On-chip Rotated Polarization Directional Coupler Fabricated by Femtosecond Laser Direct Writing

We present a rotated polarization directional coupler (RPDC) on a photonic chip. We demonstrate a double-track approach to modify the distribution of refractive index between adjacent tracks and form a single waveguide with arbitrary birefringent optical axis. We construct a RPDC with the two axis-rotated waveguides coupled in a strong regime. The obtained extinction ratios on average are about 16dB and 20dB for the corresponding orthogonal polarizations. We perform the reconstruction of Stokes vector to test the projection performance of our RPDC, and observe the average fidelities up to 98.1% and 96.0% for the perfectly initialized states in 0$^\circ$ and 45$^\circ$ RPDCs respectively.Comment: 6 pages, 4 figure

Reconstruction of the Real Quantum Channel via Convex Optimization

Quantum process tomography is often used to completely characterize an unknown quantum process. However, it may lead to an unphysical process matrix, which will cause the loss of information respect to the tomography result. Convex optimization, widely used in machine learning, is able to generate a global optimal model that best fits the raw data while keeping the process tomography in a legitimate region. Only by correctly revealing the original action of the process can we seek deeper into its properties like its phase transition and its Hamiltonian. Thus, we reconstruct the real quantum channel using convex optimization from our experimental result obtained in free-space seawater. In addition, we also put forward a criteria, state deviation, to evaluate how well the reconstructed process fits the tomography result. We believe that the crossover between quantum process tomography and convex optimization may help us move forward to machine learning of quantum channels.Comment: 5 pages, 3 figures, 1 tabl

Towards Quantum Communication in Free-Space Seawater

Long-distance quantum channels capable of transferring quantum states faithfully for unconditionally secure quantum communication have been so far confirmed feasible in both fiber and free-space air. However, it remains unclear whether seawater, which covers more than 70% of the earth, can also be utilized, leaving global quantum communication incomplete. Here we experimentally demonstrate that polarization quantum states including general qubits and entangled states can well survive after travelling through seawater. We performed experiments in a 3.3-meter-long tube filled with seawater samples collected in a range of 36 kilometers in Yellow sea, which conforms to Jerlov water type I. For single photons at 405 nm in blue-green window, we obtained average process fidelity above 98%. For entangled photons at 810 nm, even with high loss, we observe violation of Bell inequality with 33 standard deviations. This work confirms feasibility of seawater quantum channel, representing the first step towards underwater quantum communication.Comment: 22 pages, 4 figures, 1 table, comments welcom

Topological Protection of Two-photon Quantum Correlation on a Photonic Chip

Low-decoherence regime plays a key role in constructing multi-particle quantum systems and has therefore been constantly pursued in order to build quantum simulators and quantum computers in a scalable fashion. Quantum error correction and quantum topological computing have been proved being able to protect quantumness but haven't been experimentally realized yet. Recently, topological boundary states are found inherently stable and are capable of protecting physical fields from dissipation and disorder, which inspires the application of such a topological protection on quantum correlation. Here, we present an experimental demonstration of topological protection of two-photon quantum states on a photonic chip. By analyzing the quantum correlation of photons out from the topologically nontrivial boundary state, we obtain a high cross-correlation and a strong violation of Cauchy-Schwarz inequality up to 30 standard deviations. Our results, together with our integrated implementation, provide an alternative way of protecting quantumness, and may inspire many more explorations in 'quantum topological photonics', a crossover between topological photonics and quantum information.Comment: 6 pages, 4 figures, 1 tabl

Asymmetric angular dependence of spin-transfer torques in CoFe/Mg-B-O/CoFe magnetic tunnel junctions

Using a first-principles noncollinear wave-function-matching method, we studied the spin-transfer torques (STTs) in CoFe/Mg-B-O/CoFe(001) magnetic tunnel junctions (MTJs), where three different types of B-doped MgO in the spacer are considered, including B atoms replacing Mg atoms (Mg$_3$BO$_4$), B atoms replacing O atoms (Mg$_4$BO$_3$), and B atoms occupying interstitial positions (Mg$_4$BO$_4$) in MgO. A strong asymmetric angular dependence of STT can be obtained both in ballistic CoFe/Mg$_3$BO$_4$ and CoFe/Mg$_4$BO$_4$ based MTJs, whereas a nearly symmetric STT curve is observed in the junctions based on CoFe/Mg$_4$BO$_3$. Furthermore, the asymmetry of the angular dependence of STT can be suppressed significantly by the disorder of B distribution. Such skewness of STTs in the CoFe/Mg-B-O/CoFe MTJs could be attributed to the interfacial resonance states induced by the B diffusion into MgO spacer. The present investigation demonstrates the feasibility of effectively enhancing microwave output power in MgO based spin torque oscillator (STO) by doping the B atoms into MgO spacer.Comment: 8 pages, 8 figure

Non-classical photon correlation in a two-dimensional photonic lattice

Quantum interference and quantum correlation, as two main features of quantum optics, play an essential role in quantum information applications, such as multi-particle quantum walk and boson sampling. While many experimental demonstrations have been done in one-dimensional waveguide arrays, it remains unexplored in higher dimensions due to tight requirement of manipulating and detecting photons in large-scale. Here, we experimentally observe non-classical correlation of two identical photons in a fully coupled two-dimensional structure, i.e. photonic lattice manufactured by three-dimensional femtosecond laser writing. Photon interference consists of 36 Hong-Ou-Mandel interference and 9 bunching. The overlap between measured and simulated distribution is up to $0.890\pm0.001$. Clear photon correlation is observed in the two-dimensional photonic lattice. Combining with controllably engineered disorder, our results open new perspectives towards large-scale implementation of quantum simulation on integrated photonic chips.Comment: 10 pages, 5 figure

Invisibility Cloak Printed on a Photonic Chip

Invisibility cloak capable of hiding an object can be achieved by properly manipulating electromagnetic field. Such a remarkable ability has been shown in transformation and ray optics. Alternatively, it may be realistic to create a spatial cloak by means of confining electromagnetic field in three-dimensional arrayed waveguides and introducing appropriate collective curvature surrounding an object. We realize the artificial structure in borosilicate by femtosecond laser direct writing, where we prototype up to 5000 waveguides to conceal millimeter-scale volume. We characterize the performance of the cloak by normalized cross correlation, tomography analysis and continuous three-dimensional viewing angle scan. Our results show invisibility cloak can be achieved in waveguide optics. Furthermore, directly printed invisibility cloak on a photonic chip may enable controllable study and novel applications in classical and quantum integrated photonics, such as invisualising a coupling or swapping operation with on-chip circuits of their own.Comment: 9 pages, 6 figure

Direct Observation of Topology from Single-photon Dynamics on a Photonic Chip

Topology manifesting in many branches of physics deepens our understanding on state of matters. Topological photonics has recently become a rapidly growing field since artificial photonic structures can be well designed and constructed to support topological states, especially a promising large-scale implementation of these states using photonic chips. Meanwhile, due to the inapplicability of Hall conductance to photons, it is still an elusive problem to directly measure the integer topological invariants and topological phase transitions for photons. Here, we present a direct observation of topological winding numbers by using bulk-state photon dynamics on a chip. Furthermore, we for the first time experimentally observe the topological phase transition points via single-photon dynamics. The integrated topological structures, direct measurement in the single-photon regime and strong robustness against disorder add the key elements into the toolbox of `quantum topological photonics' and may enable topologically protected quantum information processing in large scale.Comment: 7 pages, 4 figures, comments welcom

Mapping Twisted Light into and out of a Photonic Chip

Twisted light carrying orbital angular momentum (OAM) provides an additional degree of freedom for modern optics and an emerging resource for both classical and quantum information technologies. Its inherently infinite dimensions can potentially be exploited by using mode multiplexing to enhance data capacity for sustaining the unprecedented growth in big data and internet traffic, and can be encoded to build large-scale quantum computing machines in high-dimensional Hilbert space. While the emission of twisted light from the surface of integrated devices to free space has been widely investigated, the transmission and processing inside a photonic chip remain to be addressed. Here, we present the first laser-direct-written waveguide being capable of supporting OAM modes and experimentally demonstrate a faithful mapping of twisted light into and out of a photonic chip. The states OAM$_{0}$, OAM$_{-1}$, OAM$_{+1}$ and their superpositions can transmit through the photonic chip with a total efficiency up to 60% with minimal crosstalk. In addition, we present the transmission of quantum twisted light states of single photons and measure the output states with single-photon imaging. Our results may add OAM as a new degree of freedom to be transmitted and manipulated in a photonic chip for high-capacity communication and high-dimensional quantum information processing.Comment: 8 pages, 8 figure

Quantum Computation for Pricing the Collateralized Debt Obligations

Collateralized debt obligation (CDO) has been one of the most commonly used structured financial products and is intensively studied in quantitative finance. By setting the asset pool into different tranches, it effectively works out and redistributes credit risks and returns to meet the risk preferences for different tranche investors. The copula models of various kinds are normally used for pricing CDOs, and the Monte Carlo simulations are required to get their numerical solution. Here we implement two typical CDO models, the single-factor Gaussian copula model and Normal Inverse Gaussian copula model, and by applying the conditional independence approach, we manage to load each model of distribution in quantum circuits. We then apply quantum amplitude estimation as an alternative to Monte Carlo simulation for CDO pricing. We demonstrate the quantum computation results using IBM Qiskit. Our work addresses a useful task in finance instrument pricing, significantly broadening the application scope for quantum computing in finance.Comment: 19 pages, 18 figures, 4 table