Deterministic Generation of Orbital-Angular-Momentum Multiplexed Tripartite Entanglement

Phase-insensitive amplifier gain estimation at Cramér-Rao bound for two-mode squeezed state of light

Phase-insensitive amplifiers (PIAs), as a class of important quantum devices, have found significant applications in the subtle manipulation of multiple quantum correlation and multipartite quantum entanglement. Gain is a very important parameter for quantifying the performance of a PIA. Its absolute value can be defined as the ratio of the output light beam power to the input light beam power, while its estimation precision has not been extensively investigated yet. Therefore, in this work, we theoretically study the estimation precision from the vacuum two-mode squeezed state (TMSS), the estimation precision of the coherent state, and the bright TMSS scenario, which has the following two advantages: it has more probe photons than the vacuum TMSS and higher estimation precision than the coherent state. The advantage in terms of estimation precision of the bright TMSS compared with the coherent state is researched. We first simulate the effect of noise from another PIA with gain M on the estimation precision of the bright TMSS, and we find that a scheme in which the PIA is placed in the auxiliary light beam path is more robust than two other schemes. Then, a fictitious beam splitter with transmission T is used to simulate the noise effects of propagation loss and imperfect detection, and the results show that a scheme in which the fictitious beam splitter is placed before the original PIA in the probe light beam path is the most robust. Finally, optimal intensity difference measurement is confirmed to be an accessible experimental technique to saturate estimation precision of the bright TMSS. Therefore, our present study opens a new avenue for quantum metrology based on PIAs.

Enhancing and flattening multiplexed quantum entanglement by utilizing perfect vortex modes

We experimentally demonstrate a method for enhancing and flattening multiplexed entanglement in the four-wave mixing (FWM) process, which is implemented by replacing Laguerre-Gaussian (LG) modes with perfect vortex (PV) modes. For the topological charge l ranging from -5 to 5, the entanglement degrees of orbital angular momentum (OAM) multiplexed entanglement with PV modes are all larger than those of OAM multiplexed entanglement with LG modes. More importantly, for OAM multiplexed entanglement with PV modes, the degree of entanglement almost does not change with the topology value. In other words, we experimentally flatten the OAM multiplexed entanglement, which cannot be achieved in OAM multiplexed entanglement with LG modes based on the FWM process. In addition, we experimentally measure the entanglement with coherent superposition OAM modes. Our scheme provides a new, to the best of our knowledge, platform to construct an OAM multiplexed system and may find potential applications in realizing the parallel quantum information protocols.

Experimental measurement of quadrature squeezing in quadripartite entanglement

Multipartite entanglement is one of the most fundamental and important resources for quantum information processing in both discrete variable and continuous variable (CV) regimes. For its applications in the CV regime, such as the realization of quantum teleportation networks and quantum dense coding, the quadrature squeezing of multipartite entanglement plays a significant role. Here, we report the first, to the best of our knowledge, experimental measurement of the quadrature squeezing in the quadripartite entanglement generated by the two-beam pumped cascaded four-wave mixing process in a ⁸⁵ R b vapor cell. Moreover, we find that the quadrature squeezing is nonexistent in each pair of beams, but exists in the whole quadripartite entanglement. Our results may find potential applications in building a multi-user quantum secret sharing network.

Deterministic manipulation of steering between distant quantum network nodes

Multipartite Einstein-Podolsky-Rosen (EPR) steering is a key resource in a quantum network. Although EPR steering between spatially separated regions of ultracold atomic systems has been observed, deterministic manipulation of steering between distant quantum network nodes is required for a secure quantum communication network. Here, we propose a feasible scheme to deterministically generate, store, and manipulate one-way EPR steering between distant atomic cells by a cavity-enhanced quantum memory approach. While optical cavities effectively suppress the unavoidable noises in electromagnetically induced transparency, three atomic cells are in a strong Greenberger-Horne-Zeilinger state by faithfully storing three spatially separated entangled optical modes. In this way, the strong quantum correlation of atomic cells guarantees one-to-two node EPR steering is achieved, and can perserve the stored EPR steering in these quantum nodes. Furthermore, the steerability can be actively manipulated by the temperature of the atomic cell. This scheme provides the direct reference for experimental implementation for one-way multipartite steerable states, which enables an asymmetric quantum network protocol.

Experimental realization of multimode nonlinear parametric amplification from cascading four-wave mixing of dressed atoms

The nonlinear parametric process is of great significance for achieving high-quality coherent optical signals and quantum correlated photons. With the development of classical and quantum information processing, the study of the properties of parametric processes is evolving in complex scenarios of multimode, which is limited in conventional nonlinear media due to strict phase matching, e.g. nonlinear crystals. Here we study the dressing-energy-level-cascaded four-wave mixing process to generate multimode optical parametric signals. Via cascading double-Λ type configuration of ⁸⁵Rb D₁ line, the non-degenerate energy-level-cascaded FWM is constructed to generate multimode self-parametric amplification. Moreover, with the dressing effects based on atomic coherence, the spatial and frequency multimode characteristics of energy-level-cascaded FWM parametric amplification, i.e., the modes number and pattern, are actively modulated by the pump fields detuning. Also, the spatial modes from the coupling of two coexisting spontaneous parametric FWMs can be controlled to reach tremendous scalability via the atomic coherence and Kerr non-linearity. The atomic coherence effects and unique phase-matching symmetry nature allow flexible modulation of the multimode property of the generated parametric signals within a nonlinear device, which paves a way for multimode classical and quantum information processing.

Ultra-Large-Scale Deterministic Entanglement Containing 2×20 400 Optical Modes Based on Time-Delayed Quantum Interferometer

Quantum entanglement is an indispensable resource for implementing quantum information processing. The scale of quantum entanglement directly determines its quantum information processing capability. Therefore, it is of great importance to generate ultra-large-scale (ULS) quantum entanglement for the development of quantum information science and technology. Many efforts have been made to increase the scale of quantum entanglement. Recently, time-domain multiplexing has been introduced into continuous-variable (CV) quantum systems to greatly enlarge the scale of quantum entanglement. In this Letter, based on a time-delayed quantum interferometer, we theoretically propose and experimentally demonstrate a scheme for generating an ULS CV deterministic entanglement containing 2×20 400 optical modes. In addition, such ULS entanglement contains 81 596 squeezed modes. Our results provide a new platform for implementing ULS CV quantum information processing.

Manipulation of continuous variable orbital angular momentum squeezing and entanglement by pump shaping

Spatially structured quantum states, such as orbital angular momentum (OAM) squeezing and entanglement, is currently a popular topic in quantum optics. The method of generating and manipulating spatial quantum states on demand needs to be explored. In this paper, we generated OAM mode squeezed states of -5.4 dB for the L G0+1 mode and -5.3 dB for the L G0-1 mode directly by an optical parametric oscillator (OPO) for the first time. Additionally, we demonstrated that the OAM mode squeezed and entangled states were respectively generated by manipulating the nonlinear process of the OPO by controlling the relative phase of two beams of different modes, thus making two different spatial multimode pump beams. We characterized the Laguerre-Gaussian (LG) entangled states by indirectly measuring the squeezing for the H G _10(45^∘) mode and H G _10(135^∘) mode, and directly measuring the entanglement between the L G0+1 and L G0-1 modes. The effective manipulation of the OAM quantum state provides a novel insight into the continuous variable quantum state generation and construction on demand for high-dimensional quantum information and quantum metrology.

Programmable time-multiplexed squeezed light source

One of the leading approaches to large-scale quantum information processing (QIP) is the continuous-variable (CV) scheme based on time multiplexing (TM). As a fundamental building block for this approach, quantum light sources to sequentially produce time-multiplexed squeezed-light pulses are required; however, conventional CV TM experiments have used fixed light sources that can only output the squeezed pulses with the same squeezing levels and phases. We here demonstrate a programmable time-multiplexed squeezed light source that can generate sequential squeezed pulses with various squeezing levels and phases at a time interval below 100 ns. The generation pattern can be arbitrarily chosen by software without changing its hardware configuration. This is enabled by using a waveguide optical parametric amplifier and modulating its continuous pump light. Our light source will implement various large-scale CV QIP tasks.

Optimal bright multimode quantum squeezing via multi-seeding energy-level cascaded four-wave mixing

Quantum Squeezing is one of the most important quantum resources in quantum optics and quantum information. In particular, multimode quantum squeezing, with ultra-low quantum fluctuations and quantum correlations amongst many optical modes, is essential for realizing multipartite entanglement and quantum precision measurements. In this paper, we propose an all-optically controlled scheme to generate three-mode bright quantum correlated beams from energy-level cascaded four-wave mixing (ELC-FWM). By using a linear modes transform approach, the input-output relation and the covariance matrix of the produced states are obtained. Moreover, single-, double- and triple-seeding conditions are investigated to measure the quantum squeezing properties. We find that various permutations of two- and three-mode quadrature squeezing can be generated and optimized to reach the corresponding limit, via only modulating the ratio of the multiple seeds, without need of any post-operating linear optics, e.g., beam splitters. Such weak seeding light controlled scheme suggests the modulation and the optimization of multimode quantum states might be operated at photons-level, providing a reconfigurable and integrated strategy for complex quantum information processing and quantum metrology.

Time-varying orbital angular momentum in tight focusing of ultrafast pulses

The orbital angular momentum (OAM) of light has important applications in a variety of fields, including optical communication, quantum information, super-resolution microscopic imaging, particle trapping, and others. However, the temporal properties of OAM in ultrafast pulses and in the evolution process of spin-orbit coupling has yet to be revealed. In this work, we theoretically studied the spatiotemporal property of time-varying OAM in the tightly focused field of ultrafast light pulses. The focusing of an incident light pulse composed of two time-delayed femtosecond sub-pulses with the same OAM but orthogonal spin states is investigated, and the ultrafast dynamicsa time delay of OAM variation during the focusing process driven by the spin-orbit coupling is visualized. Temporal properties of three typical examples, including formation, increase, and transformation of topological charge are investigated to reveal the non-uniform evolutions of phase singularities, local topological charges, self-torques, and time-varying OAM per photon. This work could deepen the understanding of spin-orbit coupling in time domain and promote many promising applications such as ultrafast OAM modulation, laser micromachining, high harmonic generation, and manipulation of molecules and nanostructures.

Deterministic distribution of multipartite entanglement in a quantum network by continuous-variable polarization states

Quantum network plays a vitally important role in the practical application of quantum information, which requires the deterministic entanglement distribution among multiple remote users. Here, we propose a feasible scheme to deterministically distribute quadripartite entanglement by continuous-variable (CV) polarization states. The quantum server prepares the quadripartite CV polarization entanglement and distributes them to four remote users via optical fiber. In this way, the measurement of CV polarization entanglement is local oscillation free, which makes the long distance entanglement distribution in commercial optical fiber communication networks possible. Furthermore, both the Greenberger-Horne-Zeilinger-like (GHZ-like) and cluster-like polarization entangled states can be distributed among four users by controlling the beam splitter network in quantum server, which are confirmed by the extended criteria for polarization entanglement of multipartite optical modes. The protocol provides the direct reference for experimental implementation and can be directly extended to quantum network with more users, which is essential for a metropolitan quantum network.

Orbital Angular Momentum Multiplexed Quantum Dense Coding

To beat the channel capacity limit of conventional quantum dense coding (QDC) with fixed quantum resources, we experimentally implement the orbital angular momentum (OAM) multiplexed QDC (MQDC) in a continuous variable system based on a four-wave mixing process. First, we experimentally demonstrate that the Einstein-Podolsky-Rosen entanglement source coded on OAM modes can be used in a single channel to realize the QDC scheme. Then, we implement the OAM MQDC scheme by using the Einstein-Podolsky-Rosen entanglement source coded on OAM superposition modes. In the end, we make an explicit comparison of channel capacities for four different schemes and find that the channel capacity of the OAM MQDC scheme is substantially enhanced compared to the conventional QDC scheme without multiplexing. The channel capacity of our OAM MQDC scheme can be further improved by increasing the squeezing parameter and the number of multiplexed OAM modes in the channel. Our results open an avenue to construct high-capacity quantum communication networks.

Multidimensional four-wave mixing signals detected by quantum squeezed light

Quantum light and its statistics provide powerful tools for the study of properties of matter that are difficult to retrieve with classical light. Novel spectroscopic and sensing techniques based on quantum light sources can reveal information about complex material systems that is not accessible by varying the frequencies or time delays of classical light pulses. Here, based on a four-wave mixing process, we report an experimental study of the 2D quantum noise spectra of two-beam intensity difference squeezing. External noise erodes the resolution of classical measurements, while quantum signals remain intact. Our results pave the way for exploiting quantum correlations of squeezed light for spectroscopic applications.

Four-wave mixing (FWM) of optical fields has been extensively used in quantum information processing, sensing, and memories. It also forms a basis for nonlinear spectroscopies such as transient grating, stimulated Raman, and photon echo where phase matching is used to select desired components of the third-order response of matter. Here we report an experimental study of the two-dimensional quantum noise intensity difference spectra of a pair of squeezed beams generated by FWM in hot Rb vapor. The measurement reveals details of the χ(3) susceptibility dressed by the strong pump field which induces an AC Stark shift, with higher spectral resolution compared to classical measurements of probe and conjugate beam intensities. We demonstrate how quantum correlations of squeezed light can be utilized as a spectroscopic tool which unlike their classical counterparts are robust to external noise.

Experimental Demonstration of a Multifunctional All-Optical Quantum State Transfer Machine

Quantum information protocol with quantum resources shows a great advantage in substantially improving security, fidelity, and capacity of information processing. Various quantum information protocols with diverse functionalities have been proposed and implemented. However, in general, the present quantum information system can only carry out a single information protocol or deal with a single communication task, which limits its practical application in the future. Therefore, it is essential to develop a multifunctional platform compatible with multiple different quantum information protocols. In this Letter, by utilizing an all-optical platform consisting of a gain-tunable parametric amplifier, a beam splitter, and an entanglement source, we experimentally realize the partially disembodied quantum state transfer protocol, which links the all-optical quantum teleportation protocol and the optimal 1→N coherent state cloning protocol. As a result, these three protocols, which have different physical essences and functionalities, are implemented in a single all-optical machine. In particular, we demonstrate that the partially disembodied quantum state transfer protocol can enhance the state transfer fidelity compared with all-optical quantum teleportation under the same strength of entanglement. Our all-optical quantum state transfer machine paves a way to implement the multifunctional quantum information system.

Spatially dependent hyper-Raman scattering in five-level cold atoms

We demonstrate a scheme to control the spatially dependent hyper-Raman scattering based on electromagnetically induced transparency in a cold atomic system. By adjusting the different system parameters, one can effectively modulate the phase and intensity of the generated Raman field. Specifically, we show that electromagnetically induced transparency creates quantum interference, which results in greatly enhanced efficiency for the generated Raman field. Such improvement in Raman efficiency makes our scheme suitable for generation of short-wavelength coherent radiation, conversion of frequency, and nonlinear spectroscopy based on orbital angular momentum light.

Nonlinear interferometric surface-plasmon-resonance sensor

A nonlinear interferometer can be constructed by replacing the beam splitter in the Mach-Zehnder interferometer with four-wave mixing (FWM) process. Meanwhile, the conventional surface plasmon resonance (SPR) sensors can be extensively used to infer the information of refractive index of the sample to be measured via either angle demodulation technique or intensity demodulation technique. Combined with a single FWM process, a quantum SPR sensor has been realized, whose noise floor is reduced below standard quantum limit with sensitivity unobtainable with classical SPR sensor. Therefore, in this work we have theoretically proposed a nonlinear interferometric SPR sensor, in which a conventional SPR sensor is placed inside nonlinear interferometer, which is called as I-type nonlinear interferometric SPR sensor. We demonstrate that near resonance angle I-type nonlinear interferometric SPR sensor has the following advantages: its degree of intensity-difference squeezing, estimation precision ratio, and signal-noise-ratio are improved by the factors of 4.6 dB, 2.3 dB, and 4.6 dB respectively than that obtained with a quantum SPR sensor based on a single FWM process. In addition, the theoretical principle of this work can also be expanded to other types of sensing, such as bending, pressure, and temperature sensors based on a nonlinear interferometer.

Near-Field Vortex Beams Diffraction on Surface Micro-Defects and Diffractive Axicons for Polarization State Recognition

The diffraction of vortex Gaussian laser beams by elementary objects of micro-optics (surface micro-defects) to recognize the type of polarization (linear, circular, radial, azimuthal) of the input radiation was investigated in this paper. We considered two main types of defects (protrusion and depression in the form of a circle and a square) with different sizes (the radius and height were varied). Light propagation (3D) through the proposed micro-defects was modeled using the finite difference time domain (FDTD) method. The possibility of recognizing (including size change) of surface micro-defects (protrusions and depressions) and all the above types of polarization are shown. Thus, micro-defects act as sensors for the polarization state of the illuminating beam. The focusing properties of micro-defects are compared with diffractive axicons with different numerical apertures (NAs). The possibility of sub-wavelength focusing with element height change is demonstrated. In particular, it is numerically shown that a silicon cylinder (protrusion) forms a light spot with a minimum size of the all intensity FWHM of 0.28λ.

Characterization of quantum squeezing generated from the phase-sensitive and phase-insensitive amplifiers in the ultra-low average input photon number regime

We give the general expressions of intensity-difference squeezing (IDS) generated from two types of optical parametric amplifiers [i.e. phase-sensitive amplifier (PSA) and phase-insensitive amplifier (PIA)] based on the four-wave mixing process, which clearly shows the IDS transition between the ultra-low average input photon number regime and the ultra-high average input photon number regime. We find that both the IDS of the PSA and the IDS of the PIA get enhanced with the decrease of the average input photon number especially in the ultra-low average input photon number regime. This result is substantially different from the result in the ultra-high average input photon number regime where the IDS does not vary with the average input photon number. Moreover, under the same intensity gain, we find that the optimal IDS of the PSA is better than the IDS of the PIA in the ultra-low average input photon number regime. Our theoretical work predicts the presence of strong quantum correlation in the ultra-low average input photon number regime, which may have potential applications for probing photon-sensitive biological samples.

Large-Scale Quantum Network over 66 Orbital Angular Momentum Optical Modes

Multipartite entanglement (ME) is the fundamental ingredient for building quantum networks. The scale of ME determines its quantum information carrying and processing capability. Most of the current efforts for boosting the scale of ME focus on increasing the number of entangled nodes. However, the number of channels for broadcasting ME is also an important index for characterizing its scale. In this Letter, we experimentally exploit orbital angular momentum multiplexing and the spatial pump shaping technique to simultaneously and deterministically generate 11 channels of individually accessible and mutually orthogonal continuous variable (CV) spatially separated hexapartite entangled states over 66 optical modes in a single quantum system. These results suggest that our method can greatly expand the scale of ME and provide a new perspective and platform to construct a CV quantum network.

High-fidelity heralded quantum squeezing gate based on entanglement

Squeezing operation is critical in Gaussian quantum information. A high-fidelity heralded squeezing gate was recently realized using a noiseless linear amplifier with moderate ancillary squeezing. Here we analyze the heralded scheme based on squeezing [J. Zhao, Nat. Photonics, 14, 306 (2020)] and find that its fidelity depends heavily on the purity of auxiliary squeezing, and even the fidelity with a 6 dB pure squeezed state is better than with a 15 dB thermal squeezed state. On this basis, we construct a new heralded squeezing gate based on teleportation, which can overcome the shortcomings of the heralded scheme based on squeezing and is immune to the purity of input squeezing. It can better use the current best available squeezing (15 dB) to realize a perfect squeezing gate for fault-tolerant continuous-variable quantum computation. This scheme is promising to realize other single-mode Gaussian operations and non-classical state squeezing operations.

Topological charge of asymmetric optical vortices

We obtain theoretical relationships to define topological charge (TC) of vortex laser beams devoid of radial symmetry, namely asymmetric Laguerre-Gaussian (LG), asymmetric Bessel-Gaussian (BG), and asymmetric Kummer beams, as well as Hermite-Gaussian (HG) vortex beams. Although they are obtained as superposition of respective conventional LG, BG, and HG beams, these beams have the same TC equal to that of a single mode, n. At the same time, the normalized orbital angular momentum (OAM) that the beams carry is different, differently responding to the variation of the beam's asymmetry degree. However, whatever the asymmetry degree, TC of the beams remains unchanged and equals n. Although separate HG beam does not have OAM and TC, superposition of only two HG modes with adjacent numbers (n, n + 1) and a π/2-phase shift produces a modal beam whose TC is -(2n + 1). Theoretical findings are validated via numerical simulation.

Observation of the interplay between seeded and self-seeded nondegenerate four-wave mixing in cesium vapor

Nondegenerate four-wave mixing (NFWM) is a practical and effective technique for generating or amplifying light fields at different wavelengths, and could be used to create color correlation and entanglement. Here we experimentally investigate the NFWM process in diamond atomic system via two-photon excitation with two pumps at 852 nm and 921 nm, demonstrating that a seeded NFWM with a third laser at 895 nm and two self-seeded NFWMs due to amplified spontaneous emission (ASE) occur simultaneously. We compare the two kinds of processes and show that the single- and two-photon detunings hold the key role in distinguishing them. As a result, the enhancement of seeded NFWM is obtained by selecting large one- and two-photon detunings, in which case the ASE induced self-seeded NFWM can be largely suppressed. In contrast, the ASE and its induced NFWM are effectively achieved with one- and two-photon resonant excitations allowing for population inversion for efficient ASE.

Enhancement of quantum correlations using correlation injection scheme in a cascaded four-wave mixing processes

Quantum correlations and entanglement shared among multiple quantum beams are important for both fundamental science and the development of quantum technologies. The enhancement for them is necessary and important to implement the specific quantum tasks and goals. Here, we report a correlation injection scheme (CIS) which is an effective method to enhance the quantum correlations and entanglement in the symmetrical cascaded four-wave mixing processes, and the properties of quantum correlations and entanglement can be characterized by the values of the degree of intensity-difference squeezing (DS) and the smallest symplectic eigenvalues, respectively. Our results show that the CIS can enhance the quantum correlations and entanglement under certain conditions, while for other conditions it can only decrease the values of the DS and the smallest symplectic eigenvalues to the level of standard quantum limit, respectively. We believe that our scheme is experimentally accessible and will contribute to a deeper understanding of the manipulations of the quantum correlations and entanglement in various quantum networks.