DOCSLIB.ORG

Quantum Phase-Sensitive Diffraction and Imaging Using Entangled Photons

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Phase-Sensitive Diffraction and Imaging Using Entangled Photons Quantum phase-sensitive diffraction and imaging using entangled photons Shahaf Asbana,b,1, Konstantin E. Dorfmanc,1, and Shaul Mukamela,b,1 aDepartment of Chemistry, University of California, Irvine, CA 92697-2025; bDepartment of Physics and Astronomy, University of California, Irvine, CA 92697-2025; and cState Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China Contributed by Shaul Mukamel, April 18, 2019 (sent for review March 21, 2019; reviewed by Sharon Shwartz and Ivan A. Vartanyants) (1) R ∗ (2) R 2 We propose a quantum diffraction imaging technique whereby Here βnm = dr un (r)σ(r)um (r), βnm = dr un (r) jσ(r)j ∗ one photon of an entangled pair is diffracted off a sample and um (r), and ρ¯i is a two-dimensional vector in the transverse detected in coincidence with its twin. The image is obtained by detection plane. σ (r) is the charge density of the target object scanning the photon that did not interact with matter. We show prepared by an actinic pulse and p = (1, 2) represents the that when a dynamical quantum system interacts with an external order in σ (r). For large diffraction angles and frequency- field, the phase information is imprinted in the state of the field resolved signal, thep phase-dependent image is modified to in a detectable way. The contribution to the signal from photons P1 ∗ S [ρ¯i ]/ Re nm γnm λn λm vn (ρ¯i )vm (ρ¯i ), where γnm has a 1=2 (1) that interact with the sample scales as / Ip , where Ip is the source similar structure to βnm modulated by the Fourier decomposi- intensity, compared with / Ip of classical diffraction. This makes tion of the Schmidt basis. γnm is phase dependent, contrast to imaging with weak fields possible, providing high signal-to-noise diffraction with classical sources. ratio, avoiding damage to delicate samples. A Schmidt decomposi- Our second main result tackles the spatial resolution enhance- tion of the state of the field can be used for image enhancement by ment. In entanglement-based imaging, the resolution is lim- reweighting the Schmidt modes contributions. ited by the degree of correlation of the two beams. Schmidt decomposition of the image allows us to enhance desired spa- quantum imaging j entangled photons j quantum diffraction j tial features of the charge density. High-order Schmidt modes phase-sensitive imaging (which correspond to angular momentum transverse modes with PHYSICS high topological charge) offer more detailed matter information. apid advances in short-wavelength ultrafast light sources Reweighting of Schmidt modes maximizes modal entropy which Rhave revolutionized our ability to observe the microscopic yields matter information gain and reveals fine details of the world. With bright free-electron lasers and high-harmonics table- charge density. Moreover, S(1) in Eq. 1 has no classical analog; top sources, short time (femtosecond) and length (subnanome- the contribution to the overall image from the signal photons ter) scales become accessible experimentally. These offer new 1=2 scales as Ip , where Ip is the intensity of the source. This is exciting possibilities to study spatio-spectral properties of quan- a unique signature of the linear quantum diffraction (13). The tum systems driven out of equilibrium and monitor dynamical overall detected signal is obtained in coincidence and scales as relaxation processes and chemical reactions. The spatial fea- 3=2 tures of small-scale charge distributions can be recorded in time. / Ip . Classical diffraction in contrast requires two interactions Far-field off-resonant X-ray diffraction measurements provide with the incoming field and therefore scales as Ip , and the corre- 2 (2) useful information on the charge density σ (Q), where Q is the sponding coincidence scales as / Ip , which also applies for S . diffraction wavevector. The observed diffraction pattern S (Q) 2 is given by the modulus square S (Q)/ jσ (Q)j . Inverting these Significance signals to real-space σ (r) requires a Fourier transform. Since σ ( ) the phase of Q is not available, the inversion requires phase A quantum diffraction imaging technique is proposed, retrieval which can be done using either algorithmic solutions whereby one photon of an entangled pair is diffracted off (1, 2) or more sophisticated and costly experimental setups such a sample and detected in coincidence with its twin. Scan- as heterodyne measurements (3). Correlated beam techniques ning the photon that did not interact with matter, we show (4–10) in the visible regime have been shown to circumvent that the phase information imprinted in the state of the this problem by producing the real-space image of mesoscopic field is detectable. We discuss several experimental applica- objects. Such techniques have classical analogs using correlated tions: (i) Obtaining real-space images in diffraction imaging light. They reveal the modulus square of the studied object 1=2 2 avoids the “phase problem.” (ii) The image scales as / I jσ (r)j (11, 12). p I In this paper we consider the setup shown in Fig. 1. We focus with the interacting photons, where p is the source inten- / on off-resonant scattering of entangled photons in which only sity, compared with Ip of classical diffraction. This makes one photon, denoted as the “signal,” interacts with a sample. weak-field imaging possible, avoiding damage to delicate Its entangled counterpart, the “idler,” is spatially scanned and samples. (iii) A Schmidt decomposition of the field can be used measured in coincidence with the arrival of the signal photon. for image enhancement by reweighting the Schmidt modes The idler reveals the image and also uncovers phase informa- contributions. tion, as was recently shown in ref. 13 for linear diffraction where Author contributions: S.A., K.E.D., and S.M. designed research; S.A. performed research; heterodyne-like detection has been achieved due to vacuum S.A. analyzed data; and S.A., K.E.D., and S.M. wrote the paper.y fluctuation of the detector. Reviewers: S.S., Bar Ilan University; and I.A.V., Deutsches Elektronen-Synchrotron (DESY).y Our first main result is that for small diffraction angles, The authors declare no conflict of interest.y using Schmidt decomposition of the two-photon amplitude p Published under the PNAS license.y Φ(q , q ) = P1 λ u (q )v (q ) λ s i n n n s n i , where n is the respective 1 To whom correspondence may be addressed. Email: [email protected], sasban@ mode weight, reads uci.edu, or [email protected] This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. (p) X p (p) ∗ 1073/pnas.1904839116/-/DCSupplemental.y S [ρ¯i ] / Re λn λm βnm vn (ρ¯i )vm (ρ¯i ): [1] Published online May 23, 2019. nm www.pnas.org/cgi/doi/10.1073/pnas.1904839116 PNAS j June 11, 2019 j vol. 116 j no. 24 j 11673–11678 Downloaded by guest on September 26, 2021 the field amplitude Φ into a product of single-photon amplitude; all of the interesting quantum optical effects discussed below are derivatives of this feature. Φ can be represented as a super- position of separable states using the Schmidt decomposition (19–21) 1 X p Φ(qs , qi ) = λn un (qs )vn (qi ), [5] n where the Schmidt modes un (qs ) and vn (qi ) are the eigenvec- tors of the signal and the idler reduced density matrices, and P the eigenvalues λn satisfy the normalization n λn = 1 (20). The number of relevant modes serves as an indicator for the degree of inseparability of the amplitude, i.e., photon entangle- ment. Common measures for entanglement include the entropy P −1 P 2 Sent = − n λn log2 λn or the Schmidt number κ ≡ n λn . The latter is also known as the inverse participation ratio as it quantifies the number of important Schmidt modes or the effec- Fig. 1. Sketch of the proposed quantum imaging setup. A broadband (2) tive joint Hilbert space size of the two photons. In a maximally pump pulse with the wavevector kp propagates through a χ crystal, gen- erating an entangled photon pair denoted as signal and idler. The photons entangled wavefunction, all modes contribute equally. are distinguished either by polarization (type II) or by frequency (type I) and The spatial profile of the photons in the transverse plane are separated by a beam splitter (BS). The signal photon interacts with the (perpendicular to the propagation direction) can be expanded sample and can be further frequency dispersed and collected by a “bucket” and measured using a variety of basis functions; e.g., Laguerre– detector Ds with no spatial resolution. The idler is spatially resolved in Gauss (LG) or Hermite–Gauss (HG) has been demonstrated the transverse plane by the detector Di. The two photons are detected in experimentally (22, 23). These sets satisfy orthonormality coincidence (Eq. 12). R 2 P 0 d q un (q)vk (q)= δnk and closure relations n un (q)vn (q )= (2) 0 δ (q − q ). The deviation of λn from a uniform (flat) dis- tribution reflects the degree of entanglement. Perfect quan- Thanks to favorable scaling, weak fields can be used to study tum correlations correspond to maximal entanglement entropy fragile samples to avoid damage. and thus a flat distribution of modes. This is further clarified by the closure relations, which demonstrate the convergence Spatial Entanglement into a point-to-point mapping in the limit of perfect trans- Various sources of entangled photons are available, from quan- verse entanglement. The biphoton amplitude exhibits two lim- tum dots (14) to cold atomic gases (15) and nonlinear crystals, iting cases for the infinite inverse participation ratio which are and are reviewed in ref.
Load more

Recommended publications
  • Many Physicists Believe That Entanglement Is The
    NEWS FEATURE SPACE. TIME. ENTANGLEMENT. n early 2009, determined to make the most annual essay contest run by the Gravity Many physicists believe of his first sabbatical from teaching, Mark Research Foundation in Wellesley, Massachu- Van Raamsdonk decided to tackle one of setts. Not only did he win first prize, but he also that entanglement is Ithe deepest mysteries in physics: the relation- got to savour a particularly satisfying irony: the the essence of quantum ship between quantum mechanics and gravity. honour included guaranteed publication in After a year of work and consultation with col- General Relativity and Gravitation. The journal PICTURES PARAMOUNT weirdness — and some now leagues, he submitted a paper on the topic to published the shorter essay1 in June 2010. suspect that it may also be the Journal of High Energy Physics. Still, the editors had good reason to be BROS. ENTERTAINMENT/ WARNER In April 2010, the journal sent him a rejec- cautious. A successful unification of quantum the essence of space-time. tion — with a referee’s report implying that mechanics and gravity has eluded physicists Van Raamsdonk, a physicist at the University of for nearly a century. Quantum mechanics gov- British Columbia in Vancouver, was a crackpot. erns the world of the small — the weird realm His next submission, to General Relativity in which an atom or particle can be in many BY RON COWEN and Gravitation, fared little better: the referee’s places at the same time, and can simultaneously report was scathing, and the journal’s editor spin both clockwise and anticlockwise. Gravity asked for a complete rewrite.
    [Show full text]
  • Multi-Wavelength Compressive Computational Ghost Imaging
    Multi-wavelength compressive computational ghost imaging Stephen S. Welsha , Matthew P. Edgara, Phillip Jonathanb , Baoqing Suna , Miles. J. Padgetta aUniversity of Glasgow, Kelvin Building University Avenue G12 8QQ, Glasgow, UK; bDepartment of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK; ABSTRACT The field of ghost imaging encompasses systems which can retrieve the spatial information of an object through correlated measurements of a projected light field, having spatial resolution, and the associated reflected or trans- mitted light intensity measured by a photodetector. By employing a digital light projector in a computational ghost imaging system with multiple spectrally filtered photodetectors we obtain high-quality multi-wavelength reconstructions of real macroscopic objects. We compare different reconstruction algorithms and reveal the use of compressive sensing techniques for achieving sub-Nyquist performance. Furthermore, we demonstrate the use of this technology in non-visible and fluorescence imaging applications. Keywords: Ghost Imaging, Single Pixel Detectors, DLP Technologies, Multi-wavelength Imaging, Non-visible Imaging, Fluorescence Imaging 1. INTRODUCTION Ghost imaging (GI) has been an active research area for nearly two decades. First demonstrated utilizing spatially entangled photons,1 it was later shown possible using classical correlations of pseudo-thermal light sources.2{5 Early demonstrations of so called `classical GI' used a laser beam propagated through a ground glass diffuser in order to produce a pseudo-thermal speckle field. A beam splitter was used to produce two identical copies of the field which were subsequently propagated along two different paths: the test path and the reference path. The test path contained a partially transmissive or reflective object (typically planar) and a single-pixel photodetector (SPD) with no spatial resolution, whereas the reference path contained a detector with spatial resolution, typically a charged coupled device (CCD).
    [Show full text]
  • A Live Alternative to Quantum Spooks
    International Journal of Quantum Foundations 6 (2020) 1-8 Original Paper A live alternative to quantum spooks Huw Price1;∗ and Ken Wharton2 1. Trinity College, Cambridge CB2 1TQ, UK 2. Department of Physics and Astronomy, San José State University, San José, CA 95192-0106, USA * Author to whom correspondence should be addressed; E-mail:[email protected] Received: 14 December 2019 / Accepted: 21 December 2019 / Published: 31 December 2019 Abstract: Quantum weirdness has been in the news recently, thanks to an ingenious new experiment by a team led by Roland Hanson, at the Delft University of Technology. Much of the coverage presents the experiment as good (even conclusive) news for spooky action-at-a-distance, and bad news for local realism. We point out that this interpretation ignores an alternative, namely that the quantum world is retrocausal. We conjecture that this loophole is missed because it is confused for superdeterminism on one side, or action-at-a-distance itself on the other. We explain why it is different from these options, and why it has clear advantages, in both cases. Keywords: Quantum Entanglement; Retrocausality; Superdeterminism Quantum weirdness has been getting a lot of attention recently, thanks to a clever new experiment by a team led by Roland Hanson, at the Delft University of Technology.[1] Much of the coverage has presented the experiment as good news for spooky action-at-a-distance, and bad news for Einstein: “The most rigorous test of quantum theory ever carried out has confirmed that the ‘spooky action-at-a-distance’ that [Einstein] famously hated .
    [Show full text]
  • Lensless Imaging with Compressive Ultrafast Sensing Guy Satat, Matthew Tancik and Ramesh Raskar
    1 Lensless Imaging with Compressive Ultrafast Sensing Guy Satat, Matthew Tancik and Ramesh Raskar Abstract—Lensless imaging is an important and challenging time: the physics-based approach is done in one shot (i.e. all problem. One notable solution to lensless imaging is a single the sensing is done in parallel). The single pixel camera and pixel camera which benefits from ideas central to compressive its variants require hundreds of consecutive acquisitions, which sampling. However, traditional single pixel cameras require many illumination patterns which result in a long acquisition process. translates into a substantially longer overall acquisition time. Here we present a method for lensless imaging based on compres- Recently, time-resolved sensors enabled new imaging ca- sive ultrafast sensing. Each sensor acquisition is encoded with a pabilities. Here we consider a time-resolved system with different illumination pattern and produces a time series where pulsed active illumination combined with a sensor with a time is a function of the photon’s origin in the scene. Currently time resolution on the order of picoseconds. Picosecond time available hardware with picosecond time resolution enables time tagging photons as they arrive to an omnidirectional sensor. resolution allows distinguishing between photons that arrive This allows lensless imaging with significantly fewer patterns from different parts of the target with mm resolution. The compared to regular single pixel imaging. To that end, we develop sensor provides more information per acquisition (compared a framework for designing lensless imaging systems that use to regular pixel), and so fewer masks are needed. Moreover, the ultrafast detectors. We provide an algorithm for ideal sensor time-resolved sensor is characterized by a measurement matrix placement and an algorithm for optimized active illumination patterns.
    [Show full text]
  • Quantum Entanglement and Bell's Inequality
    Quantum Entanglement and Bell’s Inequality Christopher Marsh, Graham Jensen, and Samantha To University of Rochester, Rochester, NY Abstract – Christopher Marsh: Entanglement is a phenomenon where two particles are linked by some sort of characteristic. A particle such as an electron can be entangled by its spin. Photons can be entangled through its polarization. The aim of this lab is to generate and detect photon entanglement. This was accomplished by subjecting an incident beam to spontaneous parametric down conversion, a process where one photon produces two daughter polarization entangled photons. Entangled photons were sent to polarizers which were placed in front of two avalanche photodiodes; by changing the angles of these polarizers we observed how the orientation of the polarizers was linked to the number of photons coincident on the photodiodes. We dabbled into how aligning and misaligning a phase correcting quartz plate affected data. We also set the polarizers to specific angles to have the maximum S value for the Clauser-Horne-Shimony-Holt inequality. This inequality states that S is no greater than 2 for a system obeying classical physics. In our experiment a S value of 2.5 ± 0.1 was calculated and therefore in violation of classical mechanics. 1. Introduction – Graham Jensen We report on an effort to verify quantum nonlocality through a violation of Bell’s inequality using polarization-entangled photons. When light is directed through a type 1 Beta Barium Borate (BBO) crystal, a small fraction of the incident photons (on the order of ) undergo spontaneous parametric downconversion. In spontaneous parametric downconversion, a single pump photon is split into two new photons called the signal and idler photons.
    [Show full text]
  • Relational Quantum Mechanics Relational Quantum Mechanics A
    Provisional chapter Chapter 16 Relational Quantum Mechanics Relational Quantum Mechanics A. Nicolaidis A.Additional Nicolaidis information is available at the end of the chapter Additional information is available at the end of the chapter http://dx.doi.org/10.5772/54892 1. Introduction Quantum mechanics (QM) stands out as the theory of the 20th century, shaping the most diverse phenomena, from subatomic physics to cosmology. All quantum predictions have been crowned with full success and utmost accuracy. Yet, the admiration we feel towards QM is mixed with surprise and uneasiness. QM defies common sense and common logic. Various paradoxes, including Schrodinger’s cat and EPR paradox, exemplify the lurking conflict. The reality of the problem is confirmed by the Bell’s inequalities and the GHZ equalities. We are thus led to revisit a number of old interlocked oppositions: operator – operand, discrete – continuous, finite –infinite, hardware – software, local – global, particular – universal, syntax – semantics, ontological – epistemological. The logic of a physical theory reflects the structure of the propositions describing the physical system under study. The propositional logic of classical mechanics is Boolean logic, which is based on set theory. A set theory is deprived of any structure, being a plurality of structure-less individuals, qualified only by membership (or non-membership). Accordingly a set-theoretic enterprise is analytic, atomistic, arithmetic. It was noticed as early as 1936 by Neumann and Birkhoff that the quantum real needs a non-Boolean logical structure. On numerous cases the need for a novel system of logical syntax is evident. Quantum measurement bypasses the old disjunctions subject-object, observer-observed.
    [Show full text]
  • Fast First-Photon Ghost Imaging
    www.nature.com/scientificreports OPEN Fast frst-photon ghost imaging Xialin Liu, Jianhong Shi, Xiaoyan Wu & Guihua Zeng Conventional imaging at low light levels requires hundreds of detected photons per pixel to suppress the Poisson noise for accurate refectivity inference. We propose a high-efciency photon-limited imaging technique, called fast frst-photon ghost imaging, which recovers the image by conditional Received: 11 December 2017 averaging of the reference patterns selected by the frst-photon detection signal. Our technique merges the physics of low-fux measurements with the framework of computational ghost imaging. Accepted: 9 March 2018 Experimental results demonstrate that it can reconstruct an image from less than 0.1 detected photon Published: xx xx xxxx per pixel, which is three orders of magnitude less than conventional imaging techniques. A signal- to-noise ratio model of the system is established for noise analysis. With less data manipulation and shorter time requirements, our technique has potential applications in many felds, ranging from biological microscopy to remote sensing. Photon-limited imaging has attracted great interest on account of its important applications under extreme envi- ronments, such as night vision1, biological imaging2, remote sensing3, and so forth, when of-the-shelf methods fail due to photon-limited data. Conventionally, the transverse spatial image is recovered by either a spatially resolving detector array with foodlight illumination or a single detector with raster-scanned point-by-point illumination. In this way, even with time-resolved single-photon detectors, hundreds of photons per pixel are necessary to suppress the Poisson noise that is inherent in photon counting to obtain accurate intensity values.
    [Show full text]
  • What Can Bouncing Oil Droplets Tell Us About Quantum Mechanics?
    What can bouncing oil droplets tell us about quantum mechanics? Peter W. Evans∗1 and Karim P. Y. Th´ebault†2 1School of Historical and Philosophical Inquiry, University of Queensland 2Department of Philosophy, University of Bristol June 16, 2020 Abstract A recent series of experiments have demonstrated that a classical fluid mechanical system, constituted by an oil droplet bouncing on a vibrating fluid surface, can be in- duced to display a number of behaviours previously considered to be distinctly quantum. To explain this correspondence it has been suggested that the fluid mechanical system provides a single-particle classical model of de Broglie’s idiosyncratic ‘double solution’ pilot wave theory of quantum mechanics. In this paper we assess the epistemic function of the bouncing oil droplet experiments in relation to quantum mechanics. We find that the bouncing oil droplets are best conceived as an analogue illustration of quantum phe- nomena, rather than an analogue simulation, and, furthermore, that their epistemic value should be understood in terms of how-possibly explanation, rather than confirmation. Analogue illustration, unlike analogue simulation, is not a form of ‘material surrogacy’, in which source empirical phenomena in a system of one kind can be understood as ‘stand- ing in for’ target phenomena in a system of another kind. Rather, analogue illustration leverages a correspondence between certain empirical phenomena displayed by a source system and aspects of the ontology of a target system. On the one hand, this limits the potential inferential power of analogue illustrations, but, on the other, it widens their potential inferential scope. In particular, through analogue illustration we can learn, in the sense of gaining how-possibly understanding, about the putative ontology of a target system via an experiment.
    [Show full text]
  • Disentangling the Quantum World
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Apollo Entropy 2015, 17, 7752-7767; doi:10.3390/e17117752 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Disentangling the Quantum World Huw Price 1;y;* and Ken Wharton 2;y 1 Trinity College, Cambridge CB2 1TQ, UK 2 San José State University, San José, CA 95192-0106, USA; E-Mail: [email protected] y These authors contributed equally to this work. * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +44-12-2333-2987. Academic Editors: Gregg Jaeger and Andrei Khrennikov Received: 22 September 2015 / Accepted: 6 November 2015 / Published: 16 November 2015 Abstract: Correlations related to quantum entanglement have convinced many physicists that there must be some at-a-distance connection between separated events, at the quantum level. In the late 1940s, however, O. Costa de Beauregard proposed that such correlations can be explained without action at a distance, so long as the influence takes a zigzag path, via the intersecting past lightcones of the events in question. Costa de Beauregard’s proposal is related to what has come to be called the retrocausal loophole in Bell’s Theorem, but—like that loophole—it receives little attention, and remains poorly understood. Here we propose a new way to explain and motivate the idea. We exploit some simple symmetries to show how Costa de Beauregard’s zigzag needs to work, to explain the correlations at the core of Bell’s Theorem. As a bonus, the explanation shows how entanglement might be a much simpler matter than the orthodox view assumes—not a puzzling feature of quantum reality itself, but an entirely unpuzzling feature of our knowledge of reality, once zigzags are in play.
    [Show full text]
  • Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars
    PHYSICAL REVIEW LETTERS 121, 080403 (2018) Editors' Suggestion Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars Dominik Rauch,1,2,* Johannes Handsteiner,1,2 Armin Hochrainer,1,2 Jason Gallicchio,3 Andrew S. Friedman,4 Calvin Leung,1,2,3,5 Bo Liu,6 Lukas Bulla,1,2 Sebastian Ecker,1,2 Fabian Steinlechner,1,2 Rupert Ursin,1,2 Beili Hu,3 David Leon,4 Chris Benn,7 Adriano Ghedina,8 Massimo Cecconi,8 Alan H. Guth,5 † ‡ David I. Kaiser,5, Thomas Scheidl,1,2 and Anton Zeilinger1,2, 1Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria 2Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria 3Department of Physics, Harvey Mudd College, Claremont, California 91711, USA 4Center for Astrophysics and Space Sciences, University of California, San Diego, La Jolla, California 92093, USA 5Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 6School of Computer, NUDT, 410073 Changsha, China 7Isaac Newton Group, Apartado 321, 38700 Santa Cruz de La Palma, Spain 8Fundación Galileo Galilei—INAF, 38712 Breña Baja, Spain (Received 5 April 2018; revised manuscript received 14 June 2018; published 20 August 2018) In this Letter, we present a cosmic Bell experiment with polarization-entangled photons, in which measurement settings were determined based on real-time measurements of the wavelength of photons from high-redshift quasars, whose light was emitted billions of years ago; the experiment simultaneously ensures locality. Assuming fair sampling for all detected photons and that the wavelength of the quasar photons had not been selectively altered or previewed between emission and detection, we observe statistically significant violation of Bell’s inequality by 9.3 standard deviations, corresponding to an estimated p value of ≲7.4 × 10−21.
    [Show full text]
  • Quantum Fisher Information and Entanglement of Moving Two Two-Level Atoms Under the Influence of Environmental Effects
    Article Quantum Fisher Information and Entanglement of Moving Two Two-Level Atoms under the Influence of Environmental Effects Syed Jamal Anwar , M. Usman, M. Ramzan and M. Khalid Khan * Department of Physics, Quaid-i-Azam University, 45320 Islamabad, Pakistan; [email protected] (S.J.A.); [email protected] (M.U.); [email protected] (M.R.) * Correspondence: [email protected] Received: 13 March 2019; Accepted: 20 May 2019; Published: 5 June 2019 Abstract: We have investigated numerically the dynamics of quantum Fisher information (QFI) and quantum entanglement (QE) of a two moving two-level atomic systems interacting with a coherent and thermal field in the presence of intrinsic decoherence (ID) and Kerr (non-linear medium) and Stark effects. The state of the entire system interacting with coherent and thermal fields is evaluated numerically under the influence of ID and Kerr (nonlinear) and Stark effects. QFI and von Neumann entropy (VNE) decrease in the presence of ID when the atomic motion is neglected. QFI and QE show an opposite response during its time evolution in the presence of a thermal environment. QFI is found to be more susceptible to ID as compared to QE in the presence of a thermal environment. The decay of QE is further damped at greater time-scales, which confirms the fact that ID heavily influences the system’s dynamics in a thermal environment. However, a periodic behavior of entanglement is observed due to atomic motion, which becomes modest under environmental effects. It is found that a non-linear Kerr medium has a prominent effect on the VNE but not on the QFI.
    [Show full text]
  • A Route Towards Ghost Imaging with Inelastically Scattered Electrons
    One-dimensional ghost imaging with an electron microscope: a route towards ghost imaging with inelastically scattered electrons E. Rotunno1, S. Gargiulo2, G. M. Vanacore3, C. Mechel4, A. H. Tavabi5, R. E. Dunin-Borkowski5, F. Carbone2,I Maidan2, M. Zanfrognini6, S. Frabboni6, T. Guner7, E. Karimi7, I. Kaminer4 and V. Grillo1* 1 Centro S3, Istituto di Nanoscienze-CNR, 41125 Modena, Italy 2 Institute of Physics, Laboratory for Ultrafast Microscopy and Electron Scattering (LUMES), École Polytechnique Fédérale de Lausanne, Station 6, Lausanne, 1015, Switzerland 3 Department of Materials Science, University of Milano-Bicocca, Via Cozzi 55, 20121, Milano, Italy 4 Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel 5 Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany 6 Dipartimento FIM, Universitá di Modena e Reggio Emilia, 41125 Modena, Italy 7 Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada *email: [email protected] In quantum mechanics, entanglement and correlations are not sporadic curiosities but ubiquitous phenomena that are at the basis of interacting quantum systems. In electron microscopy, such concepts have not yet been explored extensively. For example, inelastic scattering can be reanalyzed in terms of correlations between an electron beam and a sample. Whereas classical inelastic scattering results in a loss of coherence in the electron beam, a joint measurement performed on both the electron beam and the sample excitation could restore the coherence and “lost information.” Here, we propose to exploit joint measurement in electron microscopy to achieve a counterintuitive application of the concept of ghost imaging, which was first proposed in quantum photonics.
    [Show full text]