Multipartite Continuous-variable Entanglement Research Articles

Sculpting bosonic states with arithmetic subtractions

Continuous-variable (CV) encoding allows information to be processed compactly and efficiently on quantum processors. Recently developed techniques such as controlled beam-splitter operations and the near deterministic phonon subtractions make trapped ion systems attractive for exploring CV quantum computing. Here we propose a probabilistic scheme based on the boson sculpting technique for generating multipartite highly entangled states of motional modes of trapped ion systems. We also investigate the effects of decoherence on the fidelity of the generated state by performing numerical simulations with realistic noise parameters. Our work is a step towards generating multipartite CV entanglement.

Generation of multiple entangled fields via mechanical oscillator displacement

We present a convenient and efficient scheme to generate arbitrarily multipartite continuous-variable entanglement via mechanical oscillator displacement induced by two strong input pump fields in the conventional single-cavity optomechanical system. It is shown that multipartite entanglement among the outputs of the two pump fields and any number of relatively weak probe fields can be realized and optimized when the two pump fields with suitable amplitude ratio and relative initial phase are, respectively, tuned to the red and blue mechanical sidebands of a single cavity mode and each probe field is red-detuned by the mechanical frequency with respect to a different neighboring cavity mode. This method can, in principle, be extended to flexibly and conveniently generate arbitrarily multiple nondegenerate bright entangled fields by using only coherent laser fields, and may find promising applications in realistic quantum communication and networks.

Continuous-variable entangled states of light carrying orbital angular momentum

The orbital angular momentum of light, unlike spin, is an infinite-dimensional discrete variable and may hence offer enhanced performances for encoding, transmitting, and processing quantum information. Hitherto, this degree of freedom of light has been studied mainly in the context of quantum states with definite number of photons. On the other hand, field-quadrature continuous-variable quantum states of light allow implementing many important quantum protocols not accessible with photon-number states. Here, we realize a scheme based on a $q$-plate device for endowing a bipartite continuous-variable Gaussian entangled state with nonzero orbital angular momentum. We then apply a reconfigurable homodyne detector working directly with such nonzero orbital angular momentum modes in order to retrieve experimentally their entire quantum-state covariance matrix, thus providing a full characterization of their quantum fluctuation properties. Our work is a step towards generating multipartite continuous-variable entanglement in a single optical beam.

Bright four-color quadripartite entanglement from quasi-phase-matching cascaded nonlinear optical frequency conversion

We propose an experimentally feasible scheme to produce bright four-color continuous-variable entanglement by intracavity quasi-phase-matching cascaded nonlinear optical frequency conversion in only one optical superlattice. The second, third and fourth harmonics can be generated by frequency doubling of the input fundamental field at frequency , the sum frequency of fundamental and second harmonic fields, and frequency doubling of the second harmonic field, respectively. The entanglement properties influenced by system parameters are theoretically discussed according to the sufficient inseparability criterion proposed by van Loock and Furusawa. Such compact multipartite continuous-variable entanglement has potential applications in quantum communication and computation networks.

Zero supermode-based multipartite entanglement in χ(2) nonlinear waveguide arrays

We show that arrays of $\chi^{(2)}$ nonlinear waveguides in the second harmonic generation regime are a promising source of continuous-variable entanglement. We indeed demonstrate analytically that optical arrays with odd number of waveguides injected with the zero-eigenvalue fundamental supermode entangle this fundamental supermode with a collective harmonic field. Moreover the fundamental individual modes are multipartite entangled and their entanglement grows with propagation length. The device is scalable, robust to losses, does not rely on specific values of nonlinearity and coupling and is easily realized with current technology. It thus stands as an unprecedented candidate for generation of multipartite continuous-variable entanglement for optical quantum information processing.

Characterizing the multipartite continuous-variable entanglement structure from squeezing coefficients and the Fisher information

Understanding the distribution of quantum entanglement over many parties is a fundamental challenge of quantum physics and is of practical relevance for several applications in the field of quantum information. The Fisher information is widely used in quantum metrology since it is related to the quantum gain in metrology measurements. Here, we use methods from quantum metrology to microscopically characterize the entanglement structure of multimode continuous-variable states in all possible multi-partitions and in all reduced distributions. From experimentally measured covariance matrices of Gaussian states with 2, 3, and 4 photonic modes with controllable losses, we extract the metrological sensitivity as well as an upper separability bound for each partition. An entanglement witness is constructed by comparing the two quantities. Our analysis demonstrates the usefulness of these methods for continuous-variable systems and provides a detailed geometric understanding of the robustness of cluster-state entanglement under photon losses.

Implementation of bright six-partite entanglement by coupled intracavity sum frequency generation

Bright six-partite continuous-variable (CV) entanglement generated by the coupled intracavity sum frequency generation is investigated. The entanglement characteristics of reflected pump fields and the output sum frequency fields are discussed theoretically in symmetric and asymmetric cases by applying van Loock and Furusawa criteria for multipartite CV entanglement. Such compact tunable multipartite CV entanglement, generated from an experimentally feasible coupled system, could be used in integrated quantum communication and networks.

Bright six-partite entanglement from coupled intracavity nondegenerate parametric down-conversion

We propose an experimentally feasible scheme to produce bright six-partite continuous-variable (CV) entanglement by coupled intracavity non-degenerate parametric down-conversion operating above-threshold. The six-partite entanglement properties of the output fields are theoretically analyzed according to the sufficient inseparability criterion for multipartite CV entanglement. Such compact tunable multipartite CV entanglement, generated from a coupled system, could be used in quantum communications and networks.

Systematic construction of genuine-multipartite-entanglement criteria in continuous-variable systems using uncertainty relations

A general procedure to construct criteria for identifying genuine multipartite continuous variable entanglement is presented. It relies on the proper definition of adequate global operators describing the multipartite system, the positive partial transpose criterion of separability, and quantum mechanical uncertainty relations. As a consequence, each criterion encountered consists of a single inequality that is nicely computable and experimentally feasible, and that when violated is sufficient condition for genuine multipartite entanglement. Additionally we show that the previous work of van Loock and Furusawa [Phys. Rev. A, 67, 052315 (2003)] is a special case of our result that includes strongest criteria to detect entanglement.

Multipartite continuous-variable entanglement in a multi-mode period pumping non-degenerate optical parametric amplifier

The multipartite continuous-variable (CV) entanglement characteristic of a multi-mode phased-locked period pumping non-degenerate optical parametric amplification system was investigated for the case when finite bandwidth is considered. A continuously modulated pumping with a sinusoidal envelope can produce an improvement in the minimum values of the multipartite CV entanglement. The minimum variances can be described approximately by the linear theory formula . We should take a proper bandwidth Δω in order to obtain a long-term entanglement. The larger values of pump parameter μ and particle number N result in long-term entanglement.

Effect of the dispersion on multipartite continuous-variable entanglement in optical parametric amplifier**Project supported by the State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China (Grant No. KF201401) and the National Natural Science Foundation of China (Grant No. 11404084).

Based on the quantum fluctuations, we adopt the method of generalized V1 criterion to investigate multipartite entanglement characteristics in an optical parametric amplification system with the consideration of dispersion. The nonlinear interaction becomes strong because of the existence of dispersion coefficient σ . Considering the influence of dispersion factor σ , with increasing the pump parameter μ , the value of minimum variance V1 decreases and the squeezing curve nearly equals 1/(1 + μ ). The larger particle number N results in a smaller variance and higher entanglement.

Generation of multipartite continuous-variable entanglement via atomic spin wave: Heisenberg-Langevin approach

We conduct theoretical studies on the effects of various parameters on generation of multipartite continuous-variable entanglement via atomic spin wave induced by the strong coupling and probe fields in the Λ-type electromagnetically induced transparency configuration in a realistic atomic ensemble by using the Heisenberg-Langevin formalism. It is shown that the increase of the atomic density and/or Rabi frequencies of the scattering fields, as well as the decrease of the coherence decay rate of the lower doublet would strengthen the degree of multipartite entanglement. This provides a clear evidence that the creation of multicolor multipartite entangled narrow-band fields to any desired number with a long correlation time can be achieved conveniently by using atomic spin wave in an atomic ensemble with large optical depth, which may find interesting applications in quantum information processing and quantum networks.

Implementation of bright two-color quadripartite continuous-variable entanglement by the quantum optical dimer

An experimentally feasible intracavity coupler scheme is proposed to generate bright quadripartite continuous-variable (CV) entanglement by the coupled second-harmonic generation processes. By solving the steady-state equations and calculating the correlation spectra of the four output beams, we show that the four output beams are all entangled with each other according to the sufficient inseparability criterion for multipartite CV entanglement. By utilizing the upconversion process, the generated four entanglement fields have macroscopic intensities as soon as the input fields are turned on.

Generation of six-partite continuous-variable entanglement using a nonlinear photonic crystal by frequency conversions

We theoretically show that six-partite continuous-variable entanglement can be generated by nonlinear optical processes conducted in a designed photonic crystal-like periodically poled lithium niobat (PPLN). The processes consist of a nonlinear parametric down-conversion and four sum-frequency processes. The characteristics of the six-partite entanglement among the six beams are analyzed both above and below the threshold by applying a sufficient inseparability criterion for multipartite continuous-variable entanglement. We investigated our proposal for a specific case of a PPLN optical superlattice with fixed light and material properties.

The influence of pump depletion on multipartite continuous-variable entanglement in a frequency non-degenerate parametric amplifier

The multipartite continuous variable (CV) entanglement characteristic of a frequency non-degenerate optical parametric amplification (FNOPA) system was investigated for the case when pump depletion is considered. The multipartite CV entanglement depends on the pump parameter, μ, the squeezed parameter, r, and particle number, N. Larger values of pump parameter μ and particle number N result in a very small variance, , and a long-term entanglement.

Scalable network of quadrangle entanglements via multiple phase-dependent electromagnetically induced transparency

One important class of multipartite continuous variable entanglement is described by a closed polygon, where every vertex represents one optical field and every side corresponds to the entanglement between the two connected vertices. Here we show that it is possible to obtain a scalable network of quadrangle entanglements by using multiple phase-dependent electromagnetically induced transparency. For $4,6,8,\dots{},2n (n\ensuremath{\geqslant}2)$ mode cases the network consists of $1,9,36,\dots{},\frac{1}{4}{n}^{2} (n\ensuremath{-}1){}^{2}$ quadrangles, respectively. This suggests an efficient way of creating complex quantum networks and has great potentials for quantum information and computation.

Scheme to generate three-mode continuous-variable entanglement in cavity quantum electrodynamics

We propose a theoretical method of generating a three-mode continuous-variable entanglement in an optical cavity with an atomic cloud. The scheme uses Raman transitions between stable atomic ground states and under the input–output theory a three-mode entangled light of the output fields can be produced. The characters of the tripartite entanglement, the degree of the quadrature-phase amplitude correlations among the three modes are discussed by applying a sufficient inseparability criterion for multipartite continuous-variable entanglement, which was proposed by van Loock and Furusawa. The dependences of the correlation on the effective coupling constants are theoretically analyzed.

Scheme to generate continuous-variable quadripartite entanglement by intracavity down-conversion cascaded with double sum-frequency generations

We theoretically show that continuous-variable genuine quadripartite entanglement can be generated by intracavity cascaded nonlinear optical interactions. The process consists of a parametric down-conversion, a sum-frequency generation of pump and signal and a sum-frequency generation of pump and idler. The characteristics of the quadripartite entanglement among the signal, the idler, and two sum-frequency modes are analyzed by applying a sufficient inseparability criterion for multipartite continuous-variable entanglement proposed by Van Loock and Furusawa. The threshold properties of the system are also discussed.

Manipulating quantum information by propagation

We study creation of bi- and multipartite continuous variable entanglement in structures of coupled quantum harmonic oscillators. By adjusting the interaction strengths between nearest neighbors we show how to maximize the entanglement production between the arms in a Y-shaped structure where an initial single mode squeezed state is created in the first oscillator of the input arm. We also consider the action of the same structure as an approximate quantum cloner. For a specific time in the system dynamics the last oscillators in the output arms can be considered as imperfect copies of the initial state. By increasing the number of arms in the structure, multipartite entanglement is obtained, as well as 1 to M cloning. Finally, we are considering configurations that implement the symmetric splitting of an initial entangled state. All calculations are carried out within the framework of the rotating wave approximation in quantum optics, and our predictions could be tested with current available experimental techniques.

Observation of triply coincident nonlinearities in periodically poled KTiOPO_4

We report the simultaneous quasi-phase-matching of all three possible nonlinearities for propagation along the X axis of periodocally poled (PP) KTiOPO4 (KTP) for second-harmonic generation of 745 nm pulsed light from 1490nm subpicosecond pulses in a PPKTP crystal with a 45.65 micrometer poling period. This confirms the recent Sellmeier fits of KTP by K. Kato and E. Takaoka [Appl. Opt. 41, 5040 (2002)]. Such coincident nonlinearities are of importance for realizing compact sources of multipartite continuous-variable entanglement [Pfister et al., Phys. Rev. A 70, 020302 (2004)] and we propose a new simpler method for entangling four fields, based on this triple coincidence.