical noise couples to the resonator (on top of the quantum vacuum), for example via dissipative \internal modes, then the resulting spectrum of the photons in the cavity will present two strongly asymmetric branches. However, according to the theory of the dynamical Casimir efiect, these branches should be symmetric, a prediction which is conflrmed by our ex- perimental data. The simulation presented here therefore shows that the origin of the photons generated in our experiment with Josephson metamaterials is the quantum vacuum, and not a spurious classical noise source. The picture about vacuum that emerges from modern quantum fleld theory is very difierent from that ofiered by classical physics. In classical fleld theory, the vacuum is the zero-energy state of the fleld, deflned by the absence of any excitation. In quantum fleld theory, the vacuum state has a flnite zero-point energy associated with it, and the uncertainty principle indicates that ∞uctuations exist even in this state. Due to the existence of ∞uctuations, the quantum vacuum can become unstable under certain perturbations, and the energy of the perturbation is converted into creation of real particles (1). In the Schwinger efiect for example, a static intense electric fleld can create pairs of electrons and positrons. In very strong gravitational flelds, at the event horizon of black holes, the vacuum becomes unstable and energy is radiated away (Hawking efiect). By the equivalence principle, an accelerated observer in the Minkowski vacuum will detect a flnite-temperature fleld (Unruh efiect). In a previous paper, we reported the observation of the dynamical Casimir efiect using a ∞ux- biased Josephson metamaterial embedded in a microwave cavity at 5.4GHz (2). A non-adiabatic change in the index of refraction of the cavity (or in the electrical length) was realized by modulat- ing the ∞ux at values close to double the resonant frequency of the cavity. We measured also the frequency-correlated photons emitted from the cavity (which is kept at a temperature T = 50mK), and we obtained a power spectrum displaying a bimodal, \sparrow-tail distribution, with two sym- metric branches. Furthermore, we demonstrated that the generated photons are squeezed below the vacuum level and that the state of the two-photon fleld is nonseparable. The experimental results are in excellent agreement with the theoretical predictions. An alternative realization of the dynam- ical Casimir efiect consists in modulating an efiective boundary condition, realized experimentally as a SQUID structure placed at the end of a coplanar waveguide resonator (3). Remarkably, the experiments presented in Refs. (2,3) are the only existing measurements of the dynamical Casimir efiect, which was predicted theoretically in 1970 (4).