Stimulated emission of polarization-entangled photons

Localization-enhanced moiré exciton in twisted transition metal dichalcogenide heterotrilayer superlattices

The stacking of twisted two-dimensional (2D) layered materials has led to the creation of moiré superlattices, which have become a new platform for the study of quantum optics. The strong coupling of moiré superlattices can result in flat minibands that boost electronic interactions and generate interesting strongly correlated states, including unconventional superconductivity, Mott insulating states, and moiré excitons. However, the impact of adjusting and localizing moiré excitons in Van der Waals heterostructures has yet to be explored experimentally. Here, we present experimental evidence of the localization-enhanced moiré excitons in the twisted WSe₂/WS₂/WSe₂ heterotrilayer with type-II band alignments. At low temperatures, we observed multiple excitons splitting in the twisted WSe₂/WS₂/WSe₂ heterotrilayer, which is manifested as multiple sharp emission lines, in stark contrast to the moiré excitonic behavior of the twisted WSe₂/WS₂ heterobilayer (which has a linewidth 4 times wider). This is due to the enhancement of the two moiré potentials in the twisted heterotrilayer, enabling highly localized moiré excitons at the interface. The confinement effect of moiré potential on moiré excitons is further demonstrated by changes in temperature, laser power, and valley polarization. Our findings offer a new approach for localizing moiré excitons in twist-angle heterostructures, which has the potential for the development of coherent quantum light emitters.

Unconditional and Robust Quantum Metrological Advantage beyond N00N States

Quantum metrology employs quantum resources to enhance the measurement sensitivity beyond that can be achieved classically. While multiphoton entangled N00N states can in principle beat the shot-noise limit and reach the Heisenberg limit, high N00N states are difficult to prepare and fragile to photon loss which hinders them from reaching unconditional quantum metrological advantages. Here, we combine the idea of unconventional nonlinear interferometers and stimulated emission of squeezed light, previously developed for the photonic quantum computer Jiuzhang, to propose and realize a new scheme that achieves a scalable, unconditional, and robust quantum metrological advantage. We observe a 5.8(1)-fold enhancement above the shot-noise limit in the Fisher information extracted per photon, without discounting for photon loss and imperfections, which outperforms ideal 5-N00N states. The Heisenberg-limited scaling, the robustness to external photon loss, and the ease-of-use of our method make it applicable in practical quantum metrology at a low photon flux regime.

Microtubules as a potential platform for energy transfer in biological systems: a target for implementing individualized, dynamic variability patterns to improve organ function

Variability characterizes the complexity of biological systems and is essential for their function. Microtubules (MTs) play a role in structural integrity, cell motility, material transport, and force generation during mitosis, and dynamic instability exemplifies the variability in the proper function of MTs. MTs are a platform for energy transfer in cells. The dynamic instability of MTs manifests itself by the coexistence of growth and shortening, or polymerization and depolymerization. It results from a balance between attractive and repulsive forces between tubulin dimers. The paper reviews the current data on MTs and their potential roles as energy-transfer cellular structures and presents how variability can improve the function of biological systems in an individualized manner. The paper presents the option for targeting MTs to trigger dynamic improvement in cell plasticity, regulate energy transfer, and possibly control quantum effects in biological systems. The described system quantifies MT-dependent variability patterns combined with additional personalized signatures to improve organ function in a subject-tailored manner. The platform can regulate the use of MT-targeting drugs to improve the response to chronic therapies. Ongoing trials test the effects of this platform on various disorders.

Menezes L, Tittl A, Ren H, Maier SA. Optical Metasurfaces for Energy Conversion

Nanostructured surfaces with designed optical functionalities, such as metasurfaces, allow efficient harvesting of light at the nanoscale, enhancing light-matter interactions for a wide variety of material combinations. Exploiting light-driven matter excitations in these artificial materials opens up a new dimension in the conversion and management of energy at the nanoscale. In this review, we outline the impact, opportunities, applications, and challenges of optical metasurfaces in converting the energy of incoming photons into frequency-shifted photons, phonons, and energetic charge carriers. A myriad of opportunities await for the utilization of the converted energy. Here we cover the most pertinent aspects from a fundamental nanoscopic viewpoint all the way to applications.

Nonreciprocity in Photon Pair Correlations of Classically Reciprocal Systems

Nonreciprocal optical systems have found many applications altering the linear transmission of light as a function of its propagation direction. Here, we consider a new class of nonreciprocity which appears in photon pair correlations and not in linear transmission. We experimentally demonstrate and theoretically verify this nonreciprocity in the second-order coherence functions of photon pairs produced by spontaneous four-wave mixing in a silicon microdisk. Reversal of the pump propagation direction can result in substantial extinction of the coherence functions without altering pump transmission.

Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light

We report phase-programmable Gaussian boson sampling (GBS) which produces up to 113 photon detection events out of a 144-mode photonic circuit. A new high-brightness and scalable quantum light source is developed, exploring the idea of stimulated emission of squeezed photons, which has simultaneously near-unity purity and efficiency. This GBS is programmable by tuning the phase of the input squeezed states. The obtained samples are efficiently validated by inferring from computationally friendly subsystems, which rules out hypotheses including distinguishable photons and thermal states. We show that our GBS experiment passes a nonclassicality test based on inequality constraints, and we reveal nontrivial genuine high-order correlations in the GBS samples, which are evidence of robustness against possible classical simulation schemes. This photonic quantum computer, Jiuzhang 2.0, yields a Hilbert space dimension up to ∼10^{43}, and a sampling rate ∼10^{24} faster than using brute-force simulation on classical supercomputers.

Resonant Coupling of a Moiré Exciton to a Phonon in a WSe2/MoSe2 Heterobilayer

Moiré patterns with an angular mismatch in van der Waals heterostructures are a fascinating platform to engineer optically generated excitonic properties. The moiré pattern can give rise to spatially ordered exciton ensembles, which offer the possibility for coherent quantum emitters and quantum simulation of many-body physics. The intriguing moiré exciton properties are affected by their dynamics and exciton-phonon interaction. Here, we report the moiré exciton and phonon interaction in a twisted WSe₂/MoSe₂ heterobilayer. By tuning the excitation energy, we realized the selective excitation of the moiré exciton at phonon resonances and the otherwise negligible small absorption. Furthermore, we revealed the relaxation of moiré exciton ensembles between different potential minima via the resonant phonon scattering process. Our findings highlight resonant coupling of a moiré exciton to a phonon and could pave a new way for the exploration of novel quantum phenomena of the moiré exciton.

Experimentally Demonstrate the Spin-1 Information Entropic Inequality Based on Simulated Photonic Qutrit States

Quantum correlations of higher-dimensional systems are an important content of quantum information theory and quantum information application. The quantification of quantum correlation of high-dimensional quantum systems is crucial, but difficult. In this paper, using the second-order nonlinear optical effect and multiphoton interference enhancement effect, we experimentally implement the photonic qutrit states and demonstrate the spin-1 information entropic inequality for the first time to quantitative quantum correlation. Our work shows that information entropy is an important way to quantify quantum correlation and quantum information processing.

Hanbury Brown-Twiss Correlations for a Driven Superatom

Hanbury Brown-Twiss interference and stimulated emission, two fundamental processes in atomic physics, have been studied in a wide range of applications in science and technology. We study interference effects that occur when a weak probe is sent through a gas of two-level atoms that are prepared in a singly excited collective (Dicke or "superatom") state and for atoms prepared in a factorized state. We measure the time-integrated second-order correlation function g^{(2)} of the output field as a function of the delay τ between the input probe field and radiation emitted by the atoms and find that, for the Dicke state, g^{(2)} is twice as large for τ=0 as it is for γ_{e}τ≫1 (γ_{e} is an excited state decay rate), while for the product state, this ratio is equal to 3/2. The results agree with those of a theoretical model in which any effects related to stimulated emission are totally neglected-the coincidence counts measured in our experiment arise from Hanbury Brown-Twiss interference between the input field and the field radiated by the atoms.

Interlayer valley excitons in heterobilayers of transition metal dichalcogenides

Stacking different two-dimensional crystals into van der Waals heterostructures provides an exciting approach to designing quantum materials that can harness and extend the already fascinating properties of the constituents. Heterobilayers of transition metal dichalcogenides are particularly attractive for low-dimensional semiconductor optics because they host interlayer excitons-with electrons and holes localized in different layers-which inherit valley-contrasting physics from the monolayers and thereby possess various novel and appealing properties compared to other solid-state nanostructures. This Review presents the contemporary experimental and theoretical understanding of these interlayer excitons. We discuss their unique optical properties arising from the underlying valley physics, the strong many-body interactions and electrical control resulting from the electric dipole moment, and the unique effects of a moiré superlattice on the interlayer exciton potential landscape and optical properties.

Quantum interferometric generation of polarization entangled photons

Quantum interference, like Hong-Ou-Mandel interference, has played an important role to test fundamental concepts in quantum physics. We experimentally show that the multiple quantum interference effects enable the generation of high-performance polarization entangled photons. These photons have a high-emission rate, are degenerate, have a broadband distribution, and are postselection free. A quantum interferometric scheme, based on a round-trip configuration of a double-pass polarization Sagnac interferometer, makes it possible to use the large generation efficiency of polarization entangled photons in the process of parametric down-conversion and to separate degenerate photon pairs into different optical modes with no requirement of postselection. We demonstrate experimentally that multiple quantum interference is not only an interesting fundamental quantum optical phenomenon but can be used for novel photonic quantum information technologies.

Scalable symmetry detector and its applications by using beam splitters and weak nonlinearities

We describe a method to detect twin-beam multiphoton entanglement based on a beam splitter and weak nonlinearities. For the twin-beam four-photon entanglement, we explore a symmetry detector. It works not only for collecting two-pair entangled states directly from the spontaneous parametric down-conversion process, but also for generating them by cascading these symmetry detectors. Surprisingly, by calculating the iterative coefficient and the success probability we show that with a few iterations the desired two-pair can be obtained from a class of four-photon entangled states. We then generalize the symmetry detector to n-pair emissions and show that it is capable of determining the number of the pairs emitted indistinguishably from the spontaneous parametric down-conversion source, which may contribute to explore multipair entanglement with a large number of photons.

Moiré excitons: From programmable quantum emitter arrays to spin-orbit-coupled artificial lattices

Highly uniform and ordered nanodot arrays are crucial for high-performance quantum optoelectronics, including new semiconductor lasers and single-photon emitters, and for synthesizing artificial lattices of interacting quasiparticles toward quantum information processing and simulation of many-body physics. Van der Waals heterostructures of two-dimensional semiconductors are naturally endowed with an ordered nanoscale landscape, that is, the moiré pattern that laterally modulates electronic and topographic structures. We find that these moiré effects realize superstructures of nanodot confinements for long-lived interlayer excitons, which can be either electrically or strain tuned from perfect arrays of quantum emitters to excitonic superlattices with giant spin-orbit coupling (SOC). Besides the wide-range tuning of emission wavelength, the electric field can also invert the spin optical selection rule of the emitter arrays. This unprecedented control arises from the gauge structure imprinted on exciton wave functions by the moiré, which underlies the SOC when hopping couples nanodots into superlattices. We show that the moiré hosts complex hopping honeycomb superlattices, where exciton bands feature a Dirac node and two Weyl nodes, connected by spin-momentum-locked topological edge modes.

Observation of Four-Photon Orbital Angular Momentum Entanglement

We demonstrate genuine multipartite quantum entanglement of four photons in their orbital angular momentum degrees of freedom, where a high-dimensional discrete Hilbert space is attached to each photon. This can encode more quantum information compared to the qubit case, but it is a long-standing problem to entangle more than two such photons. In our experiment we use pulsed spontaneous parametric down-conversion to produce the photon quadruplets, which allows us to detect about one four-photon event per second. By means of quantum state reconstruction and a suitable witness operator we find that the photon quadruplets form a genuine multipartite entangled symmetric Dicke state. This opens a new tool for addressing foundational questions in quantum mechanics, and for exploration of novel high-dimensional multiparty quantum information applications such as secret sharing.

Loss resilience for two-qubit state transmission using distributed phase sensitive amplification

We transmit phase-encoded non-orthogonal quantum states through a 5-km long fibre-based distributed optical phase-sensitive amplifier (OPSA) using telecom-wavelength photonic qubit pairs. The gain is set to equal the transmission loss to probabilistically preserve input states during transmission. While neither state is optimally aligned to the OPSA, each input state is equally amplified with no measurable degradation in state quality. These results promise a new approach to reduce the effects of loss by encoding quantum information in a two-qubit Hilbert space which is designed to benefit from transmission through an OPSA.

A quantum dot single-photon source with on-the-fly all-optical polarization control and timed emission

Sources of single photons are key elements for applications in quantum information science. Among the different sources available, semiconductor quantum dots excel with their integrability in semiconductor on-chip solutions and the potential that photon emission can be triggered on demand. Usually, the photon is emitted from a single-exciton ground state. Polarization of the photon and time of emission are either probabilistic or pre-determined by electronic properties of the system. Here, we study the direct two-photon emission from the biexciton. The two-photon emission is enabled by a laser pulse driving the system into a virtual state inside the band gap. From this intermediate state, the single photon of interest is then spontaneously emitted. We show that emission through this higher-order transition provides a versatile approach to generate a single photon. Through the driving laser pulse, polarization state, frequency and emission time of the photon can be controlled on-the-fly.

Single photon sources are important for applications in quantum information. Here, the authors exploit higher-order transitions from a biexciton state to the ground state of a semiconductor quantum dot to emit single photons with all-optical control of their frequency, polarization and emission time.

Exploration of photon-number entangled states using weak nonlinearities

A method for exploring photon-number entangled states with weak nonlinearities is described. We show that it is possible to create and detect such entanglement at various scales, ranging from microscopic to macroscopic systems. In the present architecture, we suggest that the maximal phase shift induced in the process of interaction between photons is proportional to photon numbers. Also, in the absence of decoherence we analyze maximum error probability and show its feasibility with current technology.

Giant narrowband twin-beam generation along the pump-energy propagation direction

Walk-off effects, originating from the difference between the group and phase velocities, limit the efficiency of nonlinear optical interactions. While transverse walk-off can be eliminated by proper medium engineering, longitudinal walk-off is harder to avoid. In particular, ultrafast twin-beam generation via pulsed parametric down-conversion and four-wave mixing is only possible in short crystals or fibres. Here we show that in high-gain parametric down-conversion, one can overcome the destructive role of both effects and even turn them into useful tools for shaping the emission. In our experiment, one of the twin beams is emitted along the pump Poynting vector or its group velocity matches that of the pump. The result is markedly enhanced generation of both twin beams, with the simultaneous narrowing of angular and frequency spectrum. The effect will enable efficient generation of ultrafast twin photons and beams in cavities, waveguides and whispering-gallery mode resonators.

Nonlinear interactions such as parametric down-conversion and four-wave mixing are limited by transverse and longitudinal walk-off effects. Here, Pérez et al. demonstrate bright, tunable, diffraction-limited twin-beam radiation by ensuring that signal or idler pulse propagates in the direction or velocity of the pump.

Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam

The interplay between light polarization and matter is the basis of many fundamental physical processes and applications. However, the electromagnetic wave nature of light in free space sets a fundamental limit on the three-dimensional polarization orientation of a light beam. Although a high numerical aperture objective can be used to bend the wavefront of a radially polarized beam to generate the longitudinal polarization state in the focal volume, the arbitrary three-dimensional polarization orientation of a beam has not been achieved yet. Here we present a novel technique for generating arbitrary three-dimensional polarization orientation by a single optically configured vectorial beam. As a consequence, by applying this technique to gold nanorods, orientation-unlimited polarization encryption with ultra-security is demonstrated. These results represent a new landmark of the orientation-unlimited three-dimensional polarization control of the light–matter interaction.

Generating arbitrary orientation of light polarization has been an elusive goal, yet it is important to light interactions with nano-objects. By combining azimuthally and radially polarized beams, Li et al. overcome this obstacle and demonstrate its use for polarization-based encryption with gold nanorods.

Polarization-entangled light pulses of 10(5) photons

We experimentally demonstrate polarization entanglement for squeezed vacuum pulses containing more than 10(5) photons. We also study photon-number entanglement by calculating the Schmidt number and measuring its operational counterpart. Theoretically, our pulses are the more entangled the brighter they are. This promises important applications in quantum technologies, especially photonic quantum gates and quantum memories.

Stimulated emission from a single excited atom in a waveguide

We study stimulated emission from an excited two-level atom coupled to a waveguide containing an incident single-photon pulse. We show that the strong photon correlation, as induced by the atom, plays a very important role in stimulated emission. Additionally, the temporal duration of the incident photon pulse is shown to have a marked effect on stimulated emission and atomic lifetime.

The biaxial nonlinear crystal BiB₃O₆ as a polarization entangled photon source using non-collinear type-II parametric down-conversion

We describe the full characterization of the biaxial nonlinear crystal BiB₃O₆ (BiBO) as a polarization entangled photon source using non-collinear type-II parametric down-conversion. We consider the relevant parameters for crystal design, such as cutting angles, polarization of the photons, effective nonlinearity, spatial and temporal walk-offs, crystal thickness and the effect of the pump laser bandwidth. Experimental results showing entanglement generation with high rates and a comparison to the well investigated β-BaB₂O₄ (BBO) crystal are presented as well. Changing the down-conversion crystal of a polarization entangled photon source from BBO to BiBO enhances the generation rate as if the pump power was increased by 2.5 times. Such an improvement is currently required for the generation of multiphoton entangled states.

Projection of two biphoton qutrits onto a maximally entangled state

Bell state measurements, in which two quantum bits are projected onto a maximally entangled state, are an essential component of quantum information science. We propose and experimentally demonstrate the projection of two quantum systems with three states (qutrits) onto a generalized maximally entangled state. Each qutrit is represented by the polarization of a pair of indistinguishable photons-a biphoton. The projection is a joint measurement on both biphotons using standard linear optics elements. This demonstration enables the realization of quantum information protocols with qutrits, such as teleportation and entanglement swapping.

Parameter estimation with entangled photons produced by parametric down-conversion

We explore the advantages offered by twin light beams produced in parametric down-conversion for precision measurement. The symmetry of these bipartite quantum states, even under losses, suggests that monitoring correlations between the divergent beams permits a high-precision inference of any symmetry-breaking effect, e.g., fiber birefringence. We show that the quantity of entanglement is not the key feature for such an instrument. In a lossless setting, scaling of precision at the ultimate "Heisenberg" limit is possible with photon counting alone. Even as photon losses approach 100% the precision is shot-noise limited, and we identify the crossover point between quantum and classical precision as a function of detected flux. The predicted hypersensitivity is demonstrated with a Bayesian simulation.

Stimulated emission as a result of multiphoton interference

By performing an experiment on stimulated emission by two photons in the parametric amplification process and comparing it to a three-photon interference scheme, we present evidence in support of the idea that the underlying physics of stimulated emission is simply the constructive interference due to photon indistinguishability. So the observed signal enhancement upon the input of photons can be interpreted as a result of multiphoton interference of the input photons and the otherwise spontaneously emitted photon from the amplifier.

Entanglement generation by Fock-state filtration

We demonstrate a Fock-state filter which is capable of preferentially blocking single photons over photon pairs. The large conditional nonlinearities are based on higher-order quantum interference, using linear optics, an ancilla photon, and measurement. We demonstrate that the filter acts coherently by using it to convert unentangled photon pairs to a path-entangled state. We quantify the degree of entanglement by transforming the path information to polarization information; applying quantum state tomography we measure a tangle of T=(20+/-9)%.

Signatures for generalized macroscopic superpositions

We develop criteria sufficient to enable detection of macroscopic coherence where there are not just two macroscopically distinct outcomes for a pointer measurement, but rather a spread of outcomes over a macroscopic range. The criteria provide a means to distinguish a macroscopic quantum description from a microscopic one based on mixtures of microscopic superpositions of pointer-measurement eigenstates. The criteria are applied to Gaussian-squeezed and spin-entangled states.

Observation of bunching of two bell states

The bunching of two single photons on a beam splitter is a fundamental quantum effect, first observed by Hong, Ou, and Mandel. It is a unique interference effect that relies only on the photons' indistinguishability and not on their relative phase. We generalize this effect by demonstrating the bunching of two Bell states, created in two passes of a nonlinear crystal, each composed of two photons. When the two Bell states are indistinguishable, phase-insensitive destructive interference prevents the outcome of fourfold coincidence between the four spatial-polarization modes. For certain combinations of the two Bell states, we demonstrate the opposite effect of antibunching. We relate this result to the number of distinguishable modes in parametric down-conversion.

Multiphoton path entanglement by nonlocal bunching

Multiphoton path entanglement is created without applying postselection, by manipulating the state of stimulated parametric down-conversion. A specific measurement on one of the two output spatial modes leads to the nonlocal bunching of the photons of the other mode, forming the desired multiphoton path entangled state. We present experimental results for the case of a heralded two-photon path entangled state and show how to extend this scheme to higher photon numbers.

Quantum entanglement of a large number of photons

A bipartite multiphoton entangled state is created through stimulated parametric down-conversion of strong laser pulses in a nonlinear crystal. It is shown how detectors that do not resolve the photon number can be used to analyze such multiphoton states. Entanglement of up to 12 photons is detected using both the positivity of the partially-transposed density matrix and a newly derived criteria. Furthermore, evidence is provided for entanglement of up to 100 photons. The multiparticle quantum state is such that even in the case of an overall photon collection and detection efficiency as low as a few percent, entanglement remains and can be detected.

De Broglie wavelength of a non-local four-photon state

Superposition is one of the most distinctive features of quantum theory and has been demonstrated in numerous single-particle interference experiments. Quantum entanglement, the coherent superposition of states in multi-particle systems, yields more complex phenomena. One important type of multi-particle experiment uses path-entangled number states, which exhibit pure higher-order interference and the potential for applications in metrology and imaging; these include quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit, or quantum lithography beyond the classical diffraction limit. It has been generally understood that in optical implementations of such schemes, lower-order interference effects always decrease the overall performance at higher particle numbers. Such experiments have therefore been limited to two photons. Here we overcome this limitation, demonstrating a four-photon interferometer based on linear optics. We observe interference fringes with a periodicity of one-quarter of the single-photon wavelength, confirming the presence of a four-particle mode-entangled state. We anticipate that this scheme should be extendable to arbitrary photon numbers, holding promise for realizable applications with entanglement-enhanced performance.

Distinguishing genuine entangled two-photon-polarization sfrom independently generated pairs of entangled photons

A scheme to distinguish entangled two-photon-polarization (ETP) states from two independent entangled one-photon-polarization (EOP) states is proposed. Using this scheme, the experimental generation of ETP by parametric down-conversion is confirmed through the anticorrelations among three orthogonal two-photon-polarization states. The estimated fraction of ETP among the correlated photon pairs is 37% in the present experimental setup.

Theory of an entanglement laser

We consider the creation of polarization entangled light from parametric down-conversion driven by an intense pulsed pump field inside a cavity. The multiphoton states produced are close approximations to singlet states of two very large spins. A criterion is derived to quantify the entanglement of such states. We study the dynamics of the system in the presence of losses and other imperfections, concluding that the creation of strongly entangled states with photon numbers up to a million seems achievable.

Violation of Bell's inequality with photons from independent sources

We report a violation of Bell's inequality using one photon from a parametric down-conversion source and a second photon from an attenuated laser beam. The two photons were entangled at a beam splitter using the postselection technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]]. A quantum interference pattern with a visibility of 91% was obtained using the photons from these independent sources, as compared with a visibility of 99.4% using two photons from a central parametric down-conversion source.

Experimental observation of four-photon entanglement from parametric down-conversion

We observe polarization entanglement between four photons produced from a single down-conversion source. The nonclassical correlations between the measurement results violate a generalized Bell inequality for four qubits. The characteristic properties and its easy generation with high interferometric contrast make the observed four-photon state well suited for implementing advanced quantum communication schemes such as multiparty quantum key distribution, secret sharing, and telecloning.

Long-distance teleportation of qubits at telecommunication wavelengths

Matter and energy cannot be teleported (that is, transferred from one place to another without passing through intermediate locations). However, teleportation of quantum states (the ultimate structure of objects) is possible: only the structure is teleported--the matter stays at the source side and must be already present at the final location. Several table-top experiments have used qubits (two-dimensional quantum systems) or continuous variables to demonstrate the principle over short distances. Here we report a long-distance experimental demonstration of probabilistic quantum teleportation. Qubits carried by photons of 1.3 micro m wavelength are teleported onto photons of 1.55 micro m wavelength from one laboratory to another, separated by 55 m but connected by 2 km of standard telecommunications fibre. The first (and, with foreseeable technologies, the only) application of quantum teleportation is in quantum communication, where it could help to extend quantum cryptography to larger distances.

Coherent collisions between Bose-Einstein condensates

We study the nondegenerate parametric amplifier for matter waves, implemented by colliding two Bose-Einstein condensates. The coherence of the amplified waves is shown by observing high contrast interference with a reference wave and by reversing the amplification process. Since our experiments also place limits on all known sources of decoherence, we infer that relative number squeezing is most likely present between the amplified modes. Finally, we suggest that reversal of the amplification process may be used to detect relative number squeezing without requiring subshot-noise detection.

Experimental extraction of an entangled photon pair from two identically decohered pairs

Entanglement is considered to be one of the most important resources in quantum information processing schemes, including teleportation, dense coding and entanglement-based quantum key distribution. Because entanglement cannot be generated by classical communication between distant parties, distribution of entangled particles between them is necessary. During the distribution process, entanglement between the particles is degraded by the decoherence and dissipation processes that result from unavoidable coupling with the environment. Entanglement distillation and concentration schemes are therefore needed to extract pairs with a higher degree of entanglement from these less-entangled pairs; this is accomplished using local operations and classical communication. Here we report an experimental demonstration of extraction of a polarization-entangled photon pair from two decohered photon pairs. Two polarization-entangled photon pairs are generated by spontaneous parametric down-conversion and then distributed through a channel that induces identical phase fluctuations to both pairs; this ensures that no entanglement is available as long as each pair is manipulated individually. Then, through collective local operations and classical communication we extract from the two decohered pairs a photon pair that is observed to be polarization-entangled.

Polarization entanglement purification using spatial entanglement

We present a scheme for entanglement purification with linear optics that works for currently available parametric down-conversion sources, in contrast to a previous scheme [J. W. Pan, Nature (London) 410, 1067 (2001)]] that relied on ideal single-pair sources. The present scheme makes use of spatial entanglement in order to purify polarization entanglement. Surprisingly, spatial entanglement as an additional resource also leads to a substantial improvement in entanglement output compared to the previous scheme.

Trapped-ion quantum simulator: experimental application to nonlinear interferometers

We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of two nth order nonlinear optical beam splitters comprising an interferometer sensitive to phase shift in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with n, and the simulation demonstrates that the use of nonlinear beam splitters (n=2,3) enhances this sensitivity compared to the standard quantum limit imposed by a linear beam splitter (n=1).

N-particle N-level singlet States: some properties and applications

Three apparently unrelated problems which have no solution using classical tools are described: the "N-strangers," "secret sharing," and "liar detection" problems. A solution for each of them is proposed. Common to all three solutions is the use of quantum states of total spin zero of N spin-(N-1)/2 particles.

Multiphoton entanglement concentration and quantum cryptography

Multiphoton states from parametric down-conversion can be entangled both in polarization and photon number. Maximal high-dimensional entanglement can be concentrated postselectively from these states via photon counting. This makes them natural candidates for quantum key distribution, where the presence of more than one photon per detection interval has up to now been considered undesirable. We propose a simple multiphoton cryptography protocol for the case of low losses.

Experimental violation of a spin-1 bell inequality using maximally entangled four-photon states

We demonstrate the experimental violation of a spin-1 Bell inequality. The spin-1 inequality is based on the Clauser, Horne, Shimony, and Holt formalism. For entangled spin-1 particles, the maximum quantum-mechanical prediction is 2.55 as opposed to a maximum of 2, predicted using local hidden variables. We obtained an experimental value of 2.27+/-0.02 using the four-photon state generated by pulsed, type-II, stimulated parametric down-conversion. This is a violation of the spin-1 Bell inequality by more than 13 standard deviations.