Two-photon States Research Articles

Experimental entanglement characterization of two-rebit states

We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply rooted, yet rarely discussed question of why quantum states are described via complex numbers. With our experiment, we then realize two-photon polarization states that are entangled with respect to the notion of two rebits, comprising two two-level systems over real numbers. At the same time, the generated states are separable with respect to two complex qubits. Among other results, we reconstruct the best approximation of the generated states in terms of a real-valued, local expansion and show that this yields an incomplete description of our data. Conversely, the generated states are shown to be fully decomposable in terms of tensor-product states with complex wave functions. Thereby, we probe paradigms of quantum physics with modern theoretical tools and experimental platforms that are relevant for applications in quantum information science and technology and connected to the fundamentals of the quantum description of nature.

Heterochromatic Nonlinear Optical Responses in Upconversion Nanoparticles for Super-Resolution Nanoscopy.

Point spread function (PSF) engineering by an emitter's response can code higher-spatial-frequency information of an image for microscopy to achieve super-resolution. However, complexed excitation optics or repetitive scans are needed, which explains the issues of low speed, poor stability, and operational complexity associated with the current laser scanning microscopy approaches. Here, the diverse emission responses of upconversion nanoparticles (UCNPs) are reported for super-resolution nanoscopy to improve the imaging quality and speed. The method only needs a doughnut-shaped scanning excitation beam at an appropriate power density. By collecting the four-photon emission of single UCNPs, the high-frequency information of a super-resolution image can be resolved through the doughnut-emission PSF. Meanwhile, the two-photon state of the same nanoparticle is oversaturated, so that the complementary lower-frequency information of the super-resolution image can be simultaneously collected by the Gaussian-like emission PSF. This leads to a method of Fourier-domain heterochromatic fusion, which allows the extended capability of the engineered PSFs to cover both low- and high-frequency information to yield optimized image quality. This approach achieves a spatial resolution of 40nm, 1/24th of the excitation wavelength. This work suggests a new scope for developing nonlinear multi-color emitting probes in super-resolution nanoscopy.

Positive operator-valued measure for two-photon detection via sum-frequency generation

Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process effects a generalized measurement on the input two-photon state. We describe the positive-operator-valued measure (POVM) associated with such a measurement, and show that its elements are proportional to the two-photon states produced by the time-reversed PDC process. Such a detection acts as a joint measurement on two photons, and is thus an important component of many quantum information processing protocols relying on photonic entanglement. Using the retrodictive approach, we analyze the properties of the two-photon POVM that are relevant for quantum protocols exploiting two-photon states and measurements.

Topological protection versus degree of entanglement of two-photon light in photonic topological insulators

Topological insulators combine insulating properties in the bulk with scattering-free transport along edges, supporting dissipationless unidirectional energy and information flow even in the presence of defects and disorder. The feasibility of engineering quantum Hamiltonians with photonic tools, combined with the availability of entangled photons, raises the intriguing possibility of employing topologically protected entangled states in optical quantum computing and information processing. However, while two-photon states built as a product of two topologically protected single-photon states inherit full protection from their single-photon “parents”, a high degree of non-separability may lead to rapid deterioration of the two-photon states after propagation through disorder. In this work, we identify physical mechanisms which contribute to the vulnerability of entangled states in topological photonic lattices. Further, we show that in order to maximize entanglement without sacrificing topological protection, the joint spectral correlation map of two-photon states must fit inside a well-defined topological window of protection.

In English

In this paper, we used high-resolution IR absorption spectra to investigate 1D and 2D polaritons in periodical 2D macroporous silicon structures with nano-coatings of SiO2 and CdS, ZnO nanoparticles. The application of high-resolution IR absorption spectroscopy resulted in detection of dipole-active TO vibrations, photon splitting and giant two-polar absorption oscillations with amplitudes of ±107arb.un. As a result, the dispersion law in yz surfaces of macropores change to z direction along macropores. It means additional degree of freedom as vertically polarized light in z direction and horizontally polarized light in x direction resulted in beams splitting and two-photon interference - Hong-Ou-Mandel effect. In our case, 2D resonances of Wannier-Stark electro-optical effect in yz plane correspond to constructive interference of the two-photon states (bosonic behavior), and two-polar resonances in ±z direction are determined by destructive interference of the two-photon states (fermionic behavior). Two-polar oscillations of 1D -polaritons have the ultra-small half-width 0.4–0.6 сm–1 and minimal Rabi frequency of samples 1.0 сm–1 equaled to the resolution of spectral measurements. Furthermore, two-photon interference and 1D polaritons are perspective for high-coherent optical quantum computers on macroporous silicon with nano-coatings and, in addition, for lasers and new metamaterials.

Effects of low-lying excitations in pentalene and its derivatives in singlet fission: a model exact and density matrix renormalisation group study

ABSTRACT Low-lying excited states in oligoquinanes, a multiple-fused five-membered ring compounds, aryl fused oligoquinanes and their derivatives are investigated within Pariser–Parr–Pople (PPP) model Hamiltonian. The calculated low-lying singlet excited states are in very good agreement with the experimental values reported in the literature. The lowest dipole allowed singlet excited state () calculated for most of the pentalene derivatives except 5,10 dihydroindolo[3,2-b]indole lies above the optically dark two-photon state resulting in the molecules to be non-fluorescent. The energy ordering of and lowest triplet energy state () for pentalene and dicyclopenta[a,e]pentalene satisfies two energy criteria for intermolecular multiexcitonic Singlet Fission (SF) process to occur.

Operational Resource Theory of Imaginarity.

Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems and their dynamics and interaction. Since the inception of quantum theory, it has been debated whether complex numbers are essential or whether an alternative consistent formulation is possible using real numbers only. Here, we attack this long-standing problem theoretically and experimentally, using the powerful tools of quantum resource theories. We show that, under reasonable assumptions, quantum states are easier to create and manipulate if they only have real elements. This gives an operational meaning to the resource theory of imaginarity. We identify and answer several important questions, which include the state-conversion problem for all qubit states and all pure states of any dimension and the approximate imaginarity distillation for all quantum states. As an application, we show that imaginarity plays a crucial role in state discrimination, that is, there exist real quantum states that can be perfectly distinguished via local operations and classical communication but that cannot be distinguished with any nonzero probability if one of the parties has no access to imaginarity. We confirm this phenomenon experimentally with linear optics, discriminating different two-photon quantum states by local projective measurements. Our results prove that complex numbers are an indispensable part of quantum mechanics.

Non-classical light in a J x photonic lattice

We report the study of non-classical light in a photonic lattice having a parabolic coupling distribution, also known as a J x photonic lattice. We focus on a two-photon Fock state, a two-photon N00N state, a single-mode squeezed state and a coherent state as inputs to the lattice. We investigate the possibility of a perfect transfer of the mean photon number as well as the quantum state from one waveguide mode to another. We study photon–photon correlation for the two-photon N00N state. For the single-mode squeezed state we perform a detailed study of the evolution of the squeezing factor and entanglement between the waveguide modes. Our findings suggest a perfect transfer of the average photon number in all cases and a perfect transfer of the quantum state in the cases of the two-photon Fock state and the two-photon N00N state only, but not in the cases of the squeezed and coherent states. Our results should have applications in the physical implementation of photonic continuous-variable quantum-information processing.

The impact of distinct loss mechanisms on multi-photon states

Quantum optics plays an important role in many contemporary applications of quantum information processing and quantum metrology. Experimental implementations of these protocols, however, inevitably exhibit loss. This loss has two distinct forms, stochastic loss and deterministic loss, which impact quantum mechanical systems in distinct ways. In this exposition, we offer a straightforward experimental illustration of the impact of both forms of loss on multi-photon states. Specifically, we show that heralding statistics for two-photon states decrease in the obvious way under stochastic loss, and yet are unchanged in the presence of deterministic loss. This demonstration offers an intuitive clarification of loss for multi-photon systems for the student familiar with elementary quantum mechanics, and emphasizes the difference between pure and mixed states in quantum theory more generally. This presentation is targeted towards advanced undergraduate students familiar with quantum optics.

Verification of complementarity relations between quantum steering criteria using an optical system

The ability that one system immediately affects another one by using local measurements is regarded as quantum steering, which can be detected by various steering criteria. Recently, Mondal et al. [Phys. Rev. A 98, 052330 (2018)] derived the complementarity relations of coherence steering criteria, and revealed that the quantum steering of a system can be observed through the average coherence of a subsystem. Here, we experimentally verify the complementarity relations between quantum steering criteria by employing two-photon Bell-like states and three Pauli operators. The results demonstrate that if prepared quantum states can violate two setting coherence steering criteria and turn out to be steerable states, then they cannot violate the complementary settings criteria. Three measurement settings inequalities, which establish a set of complementarity relations between these two coherence steering criteria, are always obeyed by all prepared quantum states in experiment. In addition, we experimentally certify that the strengths of coherence steering criteria depend on the choice of coherence measure. In comparison with two setting coherence steering criteria based on ${l}_{1}$ norm of coherence and relative entropy of coherence, our experimental results show that the steering criterion based on skew information of coherence is the strongest in detecting the steerability of two-photon Bell-like states. Thus, our experimental demonstration can deepen the understanding of the relation between the quantum steering and quantum coherence.

Development of hybrid ARQ protocol for the quantum communication system on stabilizer codes

In this paper, we develop a novel hybrid automatic-repeat-request (ARQ) protocol for the quantum communication system using quantum stabilizer codes. The quantum information is encoded by stabilizer codes to against the channel noise. The two-photon entangled state is prepared for codeword secure transmission. Hybrid ARQ protocol rules the recognition and retransmission of error codewords. In this protocol, the property of quantum entangled state ensures the security of information, the theory of hybrid ARQ system improves the reliability of transmission, the theory of quantum stabilizer codes corrects the flipping errors of codewords. Finally, we verify the security and throughput efficiency of this protocol.

Feasible time-bin entanglement purification based on sum-frequency generation.

High quality time-bin entanglement is widely exploited to achieve the purposes of fundamental tests of physics and the implementation of quantum communication protocols both in free space and optical fiber propagation. However, the imperfect approaches of generating time-bin entangled state will degrade its quality and limit its practical application. Entanglement purification is to distill high quality entangled states from low quality entangled states. In this paper, we present the first entanglement purification protocol (EPP) for time-bin entanglement. We first explain this EPP for two-photon time-bin entangled state and then extend it to the system of multi-photon time-bin entangled state. We also design a possible realization of this EPP with practical spontaneous parametric down conversion (SPDC) source. Differ from the conventional EPPs, this EPP does not require the sophisticated controlled-not (CNOT) gate or similar operations, and it uses the feasible sum-frequency generation (SFG) to perform the purification. Moreover, the double-pair noise emitted from the SPDC source can be eliminated automatically which is the other advantage of this EPP. If we combine with the faithful entanglement swapping, this EPP may have potential to be a part of full quantum repeaters.

Collapse of Xe polarized atomic states in magnetic fields

Ionization of two-photon excited states $$5p^{\mathrm {5}}(^{\mathrm {2}}P_{\mathrm {3/2}})6\hbox {p}[^{\mathrm {3}}/_{\mathrm {2}}$$ , $$^{\mathrm {5}}/_{\mathrm {2}}]_{\mathrm {2}}$$ , $$\hbox {M}=2$$ (jl-coupling) of xenon atoms by circularly polarized probe light was studied experimentally in a supersonic beam. The observed photoionization signals revealed oscillation structure due to the Larmor precession of atomic states in an external magnetic field. We derived analytical formulas for the photoelectron current and explained the diversity in the structure of the detected oscillations in terms of the principal lines among multiplet components of optical transitions. The obtained numerical data demonstrate collapse and revival (beating) behavior of the photocurrent due to nonlinearity of Zeeman shifts in the presence of the Paschen–Back effect. Our results indicate the possibility of implementing Doppler-free spectroscopy involving bound-free transitions.

Engineering the spectral profile of photon pairs by using multi-stage nonlinear interferometers

Using the quantum interference of photon pairs in N-stage nonlinear interferometers (NLIs), the contour of the joint spectral function can be modified into an islands pattern. We perform two series of experiments. One is that all of the nonlinear fibers in pulse pumped NLIs are identical; the other is that the lengths of N pieces of nonlinear fibers are different. We not only demonstrate how the pattern of spectral function changes with the stage number N, but also characterize how the relative intensity of island peaks varies with N. The results well agree with theoretical predictions, revealing that the NLI with lengths of N pieces of nonlinear fibers following binomial distribution can provide a better active filtering function. Our investigation shows that the active filtering effect of multi-stage NLI is a useful tool for efficiently engineering the factorable two-photon state—a desirable resource for quantum information processing.

Configurable heralded two-photon Fock-states on a chip

Progress in integrated photonics enables the combination of several elementary functions on single substrates for the realization of advanced functionalized chips. We report a monolithic integrated quantum photonic realization on lithium niobate, where nonlinear optics and electro-optics properties have been harnessed simultaneously for generating heralded configurable, two-photon states. Taking advantage of a picosecond pump laser and telecom components, we demonstrate the production of various path-coded heralded two-photon states, showing 94% raw visibility for Hong-Ou-Mandel interference. The versatility and performance of such a highly integrated photonic entanglement source enable exploring more complex quantum information processing protocols finding application in communication, metrology and processing tasks.

Photonic two-particle quantum walks in Su–Schrieffer–Heeger lattices

We report on the experimental demonstration of two-photon quantum walks at the edge of a photonic Su–Schrieffer–Heeger lattice and compare them to those observed when launching photons at the edge of a homogeneous lattice. Whereas at the topological edge, one of the photons primarily remains close to the edge, both photons penetrate freely from the trivial edge into the bulk. This behavior manifests also in the average inter-particle distance, which is significantly larger at the topological edge. Hence, for a given propagation length, the entangled two-photon state launched at the topological edge extends over a wider domain of the lattice.

Higher-dimensional Hong-Ou-Mandel effect and state redistribution with linear-optical multiports

We expand the two-photon Hong-Ou-Mandel (HOM) effect onto a higher-dimensional set of spatial modes and introduce an effect that allows controllable redistribution of quantum states over these modes using directionally unbiased linear-optical four-ports without post-selection. The original HOM effect only allows photon pairs to exit in two directions in space. But when accompanied by beam splitters and phase shifters, the result is a directionally controllable two-photon HOM effect in four spatial modes, with direction controlled by changing the phases in the system. This controllable quantum amplitude manipulation also allows demonstration of a "delayed" HOM effect by exploiting phase shifters in a system of two connected multiport devices. By this means, both spatial and temporal control of the propagation of the two-photon superposition state through a network can be achieved.

Temporal filtering characteristics of gated InGaAs/InP single-photon detectors for coincidence measurement

Semiconductor single-photon avalanche detectors (SPADs) have played an important role in practical quantum communication technology due to their advantages of small size, low cost and easy operation. Among them, InGaAs/InP SPADs have been widely used in fiber-optic quantum key distribution systems due to their response wavelength range in a near-infrared optical communication band. In order to avoid the influence of dark count and afterpulsing on single photon detection, the gated quenching technologies are widely applied to the InGaAs/InP SPADs. Typically, the duration of gate pulse is set to be as short as a few nanoseconds or even less. As the detection of the arrival of single photons depends on the coincidence between the arrival time of gate pulse and the arrival time of photon, the gate pulse duration of the InGaAs/InP SPADs inevitably affects the effective detection of the single photons. Without the influence of dispersion, the temporal width of the transmitted photons is usually on the order of picoseconds or even less, which is much shorter than the gate width of the InGaAs/InP SPAD. Therefore, the gate width normally has no influence on the temporal measurement of the detected photons. However, in quantum systems involving large dispersion, such as the long-distance fiber-optic quantum communication system, the temporal width of the transmitted photons is significantly broadened by the experienced dispersion so that it may approach to or even exceed the gate width of the single-photon detector. As a result, the effect of the gate width on the recording of the arrival time of the dispersed photons should be taken into account. In this paper, the influence of the gate width coupled to the InGaAs/InP single photon detectors on the measurement of the two-photon coincidence time width is studied both theoretically and experimentally. The theoretical analysis and experimental results are in good agreement with each other, showing that the finally measured coincidence time width of the two-photon state after dispersion is not more than half of the effective gate pulses width. The maximum observable coincidence time width based on the gated single photon detector is fundamentally limited by the gate width, which restricts its applications in quantum information processing based on the two-photon temporal correlation measurement.

Observation of second-order interference beyond the coherence time with true thermal photons.

It has recently been shown that counter-intuitive Franson-like second-order interference can be observed with a pair of classically correlated pseudo thermal light beams and two separate unbalanced interferometers (UIs): the second-order interference visibility remains fixed at 1/3 even though the path length difference in each UI is increased significantly beyond the coherence length of the pseudo thermal light [Phys. Rev. Lett.119, 223603 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.223603]. However, as the pseudo thermal beam itself originated from a long-coherence laser (and by using a rotating ground disk), there exists the possibility of a classical theoretical model to account for second-order interference beyond the coherence time on the long coherence time of the original laser beam. In this work, we experimentally explore this counter-intuitive phenomenon with a true thermal photon source generated via quantum thermalization, i.e., obtaining a mixed state from a pure two-photon entangled state. This experiment not only demonstrates the unique second-order coherence properties of thermal light clearly but may also open up remote sensing applications based on such effects.

Experimental Parity-Time Symmetric Quantum Walks for Centrality Ranking on Directed Graphs.

Using quantum walks (QWs) to rank the centrality of nodes in networks, represented by graphs, is advantageous compared to certain widely used classical algorithms. However, it is challenging to implement a directed graph via QW, since it corresponds to a non-Hermitian Hamiltonian and thus cannot be accomplished by conventional QW. Here we report the realizations of centrality rankings of a three-, a four-, and a nine-vertex directed graph with parity-time (PT) symmetric quantum walks by using high-dimensional photonic quantum states, multiple concatenated interferometers, and dimension dependent loss to achieve these. We demonstrate the advantage of the QW approach experimentally by breaking the vertex rank degeneracy in a four-vertex graph. Furthermore, we extend our experiment from single-photon to two-photon Fock states as inputs and realize the centrality ranking of a nine-vertex graph. Our work shows that a PT symmetric multiphoton quantum walk paves the way for realizing advanced algorithms.