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Orbital angular momentum-entanglement frequency transducer

Entanglement is a vital resource for realizing many tasks such as teleportation, secure key distribution, metrology and quantum computations. To effectively build entanglement between different quantum systems and share information between them, a frequency transducer to convert between quantum states of different wavelengths while retaining its quantum features is indispensable. Information encoded in the photons orbital angular momentum OAM degrees of freedom is preferred in harnessing the information carrying capacity of a single photon because of its unlimited dimensions. A quantum transducer, which operates at wavelengths from 1558.3 nm to 525 nm for OAM qubits, OAMpolarization hybrid entangled states, and OAM entangled states, is reported for the first time. Nonclassical properties and entanglements are demonstrated following the conversion process by performing quantum tomography, interference, and Bell inequality measurements. Our results demonstrate the capability to create an entanglement link between different quantum systems operating in photons OAM degrees of freedoms, which will be of great importance in building a high capacity OAM quantum network.

entanglement state, information can be encoded in various degrees of freedom; entanglement can be constructed via a photon's polarization [5], in time-bins [6], and in orbital angular momentum (OAM) [7]. Among these degrees of freedom of light, its OAM degrees of freedom provide unique features including the mechanical torch effect, and singularities in phase-intensity distributions, which have broad applications in micro-particle manipulations [8], high precision optical metrology [9][10][11] and potential high-capacity information encoding in optical communications [12,13].
In recent years, much effort has gone into exploiting OAM light in quantum information technologies. Since the pioneering work demonstrating entanglement in OAM degrees of freedom [7], great advances have been made in the experimental control of OAM superposition states and their use in various protocols; they include quantum cryptography [14], the demonstration of very-high dimensional entanglement [15,16], and quantum teleportation from spin to OAM degrees of freedom [17]. More recently, quantum memory for OAM qubits [18,19] and entangled states [20][21][22] were demonstrated showing the capability for high-density information encoding and processing. Beyond their fundamental significance, these experiments give testimony to the potential of OAM of light as a basic information carrier and its promise in enhanced information encoding and processing capacities. A complete high capacity quantum network operating in the photonic OAM degrees of freedom should have some basic components that serve as quantum memory, quantum processors or communication channels [1].
To realize these components, the underlying physical systems usually work at different wavelengths. Transferring information between these systems effectively requires wavelength bridges which map the frequencies of one photon to another photon while preserving its quantum features.
Such wavelength bridges can be realized using second-order nonlinear processes, in which two optical fields combine in a nonlinear medium to generate a third field [23].
Energy, linear optical momentum, and OAM are conserved in the interaction process. By using high-efficiency quasi-phase-matching nonlinear waveguides, much progress in building a wavelength bridge between various systems has been made. In 2005, Tanzilli and colleagues demonstrated that time-bin entanglement between two photons at 1555 nm and 1312 nm generated by spontaneous parametric down conversion (SPDC) was preserved after up-conversion from 1312-nm to 712.4-nm [24]; in 2010, Rakher and colleagues verified that a single telecom-band photon at 1.3 µm generated from a quantum dot can be up-converted to 710 nm [25]; in 2011, Ikuta and colleagues showed down-conversion for a polarization-entangled photon at 780 nm to 1522 nm [26]; in 2014, Vollmer and collaborators demonstrated up-conversion of a 1550-nm squeezed vacuum state to 532 nm [27]. Recent progress in up-conversion detectors allows photon detection using high-performance visible optical detectors, although in each case the light detected is a highly attenuated laser source [28]. In reviewing the above work, we find that the spatial modes used are fundamental Gaussian modes because nonlinear waveguides supporting high-order spatial mode are still unobtainable. Until recently, quantum frequency conversion of OAM quantum states had been an open problem. We demonstrated the up-conversion of heralded 1560-nm single photon OAM states to 525 nm [29].
Because an OAM entanglement state has the capability to realize more sophisticated applications in quantum information science that cannot be accomplished using single-photon OAM states, frequency conversion of an OAM entangled state would be an important step in quantum information science.
In this work, we move towards this step by successively up-converting 1558.3-nm OAM qubits, OAM-polarization hybrid-entangled states, and OAM entanglement states to 525 nm. With more advanced experimental techniques compared with those used in Ref. [29], and by performing quantum state tomography, two-photon interference, and CHSH-inequality measurements, we clearly show that the quantum superposition and entanglement of the states are retained after up-conversion. Frequency up-conversion of a quantum state can be accomplished using sum frequency generation (SFG), in which the annihilation of a strong pump photon ( p ) and a weak signal photon (  ) creating a SFG photon with frequency (     p ). The effective Hamilton operator for this process is [27,29] When condition /2 f t   holds, the input signal field is completely converted to the output SFG field 2, 1,( . As ξ strongly depends on the pump amplitude, the key point for reaching maximum conversion efficiency is to increasing the pump power. In this work, the conversion efficiency is increased using a ring cavity to enhance the pump power.
Up-conversion of OAM qubit states is investigated next.      regime, l=100 is obtained in second harmonic generation [36].
In our experiments, the l=1 mode is used only as an example.
If the conversion efficiency issue is solved, dimensional limitations on l pose no problem.
In conclusion, the experiments described above provide a , plotting of these ideal density matrices are showed in figure S2.  , the relative phase between the two superposition state is 2 , figure S3 shows the diagram of the definition of the rotation angle  . Figure S3. Diagram for the definition of the rotation angle of the phase mask applied to SLM A and B.