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Entanglement conditions for integrated-optics multi-port quantum interferometry experiments

Junghee Ryu, Marcin Marciniak, Marcin Wieśniak, Marek Żukowski

Published Jan 10, 2016• 1 citation
OpenAlex

Abstract

Integrated optics allows one to perform interferometric experiments based upon multi-port beam-splitter. To observe entanglement effects one can use multi-mode parametric down-conversion emissions. When the structure of the Hamiltonian governing the emissions has (infinitely) many equivalent Schmidt decompositions into (beams), one can have perfect EPR-like correlations of numbers of photons emitted into conjugate modes which can be monitored at spatially separated detection stations. We provide series of entanglement conditions for all prime numbers of modes, and show their violations by bright multi-mode squeezed vacuum states. One family of such conditions is given in terms of the usual intensity-related variables. Moreover, we show that an alternative series of conditions expressed in terms averages of observed rates, which is a generalization of the ones given in arXiv:1508.02368, is a much better entanglement indicator. Thus the rates seem to emerge as a powerful concept in quantum optics. Generalizations of the approach are expected.

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Journal of Physics B Atomic Molecular and Optical Physics•Nov 3, 2014•7 citations
Integrated optics allows one to perform interferometric experiments based upon multi-port beam-splitter. To observe entanglement effects one can use multi-mode parametric down-conversion emissions. When the structure of the Hamiltonian governing the emissions has (infinitely) many equivalent Schmidt decompositions into (beams), one can have perfect EPR-like correlations of numbers of photons emitted into conjugate modes which can be monitored at spatially separated detection stations. We provide series of entanglement conditions for all prime numbers of modes, and show their violations by bright multi-mode squeezed vacuum states. One family of such conditions is given in terms of the usual intensity-related variables. Moreover, we show that an alternative series of conditions expressed in terms averages of observed rates, which is a generalization of the ones given in arXiv:1508.02368, is a much better entanglement indicator. Thus the rates seem to emerge as a powerful concept in quantum optics. Generalizations of the approach are expected.
Abstract We generalize a new approach to entanglement conditions for light of undefined photons numbers given in Żukowski et al (2017 Phys. Rev. A 95 042113) for polarization correlations to a broader family of interferometric phenomena. Integrated optics allows one to perform experiments based upon multiport beamsplitters. To observe entanglement effects one can use multi-mode parametric down-conversion emissions. When the structure of the Hamiltonian governing the emissions has (infinitely) many equivalent Schmidt decompositions into modes (beams), one can have perfect EPR-like correlations of numbers of photons emitted into ‘conjugate modes’ which can be monitored at spatially separated detection stations. We provide entanglement conditions for experiments involving three modes on each side, and three-input-three-output multiport beamsplitters, and show their violations by bright squeezed vacuum states. We show that a condition expressed in terms of averages of observed rates is a much better entanglement indicator than a related one for the usual intensity variables. Thus, the rates seem to emerge as a powerful concept in quantum optics, especially for fields of undefined intensities.
Normalized quantum Stokes operators introduced in Phys. Rev. A 95, 042113 (2017) enable one to better observe non-classical correlations of entangled states of optical fields with undefined photon numbers.For a given run of an experiment the new quantum Stokes operators are defined by the differences of the measured intensities (or photon numbers) at the exits of a polarizer divided by their sum.It is this ratio that is to be averaged, and not the numerator and the denominator separately, as it is in the conventional approach.The new approach allows to construct more robust entanglement indicators against photon-loss noise, which can detect entangled optical states in situations in which witnesses using standard Stokes operators fail.Here we show an extension of this approach beyond phenomena linked with polarization.We discuss EPR-like experiments involving correlations produced by optical beams in a multi-mode bright squeezed vacuum state.EPR-inspired entanglement conditions for all prime numbers of modes are presented.The conditions are much more resistant to noise due to photon loss than similar ones which employ standard Glauber-like intensity, correlations.
Continuous variable entanglement can be produced in nonlinear systems or via interference of squeezed states. In many of optical systems, such as parametric down conversion or interference of optical squeezed states, production of two perfectly symmetric subsystems is usually used for demonstrating the existence of entanglement. This symmetry simplifies the description of the concept of entanglement. However, asymmetry in entanglement may arise naturally in a real experiment, or be intentionally introduced in a given quantum information protocol. These asymmetries can emerge from having the output beams experience different losses and environmental contamination, or from the availability of non-identical input quantum states in quantum communication protocols. In this paper, we present a visualisation of entanglement using quadrature amplitude plots of the twin beams. We quantitatively discuss the strength of asymmetric entanglement using EPR and inseparability criteria and theoretically show that the optimal beamsplitter ratio for entanglement is dependent on the asymmetries and may not be 50/50. To support this theory, we present experimental results showing one particular asymmetric entanglement where a 0.78/0.22 beamsplitter is optimal for observing entanglement.
Better versions of separability conditions for four mode optical fields, i.e. two beams with two modes of mutually orthogonal polarization are given. Our conditions involve variances. Their meaning is intuitive and their implementation is feasible. Namely, if for a given quantum state the spread of the data around its mean value is smaller than the minimal spread predicted for the set of separable states, then the given state is entangled. Our conditions are formulated for standard quantum Stokes observables and normalized Stokes observables and result to be more efficient that the previous conditions for four mode optical fields involving variances. We test our conditions for bright squeezed vacuum with (and without) induced non-gaussianity obtained by addition or subtraction of photons. Also we propose a practical experimental scheme of how to generate such states for an event-ready experiment.
Double-pair emission from type-II parametric down-conversion results in a highly entangled four-photon state. Due to interference, which is similar to bunching from thermal emission, this state is not simply a product of two pairs. The observation of this state can be achieved by splitting the two emission modes at beam splitters and subsequent detection of a photon in each output. Here we describe the features of this state and construct a Bell-type inequality, which gives a necessary and sufficient condition for a four-photon test of local realistic hidden variable theories.
Continuous variable entanglement can be produced in nonlinear systems or via the interference of squeezed states. In many optical systems such as parametric down conversion, the production of two perfectly symmetric subsystems is usually assumed when demonstrating the existence of entanglement. This symmetry simplifies the description of entanglement. However, asymmetry in entanglement may arise naturally in a real experiment, or be intentionally introduced in a given quantum information protocol. These asymmetries can emerge from having the output beams experience different losses and environmental contamination, or from the availability of non-identical input quantum states in quantum communication protocols. In this paper, we present a visualization of entanglement using quadrature amplitude plots of the twin beams. We quantitatively discuss the strength of asymmetric entanglement using EPR and inseparability criteria and theoretically show that the optimal beamsplitter ratio for entanglement is dependent on the asymmetries and may not be 50 : 50. To support this theory, we present experimental results showing one particular asymmetric entanglement where a 78 : 22 beamsplitter is optimal for observing entanglement.