Degenerate cavity supporting more than 31 Laguerre–Gaussian modes

Abstract

Photons propagating in Laguerre-Gaussian modes have characteristic orbital angular momenta, which are fundamental optical degrees of freedom. The orbital angular momentum of light has potential application in high capacity optical communication and even in quantum information processing. In this work, we experimentally construct a ring cavity with 4 lenses and 4 mirrors that is completely degenerate for LaguerreGaussian modes. By measuring the transmitted peaks and patterns of different modes, the ring cavity is shown to supporting more than 31 Laguerre-Gaussian modes. The constructed degenerate cavity opens a new way for using the unlimited resource of available angular momentum states simultaneously. The Laguerre-Gaussian (LG) modes are solutions for beam profiles with circularly symmetric. They are written in cylindrical coordinates using Laguerre polynomials and shown to obtained well-defined orbital angular momentum (OAM) [1]. The phase fronts of light beams in OAM eigenstates rotate, clockwise for positive OAM values, anti-clockwise for negative values, which could result in some unique features. The synthetic dimension with the values of OAM defined as the dimensional basis is recognized as a unique asset in many studies, including high-capacity optical communication [2,3], versatile optical tweezers [4], quantum information and quantum foundation [5][6][7]. It has been recently demonstrated quantum entanglement involving angular momenta as high as hundreds [6,8]. The manipulation and measurement of OAM states can be reached with high precision [5,[9][10][11], which leads to new applications of OAM states, such as detecting of a spinning object and lateral motion [12,13].Although, in principle, there are infinite synthetic degrees of freedom for OAM states, how to construct some functional devices by manipulating them in the synthetic dimension become a subject to be developed. Recently, a new kind of photonics simulator based on energy-degenerated optical cavities has been theoretically presented, which can support a large number of OAM modes [14]. By taking advantage of such kind of optical cavity, one can simulate photonics topological matters, as well as construct all-optical devices by manipulating in photonic synthetic dimension [15,16]. All such potentially novel applications are ascribed to set up a kind of degenerate optical cavity, which can support plenty of energy-degenerated OAM modes.Here, we present an experimental framework using numbers of OAM states in an optical cavity simultaneously, which is referred to a degenerate cavity. Different from previous works with OAM in cavities [17,18], we precisely measure the transmitted peaks and beam profles of different modes in the cavity, which is shown to supporting more than 31 LG modes. Moreover, the constructed cavity is in principle completely degenerate, which can be used to generate lasers and entangled photon sources with high dimensional LG modes [19][20][21][22] and other related fields [23][24][25].The theoretical framework of a degenera...

Synthesizing arbitrary lattice models using a single degenerate cavity

“…The first one is the beam size of the OAM modes on the cavity mirrors. Since the radius of LG modes de-pends on its topological charge l as r ∼ √ lr 0 , the maximal OAM L m allowed in the cavity is then determined by the size of cavity mirrors.Following the current experimental parameters shown in reference [19], we find that L m can reach up to 200 or more depending on the explicit setup. This indicates that degenerate OAM modes supported in current system is large enough to simulate high-dimensional lattice models, and can be act as a testbed to verify our construction ideals.…”

“…This is possible to use a modified cavity with longer optical length D. Since a round trip of optical fields inside the cavity induces a phase kD = 2mπ with m an integer number, a longer optical length indicates a larger integer m.The free spectral range of the resonator is inversely proportional to the cavity length and reads ∆v FS R = c/D. For current setup shown in reference [19], the cavity length can be tunned from 60cm to 600cm, while the FSR of the cavity can change from 500MHz to 50MHz, which is still much larger than the cavity linewidth (12MHz). This elongated cavity provides enough room for introducing different ancillary circuits into the main cavity.…”

“…For photonic systems, synthetic dimensions can be implemented using the photonic orbital angular momentum (OAM) degrees of freedom [16][17][18][19][20][21][22], or the photonic frequency comb with equal-distant level splittings [7,9,23]. Constructing photonic synthetic dimensions based on photonic OAM degrees of freedom was first proposed in [16] and discussed in more depth in Ref.…”

“…Constructing photonic synthetic dimensions based on photonic OAM degrees of freedom was first proposed in [16] and discussed in more depth in Ref. [17][18][19][20][21][22], where a cavity system supporting a large number of degenerate photonic modes with different angular momentum is constructed. The abundance of the OAM degrees of freedom becomes a sufficient resource that allows us to simulate various novel topological physics in high-dimensional systems in a very compact manner [16].…”

Convexity properties of superpositions of degenerate bipartite eigenstates

“…We consider reduced density matrices at constant values of z since the LG states in Equation 52 are not square-integrable functions. To avoid this kind of assumption it is possible to implement the calculation of reduced density matrices and the corresponding entropies using LG modes in a cavity [41,42], which are square-integrable and very similar to those in Equation 52, so the dependency on the z variable can be traced out completely.…”