DOCSLIB.ORG

Introducing 3D Transmon (PDF)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Introducing 3D Transmon (PDF) Introducing 3D transmon Hanhee Paik Department of Applied Physics Yale University Experiment W/͛Ɛ Theory Dave Schuster Lev Bishop Gerhard Kirchmair Luigi Frunzio Adam Sears Steve Girvin Gianluigi Catelani Blake Johnson Leonid Glazman Dong Zhou Matt Reagor Simon Nigg Luyan Sun Michel Devoret Eran Ginossar Matt Reed Leo DiCarlo Rob Schoelkopf Eric Holland Brian Vlastakis Outline Review : Superconducting qubits, transmon and circuit QED 3D transmon - a transmon in a waveguide cavity : Coherence improved By an order of magnitude New physics observed in superconducting qubits : What can T1 and T2 tell us? How to manipulate 3D transmons? : Single and two qubit gates using microwave driving Paik et al. Phys. Rev. Lett. 107, 240501 (2011) Superconducting Qubits Superconductor ZZ01z 12 Z12 1 nm Insulating barrier 1 Z Energy 01 0 Superconductor (Al) nonlinearity from Z ~5 10G Hz Josephson junction electromagnetic oscillator 01 (dissipationless) e2 =2 Charging E Josephson E energy C energy J 2 2C6 4e LJ Interacting with SC qubits: Circuit QED A Circuit Implementation of Cavity QED 2g = vacuum Rabi freq. N = cavity decay rate J с͞ƚƌĂŶƐǀĞƌƐĞ͟ĚĞĐĂLJƌĂƚĞ Jaynes-Cummings Hamiltonian Z HÖ Z ()aa 1 a VVÖ g()a V a H H r 2 2 z NJ Quantized Field 2-level system Electric dipole Dissipation Interaction Interacting with SC qubits: Circuit QED A Circuit Implementation of Cavity QED Strong Coupling = g !NJ out Superconducting transmission ůŝŶĞ͞ĐĂǀŝƚLJ͟ 10 Pm Superconducting artificial Microwave ͞ĂƚŽŵ͟ in Theory: Blais et al., Phys. Rev. A 69, 062320 (2004) Charge Qubits superconductor tunnel oxide layer superconductor V. Bouchiat, D. Vion, P. Joyez, D. Esteve, & M.H. Devoret, Physica Scripta T76, 165 (1998). Transmon : Outsmarting 1/f Charge Noise Cooper-pair Box ͞Transmon͟ Vg Koch et al., 2007; Houck et al., 2008 T1 can Be ~ 10 Ps EJ/EC = 1 EJ/EC = 25 - 100 Energy Energy sweet exponentially spot suppresses 1/f! Sensitive n = C V /2e to charge noise ng = CgVg/2e g g g Coherence in Conventional Transmon Qubit T1 1.5Ps Random benchmarking of 1-qubit ops Chow et al. PRL 2009: TechniQue from Knill et al. for ions * T21 23.0T Ps Error per gate = 1.2 % Similar error rates in phase qubits (UCSB): Lucero et al. PRL 100, 247001 (2007) History of Charge Qubit Coherence Number of gate operation gate Number of What is limiting coherence? d,YƵĞƐƚŝŽŶ͗tŚĞƌĞ͛Ɛthe Dissipation? Surface losses? Substrate losses? ? Junction losses? Radiation? ? ? Quasiparticles? Shunt capacitance Which element matters the most? Typical Junction: Dirt Happens Dolan Bridge Technique Qubit: two 200 x 300 nm junctions PMMA/MAA bilayer Rn~ 3.5 kOhms Al/AlOx/Al Ic ~ 40 nA Current Density ~ 30- 40 A/cm2 Surfaces Can Matter E d Nb - + + - 5 Pm D-Al2O3 ³SDUWLFLSDWLRQUDWLR´ IUDFWLRQRIHQHUJ\VWRUHGLQPDWHULDO even a thin (few nanometer) surface layer will store ~ 1/1000 of the energy If surface loss tangent is poor ( tanG ~ 10-2) would limit Q ~ 105 as shown in: Increase spacings Gao et al. 2008 (Caltech) decreases energy on surfaces 2¶&RQQHOOHWDO 8&6% Wang et al. 2009 (UCSB) increases Q Recent IBM work by Chow and Colores el at. 2012 How to Reduce the Importance of the Surface CPW/Compact Resonator* Surface participation ratio t L diel 23 L ~ 10 Pm psurf ~ 10 10 3D L ~ 5,000 Pm diel 6 t L Assume: psurf ~ 0 10 t ~ 3 nm Use 3D cavity for circuit QED experiment! A High-Q Aluminum Superconducting (3D) Cavity 11.416763635 GHz Aluminum cylindrical ɷf = 19Hz waveguide cavity : TE011 mode Q = 600M (ideally 1 Photon i Zero E field (-175dBm) Q = 510M 10B Photons c On surface) (-77dBm) ĺ QL = 275M no power dependence of Q : absence of surface dielectric loss M. Reagor, H. Paik et al. in preparation (2012) Rectangular Waveguide Cavity y0=5 mm 50 mm z0 = 36 mm x0=18 mm aluminum alloy TE101 fundamental mode (6061-T6, Tc ~ 1.5 K) Internal Q ~ 5,000,000 with 6061 aluminum alloy : - Q > 30M can be obtained with pure aluminum. Rectangular cavity - lower symmetry than a cylindrical cavity - lower density of modes in the measurement bandwidth Q) How do we couple the qubit to this cavity? JJ 250 Pm Q) How do we couple the qubit to this cavity? A) Add an antenna! Single small Al Josephson junction with a short dipole antenna JJ d d a 0.01O 250 Pm Rectangular Waveguide Cavity for circuit QED ͞ϯtransmon͟ single small Al JJ with a short dipole JJ antenna d a 0.01O 250 Pm 50 mm d x E Smaller fields compensated by larger dipole g rms h Still has same net coupling! g a 100 MHz It is a transmon! (only coherence time is longer) Antenna makes E /E ~ 50 to 100 1 MHz j c Lowerging Spec power Anharmonicity a 300 MHz Linewidth < 10 kHz 1 T * t15 Ps 2 2S'f All 3D Qubits Measured at Yale Q = 70000* Includes different configurations *Bound on conventional transmon T1 : Houck et al. Phys. Rev. Lett. 101, 080502 (2008) Strong Coupling Achieved Bare cavity Zcav g 2 F01 Dressed cavity ZZcav qubit Cavity measurement frequency (GHz) g a 140 MHz Strong coupling g !NJ Strong Dispersive Regime g oe;2n g oe;1n g oe;0n 2F n=2 n=2 n ~0 n=1 n ~0.5 n=1 n=0 n ~1 n=0 Qubit Frequency (GHz) FJN, Strong Dispersive Hamiltonian: Stark shift per photon §· H eff Zcava a ¨¸ZVqc Fa a z now > 1,000 ©¹2 State dependent frequency shift linewidths What do we learn about Josephson junctions from 3D transmon? Quality Factor of Josephson Inductance delay T1 = 60 Ps S f = 6.808 GHz Q ZT1 |2,000,000 Most stringent bound on QLj t 2,000,000 the quality of Josephson Q inductance C t 2,000,000 The Josephson junction has not been limiting the SC qubit coherence Quasiparticles in Josephson Junction Fractional quasiparticle density 2S kT x x e'/kT qp ne ' Bound for non-eq 12Z ' x Quasiparticle density qp T1 SZ = 1/Pm3 ''f xqp §·12 ¨¸ 1 f 2 ©¹SZ T1 and frequency shift agree with theory By Catelani et al.* One free parameter *Catelani et al. PRL 106, 077002 (2011) - gap ' PV Coherence Dominated by Non-1/f noise Conventional Ramsey transmon T*2 improved By X 10 3D T*2 = 14 Ps Ramsey with echo Techo = 25 Ps Exponential Ramsey envelope : Absence of 1/f noise T*2 = 17 Ps Dephasing not yet limited by 1/f critical current noise Reported 1/f critical current noise model** does not explain this behavior. 0 **D. J. Van Harlingen et al., Phys. Rev. B 70, 064517 (2004) tŚĂƚ͛ƐůŝŵŝƚŝŶŐdΎ2? T*2 is not T1 limited - source of dephasing? Fluctuations of photons in the cavity 0 ge;0n ge;1n ge;2n The qubit dephases when the photon state changes *A. Sears et al. in preparation (2012) tŚĂƚ͛ƐůŝŵŝƚŝŶŐdΎ2? T*2 is not T1 limited - source of dephasing? Fluctuations of photons in the cavity 0 ge;0n ge;1n ge;2n 1 TM ~ nN *A. Sears et al. in preparation (2012) tŚĂƚ͛ƐůŝŵŝƚŝŶŐdΎ2? T*2 is not T1 limited - source of dephasing? Fluctuations of photons in the cavity 0 ge;0n ge;1n ge;2n 111 n * ¦ iNi T 22T 1TM ,int i with thermal population of photons at each n i cavity modes i. *A. Sears et al. in preparation (2012) Stability of Josephson Junction T1 ranges from 50 Ps to 70 Ps 0 * T*2 ranges from 10 Ps to 25 Ps 0 f01 = 6 808 737 605 (608) Hz 'f ~4kHzor~0.7ppm Frequency stable < 600 Hz : Stability in EJ or Ec - 80 ppb Breakthrough in SC Qubit Coherence This work Number of gate operation Number of gate By introducing 3D circuit QED architecture Charge Qubit Coherence : Saga continues This work Number of gate operation Number of gate No evidence found that the Josephson junction is limiting the qubit coherence Coherent control of 3D transmons Use microwave to perform single/two qubit gates Phase Gate using Off-Resonant Cavity Driving Zee Zeg Zge Zgg Cavity drive Cavity transmission Cavity Frequency (2)Zc FV z a a Use a qubit state-dependent cavity coherent states When the cavity is driven, cavity coherent state evolves giving phase to each qubit state. Phase of Driven Harmonic Oscillator Q H(t) Apply off-resonant drive to displace the cavity I DD(T ) eiI ()T (0) iDDH ' ()t ' ZZc d T T IDDD()T Im [*2 ]dt ' | |dt ³³00 Geometric origin Dynamical origin (Area) (energy) Single-Qubit Phase Gate (z-gate) Two coherent states Dg and De Q corresponding to |g> and |e> T T *2 IDDDg ()T Im g g dt 'g |g |dt ³³00 I T T *2 IDDDe ()T Im e e dt 'e |e |dt ³³00 If : Z-gate Also single qubit geometric phase demonstrated By M. Pechal, et al. arXiv:1109.1157 (2011) Single-Qubit Phase Gate - 13.5 dBm Ramsey experiment Msmt D gate S/2 S/2M IDvv||||22 H - 33.5 dBm Phase is proportional No driving to the driving power. SSSSS Angle of last S/2 pulse Detuning f =60 MHz Single Qubit z-gate No reduction in Ramsey Z-gate contrast after the gate 0 0.5 1 1.5 2 0 0.5 1 1.5 2 |D|2 |D|2 Two-Qubit Phase gate Cavity Zee Zeg Zge Zgg drive Dee Deg D ge D gg Frequency gg ge eg ee 0 o gg eiIIIIIge ge ei eg eg ei ge eg ee ee 0 If ISee : cPhase Ramsey experiments to measure two qubit phase Applying Ramsey IIee ge gate Ramsey Applying Ige gate Difference in phases gives two qubit phase Iee Ramsey experiments to estimate gate fidelity NOT Applying gate Applying Ramsey gate 0 I ge Comparing Ramsey contrast gives estimate on gate fidelity Demonstrating cPhase gate IIee ge Grey is a single qubit Ramsey w/o gate ISee Ige IIee eg Ramsey contrast a 90% Ieg SSSSS Angle of last Spulse Tgate = 200ns, ' = 80 MHz, P = 1.2 dBm Paik et al.
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]
  • Quantum Computers
    Quantum Computers ERIK LIND. PROFESSOR IN NANOELECTRONICS Erik Lind EIT, Lund University 1 Disclaimer Erik Lind EIT, Lund University 2 Quantum Computers Classical Digital Computers Why quantum computers? Basics of QM • Spin-Qubits • Optical qubits • Superconducting Qubits • Topological Qubits Erik Lind EIT, Lund University 3 Classical Computing • We build digital electronics using CMOS • Boolean Logic • Classical Bit – 0/1 (Defined as a voltage level 0/+Vdd) +vDD +vDD +vDD Inverter NAND Logic is built by connecting gates Erik Lind EIT, Lund University 4 Classical Computing • We build digital electronics using CMOS • Boolean Logic • Classical Bit – 0/1 • Very rubust! • Modern CPU – billions of transistors (logic and memory) • We can keep a logical state for years • We can easily copy a bit • Mainly through irreversible computing However – some problems are hard to solve on a classical computer Erik Lind EIT, Lund University 5 Computing Complexity Searching an unsorted list Factoring large numbers Grovers algo. – Shor’s Algorithm BQP • P – easy to solve and check on a 푛 classical computer ~O(N) • NP – easy to check – hard to solve on a classical computer ~O(2N) P P • BQP – easy to solve on a quantum computer. ~O(N) NP • BQP is larger then P • Some problems in P can be more efficiently solved by a quantum computer Simulating quantum systems Note – it is still not known if 푃 = 푁푃. It is very hard to build a quantum computer… Erik Lind EIT, Lund University 6 Basics of Quantum Mechanics A state is a vector (ray) in a complex Hilbert Space Dimension of space – possible eigenstates of the state For quantum computation – two dimensional Hilbert space ۧ↓ Example - Spin ½ particle - ȁ↑ۧ 표푟 Spin can either be ‘up’ or ‘down’ Erik Lind EIT, Lund University 7 Basics of Quantum Mechanics • A state of a system is a vector (ray) in a complex vector (Hilbert) Space.
    [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]
  • 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]
  • Superconducting Transmon Machines
    Quantum Computing Hardware Platforms: Superconducting Transmon Machines • CSC591/ECE592 – Quantum Computing • Fall 2020 • Professor Patrick Dreher • Research Professor, Department of Computer Science • Chief Scientist, NC State IBM Q Hub 3 November 2020 Superconducting Transmon Quantum Computers 1 5 November 2020 Patrick Dreher Outline • Introduction – Digital versus Quantum Computation • Conceptual design for superconducting transmon QC hardware platforms • Construction of qubits with electronic circuits • Superconductivity • Josephson junction and nonlinear LC circuits • Transmon design with example IBM chip layout • Working with a superconducting transmon hardware platform • Quantum Mechanics of Two State Systems - Rabi oscillations • Performance characteristics of superconducting transmon hardware • Construct the basic CNOT gate • Entangled transmons and controlled gates • Appendices • References • Quantum mechanical solution of the 2 level system 3 November 2020 Superconducting Transmon Quantum Computers 2 5 November 2020 Patrick Dreher Digital Computation Hardware Platforms Based on a Base2 Mathematics • Design principle for a digital computer is built on base2 mathematics • Identify voltage changes in electrical circuits that map base2 math into a “zero” or “one” corresponding to an on/off state • Build electrical circuits from simple on/off states that apply these basic rules to construct digital computers 3 November 2020 Superconducting Transmon Quantum Computers 3 5 November 2020 Patrick Dreher From Previous Lectures It was
    [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]
  • Uncertainty Relations for Quantum Coherence
    Article Uncertainty Relations for Quantum Coherence Uttam Singh 1,*, Arun Kumar Pati 1 and Manabendra Nath Bera 2 1 Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India; [email protected] 2 ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain; [email protected] * Correspondence: [email protected]; Tel.: +91-532-2274-407; Fax: +91-532-2567-748 Academic Editors: Paul Busch, Takayuki Miyadera and Teiko Heinosaari Received: 4 April 2016; Accepted: 9 July 2016; Published: 16 July 2016 Abstract: Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can there be some trade-off relation between the coherence measures in different reference bases? We show that the quantum coherence of a state as quantified by the relative entropy of coherence in two or more noncommuting reference bases respects uncertainty like relations for a given state of single and bipartite quantum systems. In the case of bipartite systems, we find that the presence of entanglement may tighten the above relation. Further, we find an upper bound on the sum of the relative entropies of coherence of bipartite quantum states in two noncommuting reference bases. Moreover, we provide an upper bound on the absolute value of the difference of the relative entropies of coherence calculated with respect to two incompatible bases. Keywords: uncertainty relations; coherence; quantum correlations 1. Introduction The linearity of quantum mechanics gives rise to the concept of superposition of quantum states of a quantum system and is one of the characteristic properties that makes a clear distinction between the ways a classical and a quantum system can behave.
    [Show full text]
  • Caputo Fractional Derivative and Quantum-Like Coherence
    entropy Article Caputo Fractional Derivative and Quantum-Like Coherence Garland Culbreth 1,* , Mauro Bologna 2, Bruce J. West 3 and Paolo Grigolini 1 1 Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, TX 76201, USA; [email protected] 2 Departamento de Ingeniería Eléctrica-Electrónica, Universidad de Tarapacá, 1000000 Arica, Chile; [email protected] 3 Army Research Office, DEVCOM US Army Research Laboratory, Research Triangle Park, NC 27708, USA; [email protected] * Correspondence: [email protected] Abstract: We study two forms of anomalous diffusion, one equivalent to replacing the ordinary time derivative of the standard diffusion equation with the Caputo fractional derivative, and the other equivalent to replacing the time independent diffusion coefficient of the standard diffusion equation with a monotonic time dependence. We discuss the joint use of these prescriptions, with a phenomenological method and a theoretical projection method, leading to two apparently different diffusion equations. We prove that the two diffusion equations are equivalent and design a time series that corresponds to the anomalous diffusion equation proposed. We discuss these results in the framework of the growing interest in fractional derivatives and the emergence of cognition in nature. We conclude that the Caputo fractional derivative is a signature of the connection between cognition and self-organization, a form of cognition emergence different from the other source of anomalous diffusion, which is closely related to quantum coherence. We propose a criterion to detect the action of self-organization even in the presence of significant quantum coherence. We argue that statistical analysis of data using diffusion entropy should help the analysis of physiological processes hosting both forms of deviation from ordinary scaling.
    [Show full text]
  • Measurement of Superconducting Qubits and Causality Alexander Korotkov University of California, Riverside
    Michigan State Univ., 09/21/15 Measurement of superconducting qubits and causality Alexander Korotkov University of California, Riverside Outline: Introduction (causality, POVM measurement) Circuit QED setup for measurement of superconducting qubits (transmons, Xmons) Qubit evolution due to measurement in circuit QED (simple and better theories) Experiments Alexander Korotkov University of California, Riverside Causality principle in quantum mechanics objects a and b observers A and B (and C) observers have “free will”; A B they can choose an action A choice made by observer A can affect light a b evolution of object b “back in time” cones time However, this retroactive control cannot pass space “useful” information to B (no signaling) C Randomness saves causality (even C Our focus: continuous cannot predict result of A measurement) |0 collapse Ensemble-averaged evolution of object b cannot depend on actions of observer A |1 Alexander Korotkov University of California, Riverside Werner Heisenberg Books: Physics and Philosophy: The Revolution in Modern Science Philosophical Problems of Quantum Physics The Physicist's Conception of Nature Across the Frontiers Niels Bohr Immanuel Kant (1724-1804), German philosopher Critique of pure reason (materialism, but not naive materialism) Nature - “Thing-in-itself” (noumenon, not phenomenon) Humans use “concepts (categories) of understanding”; make sense of phenomena, but never know noumena directly A priori: space, time, causality A naïve philosophy should not be a roadblock for good physics,
    [Show full text]