Relativistic Frame-Dragging and the Hong-Ou-Mandel Dip $-$ a Primitive to Gravitational Effects in Multi-Photon Quantum-Interference

Total Page:16

File Type:pdf, Size:1020Kb

Relativistic Frame-Dragging and the Hong-Ou-Mandel Dip $-$ a Primitive to Gravitational Effects in Multi-Photon Quantum-Interference Relativistic frame-dragging and the Hong-Ou-Mandel dip | a primitive to gravitational effects in multi-photon quantum-interference Anthony J. Brady∗ and Stav Haldar Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana, 70803, USA (Dated: June 9, 2020) We investigate the Hong-Ou-Mandel (HOM) effect { a two-photon quantum-interference effect { in the space-time of a rotating spherical mass. In particular, we analyze a common-path HOM setup restricted to the surface of the earth and show that, in principle, general-relativistic frame-dragging induces observable shifts in the HOM dip. For completeness and correspondence with current literature, we also analyze the emergence of gravitational time-dilation effects in HOM interference, for a dual-arm configuration. The formalism thus presented establishes a basis for encoding general- relativistic effects into local, multi-photon, quantum-interference experiments. Demonstration of these instances would signify genuine observations of quantum and general relativistic effects, in tandem, and would also extend the domain of validity of general relativity, to the arena of quantized electromagnetic fields. I. INTRODUCTION i.e., in Hong-Ou-Mandel (HOM) interference [11{13]{ for various interferometric configurations. We show, General relativity and quantum mechanics constitute in general, how to encode general-relativistic effects the foundation of modern physics, yet at seemingly dis- (frame-dragging and gravitational time-dilation) into parate scales. On the one hand, general relativity pre- multi-photon quantum-interference phenomena, and we dicts deviations from the Newtonian concepts of abso- show, in particular, that the background structure of lute space and time { due to the mass-energy distribu- curved space-time induces observable changes in a HOM- tion of nearby matter and by way of the equivalence interference signature. principle [1,2] { which appear observable only at large- The motivation behind our investigation is twofold. distance scales or with high-precision measurement de- For one, HOM interference is simple to analyze, yet is vices [3]. On the other hand, quantum mechanics pre- a primitive to bosonic many-body quantum-interference dicts deviations from Newtonian concepts of determin- phenomena [13{15] and even \lies at the heart of linear istic reality and locality [4] and appears to dominate in optical quantum computing" [16]. Furthermore, there regimes in which general relativistic effects are typically exists a simple yet sharp criterion partitioning the suf- and safely ignored. This dichotomous paradigm of mod- ficiency of classical and quantum explanations. Namely, ern physics is, however, rapidly changing due to a) the if the visibility V of the HOM-interference experiment ever-increasing improvement of quantum measurement is greater than 1/2, a quantum description for the fields strategies and precise control of quantum technologies is sufficient, whereas a classical description fails to ad- [5,6] and b) current efforts to extend quantum mechan- here to observations ([12, 13]; though, see [17] for recent ical demonstrations to large-distance scales { like, e.g., criticism of the visibility criterion). For two, the emer- bringing the quantum to space [7,8]. gence of gravitational effects in photonic demonstra- The maturation of quantum technologies complements tions beckons general-relativistic explanations { whereas, the theoretical maturation of quantum fields in curved- for massive particles, the boundary between general- space { a formalism describing the evolution of quantum relativistic and Newtonian explanations is oft-blurred. fields on the (classical) background space-time of gen- As rightly pointed-out and emphasized by the authors of eral relativity { which has been finely developed over refs. [18, 19], within any quantum demonstration claim- arXiv:2006.04221v1 [quant-ph] 7 Jun 2020 last fifty-odd years [9, 10]. Alas, even with such develop- ing the emergence of general-relativistic effects, a concur- ments, there has not yet been a physical observation re- rent, clear-cut distinction between classical and quantum quiring the principles of both general relativity and quan- explanations as well as between Newtonian and general- tum mechanics for its explanation. With these consider- relativistic explanations must exist, in order to assert ations in mind, the present thus seems a ripe time to fur- that principles of general relativity and quantum me- nish potential proof-of-principle experiments capable of chanics are at play, in tandem. and unambiguously exploring the cohesion of general rel- To place our work in a sharper context, observe that ativity and quantum mechanics, in the near-term. Such one may broadly decompose the mutual arena of gravi- is the aim of our work. tation/relativity (beyond rectilinear motion) and quan- In this report, we investigate the emergence of grav- tum mechanics into four classes: (i) classical Newtonian itational effects in two-photon quantum interference { gravity in quantum mechanics [20{23], (ii) non-inertial reference frames in quantum mechanics [24{28], (iii) clas- sical general relativity in quantum mechanics [18, 19, 29{ 34], and (iv) the quantum nature of gravity [35{39]. Al- ∗ Corresponding author: [email protected] though there has been a great deal of theoretical investi- 2 gation in these areas, there has only been observational about. The wave equation (II.1) in the geometric op- evidence for (i) and (ii) (see, e.g., refs. [20{23] and [24{ tics approximation yields transport equations along the 0 27], respectively), which indeed has supported consis- vector field rµSk, tency between these formalisms when they are concur- rently considered { e.g., consistency between Newton's µ 0 0 theory of gravitation and standard non-relativistic quan- (r Sk)(rµSk) = 0 (II.3) tum theory, in regimes where both are prevalent. Our 1 (rµS0 )(r ln α0 ) = − rµr S0: (II.4) work serves as a contribution to (iii) { where one must k µ k 2 µ describe the gravitational field by a classical metric the- 0 ory of gravity and physical probe-systems via quantum The first equation implies that rµSk is a null vector. mechanical principles. One can show that it also satisfies a geodesic equation We compartmentalize our paper in the following way. (rµS0 ) r (r S0 ) = 0: In Section IIA, we provide a model for the electro- k µ ν k magnetic field in curved space-time, in the weak-field Thus, the transport equations, (II.3) and (II.4), deter- regime and proceed to quantize the field under suitable mine how the eikonal and amplitude, respectively, evolve 0 approximations. One can consider this formalism, in along the null ray drawn out by rµSk. Observe that the succinct terms, as geometric quantum-optics in curved evolution of the eikonal along the ray is sufficient to de- space-time, in the weak-field regime. In Section IIB, termine the field φ entirely. These are the main results we discuss the metric local to an observer and its re- of geometric optics. lation to the background Post-Newtonian (PN) metric, Lastly, from the transport equations, one may derive thus prescribing the space-time upon which the quan- a conservation equation tum field of section IIA propagates. In Section IIC, µ 0 0 2 we provide some background on HOM interference and r rµSkjαkj = 0; (II.5) comment on interferometric noise and gravitational de- coherence in context. In Section III, we combine and which, via Gauss's theorem, leads to a conserved `charge' apply the formalism of previous sections to various inter- ferometric configurations, explicitly showing that gravi- µ 0 0 2 Qk := dΣ (rµSk) jαkj ; (II.6) tational effects, in principle, induce observable changes ˆΣ in HOM-interference signatures. We also provide order- with Σ being a spacelike hypersurface. Physically, the of-magnitude estimates for these effects and briefly dis- conservation equation is a conservation of photon flux cuss observational potentiality. Finally, in SectionIV, such that the number of photons Q is a constant for all we summarize our work. k time. The equations thus posed are precisely that of geo- II. METHODS metric optics in curved space-time, excepting a transport equation for the polarization vector of the field (see, e.g., refs. [1, 40]). A. Modeling quantum optics in curved space-time 1. Geometric optics in curved space: a brief review 2. Geometric optics in the weak-field regime We model the electromagnetic field by a free, massless, We work with laboratory or near-earth experiments scalar field φ satisfying the (minimally coupled) Klein- in mind. Therefore, it is sufficient to consider general Gordon equation relativity in the weak-field regime. We assume local gravitational fields, accelerations, etc. µ are sufficiently weak and consider first-order perturba- r rµφ = 0; (II.1) tions hµν about the Minkowski metric ηµν such that the space-time metric g , in some local region in space, can where r is the metric compatible covariant derivative of µν µ be written as general relativity. Such a model disregards polarization- dependent effects but accurately accounts for the ampli- gµν = ηµν + hµν : (II.7) tude and phase of the field. We assume the field to be quasi-monochromatic in the The metric perturbation induce perturbations of the geometric optics approximation [1, 40] so that it can be eikonal and amplitude about the Minkowski values rewritten (in complex form) as (Sk; αk), i.e. 0 0 0 iSk S = S + δS (II.8) φk = αke ; (II.2) k k k 0 αk = αk(1 + "k); (II.9) with S0 the eikonal (or phase), α0 a slowly-varying am- plitude with respect to variations of the eikonal, and with (δSk;"k) being the leading perturbations of O(h). k denoting the wave-vector mode which φk is centered Defining kµ := @µSk as the Minkowski wave-vector, we 3 FIG. 1. Schematic of a Hong-Ou-Mandel interferometer, in a common-path configuration, located on the earth's surface.
Recommended publications
  • Thomas Precession and Thomas-Wigner Rotation: Correct Solutions and Their Implications
    epl draft Header will be provided by the publisher This is a pre-print of an article published in Europhysics Letters 129 (2020) 3006 The final authenticated version is available online at: https://iopscience.iop.org/article/10.1209/0295-5075/129/30006 Thomas precession and Thomas-Wigner rotation: correct solutions and their implications 1(a) 2 3 4 ALEXANDER KHOLMETSKII , OLEG MISSEVITCH , TOLGA YARMAN , METIN ARIK 1 Department of Physics, Belarusian State University – Nezavisimosti Avenue 4, 220030, Minsk, Belarus 2 Research Institute for Nuclear Problems, Belarusian State University –Bobrujskaya str., 11, 220030, Minsk, Belarus 3 Okan University, Akfirat, Istanbul, Turkey 4 Bogazici University, Istanbul, Turkey received and accepted dates provided by the publisher other relevant dates provided by the publisher PACS 03.30.+p – Special relativity Abstract – We address to the Thomas precession for the hydrogenlike atom and point out that in the derivation of this effect in the semi-classical approach, two different successions of rotation-free Lorentz transformations between the laboratory frame K and the proper electron’s frames, Ke(t) and Ke(t+dt), separated by the time interval dt, were used by different authors. We further show that the succession of Lorentz transformations KKe(t)Ke(t+dt) leads to relativistically non-adequate results in the frame Ke(t) with respect to the rotational frequency of the electron spin, and thus an alternative succession of transformations KKe(t), KKe(t+dt) must be applied. From the physical viewpoint this means the validity of the introduced “tracking rule”, when the rotation-free Lorentz transformation, being realized between the frame of observation K and the frame K(t) co-moving with a tracking object at the time moment t, remains in force at any future time moments, too.
    [Show full text]
  • Covariant Calculation of General Relativistic Effects in an Orbiting Gyroscope Experiment
    PHYSICAL REVIEW D 67, 062003 ͑2003͒ Covariant calculation of general relativistic effects in an orbiting gyroscope experiment Clifford M. Will* McDonnell Center for the Space Sciences, Department of Physics, Washington University, St. Louis, Missouri 63130 ͑Received 17 December 2002; published 26 March 2003͒ We carry out a covariant calculation of the measurable relativistic effects in an orbiting gyroscope experi- ment. The experiment, currently known as Gravity Probe B, compares the spin directions of an array of spinning gyroscopes with the optical axis of a telescope, all housed in a spacecraft that rolls about the optical axis. The spacecraft is steered so that the telescope always points toward a known guide star. We calculate the variation in the spin directions relative to readout loops rigidly fixed in the spacecraft, and express the variations in terms of quantities that can be measured, to sufficient accuracy, using an Earth-centered coordi- nate system. The measurable effects include the aberration of starlight, the geodetic precession caused by space curvature, the frame-dragging effect caused by the rotation of the Earth and the deflection of light by the Sun. DOI: 10.1103/PhysRevD.67.062003 PACS number͑s͒: 04.80.Cc I. INTRODUCTION by the on-board telescope, which is to be trained on a star IM Pegasus ͑HR 8703͒ in our galaxy. One important feature of Gravity Probe B—the ‘‘gyroscope experiment’’—is a this star is that it is also a strong radio source, so that its NASA space experiment designed to measure the general direction and proper motion relative to the larger system of relativistic effect known as the dragging of inertial frames.
    [Show full text]
  • The Case for Quantum Key Distribution
    The Case for Quantum Key Distribution Douglas Stebila1, Michele Mosca2,3,4, and Norbert Lütkenhaus2,4,5 1 Information Security Institute, Queensland University of Technology, Brisbane, Australia 2 Institute for Quantum Computing, University of Waterloo 3 Dept. of Combinatorics & Optimization, University of Waterloo 4 Perimeter Institute for Theoretical Physics 5 Dept. of Physics & Astronomy, University of Waterloo Waterloo, Ontario, Canada Email: [email protected], [email protected], [email protected] December 2, 2009 Abstract Quantum key distribution (QKD) promises secure key agreement by using quantum mechanical systems. We argue that QKD will be an important part of future cryptographic infrastructures. It can provide long-term confidentiality for encrypted information without reliance on computational assumptions. Although QKD still requires authentication to prevent man-in-the-middle attacks, it can make use of either information-theoretically secure symmetric key authentication or computationally secure public key authentication: even when using public key authentication, we argue that QKD still offers stronger security than classical key agreement. 1 Introduction Since its discovery, the field of quantum cryptography — and in particular, quantum key distribution (QKD) — has garnered widespread technical and popular interest. The promise of “unconditional security” has brought public interest, but the often unbridled optimism expressed for this field has also spawned criticism and analysis [Sch03, PPS04, Sch07, Sch08]. QKD is a new tool in the cryptographer’s toolbox: it allows for secure key agreement over an untrusted channel where the output key is entirely independent from any input value, a task that is impossible using classical1 cryptography. QKD does not eliminate the need for other cryptographic primitives, such as authentication, but it can be used to build systems with new security properties.
    [Show full text]
  • Thomas Precession Is the Basis for the Structure of Matter and Space Preston Guynn
    Thomas Precession is the Basis for the Structure of Matter and Space Preston Guynn To cite this version: Preston Guynn. Thomas Precession is the Basis for the Structure of Matter and Space. 2018. hal- 02628032 HAL Id: hal-02628032 https://hal.archives-ouvertes.fr/hal-02628032 Submitted on 26 May 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Thomas Precession is the Basis for the Structure of Matter and Space Einstein's theory of special relativity was incomplete as originally formulated since it did not include the rotational effect described twenty years later by Thomas, now referred to as Thomas precession. Though Thomas precession has been accepted for decades, its relationship to particle structure is a recent discovery, first described in an article titled "Electromagnetic effects and structure of particles due to special relativity". Thomas precession acts as a velocity dependent counter-rotation, so that at a rotation velocity of 3 / 2 c , precession is equal to rotation, resulting in an inertial frame of reference. During the last year and a half significant progress was made in determining further details of the role of Thomas precession in particle structure, fundamental constants, and the galactic rotation velocity.
    [Show full text]
  • Einstein's Gravitational Field
    Einstein’s gravitational field Abstract: There exists some confusion, as evidenced in the literature, regarding the nature the gravitational field in Einstein’s General Theory of Relativity. It is argued here that this confusion is a result of a change in interpretation of the gravitational field. Einstein identified the existence of gravity with the inertial motion of accelerating bodies (i.e. bodies in free-fall) whereas contemporary physicists identify the existence of gravity with space-time curvature (i.e. tidal forces). The interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with. 1 Author: Peter M. Brown e-mail: [email protected] 2 INTRODUCTION Einstein’s General Theory of Relativity (EGR) has been credited as the greatest intellectual achievement of the 20th Century. This accomplishment is reflected in Time Magazine’s December 31, 1999 issue 1, which declares Einstein the Person of the Century. Indeed, Einstein is often taken as the model of genius for his work in relativity. It is widely assumed that, according to Einstein’s general theory of relativity, gravitation is a curvature in space-time. There is a well- accepted definition of space-time curvature. As stated by Thorne 2 space-time curvature and tidal gravity are the same thing expressed in different languages, the former in the language of relativity, the later in the language of Newtonian gravity. However one of the main tenants of general relativity is the Principle of Equivalence: A uniform gravitational field is equivalent to a uniformly accelerating frame of reference. This implies that one can create a uniform gravitational field simply by changing one’s frame of reference from an inertial frame of reference to an accelerating frame, which is rather difficult idea to accept.
    [Show full text]
  • Theory of Relativity
    Christian Bar¨ Theory of Relativity Summer Term 2013 OTSDAM P EOMETRY IN G Version of August 26, 2013 Contents Preface iii 1 Special Relativity 1 1.1 Classical Kinematics ............................... 1 1.2 Electrodynamics ................................. 5 1.3 The Lorentz group and Minkowski geometry .................. 7 1.4 Relativistic Kinematics .............................. 20 1.5 Mass and Energy ................................. 36 1.6 Closing Remarks about Special Relativity .................... 41 2 General Relativity 43 2.1 Classical theory of gravitation .......................... 43 2.2 Equivalence Principle and the Einstein Field Equations ............. 49 2.3 Robertson-Walker spacetime ........................... 55 2.4 The Schwarzschild solution ............................ 66 Bibliography 77 Index 79 i Preface These are the lecture notes of an introductory course on relativity theory that I gave in 2013. Ihe course was designed such that no prior knowledge of differential geometry was required. The course itself also did not introduce differential geometry (as it is often done in relativity classes). Instead, students unfamiliar with differential geometry had the opportunity to learn the subject in another course precisely set up for this purpose. This way, the relativity course could concentrate on its own topic. Of course, there is a price to pay; the first half of the course was dedicated to Special Relativity which does not require much mathematical background. Only the second half then deals with General Relativity. This gave the students time to acquire the geometric concepts. The part on Special Relativity briefly recalls classical kinematics and electrodynamics empha- sizing their conceptual incompatibility. It is then shown how Minkowski geometry is used to unite the two theories and to obtain what we nowadays call Special Relativity.
    [Show full text]
  • Post-Newtonian Approximations and Applications
    Monash University MTH3000 Research Project Coming out of the woodwork: Post-Newtonian approximations and applications Author: Supervisor: Justin Forlano Dr. Todd Oliynyk March 25, 2015 Contents 1 Introduction 2 2 The post-Newtonian Approximation 5 2.1 The Relaxed Einstein Field Equations . 5 2.2 Solution Method . 7 2.3 Zones of Integration . 13 2.4 Multi-pole Expansions . 15 2.5 The first post-Newtonian potentials . 17 2.6 Alternate Integration Methods . 24 3 Equations of Motion and the Precession of Mercury 28 3.1 Deriving equations of motion . 28 3.2 Application to precession of Mercury . 33 4 Gravitational Waves and the Hulse-Taylor Binary 38 4.1 Transverse-traceless potentials and polarisations . 38 4.2 Particular gravitational wave fields . 42 4.3 Effect of gravitational waves on space-time . 46 4.4 Quadrupole formula . 48 4.5 Application to Hulse-Taylor binary . 52 4.6 Beyond the Quadrupole formula . 56 5 Concluding Remarks 58 A Appendix 63 A.1 Solving the Wave Equation . 63 A.2 Angular STF Tensors and Spherical Averages . 64 A.3 Evaluation of a 1PN surface integral . 65 A.4 Details of Quadrupole formula derivation . 66 1 Chapter 1 Introduction Einstein's General theory of relativity [1] was a bold departure from the widely successful Newtonian theory. Unlike the Newtonian theory written in terms of fields, gravitation is a geometric phenomena, with space and time forming a space-time manifold that is deformed by the presence of matter and energy. The deformation of this differentiable manifold is characterised by a symmetric metric, and freely falling (not acted on by exter- nal forces) particles will move along geodesics of this manifold as determined by the metric.
    [Show full text]
  • A Semiclassical Kinetic Theory of Dirac Particles and Thomas
    A Semiclassical Kinetic Theory of Dirac Particles and Thomas Precession Omer¨ F. DAYI and Eda KILINC¸ARSLAN Physics Engineering Department, Faculty of Science and Letters, Istanbul Technical University, TR-34469, Maslak–Istanbul, Turkey1 Kinetic theory of Dirac fermions is studied within the matrix valued differential forms method. It is based on the symplectic form derived by employing the semiclassical wave packet build of the positive energy solutions of the Dirac equation. A satisfactory definition of the distribution matrix elements imposes to work in the basis where the helicity is diagonal which is also needed to attain the massless limit. We show that the kinematic Thomas precession correction can be studied straightforwardly within this approach. It contributes on an equal footing with the Berry gauge fields. In fact in equations of motion it eliminates the terms arising from the Berry gauge fields. 1 Introduction Dirac equation which describes massive spin-1/2 particles possesses either positive or negative energy solutions described by 4-dimensional spinors. However, to furnish a well defined one particle inter- pretation, instead of employing both type of solutions, a wave packet build of only positive energy plane wave solutions should be preferred. A nonrelativistic semiclassical dynamics can be obtained employing this wave packet. Semiclassical limit may be useful to have a better understanding of some quantum mechanical phenomena. In the massless limit Dirac equation leads to two copies of Weyl arXiv:1508.00781v1 [hep-th] 4 Aug 2015 particles which possess opposite chirality. Recently, the chiral semiclassical kinetic theory has been formulated to embrace the anomalies due to the external electromagnetic fields in 3 + 1 dimensions [1, 2].
    [Show full text]
  • Issue 2005 Volume 1
    ISSUE 2005 PROGRESS IN PHYSICS VOLUME 1 ISSN 1555-5534 The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics PROGRESS IN PHYSICS A quarterly issue scientific journal, registered with the Library of Congress (DC). ISSN: 1555-5534 (print) This journal is peer reviewed and included in the abstracting and indexing coverage of: ISSN: 1555-5615 (online) Mathematical Reviews and MathSciNet (AMS, USA), DOAJ of Lund University (Sweden), 4 issues per annum Referativnyi Zhurnal VINITI (Russia), etc. Electronic version of this journal: APRIL 2005 VOLUME 1 http://www.geocities.com/ptep_online To order printed issues of this journal, con- CONTENTS tact the Editor in Chief. Chief Editor D. Rabounski A New Method to Measure the Speed of Gravitation. 3 Dmitri Rabounski Quantum Quasi-Paradoxes and Quantum Sorites Paradoxes. 7 [email protected] F. Smarandache Associate Editors F. Smarandache A New Form of Matter — Unmatter, Composed of Particles Prof. Florentin Smarandache and Anti-Particles. 9 [email protected] L. Nottale Fractality Field in the Theory of Scale Relativity. 12 Dr. Larissa Borissova [email protected] L. Borissova, D. Rabounski On the Possibility of Instant Displacements in Stephen J. Crothers the Space-Time of General Relativity. 17 [email protected] C. Castro On Dual Phase-Space Relativity, the Machian Principle and Mod- Department of Mathematics, University of ified Newtonian Dynamics. 20 New Mexico, 200 College Road, Gallup, NM 87301, USA C. Castro, M. Pavsiˇ cˇ The Extended Relativity Theory in Clifford Spaces. 31 K. Dombrowski Rational Numbers Distribution and Resonance. 65 Copyright c Progress in Physics, 2005 S.
    [Show full text]
  • Physical Holonomy, Thomas Precession, and Clifford Algebra
    hXWWM UWThPh 1988-39 Physical Holonomy, Thomas Precession, and Clifford Algebra H. Urbantke Institut für Theoretische Physik Universität Wien Abstract After a general discussion of the physical significance of holonomy group transfor­ mations, a relation between the transports of Fermi-Walker and Levi-Civitä in Special Relativity is pointed out. A well-known example - the Thomas-Wigner angle - is red- erived in a completely frame-independent manner using Clifford algebra. 1 Introduction — Holonomy Groups in Physics Quantum Holonomy has become a rather popular concept in recent /ears, in particular through the work [1] of Berry and Simon; but it is clear that the Aharanov-Bohm effect [2] is a much earlier instance of it. The point is that here the differential geometric idea of parallel transport defined by connections in fibre bundles [3] attains rather direct physical meaning susceptible to experimentation. This is remarkable because parallel transport has been around in differential geometry since 1917, and differential geometry has invaded theoretical physics since the early days of General Relativity, with new impulses coming from Hamiltonian dynamics and gauge theory: yet the significance of connections used to be formal, the 'transformation properties' standing in the forefront, as one can see from the old 'Ricci-Calculus' as used by Einstein and Grossmann [4] or from the way non- abelian gauge fields were introduced by Yang and Mills [5]. The rather indirect 'physical' realization of parallel transport in General Relativity by Schild's 'ladder construction' [6] also stresses this fact; in non-abelian gauge theory I am aware of no physical realization at all.
    [Show full text]
  • Arxiv:2101.11503V2 [Quant-Ph] 26 Jul 2021 Bell State Is Reached
    Experimental Single-Copy Entanglement Distillation Sebastian Ecker,1, 2, ∗ Philipp Sohr,1, 2 Lukas Bulla,1, 2 Marcus Huber,1, 3 Martin Bohmann,1, 2 and Rupert Ursin1, 2, y 1Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria 2Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria 3Institute for Atomic and Subatomic Physics, Vienna University of Technology, 1020 Vienna, Austria The phenomenon of entanglement marks one of the furthest departures from classical physics and is indispensable for quantum information processing. Despite its fundamental importance, the distribution of entanglement over long distances through photons is unfortunately hindered by unavoidable decoherence effects. Entanglement distillation is a means of restoring the quality of such diluted entanglement by concentrating it into a pair of qubits. Conventionally, this would be done by distributing multiple photon pairs and distilling the entanglement into a single pair. Here, we turn around this paradigm by utilising pairs of single photons entangled in multiple degrees of freedom. Specifically, we make use of the polarisation and the energy-time domain of photons, both of which are extensively field-tested. We experimentally chart the domain of distillable states and achieve relative fidelity gains up to 13.8 %. Compared to the two-copy scheme, the distillation rate of our single-copy scheme is several orders of magnitude higher, paving the way towards high-capacity and noise-resilient quantum networks. Entanglement lies at the heart of quantum physics, two-photon CNOT gate cannot be deterministically re- reflecting the quantum superposition principle between alised with passive linear optics [19{22].
    [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]