Photonic Entanglement Based on Nonlinear Metamaterials

LETTER ARTICLE www.lpr-journal.org Photonic Entanglement Based on Nonlinear Metamaterials Yang Ming,* Wang Zhang, Jie Tang, Yuan Liu, Zilong Xia, Yushen Liu,* and Yan-qing Lu* resonance of “meta-atoms” through ma- Metamaterials consisting of deep subwavelength artificial “atoms” have been terial selection and geometry design, or utilized to demonstrate a series of novel phenomena such as negative arranging their distributions and orienta- refraction and epsilon-near-zero. In recent times, metamaterials have been tions in space.[1] The value of this char- developed as an up-and-coming platform for quantum optics. Here the acteristic has been thoroughly demonstrated in classical optics. Moreover, it generation and modulation of photonic entanglement are investigated based could play an important role in the con- on the parametric down conversion processes in metamaterials with text of quantum photonics. Especially, considerable optical nonlinearity. Through flexible nanostructure design, the recent explorations of nonlinear optical nonlinear photonic interaction in the metamaterial system can be effectively metamaterials[9] provide a potential plat- tailored. The distributions of optical parameters of the system are form for generating and manipulating entangled photon states,[10–12] which are inhomogeneous, based on which the spatial properties of the generated at the heart of quantum information photonic state can be steered as desired. The theoretical framework to processing. describe this system is established based on the nonlinear Huygens–Fresnel The development of quantum physics principle, and a differential approach is utilized to deal with the intrinsic loss presents intriguing novel concepts inex- of the system. The generation of orbital angular momentum entangled states haustibly, which brings excellent oppor- is actually considered as an illustration. This platform could be valuable for tunities to cut down the time-complexity of quantum algorithms.[13] Correspond- the practical applications of quantum information processing. ingly, the arithmetic capability is greatly improved in theory. However, the practi- cality of photonic quantum computation 1. Introduction usually requires multiparticle systems. With the increasing of photon number, the efficiency and Metamaterials are engineered structures with unique electro- operability of the systems face enormous challenges. As an al- magnetic properties and functionalities which are not attain- ternative, multidimensional systems can be exploited for certain able with naturally existing materials.[1] More recently, owing to quantum information applications.[14] The spatial degrees of the high designability and flexibility, metamaterials have been freedom of photon provide potential candidates, which can be deeply studied and exploited for novel photonic applications used to form infinite dimensional Hilbert space.[15] Compared such as negative refraction, near-zero permittivity, and wavefront with hyperbolic metamaterials[16,17] and negative-index “meta- shaping.[2–6] There are various sorts of photonic metamaterials. A waveguides,”[18,19] the meta-atom constructing systems provides typical sort is the ones with structural units consisting of dielec- an ideal platform to steer the spatial properties of photonic states tric or metallic subwavelength building blocks known as the arti- owing to the abundant and flexible micro/nano-structures. Sev- ficial “atoms.”[7,8] Accordingly, the light-matter interaction prop- eral investigations taking advantage of this unique characteristic erties of the metamaterials can be tailored by modulating the have been demonstrated.[20–22] However, so far the twin photons are generated prior to the interaction with metamaterials in most cases. In this letter article, we study utilizing nonlinear metamaterials for directly generating entangled photon states with expected characteristics. Such kind of function integra- Dr.Y.Ming,Z.Xia,Prof.Y.Liu tion could be benefit for reducing the complexity of practical School of Physics and Electronic Engineering Changshu Institute of Technology systems. Through designing and arranging of meta-atoms, Suzhou 215000, China the parametric down conversion (PDC) processes inside the E-mail: [email protected]; [email protected] nonlinear metamaterials can be controlled to effectively en- Dr. Y. Ming, W. Zhang, J. Tang, Y. Liu, Prof. Y.-q. Lu gineer the entangled states. For an exact description of such National Laboratory of Solid State Microstructures, College of a system, a theoretical framework is developed based on the Engineering and Applied Sciences combination of the nonlinear Huygens–Fresnel principle and Nanjing University Nanjing 210093, China the equivalent beam splitter approach for attenuation. The gen- E-mail: [email protected] eration of entangled orbital angular momentum (OAM) states is actually considered and calculated to be available. The nonlinear The ORCID identification number(s) for the author(s) of this article metamaterials provide a potential platform for steering photonic can be found under https://doi.org/10.1002/lpor.201900146 entanglement. DOI: 10.1002/lpor.201900146 Laser Photonics Rev. 2020, 1900146 1900146 (1 of 8) © 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.lpr-journal.org Figure 1. a) The schematic of the SRR-based nonlinear metamaterials. The insert exhibits the geometry of SRR meta-atom. b) The absolute value of (2) (2) max varies with the length L and width W of the meta-atom, and the sign of max depends on the orientation of the meta-atom. 2. Results and Discussion 1 (⃗r) = P̂ (⃗r) ⋅ Ê (⃗r) 2.1. Tuning the PDC Process with Nonlinear Metamaterials I 2 NM p 1 (2) (+) (−) (−) = (⃗r)Ê (⃗r)Ê (⃗r)Ê (⃗r)(1) Traditionally, entangled photons are generated through multi- 2 NM p s i photon interaction processes.[4] The dynamical process is controlled by the interaction Hamiltonian whose formalism In this equation, the subscripts p, s, and i represent the pump, is directly influenced by the nanostructures of the nonlinear signal, and idler photons, respectively. The nonlinear coefficient (2) E metamaterials. Therefore, Hamiltonian engineering can be re- of metamaterial medium is marked as NM. The pump field p alized through nanostructure design. Correspondingly, the PDC is usually treated as an undepleted classical field. The signal and process can be steered to generate photonic state on demand. idler fields are quantized and represented by field operators. The For actual metamaterials, there are various kinds of meta- corresponding expressions are written as atoms such as split ring resonator (SRR)[23] and nanoantenna (+) i k⃗ ⋅⃗r− t [24] E = E Ψ ⃗r e ( p p ) with N-fold rotational symmetry. The modulation of photonic p p0 pt( ) states can be realized through tuning the shape and orientation ∑ − † −i k⃗ ⋅⃗r− t E( ) = i d dk⃗ F Ψ ⃗r a e ( s s ) of the meta-atoms. In the present work, we consider a SRR ar- s ∫ s ∫ s s st( ) s ray system as is shown in Figure 1a, and the geometry of SRR ∑ meta-atom is presented in the inset. (−) † −i k⃗ ⋅⃗r− t E = i d dk⃗ F Ψ ⃗r a e ( i i ) i ∫ i ∫ i i it( ) i (2) Compared with the traditional domain-engineered ferroelectric nonlinear crystals, the distribution of nonlinear coefficient of E the SRR system can experience a continuous variation through The pump light is set to be monochromatic, and p0 is the cor- changing the geometry of SRR meta-atom.[23] As is shown in Ψ ⃗r responding amplitude, while the function pt( ) represents the Figure 1b, the absolute value of local nonlinear coefficient of F transverse shape. s(i) is the normalization parameter. Further- a meta-atom can be modulated between 0 and a maximum more, Ψ (⃗r)andΨ (⃗r) describe the transverse distributions of (2) st it max through tuning the ratio between the length of the SRR the signal and idler photons, including the amplitude and phase arm and the total effective length of the SRR. In addition, the a† profile. In addition, s(i) is the creation operator for the signal sign of nonlinear coefficient depends on the orientation of the (idler) field. The polarization state of the signal (idler) photons meta-atom. Owing to the current powerful nano-fabrication is marked by the parameter . technologies, the shape, orientation, and distribution of SRR The contribution of a point source in the generated photon meta-atoms can be tailored on demand. Correspondingly, such state could be evaluated with the evolution equation as |dΨ⟩ = a system provides a more accurate platform for controlling the − i∕ℏ ∫ dt t | ⟩ [1 ( ) I( )] 0 . The final down-converted state can be de- spatial properties of entangled photon states than the binary rived through summing the contributions over the whole volume modulation regime of the ferroelectric nonlinear crystals based of nonlinear metamaterial. For a quasi two dimensional (2D) sys- on the inversion of polarization direction. tem in which the nonlinear metamaterial is a thin slice, it is not To clarify the mechanism of PDC in SRR system, the conven- hard to obtain the form of the two-photon state with the spatial tional quasi-phase matching regime is not adequate owing to integral of |dΨ⟩ as the structural complexity, thus a more generalized theoretical framework needs to be established. Therefore, we introduce the |Ψ⟩ = d⃗r |dΨ⟩ t ∫ nonlinear Huygens–Fresnel principle.[25] That is to say, in PDC process, each point on the wavefront of the pump light acts as iE ∑ = | ⟩ + p0 dk⃗ dk⃗ F F a sub-source of secondary down-converting waves through inter- 0 ∫ s ∫ i s i′ 2ℏ ′ acting with nonlinear metamaterials. The influence of each point , source could be expressed with the Hamiltonian density as[26] ×Θk⃗ , k⃗ a† a† | ⟩ ( s i) s i′ 0 (3) Laser Photonics Rev. 2020, 1900146 1900146 (2 of 8) © 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.lpr-journal.org Figure 2. The illustration of the PDC process in nonlinear metamaterials. a) Detailed configuration of a dz-cell. The PDC process in a dz element is divided into two sub-processes.

Load more