Spontaneous Photon Production in Time-Dependent Epsilon-Near-Zero Materials

Abstract

Quantum field theory predicts that a spatially homogeneous but temporally varying medium will excite photon pairs out of the vacuum state. However, this important theoretical prediction lacks experimental verification due to the difficulty in attaining the required nonadiabatic and large amplitude changes in the medium. Recent work has shown that in epsilon-near-zero (ENZ) materials it is possible to optically induce changes of the refractive index of the order of unity, in femtosecond time scales. By studying the quantum field theory of a spatially homogeneous, time-varying ENZ medium, we theoretically predict photon-pair production that is up to several orders of magnitude larger than in non-ENZ time-varying materials. We also find that while in standard materials the emission spectrum depends on the time scale of the perturbation, in ENZ materials the emission is always peaked at the ENZ wavelength. These studies pave the way to technologically feasible observation of photon-pair emission from a time-varying background with implications for quantum field theories beyond condensed matter systems and with potential applications as a new source of entangled light. DOI: 10.1103/PhysRevLett.118.133904 Introduction.-Epsilon-near-zero (ENZ) materials are characterised by relative dielectric permittivity, whose real part, ε r , attains near-zero values around a given frequency ω ENZ [1,2]. A natural example of ENZ materials are commercially available transparent conducting oxides, e.g., indium-tin-oxide (ITO) or Al-doped ZnO (AZO), where ε r crosses 0 near the plasma frequency, whereas the imaginary part ε i is small. These materials are attracting attention for their rather remarkable properties, ranging from a geometric invariance of resonant structures to novel light propagation regimes and light emission geometries [2-10]. Recent work pioneered by Engheta et al. has started to focus on the quantum properties of these materials, including quantum emission in ENZ cavities and limitation or even complete suppression of vacuum modes [11,12].Alongside the fascinating linear optical properties of these materials, the nonlinear optical response exhibits an enhancement for frequencies close to ω ENZ [13][14][15][16][17][18][19]. In these first studies, the main enhancement mechanism of the nonlinearity is related to an enhancement of the z component (directed along the optical propagation axis) of the electrical field of the intense optical pump beam.An alternative nonlinear enhancement mechanism has also been reported that is based on the simple realization that in the ENZ region even a small change of permittivity Δε, induced by a third-order Kerr nonlinearity, can result in a

Broad Frequency Shift of Parametric Processes in Epsilon-Near-Zero Time-Varying Media

“…modulated, and if the temporal phase change is uniform over the pulse duration, the optical spectrum can be rigidly shifted. This effect can be interpreted as time-refraction [1,2], a phenomenon that attracted the attention of the research community owing to its link with the dynamical Casimir effect and Hawking radiation, and its implication in the formation of temporal band-gap structures and non reciprocal devices [3][4][5][6][7][8]. Strong enhancement of light-matter interaction has been observed in the spectral region where the real part of the dielectric permittivity ( [ε r ]) of a medium approaches zero (ENZ) [9][10][11].…”

Vacuum radiation and frequency-mixing in linear light-matter systems

“…Another experiment that relies on this mechanism is described in [7], where the refractive index of a thinfilm epsilon-near-zero metamaterial is changed rapidly in time, building on experiments performed in [62,68]. In light of the present results, additional physics can be expected associated with the linear frequency mixing mechanisms.…”

“…In most experimental scenarios however, the simple plane waves are not accessible, and are instead replaced by structured paraxial beams. Let us once again consider a homogeneous bulk medium where W º W ( ) x i i 2 2 , but where we restrict equation (7) to the paraxial limit, with the z-direction chosen to be the propagation direction.…”

Epsilon-Near-Zero Grids for On-chip Quantum Networks

“…As the wavelength in an ENZ material is extremely long, the phase of the eigenmode is almost constant, allowing, for example, wavefront shaping [7] for imaging applications. Another interesting feature of the ENZ materials is pronounced enhancement of nonlinearities [8,9]. It was reported that ENZ can also facilitate control over emission and interaction of quantum emitters (QE) [10] embedded in an ENZ cavity, and that emitted photons could hold substantial entanglement over large distances.…”