DOCSLIB.ORG

32. Interference and Coherence

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
32. Interference and Coherence 32. Interference and Coherence Interference • Only parallel polarizations interfere • Interference of a wave with itself The Michelson Interferometer • Fringes in delay • Measure of temporal coherence • Interference of crossed beams Coherence • Temporal coherence • Spatial coherence Albert Michelson 1852-1931 Orthogonal polarizations don’t interfere. The most general plane-wave electric field is: E rt,Reexp( E jk r t ) 0 where the amplitude is both complex and a vector: EEEE0000 xyz,, don’t forget the complex The irradiance is: conjugation! cc IEEEEEEEE**** 2200 0xx 0 0 yy 0 0 zz 0 Orthogonal polarizations don’t interfere (cont’d) Because the irradiance is given by: cc IEEEEEEEE**** 2200 0xx 0 0 yy 0 0 zz 0 combining two waves of different polarizations is different from combining waves of the same polarization. Different polarizations (e.g., x and y): c I EE** E E I I 2 11xx 2 y 2 y 12 Same polarizations (e.g. both have x polarization): cc * * IEEtotal, x total , x EEEE 1, x 2, x 1, x 2, x 22 * Therefore: This is what is III 12cE Re 12 E called a “cross term.” This cross term can give rise to very dramatic effects. The irradiance when combining a beam with a delayed replica of itself has “fringes.” * I Ic1122 Re EE I Suppose the two beams are E0 exp(jt) and E0 exp[jt)]. That is, a monochromatic wave and itself delayed by some time : * IIc200 Re E exp[ jtE ] 0 exp[ jt ( )] 2Ic Re E2 exp[ j ] 00 2 Fringes (as a function of delay) 2cos[]IcE00 I II21cos[]0 - How do we vary the delay of a beam? Varying the delay on purpose Simply moving a mirror can vary the delay of a beam by many wavelengths. Input Mirror beam E(t) Output beam E(t–) Translation stage Moving a mirror backward by a distance L yields a delay of: Note the factor of 2. 2 L /c Light must travel the extra distance to the mirror—and back! Since light travels 300 µm per ps in air, 300 µm of mirror displacement yields a delay of 2 ps. Delays of less than 0.1 fsec (10-16 sec) can be generated using this technique. We can also vary the delay using a mirror pair or a corner cube. Mirror pairs involve two E(t) Input beam reflections and displace Mirrors the return beam in space: Output But out-of-plane tilt yields E(t–) beam a nonparallel return beam. Translation stage Corner cubes involve three reflections and also displace the return beam in space. Even better, they always yield a parallel return beam: [Edmund Scientific] The Michelson Interferometer input beam The Michelson Interferometer splits a beam into two and then recombines mirror output them at the same beam splitter. beam- splitter delay Suppose the input beam is a plane wave. mirror Then the intensity measured at the output is: * IIIcEout 12 Re 0 exp jtkzkLE ( 1 ) 0 exp jtkzkL ( 2 ) 2 I00II2 0 Re exp jkLL ( 21 ) since IIIc 012 ( 0 / 2) E 0 2I0 1 cos(kL ) Iout Fringes (as a function of delay): L = L2 –L1 The Michelson Interferometer - clarification IIout 20 1 cos( kL ) If the path length difference is zero, this becomes: IIout 4 0 Are we getting more photons at the output than we put in? No! In this expression, the symbol I0 refers input to the intensity in either one of the two beam beams at this location. mirror But both beams that reach this point output beam- have passed through the 50/50 beam splitter splitter twice, thus reducing their intensity (relative to the intensity of the input delay mirror beam) by a factor of 4. Thus: II0 in 4 The Michelson-Morley experiment to measure the aether “The most famous failed experiment of all time” The Aether Wind Albert Michelson 1852-1931 Michelson’s laboratory, Case-Western University, 1887 Nobel Prize, 1907 (first American to win one of the science prizes) Interference of crossed beams x k kkcos zkˆ sin xˆ kkcos zkˆ sin xˆ z krkcos zk sin x krk cos zk sin x k * IIc200 Re E exp[j (tkrE )] 0 exp[ j ( tkr )] Cross term is proportional to: * ReE00 exp j t kz cos kx sin E exp j t kz cos kx sin Re exp 2jkx sin Fringes (as a function of x position) I (x) cos(2kx sin ) out x Big angle: small fringes. Small angle: big fringes. Large angle: The fringe spacing, : 2/(2sin) k position /(2sin ) As the angle decreases to Small angle: zero, the fringes become larger and larger, until finally, at = 0, the intensity pattern position becomes constant. You can't see the spatial fringes unless the beam angle is very small! The fringe spacing is: /(2sin ) = 0.1 mm is about the minimum fringe spacing you can see with the naked eye: sin /(2 ) 0.5mm / 200 1/ 400 rad 0.15 The Michelson Input beam x Interferometer z (Misaligned) Mirror Beam- splitter Suppose we misalign the mirrors, so the beams cross at an angle when they recombine at the beam Mirror splitter. And we won't scan the delay, so the lengths are equal. If the input beam is a plane wave, the cross term becomes: * ReEjtkzkxE00 exp cos sin exp jtkzkx cos sin Fringes (in position) Re exp 2jkx sin Iout(x) cos(2kx sin ) x Crossing beams maps delay onto position If the path length difference changes, the fringes shift. The Michelson Interferometer: input A question beam Let’s go back, for now, to the mirror output well-aligned Michelson beam- interferometer. splitter L = L2 –L1 If we move the moveable mirror = large further and further back, do we continue to see fringes forever? delay If not, then how far can we go mirror before they disappear? IIout 21cos()0 kL The Temporal Coherence Time and the Spatial Coherence Length The temporal coherence time is the time over which the beam wave- fronts remain equally spaced. Or, equivalently, over which the field remains sinusoidal with a given wavelength: The spatial coherence length is the distance over which the beam wave- fronts remain flat: Since there are two transverse dimensions, we could talk about two different coherence lengths. Instead, we define a coherence area. Spatial Spatial and Temporal and Coherence: Temporal Coherence Temporal Coherence; Spatial Incoherence Beams can be coherent or only partially coherent (or, even incoherent) Spatial in both space and in Coherence; Temporal time. Incoherence Spatial and Temporal Incoherence The coherence time of monochromatic light A nearly monochromatic light source has a large coherence time: E-field ampitude time If we know there is ...and we wait a time equal to ...then we know that we a maximum here... an integer number of periods... will find another maximum. For a perfect cosine, the integer could be as large as you want (up to infinity), and this would still be true. Thus, an ideal monochromatic light source has an infinite coherence time. In the real world: highly stabilized lasers can have coherence times on the order of a few seconds. That’s amazing! More than 1015 cycles! The coherence time of polychromatic light A polychromatic light source has a smaller coherence time. Here’s an example: an E-field composed of a superposition of several monochromatic waves, each with a slightly different frequency. 1 2 3 4 5 6 11 7 910 12 27 8 1314 15 26 16 25 17 24 18 23 19 22 20 21 What is the value of the E-field Start at this Wait N periods, at each successive value of N? maximum. where N = 1, 2, 3, ... Is it still a local maximum? The coherence time for a given waveform is the average amount of time one has to wait from an arbitrary starting point before coherence is lost. What determines the coherence time? S() sum of 3 sine waves E field time S() sum of 5 sine waves E field time S() sum of 10 sine waves E field time More spectral components = more rapid loss of coherence The coherence time is the reciprocal of the bandwidth. The coherence time is given by: c 1/v where is the light bandwidth (the width of the spectrum). Sunlight is temporally very incoherent because its bandwidth is very large (the entire visible spectrum). 1 Short optical pulses also have 2 3 small coherence times, roughly 4 equal to their duration. 5 6 “Coherence length” = (c0/n)c Why are we interested in coherence time? Because the notion is relevant to measurements that we often do. Let us suppose that we take a wave and interfere it with a copy of itself: a wave a time-delayed replica of the same wave If the time delay is zero ( = 0): perfect constructive interference at every point. The net irradiance is large. If the time delay is half the period ( = ): nearly perfect destructive interference at every point. The net irradiance is zero. If the time delay is the period ( = 2): constructive interference at every point. The net irradiance is large. What if the delay time is large? at this time, constructive interference destructive interference here a wave a time-delayed replica of the time delay same wave If the time delay is large ( > c): There is no correlation between the peaks of the wave and the peaks of the time-delayed version. Interference is sometimes constructive, sometimes destructive. The net irradiance no longer depends on the delay . Interferogram: the pattern formed by the net irradiance as a function of delay.
Load more

Recommended publications
  • The Theory of Quantum Coherence María García Díaz
    ADVERTIMENT. Lʼaccés als continguts dʼaquesta tesi queda condicionat a lʼacceptació de les condicions dʼús establertes per la següent llicència Creative Commons: http://cat.creativecommons.org/?page_id=184 ADVERTENCIA. El acceso a los contenidos de esta tesis queda condicionado a la aceptación de las condiciones de uso establecidas por la siguiente licencia Creative Commons: http://es.creativecommons.org/blog/licencias/ WARNING. The access to the contents of this doctoral thesis it is limited to the acceptance of the use conditions set by the following Creative Commons license: https://creativecommons.org/licenses/?lang=en Universitat Aut`onomade Barcelona The theory of quantum coherence by Mar´ıaGarc´ıaD´ıaz under supervision of Prof. Andreas Winter A thesis submitted in partial fulfillment for the degree of Doctor of Philosophy in Unitat de F´ısicaTe`orica:Informaci´oi Fen`omensQu`antics Departament de F´ısica Facultat de Ci`encies Bellaterra, December, 2019 “The arts and the sciences all draw together as the analyst breaks them down into their smallest pieces: at the hypothetical limit, at the very quick of epistemology, there is convergence of speech, picture, song, and instigating force.” Daniel Albright, Quantum poetics: Yeats, Pound, Eliot, and the science of modernism Abstract Quantum coherence, or the property of systems which are in a superpo- sition of states yielding interference patterns in suitable experiments, is the main hallmark of departure of quantum mechanics from classical physics. Besides its fascinating epistemological implications, quantum coherence also turns out to be a valuable resource for quantum information tasks, and has even been used in the description of fundamental biological processes.
    [Show full text]
  • Path Integrals in Quantum Mechanics
    Path Integrals in Quantum Mechanics Dennis V. Perepelitsa MIT Department of Physics 70 Amherst Ave. Cambridge, MA 02142 Abstract We present the path integral formulation of quantum mechanics and demon- strate its equivalence to the Schr¨odinger picture. We apply the method to the free particle and quantum harmonic oscillator, investigate the Euclidean path integral, and discuss other applications. 1 Introduction A fundamental question in quantum mechanics is how does the state of a particle evolve with time? That is, the determination the time-evolution ψ(t) of some initial | i state ψ(t ) . Quantum mechanics is fully predictive [3] in the sense that initial | 0 i conditions and knowledge of the potential occupied by the particle is enough to fully specify the state of the particle for all future times.1 In the early twentieth century, Erwin Schr¨odinger derived an equation specifies how the instantaneous change in the wavefunction d ψ(t) depends on the system dt | i inhabited by the state in the form of the Hamiltonian. In this formulation, the eigenstates of the Hamiltonian play an important role, since their time-evolution is easy to calculate (i.e. they are stationary). A well-established method of solution, after the entire eigenspectrum of Hˆ is known, is to decompose the initial state into this eigenbasis, apply time evolution to each and then reassemble the eigenstates. That is, 1In the analysis below, we consider only the position of a particle, and not any other quantum property such as spin. 2 D.V. Perepelitsa n=∞ ψ(t) = exp [ iE t/~] n ψ(t ) n (1) | i − n h | 0 i| i n=0 X This (Hamiltonian) formulation works in many cases.
    [Show full text]
  • Optimization of Transmon Design for Longer Coherence Time
    Optimization of transmon design for longer coherence time Simon Burkhard Semester thesis Spring semester 2012 Supervisor: Dr. Arkady Fedorov ETH Zurich Quantum Device Lab Prof. Dr. A. Wallraff Abstract Using electrostatic simulations, a transmon qubit with new shape and a large geometrical size was designed. The coherence time of the qubits was increased by a factor of 3-4 to about 4 µs. Additionally, a new formula for calculating the coupling strength of the qubit to a transmission line resonator was obtained, allowing reasonably accurate tuning of qubit parameters prior to production using electrostatic simulations. 2 Contents 1 Introduction 4 2 Theory 5 2.1 Coplanar waveguide resonator . 5 2.1.1 Quantum mechanical treatment . 5 2.2 Superconducting qubits . 5 2.2.1 Cooper pair box . 6 2.2.2 Transmon . 7 2.3 Resonator-qubit coupling (Jaynes-Cummings model) . 9 2.4 Effective transmon network . 9 2.4.1 Calculation of CΣ ............................... 10 2.4.2 Calculation of β ............................... 10 2.4.3 Qubits coupled to 2 resonators . 11 2.4.4 Charge line and flux line couplings . 11 2.5 Transmon relaxation time (T1) ........................... 11 3 Transmon simulation 12 3.1 Ansoft Maxwell . 12 3.1.1 Convergence of simulations . 13 3.1.2 Field integral . 13 3.2 Optimization of transmon parameters . 14 3.3 Intermediate transmon design . 15 3.4 Final transmon design . 15 3.5 Comparison of the surface electric field . 17 3.6 Simple estimate of T1 due to coupling to the charge line . 17 3.7 Simulation of the magnetic flux through the split junction .
    [Show full text]
  • Introduction ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Li
    This guide is designed to show someone with a basic undergraduate background in physics how to perform a presentation on the topic Introduction ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 1 of holography and how to demonstrate the making of a hologram. Although holography can be a very complex area of study, the material has been explained mostly qualitatively, so as to match the target audience’s background in mathematics and physics. The List of Equipment ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 2 target audience high school students in grades 9‐ 11 and so limited to no previous knowledge on optics, lasers or holograms is assumed. The presentation and demonstrations will teach the students about basic optics such as reflection, refraction, and interference. The Preparation for presentation ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 2‐3 students will learn the basic physics of lasers, with a focus on the apparatus set up of a laser and the necessity of a coherent light source for the creation of interference patterns. The last part of the presentation covers the two most popular types of holographic Presentation guideline ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 3‐7 production apparatuses which are reflection and transmission holograms respectively. Some historical background and fun facts are also included throughout the presentation. The module ends Demonstration guideline ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 7 with a live demonstration on how to make a hologram to give the students some exposure to the care that must be taken in experiments and to give them a taste of what higher level physics laboratories can include. The following flow chart summarizes the References ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 8 basics of how the presentation will flow. 1 First and foremost, you should find out the location you’ll Laptop be presenting at and when the presentation will take place.
    [Show full text]
  • Properties of Laser Beams
    Properties of Laser Beams 1. Laser light is highly monochromatic Monochromaticity refers to a pure spectral color of a single wavelength. A beam is more and more monochromatic if the line spread in frequency is narrow or small. This line width is an outcome of the homogeneous broadening factors and inhomogeneous broadening factors. Despite these broadening mechanisms the line width in a laser is generally very small as compared to the normal lights. A laser cavity forms a resonant system. The photons are emitted by the stimulated emission where in all the photons are in same phase and in the same state of polarization. Oscillations can sustain only at the resonance frequency of the cavity. This leads to the narrowing of the laser line width. So, the laser light is usually very pure in wavelength, and the laser is said to have the property of monochromaticity. 2. Laser light is highly coherent Two beams of light are coherent when there is a constant phase relation between the two beams or the phase difference between their waves is constant; they are incoherent if there is a random or changing phase relationship, or the phase difference is not constant. Sustained interference patterns are formed only by radiation emitted by coherent sources, generally produced by splitting a single beam into two or more beams. A laser, unlike an incandescent light source, produces a beam in which all the components bear a fixed relationship to each other i.e. the laser beam is generally coherent. For any electromagnetic (em) wave, there are two kinds of coherence viz.
    [Show full text]
  • On Coherence and the Transverse Spatial Extent of a Neutron Wave Packet
    On coherence and the transverse spatial extent of a neutron wave packet C.F. Majkrzak, N.F. Berk, B.B. Maranville, J.A. Dura, Center for Neutron Research, and T. Jach Materials Measurement Laboratory, National Institute of Standards and Technology Gaithersburg, MD 20899 (18 November 2019) Abstract In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions which are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases in which the wave function of an individual neutron in the beam must be described more accurately by a spatially localized packet, in particular with respect to its transverse extent normal to its mean direction of propagation. One such case involves the creation of orbital angular momentum (OAM) states in a neutron via interaction with a material device of a given size. It is shown in the work reported here that there exist two distinct measures of coherence of special significance and utility for describing neutron beams in scattering studies of materials in general. One measure corresponds to the coherent superposition of basis functions and their wavevectors which constitute each individual neutron packet state function whereas the other measure can be associated with an incoherent distribution of mean wavevectors of the individual neutron packets in a beam. Both the distribution of the mean wavevectors of individual packets in the beam as well as the wavevector components of the superposition of basis functions within an individual packet can contribute to the conventional notion of instrumental resolution.
    [Show full text]
  • Partial Coherence Effects on the Imaging of Small Crystals Using Coherent X-Ray Diffraction
    INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 13 (2001) 10593–10611 PII: S0953-8984(01)25635-5 Partial coherence effects on the imaging of small crystals using coherent x-ray diffraction I A Vartanyants1 and I K Robinson Department of Physics, University of Illinois, 1110 West Green Street, Urbana, IL 61801, USA Received 8 June 2001 Published 9 November 2001 Online at stacks.iop.org/JPhysCM/13/10593 Abstract Recent achievements in experimental and computational methods have opened up the possibility of measuring and inverting the diffraction pattern from a single-crystalline particle on the nanometre scale. In this paper, a theoretical approach to the scattering of purely coherent and partially coherent x-ray radiation by such particles is discussed in detail. Test calculations based on the iterative algorithms proposed initially by Gerchberg and Saxton and generalized by Fienup are applied to reconstruct the shape of the scattering crystals. It is demonstrated that partially coherent radiation produces a small area of high intensity in the reconstructed image of the particle. (Some figures in this article are in colour only in the electronic version) 1. Introduction Even in the early years of x-ray studies [1–4] it was already understood that the diffraction pattern from small perfect crystals is directly connected with the shape of these crystals through Fourier transformation. Of course, in a real diffraction experiment on a ‘powder’ sample, where many particles with different shapes and orientations are illuminated by an incoherent beam, only an averaged shape of these particles can be obtained.
    [Show full text]
  • The Paradox of Recombined Beams Frank Rioux Emeritus Professor of Chemistry CSB|SJU
    The Paradox of Recombined Beams Frank Rioux Emeritus Professor of Chemistry CSB|SJU French and Taylor illustrate the paradox of the recombined beams with a series of experiments using polarized photons in section 7-3 in An Introduction to Quantum Physics. It is my opinion that it is easier to demonstrate this so-called paradox using photons, beam splitters and mirrors. Of course, the paradox is only apparent, being created by thinking classically about a quantum phenomenon. Single photons illuminate a 50-50 beam splitter and mirrors direct the photons to detectors D1 and D2. For a statistically meaningful number of observations, it is found that 50% of the photons are detected at D1 and 50% at D2. One might, therefore, conclude that each photon is either transmitted or reflected at the beam splitter. Recombining the paths with a second beam splitter creates a Mach-Zehnder interferometer (MZI). On the basis of the previous reasoning one might expect again that each detector would fire 50% of the time. Half of the photons are in the T branch of the interferometer and they have a 50% chance of being transmitted to D2 and a 50% chance of being reflected to D1 at the second beam splitter. The same reasoning applies to the photons in the R branch. However what is observed in an equal arm MZI is that all the photons arrive at D1. The reasoning used to explain the first result is plausible, but we see that the attempt to extend it to the MZI shown below leads to a contradiction with actual experimental results.
    [Show full text]
  • Visualizing and Manipulating the Spatial and Temporal Coherence of Light with an Adjustable Light Source in an Undergraduate Experiment
    European Journal of Physics PAPER • OPEN ACCESS Visualizing and manipulating the spatial and temporal coherence of light with an adjustable light source in an undergraduate experiment To cite this article: K Pieper et al 2019 Eur. J. Phys. 40 055302 View the article online for updates and enhancements. This content was downloaded from IP address 141.52.96.103 on 10/09/2019 at 16:03 European Journal of Physics Eur. J. Phys. 40 (2019) 055302 (11pp) https://doi.org/10.1088/1361-6404/ab3035 Visualizing and manipulating the spatial and temporal coherence of light with an adjustable light source in an undergraduate experiment K Pieper1,2 , A Bergmann1, R Dengler2 and C Rockstuhl1,3 1 Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, Wolfgang-Gaede-Str. 1, D-76131 Karlsruhe, Germany 2 Institute of Physics and Technical Education, Karlsruhe University of Education, D-76133 Karlsruhe, Germany 3 Institute of Nanotechnology, Karlsruhe Institute of Technology, PO Box 3640, D-76021 Karlsruhe, Germany E-mail: [email protected] Received 14 May 2019, revised 25 June 2019 Accepted for publication 5 July 2019 Published 23 August 2019 Abstract Coherence expresses the ability of light to form interference patterns sta- tionary in time and extended over a spatial domain. The importance of coherence is undoubted but teaching coherence constitutes a challenge. In particular, there are only a few simple and clear experiments to illustrate coherence. To render the phenomena of coherence more accessible and to point out the difference between spatial and temporal coherence, we intro- duce an undergraduate experiment consisting of a light source illuminating a double-slit and a Michelson interferometer.
    [Show full text]
  • Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere
    Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere Elias Okon1 and Daniel Sudarsky2 1Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México, Mexico City, Mexico. 2Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico. Abstract: In [1] it is argued that, in order to confront outstanding problems in cosmol- ogy and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, [1] concludes that our focus on conceptual and interpretational issues, while dealing with such matters in [2], is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in quantum mechanics, such as the measurement problem or the emergence of classicality. 1 Introduction Since its inception, more than 90 years ago, quantum theory has been a source of heated debates in relation to interpretational and conceptual matters. The prominent exchanges between Einstein and Bohr are excellent examples in that regard. An avoid- ance of such issues is often justified by the enormous success the theory has enjoyed in applications, ranging from particle physics to condensed matter. However, as people like John S. Bell showed [3], such a pragmatic attitude is not always acceptable. In [2] we argue that the standard interpretation of quantum mechanics is inadequate in cosmological contexts because it crucially depends on the existence of observers external to the studied system (or on an artificial quantum/classical cut). We claim that if the system in question is the whole universe, such observers are nowhere to be found, so we conclude that, in order to legitimately apply quantum mechanics in such contexts, an observer independent interpretation of the theory is required.
    [Show full text]
  • The Paradoxes of the Interaction-Free Measurements
    The Paradoxes of the Interaction-free Measurements L. Vaidman Centre for Quantum Computation, Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford 0X1 3PU, England; School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel Reprint requests to Prof. L. V.; E-mail: [email protected] Z. Naturforsch. 56 a, 100-107 (2001); received January 12, 2001 Presented at the 3rd Workshop on Mysteries, Puzzles and Paradoxes in Quantum Mechanics, Gargnano, Italy, September 17-23, 2000. Interaction-free measurements introduced by Elitzur and Vaidman [Found. Phys. 23,987 (1993)] allow finding infinitely fragile objects without destroying them. Paradoxical features of these and related measurements are discussed. The resolution of the paradoxes in the framework of the Many-Worlds Interpretation is proposed. Key words: Interaction-free Measurements; Quantum Paradoxes. I. Introduction experiment” proposed by Wheeler [22] which helps to define the context in which the above claims, that The interaction-free measurements proposed by the measurements are interaction-free, are legitimate. Elitzur and Vaidman [1,2] (EVIFM) led to numerousSection V is devoted to the variation of the EV IFM investigations and several experiments have been per­ proposed by Penrose [23] which, instead of testing for formed [3- 17]. Interaction-free measurements are the presence of an object in a particular place, tests very paradoxical. Usually it is claimed that quantum a certain property of the object in an interaction-free measurements, in contrast to classical measurements, way. Section VI introduces the EV IFM procedure for invariably cause a disturbance of the system.
    [Show full text]
  • Lecture 21 (Interference III Thin Film Interference and the Michelson Interferometer) Physics 2310-01 Spring 2020 Douglas Fields Thin Films
    Lecture 21 (Interference III Thin Film Interference and the Michelson Interferometer) Physics 2310-01 Spring 2020 Douglas Fields Thin Films • We are all relatively familiar with the phenomena of thin film interference. • We’ve seen it in an oil slick or in a soap bubble. "Dieselrainbow" by John. Licensed under CC BY-SA 2.5 via Commons - • But how is this https://commons.wikimedia.org/wiki/File:Dieselrainbow.jpg#/media/File:Diesel rainbow.jpg interference? • What are the two sources? • Why are there colors instead of bright and dark spots? "Thinfilmbubble" by Threetwoone at English Wikipedia - Transferred from en.wikipedia to Commons.. Licensed under CC BY 2.5 via Commons - https://commons.wikimedia.org/wiki/File:Thinfilmbubble.jpg#/media/File:Thinfilmb ubble.jpg The two sources… • In thin film interference, the two sources of coherent light come from reflections from two different interfaces. • Different geometries will provide different types of interference patterns. • The “thin film” could just be an air gap, for instance. Coherence and Thin Film Interference • Why “thin film”? • Generally, when talking about thin film interference, the source light is what we would normally call incoherent – sunlight or room light. • However, most light is coherent on a small enough distance/time scale… • The book describes it like this: Coherence - Wikipedia • Perfectly coherent: "Single frequency correlation" by Glosser.ca - Own work. Licensed under CC BY-SA 4.0 via Commons - https://commons.wikimedia.org/wiki/File:Single_frequency_correlation.svg#/media/File:Single_frequency_correlation.svg • Spatially partially coherent: "Spatial coherence finite" by Original uploader was J S Lundeen at en.wikipedia - Transferred from en.wikipedia; transferred to Commons by User:Shizhao using CommonsHelper.
    [Show full text]