Nonlinear Beam Splitter Research Articles

High-probability photon catalysis with non-linear photon beam splitter

Photon catalysis (PC) is an intriguing quantum optical operation wherein the same number of photons are added to and subsequently subtracted from the relevant optical system. It is an important tool that facilitates photon number manipulation. However, most existing PC methods are suitable only for photonic states residing within few-photon subspace. In addition, the probability of PC decreases exponentially with increase in the number n of the Fock state |n〉. Thus, this study proposed a high probability PC scheme for optical quantum states with large Fock state population based on nonlinear beam splitters. The results indicate that the fidelity and the probability of PC are both substantially improved. Moreover, in case of detector inefficiency, the scheme of PC with non-linear beam splitter was more robust. Thus, the proposed method provides a useful tool for manipulating optical quantum states with large Fock number state population.

Generation of entangled photons with a second-order nonlinear photonic crystal and a beam splitter

We discuss the generation of entangled photons using a nonlinear photonic crystal and beam splitter. In our method, the photonic crystal is assumed to be composed of a material with a large second-order nonlinear optical susceptibility . Our proposal relies on two facts: (1) A nonlinear photonic crystal changes coherent incident light into squeezed light. (2) A beam splitter transforms the squeezed light into entangled light beams flying in two different directions. We estimate the yield efficiency of pairs of entangled photons per pulse of the very weak coherent light for our method at 0.0783 for a specific concrete example. Our method is more effective because the conversion efficiency (entangled biphotons per incident pump photons) in the spontaneous parametric downconversion is of the order of . The only drawback is that it requires very fine tuning of the frequency of signal photons fed into the photonic crystal; for example, an adjustment is given by Hz for the signal light of Hz. We investigate the application of entangled photons produced by our method to the BB84 quantum key distribution protocol, and we explore how to detect an eavesdropper. We suggest that our method is promising for decoy-state quantum key distribution using weak coherent light.

Testing macroscopic local realism using local nonlinear dynamics and time settings

We show how one may test macroscopic local realism where, different from conventional Bell tests, all relevant measurements need only distinguish between two macroscopically distinct states of the system being measured. Here, measurements give macroscopically distinguishable outcomes for a system observable and do not resolve microscopic properties (of order $\hbar$). Macroscopic local realism assumes: (1) macroscopic realism (the system prior to measurement is in a state which will lead to just one of the macroscopically distinguishable outcomes) and (2) macroscopic locality (a measurement on a system at one location cannot affect the macroscopic outcome of the measurement on a system at another location, if the measurement events are spacelike separated). To obtain a quantifiable test, we define $M$-scopic local realism where the outcomes are separated by an amount $\sim M$. We first show for $N$ up to $20$ that $N$-scopic Bell violations are predicted for entangled superpositions of $N$ bosons (at each of two sites). Secondly, we show violation of $M$-scopic local realism for entangled superpositions of coherent states of amplitude $\alpha$, for arbitrarily large $M=\alpha$. In both cases, the systems evolve dynamically according to a local nonlinear interaction. The first uses nonlinear beam splitters realised through nonlinear Josephson interactions; the second is based on nonlinear Kerr interactions. To achieve the Bell violations, the traditional choice between two spin measurement settings is replaced by a choice between different times of evolution at each site.

Few-photon transport in Fano-resonance waveguide geometries

We present a theoretical study of Fano interference effects in few-photon transport. Under appropriate conditions, a local defect in an optical waveguide induces a highly asymmetric transmission lineshape, characteristic of Fano interference. For a two-level emitter placed adjacent to such a defect, here modeled as a partially transmitting element, we find an analytical expression for the full time evolution of single-photon wavepackets and the emitter excitation probability. We show how the partially transmitting element affects the emitter lifetime and shifts the spectral position of the effective system resonances. Using input-output formalism, we determine the single and two-photon $ S $-matrices for both a two-level emitter and a cavity-emitter system coupled to a waveguide with a partially transmitting element. We show how the Fano interference effect can be exploited for the implementation of a Hong-Ou-Mandel switch in analogy with a tunable linear or nonlinear beam splitter.

Effect of Inter-Well Interactions on Non-Linear Beam Splitters for Matter-Wave Interferometers

We study the non-linear beam splitter in matter-wave interferometers using ultracold quantum gases in a double-well configuration in presence of non-local interactions inducing inter-well density-density coupling, as they can be realized, e.g., with dipolar gases. We explore this effect after considering different input states, in the form of either coherent, or Twin-Fock, or NOON states. We first review the non-interacting limit and the case in which only the local interaction is present, including the study of sensitivity near the self-trapping threshold. Then, we consider the two-mode model in the presence of inter-well interactions and consider the scaling of the sensitivity as a function of the non-local coupling strength. Our analysis clearly shows that non-local interactions can compensate the degradation of the sensitivity induced by local interactions, so that they may be used to restore optimal sensitivity.

Tripartite Einstein-Podolsky-Rosen steering with linear and nonlinear beamsplitters in four-wave mixing of Rubidium atoms.

Multipartite Einstein-Podolsky-Rosen (EPR) steering is an essential resource for secure one-sided device-independent quantum secret sharing. Here, we analyze the EPR steering properties exhibited in three-mode Gaussian states created by four-wave mixing (FWM) in Rubidium atoms combined with a linear beamsplitter and a nonlinear beamsplitter (second FWM), respectively. By quantifying Gaussian steerability based on a measure determined by the covariance matrix of the produced states, we compare the performance of two schemes to achieve one-way, collective, and genuine tripartite steering, as well as the monogamy constraints for distributing steering among three parties. We show that the scheme with nonlinear beamsplitter is feasible to create stronger bipartite steering and genuine tripartite steering and has more flexibility to manipulate the monogamy relation through the cooperation of the two cascaded FWM processes.

Phase sensitivity of a three-mode nonlinear interferometer

In this paper, we construct the input–output relationships of a three-mode nonlinear beam splitter (TNBS) mathematically, and a set of special solutions for the input–output equations are given. By combining two TNBSs and a phase shifter, we propose a scheme for a three-mode nonlinear interferometer (TNI) and give the input–output expression of the whole TNI. Then, we study the phase sensitivity of the TNI by giving input states and detection scheme. In addition, we also calculate the phase sensitivity of a Mach–Zehnder interferometer (MZI), SU(1,1) interferometer (SU(1,1)I) and modified Mach–Zehnder interferometer (MMZI), and we discuss the relationships of phase sensitivity between the MZI, SU(1,1)I, MMZI and TNI. Finally, in the presence of photon losses, we discuss the phase sensitivity of the four different interferometers and make detailed comparisons. It is shown that the TNI has the best robustness against photon losses under certain conditions with the same parameters.

Slow-light soliton beam splitters

We propose a scheme to realize slow-light soliton beam splitters by using a tripod-type four-level atomic system. We show that optical solitons, which have ultraslow propagation velocity and ultralow generation power, can be generated in the system via electromagnetically induced transparency and can be stored and retrieved with high efficiency and fidelity. In particular, a nonlinear beam splitter that splits one optical soliton into two or more ones can be obtained by switching on and off of two or more control laser fields subsequently. The results reported here open a route not only for active manipulation of nonlinear optical pulses in multistate quantum systems but also for promising applications in optical information processing and transmission.

Alignment-free dispersion measurement with interfering biphotons.

Measuring the dispersion of photonic devices with small dispersion-length products is challenging due to the phase-sensitive and alignment-intensive nature of conventional methods. In this Letter, we demonstrate a quantum technique to extract the second- and third-order chromatic dispersion of a short single-mode fiber using a fiber-based quantum nonlinear interferometer. The interferometer consists of two cascaded fiber-based biphoton sources, with each source acting as a nonlinear beam splitter. A fiber under test is placed between these two sources and introduces a frequency-dependent phase that is imprinted on the biphoton spectrum (interferogram) at the output of the interferometer. This interferogram contains the dispersion properties of the test fiber. Our technique has three novel features: (1)the broadband nature of the biphoton sources used in our setup allows accurate dispersion measurements on test devices with small dispersion-length products; (2)our all-fiber common-path interferometer requires no beam alignment or phase stabilization; and (3)multiple phase-matching processes supported in our biphoton sources enable dispersion measurements at different wavelengths, which yields the third-order dispersion achieved for the first time, to the best of our knowledge, using a quantum optical technique.

Quantum and high-sensitive laser technologies for polarization-optical diagnostics

The basics for highly sensitive laser and quantum technologies of polarization-optical measurements and diagnostics of ordered structures, nonlinear interfaces and nanosystems are considered. Quantum diagnostics for a nonlinear resonant beam splitter is performed. It is shown that this beam splitter operates as an optical buffer that reduces the quantum (photon) fluctuations of the reflected light.

On the Violation of Causality in Quantum Experiments

Four experimental situations are analyzed from the viewpoint of fulfilling the causality principle: instantaneous collapse of the quantum state vector of a system of entangled particles, a quantum eraser, the quantum Zeno paradox, and light transformation by a nonlinear beam splitter. The last is a planar interface of two transparent dielectrics, at least one of which possesses Kerr nonlinearity, that is, its refractive index depends on the intensity of radiation that penetrates it. It has been shown that the causality principle in the first two cases can be violated only in the sense of the instantaneousness of the manifestation of the effect with respect to the cause. For a nonlinear beam splitter, in addition to the directly opposite predictions given by the quantum and classical theories of its description for the behavior of phase fluctuations of the radiation transformed by the splitter, the causality principle is violated in the most general sense: the effect of the following event on the previous one. The quantum Zeno paradox occupies an intermediate position of democratic involvement of the cause and effect in the general cascade of two subsequent events, i.e., the first event can prevent the second event, just as the second event can prevent the first one.

A Quantum Interpretation of Light Scattering near the Boundary between Transparent Media with Kerr Nonlinearity

The transformation of light by a nonlinear beamsplitter is considered. The beamsplitter is formed by a plane interface between two transparent dielectrics, at least one of which has a Kerr nonlinearity; i.e., its refractive index depends on the intensity of the penetrating radiation. It is shown that the interpretation of the result of calculation of quantum fields at the outputs from such a beamsplitter indicates a violation of the principle of causality in the sense that a subsequent event affects the previous one.

Hybrid interferometer with nonlinear four-wave mixing process and linear beam splitter.

Optical interferometer has played an important role in optics. Up to now, many kinds of interferometers have been realized and found their applications. In this letter, we experimentally construct an interferometer by using parametric amplifier as a wave splitter and beam splitter as a wave combiner. We make measurements of interference fringes and explore the relationships between the interference visibility of the interferometer and various system parameters, such as the gain of the parametric amplifier, the one-photon detuning and the temperature of the Rb-85 vapor cell.

Quantum analysis of a beam splitter with second-order nonlinearity and generation of nonclassical light

A quantum mechanical model of a beam splitter having second-order nonlinearity is proposed and shows that nonclassical features such as squeezing and sub-Poissonian photon statistics of optical fields can be generated in output second-harmonic mode when we mix coherent light beams via such a nonlinear beam splitter.

Experimental implementation of a nonlinear beamsplitter based on a phase-sensitive parametric amplifier

Beamsplitters have played an important role in quantum optics experiments. They are often used to split and combine two beams, especially in the construct of an interferometer. In this letter, we experimentally implement a nonlinear beamsplitter using a phase-sensitive parametric amplifier, which is based on four-wave mixing in hot rubidium vapor. Here we show that, despite the different frequencies of the two input beams, the output ports of the nonlinear beamsplitter exhibit interference phenomena. We make measurements of the interference fringe visibility and study how various parameters, such as the intensity gain of the amplifier, the intensity ratio of the two input beams, and the one and two photon detunings, affect the behavior of the nonlinear beamsplitter. It may find potential applications in quantum metrology and quantum information processing.

Efficient Second Harmonic Generation in 3D Nonlinear Optical-Lattice-Like Cladding Waveguide Splitters by Femtosecond Laser Inscription.

Integrated photonic devices with beam splitting function are intriguing for a broad range of photonic applications. Through optical-lattice-like cladding waveguide structures fabricated by direct femtosecond laser writing, the light propagation can be engineered via the track-confined refractive index profiles, achieving tailored output beam distributions. In this work, we report on the fabrication of 3D laser-written optical-lattice-like structures in a nonlinear KTP crystal to implement 1 × 4 beam splitting. Second harmonic generation (SHG) of green light through these nonlinear waveguide beam splitter structures provides the capability for the compact visible laser emitting devices. With Type II phase matching of the fundamental wavelength (@ 1064 nm) to second harmonic waves (@ 532 nm), the frequency doubling has been achieved through this three-dimensional beam splitter. Under 1064-nm continuous-wave fundamental-wavelength pump beam, guided-wave SHG at 532 nm are measured with the maximum power of 0.65 mW and 0.48 mW for waveguide splitters (0.67 mW and 0.51 mW for corresponding straight channel waveguides), corresponding to a SH conversion efficiency of approximately ~14.3%/W and 13.9%/W (11.2%/W, 11.3%/W for corresponding straight channel waveguides), respectively. This work paves a way to fabricate compact integrated nonlinear photonic devices in a single chip with beam dividing functions.

Scattering of two photons on a quantum emitter in a one-dimensional waveguide: exact dynamics and induced correlations

We develop a wavefunction approach to describe the scattering of two photons on a quantum emitter embedded in a one-dimensional waveguide. Our method allows us to calculate the exact dynamics of the complete system at all times, as well as the transmission properties of the emitter. We show that the nonlinearity of the emitter with respect to incoming photons depends strongly on the emitter excitation and the spectral shape of the incoming pulses, resulting in transmission of the photons which depends crucially on their separation and width. In addition, for counter-propagating pulses, we analyze the induced level of quantum correlations in the scattered state, and we show that the emitter behaves as a nonlinear beam-splitter when the spectral width of the photon pulses is similar to the emitter decay rate.

Квантовая специфика нелинейного светоделителя

Квантовая специфика нелинейного светоделителя

Paradox of a nonlinear beam splitter and its resolution

A nonlinear beam splitter is shown to be an interesting object of investigation for the following reasons. First, the classical and quantum theories of its description give directly opposite behaviors of the phase fluctuations: according to the classical theory, the phase is unchanged; according to the quantum theory, the phase fluctuations increase or decrease, depending on the suppression or growth of amplitude fluctuations. The fundamental cause of these differences has been established. Second, the quantum fluctuations of the input mode can be separated into the amplitude and phase ones, so that the predominantly phase fluctuations are directed into one output mode, say, the reflected one, while the amplitude fluctuations are directed into the other (transmitted) mode.

Quantization of radiation emitted at discontinuities of nonlinearity

It is appropriate to base the quantum description of light propagation and down-conversion in a nonlinear medium on a Hamiltonian operator. In pumping with femtosecond pulses, which is not yet treated here, the description is so complicated that the discontinuities of the linear and nonlinear susceptibilities present a specific problem. In contrast, the analogy with a quantum nonlinear beam splitter can be utilized for the quantization of classical input–output relations. On numerical simulation, nonvanishing commutators between output field operators of different modes are revealed and a method of adaptation of these results to quantum input–output relations is also proposed.