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 parameters.
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.
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.
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…
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 detai…
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…
We present an algorithm for synchronizing two clocks based on second-order quantum interference between entangled photons generated by parametric down-conversion. The procedure is distinct from the standard Einstein two-way clock synchronization method in that photon correlations are used to define simultaneous events in the frame of reference of a Hong-Ou-Mandel (HOM) interferometer. Once the HOM interferometer is balanced, by use of an adjustable optical delay in one arm, arrival times of simultaneously generated photons are recorded by each clock. Classical information on the arrival times …
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 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…
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.
A two-particle interferometer is theoretically analyzed, to show how decoherence induced by interactions with the environment affects time correlations, a process we call time-correlation de-coherence. Specifically, on the basis of simple mathematical analysis we show how the interaction between a bipartite entangled system and a photon bath representing the environment can efface the oscillations in the coincidence-detection rate of the interferometer. We discuss the dependence of this kind of decoherence on the photon energy and density.
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 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）
We investigate quantum sensing of rotation with a multi-atom Sagnac interferometer and present multi-partite entangled states to enhance the sensitivity of rotation frequency. For studying the sensitivity, we first present a Hermitian generator with respect to the rotation frequency. The generator, which contains the Sagnac phase, is a linear superposition of a z component of the collective spin and a quadrature operator of collective bosons depicting the trapping modes, which enables us to conveniently study the quantum Fisher information (QFI) for any initial states. With the generator, we d…
We use a quantum variant of the Sagnac interferometer to argue for the quantum nature of gravity as well as to formulate a quantum version of the equivalence principle. We first present an original derivation of the phase acquired in the conventional Sagnac matter-wave interferometer, within the Hamiltonian formalism. Then we modify the interferometer in two crucial respects. The interfering matter wave is interfered along two different distances from the centre and the interferometer is prepared in a superposition of two different angular velocities. We argue that if the radial and angular de…
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…
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 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.
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…
The sensitivity of laser interferometers used for the detection of gravitational waves (GWs) is limited by quantum noise of light. An improvement is given by light with squeezed quantum uncertainties, as employed in the GW detector GEO600 since 2010. To achieve simultaneous noise reduction at all signal frequencies, however, the spectrum of squeezed states needs to be processed by 100m-scale low-loss optical filter cavities in vacuum. Here, we report on the proof-of-principle of an interferometer setup that achieves the required processed squeezed spectrum by employing Einstein-Podolsky-Rosen …
Phase measurement using a lossless Mach-Zehnder interferometer with certain entangled $N$-photon states can lead to a phase sensitivity of the order of 1/N, the Heisenberg limit. However, previously considered output measurement schemes are different for different input states to achieve this limit. We show that it is possible to achieve this limit just by the parity measurement for all the commonly proposed entangled states. Based on the parity measurement scheme, the reductions of the phase sensitivity in the presence of photon loss are examined for the various input states.
We analyze theoretically and experimentally cases of asymmetric detection, stimulation, and loss within a quantum nonlinear interferometer of entangled pairs. We show that the visibility of the SU(1,1) interference directly discerns between loss on the measured mode (signal) and the conjugated mode (idler). This asymmetry also affects the phase sensitivity of the interferometer, where coherent seeding is shown to mitigate losses that are suffered by the conjugated mode; therefore increasing the maximum threshold of loss that permits sub-shot-noise phase detection. Our findings can improve the …
This paper reports 1.5-um band time-bin entanglement generation. We employed a spontaneous four-wave mixing process in a dispersion shifted fiber, with which correlated photon pairs with very narrow bandwidths were generated efficiently. To observe two-photon interference, we used planar lightwave circuit based interferometers that were operated stably without feedback control. As a result, we obtained coincidence fringes with 99 % visibilities after subtracting accidental coincidences, and successfully distributed entangled photons over 20-km standard single-mode fiber without any deteriorati…
The quantum interference of entangled photons forms a key phenomenon underlying various quantum-optical technologies. It is known that the quantum interference patterns of entangled photon pairs can be reconstructed classically by the time-reversal method; however, the time-reversal method has been applied only to time-frequency-entangled two-photon systems in previous experiments. Here, for the first time, we apply the time-reversal method to the position-wavevector-entangled two-photon systems: the two-photon Young interferometer and the two-photon beam focusing system. We experimentally dem…
Entangled photons can be used to make measurements with an accuracy beyond that possible with classical light. While most implementations of quantum metrology have used states made up of a single colour of photons, we show that entangled states of two colours can show supersensitivity to optical phase and path-length by using a photonic crystal fibre source of photon pairs inside an interferometer. This setup is relatively simple and robust to experimental imperfections. We demonstrate sensitivity beyond the standard quantum limit and show super-resolved interference fringes using entangled st…
To acquire the best path-entangled photon Fock states for robust quantum optical metrology with parity detection, we calculate phase information from a lossy interferometer by using twin entangled Fock states. We show that (a) when loss is less than 50% twin entangled Fock states with large photon number difference give higher visibility while when loss is higher than 50% the ones with less photon number difference give higher visibility; (b) twin entangled Fock states with large photon number difference give sub-shot-noise limit sensitivity for phase detection in a lossy environment. This res…
An experimental demonstration of quantum correlations is presented. Energy and time entangled photons at wavelengths of 704 and 1310 nm are produced by parametric downconversion in KNbO3 and are sent through optical fibers into a bulk-optical (704 nm) and an all-fiber Michelson-interferometer (1310 nm), respectively. The two interferometers are located 35 meters aside from one another. Using Faraday-mirrors in the fiber-interferometer, all birefringence effects in the fibers are automatically compensated. We obtained two-photon fringe visibilities of up to 95 % from which one can project a vio…
We propose a generalized form of entangled coherent states (ECS) and apply them in a multi-arm optical interferometer to estimate multiple phase shifts. We obtain the quantum Cramer-Rao bounds for both the linear and nonlinear parameterization protocols. Through the analysis, we find that, utilizing the simultaneous estimation, this generalized form of ECS gives a better precision than the generalized NOON states [Phys. Rev. Lett. \textbf{111}, 070403 (2013)]. Moreover, comparing with the independent estimation, both the linear and nonlinear protocols have the same advantage in the relation to…
Recently, our group has demonstrated an ultrafast, low-loss, fiber-loop switch based on a nonlinear Sagnac-interferometer design, using which entangled photons were shown to be routed without any measurable degradation in their entanglement fidelity [Hall {\it et al.}, Phys. Rev. Lett. {\bf 106}, 053901 (2011)]. Such a device represents an enabling technology for a rich variety of networked quantum applications. In this paper we develop a comprehensive quantum theory for such switches in general, i.e., those based on nonlinear Sagnac interferometers, where the in-coupling of quantum noise is c…
We investigate the connection between the shot-noise limit in linear interferometers and particle entanglement. In particular, we ask whether or not sub shot-noise sensitivity can be reached with all pure entangled input states of $N$ particles if they can be optimized with local operations. Results on the optimal local transformations allow us to show that for $N=2$ all pure entangled states can be made useful for sub shot-noise interferometry while for $N>2$ this is not the case. We completely classify the useful entangled states available in a bosonic two-mode interferometer. We apply our r…
We have experimentally realized a technique to generate, control and measure entangled qutrits, 3-dimensional quantum systems. This scheme uses spontaneous parametric down converted photons and unbalanced 3-arm fiber optic interferometers in a scheme analogous to the Franson interferometric arrangement for qubits. The results reveal a source capable of generating maximally entangled states with a net state fidelity, F = 0.985 $\pm$ 0.018. Further the control over the system reveals a high, net, 2-photon interference fringe visibility, V = 0.919 $\pm$ 0.026. This has all been done at telecom wa…
By considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition states and maximally path entangled $N00N$-states. With these macroscopic states, we examine Mach-Zehnder interferometer in the context of parity measurements, in order to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio between two-body scattering length and intra-well hopping parameter can be measured with the scaling beyond t…
Heralded generation and manipulation of quantum entanglement between two macroscopic and spatially separated crystals at room temperature is theoretically studied. We show that by combining an x-ray parametric down-conversion source and x-ray interferometry with nuclear resonant scattering techniques, two macroscopic crystals hosting Mössbauer nuclei located each on an interferometer arm can be entangled for few tens of nanoseconds. The coherence time of the entanglement state can be prolonged up to values comparable to the lifetime of a single nuclear excited state, on the order of hundred na…
We propose a class of path-entangled photon Fock states for robust quantum optical metrology, imaging, and sensing in the presence of loss. We model propagation loss with beam-splitters and derive a reduced density matrix formalism from which we examine how photon loss affects coherence. It is shown that particular entangled number states, which contain a special superposition of photons in both arms of a Mach-Zehnder interferometer, are resilient to environmental decoherence. We demonstrate an order of magnitude greater visibility with loss, than possible with N00N states. We also show that t…
We experimentally demonstrate amplitude and phase modulation of a time-energy entangled two-photon wave function. The entangled photons are produced by spontaneous parametric down-conversion, spectrally dispersed in an prism compressor, modulated in amplitude and/or phase, and detected in coincidence by sum-frequency generation. First, we present a Fourier optical analysis of the optical setup yielding an analytic expression for the resulting field distribution at the exit plane of the shaping apparatus. We then introduce amplitude and/or phase shaping and present results which can only be obt…
