The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. in [Phys. Rev. A 69, 032112 (2004)], and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time dependent interaction with two radio-frequency (rf) fields. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme, yields a sinusoidal oscillation of the correlation function S, dependent on the geometric phase, such that it varies in the range between 2 and 2\sqrt{2} and, therefore, always exceeds the boundary value 2 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like-CHSH inequality, where S remains 2\sqrt2 for all settings of the geometric phase.
We demonstrate a simple, robust, and ultrabright parametric down-conversion source of polarization-entangled photons based on a polarization Sagnac interferometer. Bidirectional pumping in type-II phase-matched periodically poled KTiOPO4 yields a measured flux of 5 000 polarization-entangled pairs/s per mW of pump power in a 1-nm bandwidth at 96.8% quantum-interference visibility. The common-path arrangement of the Sagnac interferometer eliminates the need for phase stabilization for the biphoton output state.
SU(1,1) interferometer (SUI) is a novel type of interferometer that uses directly entangled quantum fields for sensing phase change. For rotational sensing, Sagnac geometry is usually adopted. However, because SUI depends on the phase sum of the two arms, traditional Sagnac geometry, when applied to SUI, will result in null signal. In this paper, we modify the traditional Sagnac interferometer by nesting SU(1,1) interferometers inside. We show that the rotational signal comes from two parts labeled as "classical" and "quantum", respectively, and the quantum part, where quantum entangled fields…
We give an analytical result for the quantum Fisher information of entangled coherent States in a lossy Mach-Zehnder Interferometer recently proposed by J. Joo et al. [Phys. Rev. Lett. 107, 083601(2011)]. For small loss of photons, we find that the entangled coherent state can surpass the Heisenberg limit. Furthermore, The formalism developed here is applicable to the study of phase sensitivity of multipartite entangled coherent states.
In this article we show that, in a two-arm interferometer, pure quantum states of perfect path distinguishability (particles) are geometrically equidistant from all states with constant path distinguishability D. This property is not shared by other states, such as perfect fringe-visibility (waves) or maximally entangled quantum states (entanglon). Indeed, the Bures distance between a particle and any other state depends only the distinguishability of the latter. On the contrary, the Bures distance between a wave or an entanglon, and any other single photon state depends on other set of parame…
Using spontaneous parametric down conversion and a 50:50 beam splitter, we generate coaxial polarization-entangled photon pairs, of which the two photons are far separated from each other. The photons are then sent one by one through one port of a modified Mach-Zehnder interferometer. We observe interference fringes with a periodicity half of the single-photon wavelength, independent of the distance between the photons. This feature can find applications in quantum-enhanced measurement.
We experimentally demonstrate a source of polarization entangled photon-pairs based on a single periodically-poled potassium titanyl phosphate (PPKTP) crystal pumped with a broadband, free running laser diode.The crystal is placed within a linear beam-displacement interferometer, and emits photon-pairs based ontype-0 spontaneous parametric downconversion (SPDC). We observe pair rates of 0.56 Mpairs/s/mW in a single spatial mode with a polarization visibility of 97.7% over a spectral range of 100 nm. This experiment demonstrates a pathway towards observing Gigacount rates of polarization entang…
We present two-photon interference experiments with polarization-entangled photon pairs in a polarization-based Franson-type interferometer. Although the two photons do not meet at a common beamsplitter, a phase-insensitive Hong-Ou-Mandel type two-photon interference peak and dip fringes are observed, resulting from the two-photon interference effect between two indistinguishable two-photon probability amplitudes leading to a coincidence detection. A spatial quantum beating fringe is also measured for nondegenerate photon pairs in the same interferometer, although the two-photon states have no…
Sources of entangled photon pairs are a key component in both fundamental tests of quantum theory and practical applications such as quantum key distribution and quantum computing. In this work, we describe and characterize a source of polarization entangled photon pairs based on two spontaneous parametric down-conversion (SPDC) crystals in a Sagnac interferometer. Our source is compact and produces high-quality entangled states in a very flexible manner. The wavelengths of the photon pairs, around 810 and 1550 nm, the phase between orthogonal components of the entangled state, and the tangle …
We demonstrate several new results for the nonlinear interferometer, which emerge from a formalism which describes in an elegant way the output field of the nonlinear interferometer as two-mode entangled coherent states. We clarify the relationship between squeezing and entangled coherent states, since a weak nonlinear evolution produces a squeezed output, while a strong nonlinear evolution produces a two-mode, two-state entangled coherent state. In between these two extremes exist superpositions of two-mode coherent states manifesting varying degrees of entanglement for arbitrary values of th…
A new type of quantum entangled interferometer was recently realized that employs parametric amplifiers as the wave splitting and recombination elements. The quantum entanglement stems from the parametric amplifiers, which produce quantum correlated fields for probing the phase change signal in the interferometer. This type of quantum entangled interferometer exhibits some unique properties that are different from traditional beam splitter-based interferometers such as Mach-Zehnder interferometers. Because of these properties, it is superior to the traditional interferometers in many aspects, …
It is discussed how systems of quantum-correlated (entangled)particles or atoms behave in external gravitational fields and what gravitational effects may exist in such systems. An experimental setup is proposed which improves the sensitivity of the Ramsey interferometer by the usage of quantum-correlated atoms. Entanglement of $n$ atoms improves the sensitivity to small phase shifts in $n^2$ times. This scheme may be used for observing gravity-induced phase shifts in laboratory.
Properties of entangled photon pairs generated in spontaneous parametric down-conversion are investigated in interference experiments. Strong energy correlations are demonstrated in a direct way. If a signal photon is detected behind a narrow spectral filter, then interference appears in the Mach-Zehnder interferometer placed in the route of the idler photon, even if the path difference in the interferometer exceeds the coherence length of the light. Narrow time correlations of the detection instants are demonstrated for the same photon-pair source using the Hong-Ou-Mandel interferometer. Both…
Entangled light can provide a seminal improvement in resolution sensitivity even without achieving Heisenberg limit in a single channel. In this paper, based on the back-of-the-envelope type calculations, I demonstrate an alternative path to space based long-arm interferometer. Its advantage with respect to LISA is that it does not require complex satellites with many active components to achieve similar resolution.
Recent experiments with identically tuned nested Mach-Zehnder interferometers which attempted to observe the location of particles inside these interferometers are analyzed. In spite of claims to the contrary, it is argued that all experiments support the same surprising picture according to which the location of the particles inside the interferometers is not described by continuous trajectories.
An experiment with nested Mach-Zehnder interferometer [Phys. Rev. Lett. 111, 240402 (2013)] has been recently implemented with neutrons [Phys. Rev. A 97, 052111 (2018)]. Which-path information has been extracted from faint traces the neutrons left, providing operational meaning to "the particle's path". The authors of the neutron interference experiment criticised the conclusions obtained by the authors of the optical experiment. I refute the criticism and argue that the results of the neutron interference experiment actually support the surprising picture of the past of the particle in the ne…
Ongoing fascination with quantum mechanics keeps driving the development of the wide field of quantum-optics, including its neutron-optics branch. Application of neutron-optical methods and, especially, neutron interferometry and polarimetry has a long-standing tradition for experimental investigations of fundamental quantum phenomena. We give an overview of related experimental efforts made in recent years.
A neutron optical experiment is presented to investigate the paths taken by neutrons in a three-beam interferometer. In various beam-paths of the interferometer, the energy of the neutrons is partially shifted so that the faint traces are left along the beam-path. By ascertaining an operational meaning to "the particle's path", which-path information is extracted from these faint traces with minimal-perturbations. Theory is derived by simply following the time evolution of the wave function of the neutrons, which clarifies the observation in the framework of standard quantum mechanics. Which-w…
We designed and implemented a novel combination of a Sagnac-interferometer with a Mach-Zehnder interferometer for a source of polarization-entangled photons. The new versatile configuration does not require multi-wavelength polarization optics, yet it performs with a good polarization quality and phase-stability over a wide wavelength range. We demonstrate the interferometer using only standard commercial optics to experimentally realize the pulsed generation of polarization-entangled photon-pairs at wavelengths of 764nm and 1221nm via type-I spontaneous four-wave mixing in a polarization-main…
We investigate quantum coherences in the presence of noise by entangling the spin and path degrees of freedom of the output neutron beam from a noisy three-blade perfect crystal neutron interferometer. We find that in the presence of dephasing noise on the path degree of freedom the entanglement of the output state reduces to zero, however the quantum discord remains non-zero for all noise values. Hence even in the presence of strong phase noise non-classical correlations persist between the spin and path of the neutron beam. This indicates that measurements performed on the spin of the neutro…
Various phase shifters and absorbers can be put into the arms of a double loop neutron interferometer. The mean intensity levels of the forward and diffracted beams behind an empty four plate interferometer of this type have been calculated. It is shown that the intensities in the forward and diffracted direction can be made equal using certain absorbers. In this case the interferometer can be regarded as a 50/50 beam splitter. Furthermore the visibilities of single and double loop interferometers are compared to each other by varying the transmission in the first loop using different absorber…
The Sagnac interferometry has been widely used to measure rotation frequency. Beyond the conventional single-particle Sagnac interferometry, we propose an atomic Sagnac interferometry via multi-particle entangled states. In our scheme, an ensemble of entangled two-state Bose atoms are moved in a ring by a state-dependent rotating potential and then are recombined for interference via Ramsey pulses after a specific time determined by the state-dependent rotating potential. The ultimate rotation sensitivity can be improved to the Heisenberg limit if the initial internal degrees of freedom are en…
For precise measurements with polarized neutrons high efficient spin-manipulation is required. We developed several neutron optical elements suitable for a new sophisticated setup, i.e., DC spin-turners and Larmor-accelerators which diminish thermal disturbances and depolarisation considerably. The gain in performance is exploited demonstrating violation of a Bell-like inequality for a spin-path entangled single-neutron state. The obtained value of S=2.365(13), which is much higher than previous measurements by neutron interferometry, is 28 $σ$ above the limit of S=2 predicted by contextual hi…
We present experimental evidence of the generation of distinct types of genuine multipartite entanglement between three degrees of freedom, two internal and one external degree of freedom, within single-neutron quantum systems. This is achieved via the development of new spin manipulation apparatuses for neutron interferometry and the genuine multipartite entanglement is detected via appropriately designed and optimized non-linear witnesses. Via the applied criteria we reveal even finer properties of the type of the genuine multipartite entanglement that is produced in the experiment. In a sub…
We theoretically investigate how entangled atomic states generated via spin-changing collisions in a spinor Bose-Einstein condensate can be designed and controllably prepared for atom interferometry that is robust against common technical issues, such as limited detector resolution. We use analytic and numerical treatments of the spin-changing collision process to demonstrate that triggering the entangling collisions with a small classical seed rather than vacuum fluctuations leads to a more robust and superior sensitivity when technical noise is accounted for, despite the generated atomic sta…
We implemented a triply entangled Greenberger-Horne-Zeilinger(GHZ)-like state and coherently manipulated the spin, path, and energy degrees of freedom in a single neutron system. The GHZ-like state was analyzed with an inequality derived by Mermin: we determined the four expectation values and finally obtained M = 2.558 +/- 0.004 > 2, which exhibits a clear violation of the noncontextual assumption and confirms quantum contextuality.
Weak values of the spin operator Sz of massive particles, more precisely neutrons, have been experimentally determined by applying a novel measurement scheme. This is achieved by coupling the neutron's spin weakly to its spatial degree of freedom in a single-neutron interferometer setup. The real and imaginary parts as well as the modulus of the weak value are obtained by a systematical variation of pre- and post-selected ensembles, which enables to study the complex properties of spin weak values.
We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by Hasegawa et al. [Phys. Rev. A 53, 2486 (1996)] to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism…
We propose a simple scheme to swap the non local correlations, characteristic of a Franson interferometric setup, between pairs of frequency entangled photons emitted by distinct non linear crystals in a parametric down conversion process. Our scheme consists of two distinct sources of frequency entangled photons. One photon of each pair is sent to a separate Mach - Zender interferometer while the other photons of the pairs are mixed by a beam splitter and then detected in a Ou - Mandel interferometer. For suitably postselected joint measuremetns, the photons sent at the Mach -Zender show a co…
A neutron interferometric test of interaction-free detection of the presence of an absorbing object in one arm of a neutron interferometer has been performed. Despite deviations from the ideal performance characteristics of a Mach-Zehnder interferometer it could be shown that information is obtained without interaction.
It is commonly assumed that no accurate experimental information can be obtained on the path taken by a particle when quantum interference between the paths is observed. However, recent progress in the measurement and control of quantum systems may provide the missing information by circumventing the conventional uncertainty limits. Here, we experimentally investigate the possibility that an individual neutron moving through a two-path interferometer may actually be physically distributed between the two paths. For this purpose, it is important to distinguish between the probability of finding…
The Kochen-Specker theorem theoretically shows evidence of the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments by using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement in a single neutron system. Here entanglement is achieved not between different particles, but between degrees of freedom, i.…
We provide a quantum information description of a proposed five-blade neutron interferometer geometry and show that it is robust against low frequency mechanical vibrations and dephasing due to the dynamical phase. The extent to which the dynamical phase affects the contrast in a neutron interferometer is experimentally shown. In our model, we consider the coherent evolution of a neutron wavepacket in an interferometer crystal blade and simulate the effect of mechanical vibrations and momentum spread of the neutron through the interferometer. The standard three-blade neutron interferometer is …
We study two different decoherence modes for entangled qubits by considering a Liouville - von Neumann master equation. Mode A is determined by projection operators onto the eigenstates of the Hamiltonian and mode B by projectors onto rotated states. We present solutions for general and for Bell diagonal states and calculate for the later the mixedness and the amount of entanglement given by the concurrence. We propose a realization of the decoherence modes within neutron interferometry by applying fluctuating magnetic fields. An experimental test of the Kraus operator decomposition describing…
We present a free-space interferometer to observe two-particle interference of a pair of atoms with entangled momenta. The source of atom pairs is a Bose--Einstein condensate subject to a dynamical instability, and the interferometer is realized using Bragg diffraction on optical lattices, in the spirit of our recent Hong--Ou--Mandel experiment. We report an observation consistent with an entangled state at the input of the interferometer. We explain how our current setup can be extended to enable a test of a Bell inequality on momentum observables.
We demonstrate pulsed polarization-entangled photons generated from a periodically poled $\mathrm{KTiOPO_4}$ (PPKTP) crystal in a Sagnac interferometer configuration at telecom wavelength. Since the group-velocity-matching (GVM) condition is satisfied, the intrinsic spectral purity of the photons is much higher than in the previous scheme at around 800 nm wavelength. The combination of a Sagnac interferometer and the GVM-PPKTP crystal makes our entangled source compact, stable, highly entangled, spectrally pure and ultra-bright. The photons were detected by two superconducting nanowire single …
We report a nonlocal interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer's unique correlation dependence on the anti-diagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. The interferometer consists of two spatially separated balanced Mach-Zehnder or Sagnac interferometers that share a polarization entangled source. Correlations between these interferometers exhibit non-local interference, while single photon interference is suppresse…
We consider a one-dimensional (1D) wire along which single conduction electrons can propagate in the presence of two spin-1/2 magnetic impurities. The electron may be scattered by each impurity via a contact-exchange interaction and thus a spin-flip generally occurs at each scattering event. Adopting a quantum waveguide theory approach, we derive the stationary states of the system at all orders in the electron-impurity exchange coupling constant. This allows us to investigate electron transmission for arbitrary initial states of the two impurity spins. We show that for suitable electron wave …
Distributed quantum phase sensing using an SU(1,1) Perelomov coherent state in a Mach-Zehnder interferometer network
Mohammed V University in Rabat（拉巴特穆罕默德五世大学）；Faculty of Sciences, Mohammed V University in Rabat（拉巴特穆罕默德五世大学理学院）；LPHE-Modeling and Simulation, Faculty of Sciences, Mohammed V University in Rabat（拉巴特穆罕默德五世大学理学院LPHE建模与模拟）；Centre of Physics and Mathematics, CPM, Faculty of Sciences, Mohammed V University in Rabat（拉巴特穆罕默德五世大学理学院物理与数学中心CPM）
Recently, different experimental methods to investigate the entangled two-photon absorption (ETPA) process in a variety of materials have been reported. The present work reports on a different approach on which the ETPA process is detected based on the changes induced on the Hong-Ou-Mandel (HOM) interferogram of two photons produced by a spontaneous parametric down conversion (SPDC) Type-II process. Using an organic solution of the laser dye Rhodamine B as a model, it is demonstrated that ETPA at 800nm can be monitored by the changes in the temporal-width and visibility of the HOM interferogra…
By selecting a certain subensemble of joint detection events in a two-particle interferometer arrangement, a formal nonlocality contradiction of the Hardy type is derived for an ensemble of particle pairs configured in the maximally entangled state. It is argued, however, that the class of experiments exhibiting this kind of contradiction does not rule out the assumption of local realism.
We examine the question of coherent perfect absorption (CPA) of single photons, and more generally, of the quantum fields by a {\it macroscopic} medium. We show the CPA of path entangled single photons in a Fabry-Perot interferometer containing an absorptive medium. The frequency of perfect absorption can be controlled by changing the interferometer parameters like the reflectivity and the complex dielectric constant of the material. We exhibit similar results for path entangled photons in micro-ring resonators. For entangled fields like the ones produced by a down converter the CPA aspect is …
A combined ferrite parametric amplifier and millimeter-wave homodyne interferometer are proposed as an ambient temperature Bell Test. It is shown that the non-linear magnetic susceptibility of the yttrium iron garnet (YIG) ferrite, on account of its narrow line-width Larmor precessional resonance, make it an ideal material for the creation of entangled photons. These can be measured using a homodyne interferometer, as the much larger number of thermally generated photons associated with ambient temperature emission can be screened out. The proposed architecture may enable YIG quantum technolog…
In 1975, two experimental groups have independently observed the 4$π$-symmetry of neutrons' spin, when passing through a static magnetic field, using a three-blade interferometer made from a single perfect Si-crystal (analogous to the Mach-Zehnder interferometer of light optics). In this article, we provide a complete analysis of the experiment, both from a theoretical and conceptual point of view. Firstly, we solve the Schrödinger equation in the weak potential approximation, to obtain the amplitude of the refracted and forward refracted beams, produced by the passage of neutrons through one …
We report the observation of phase-super resolution in a motion-sensitive spin-wave (SW) atom interferometer utilizing a NOON-type entanged state. The SW interferometer is implemented by generating a superposition of two SWs and observing the interference between them, where the interference fringe is sensitive to the atomic collective motion. By heralded generation of a second order NOON state in the SW interferometer, we clearly observe the interference pattern with phase super-resolution. The demonstrated SW interferometer can in principle be scaled up to highly entangled quantum state, and…
We demonstrate a two phase-grating, multi-beam neutron interferometer by using a modified Ronchi setup in a far-field regime. The functionality of the interferometer is based on the universal \moire effect that was recently implemented for X-ray phase-contrast imaging in the far-field regime. Interference fringes were achieved with monochromatic, bichromatic, and polychromatic neutron beams; for both continuous and pulsed beams. This far-field neutron interferometry allows for the utilization of the full neutron flux for precise measurements of potential gradients, and expands neutron phase-co…
We propose a novel interferometer by using optical transverse modes in multimode waveguide that can beat the standard quantum limit. In the scheme, the classical simulation of $N$-partical quantum entangled states is generated by using $N$ independent classical fields and linear optical elements. Similar to the quantum-enhanced measurements, the classical simulation can also achieve $\sqrt{N}$ enhancement over the precision of the measurement $N$ times for independent fields. Due to only using classical fields and linear optical elements, the scheme can be realized much more easily.
In recent years there has been an enormous progress in matter wave interferometry. The Colella- Overhauser-Werner (COW) type of neutron interferometer and the Kasevich-Chu (K-C) atom interferometer, are the prototype of such devices and the issue of whether they are sensitive to relativistic effects has recently aroused much controversy. We examine the question of to what extent the gravitational red shift, and the related twin paradox effect can be seen in both of these atom and neutron interferometers. We point out an asymmetry between the two types of devices. Because of this, the non-vanis…
Off-diagonal geometric phases acquired in the evolution of a spin-1/2 system have been investigated by means of a polarized neutron interferometer. Final counts with and without polarization analysis enable us to observe simultaneously the off-diagonal and diagonal geometric phases in two detectors. We have quantitatively measured the off-diagonal geometric phase for noncyclic evolutions, confirming the theoretical predictions. We discuss the significance of our experiment in terms of geometric phases (both diagonal and off-diagonal) and in terms of the quantum erasing phenomenon.
For a generic interferometer, the conditional probability density distribution, $p(ϕ|m)$, for the phase $ϕ$ given measurement outcome $m$, will generally have multiple peaks. Therefore, the phase sensitivity of an interferometer cannot be adequately characterized by the standard deviation, such as $Δϕ\sim 1/\sqrt{N}$ (the standard limit), or $Δϕ\sim 1/N$ (the Heisenberg limit). We propose an alternative measure of phase sensitivity--the fidelity of an interferometer--defined as the Shannon mutual information between the phase shift $ϕ$\ and the measurement outcomes $m$. As an example applicati…
In a recent article Wang et al. (Class. Quantum Grav. 23 (2006) L59), demonstrated that the phase of a particle fluctuates due to interactions with random deviations of a conformal gravitational field. Furthermore they demonstrated that atom interferometers are sensitive to these fluctuations and that sensitivity to Planck scale effects could be achieved with a sufficiently sensitive interferometer. In this paper we demonstrate that a class of entangled states, the N-atom Greenberger-Horne-Zeilinger (GHZ) states, provide a better scaling than atom interferometers and that current experiments a…
