Time-Domain Grating with a Periodically Driven Qutrit
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31 Diffraction and Interference.Pdf
Diffraction and Interference Figu These expar new .5 wave oday Isaac Newton is most famous for his new v accomplishments in mechanics—his laws of Tmotion and universal gravitation. Early in his career, however, he was most famous for his work on light. Newton pictured light as a beam of ultra-tiny material particles. With this model he could explain reflection as a bouncing of the parti- cles from a surface, and he could explain refraction as the result of deflecting forces from the surface Interference colors. acting on the light particles. In the eighteenth and nineteenth cen- turies, this particle model gave way to a wave model of light because waves could explain not only reflection and refraction, but everything else that was known about light at that time. In this chapter we will investigate the wave aspects of light, which are needed to explain two important phenomena—diffraction and interference. As Huygens' Principle origin; 31.1 pie is I constr In the late 1600s a Dutch mathematician-scientist, Christian Huygens, dimen proposed a very interesting idea about waves. Huygens stated that light waves spreading out from a point source may be regarded as die overlapping of tiny secondary wavelets, and that every point on ' any wave front may be regarded as a new point source of secondary waves. We see this in Figure 31.1. In other words, wave fronts are A made up of tinier wave fronts. This idea is called Huygens' principle. Look at the spherical wave front in Figure 31.2. Each point along the wave front AN is the source of a new wavelet that spreads out in a sphere from that point. -
Time Quasilattices in Dissipative Dynamical Systems Abstract Contents
SciPost Phys. 5, 001 (2018) Time quasilattices in dissipative dynamical systems Felix Flicker1,2 1 Rudolph Peierls Centre for Theoretical Physics, University of Oxford, Department of Physics, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK 2 Department of Physics, University of California, Berkeley, California 94720 USA fl[email protected] Abstract We establish the existence of ‘time quasilattices’ as stable trajectories in dissipative dy- namical systems. These tilings of the time axis, with two unit cells of different durations, can be generated as cuts through a periodic lattice spanned by two orthogonal directions of time. We show that there are precisely two admissible time quasilattices, which we term the infinite Pell and Clapeyron words, reached by a generalization of the period- doubling cascade. Finite Pell and Clapeyron words of increasing length provide system- atic periodic approximations to time quasilattices which can be verified experimentally. The results apply to all systems featuring the universal sequence of periodic windows. We provide examples of discrete-time maps, and periodically-driven continuous-time dy- namical systems. We identify quantum many-body systems in which time quasilattices develop rigidity via the interaction of many degrees of freedom, thus constituting dissi- pative discrete ‘time quasicrystals’. Copyright F. Flicker. Received 30-10-2017 This work is licensed under the Creative Commons Accepted 15-06-2018 Check for Attribution 4.0 International License. Published 03-07-2018 updates Published -
Arxiv:2005.03138V2 [Cond-Mat.Quant-Gas] 23 May 2020 Contents
Condensed Matter Physics in Time Crystals Lingzhen Guo1 and Pengfei Liang2;3 1Max Planck Institute for the Science of Light (MPL), Staudtstrasse 2, 91058 Erlangen, Germany 2Beijing Computational Science Research Center, 100193 Beijing, China 3Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy E-mail: [email protected] Abstract. Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time- translation symmetry in static systems is proved impossible for the equilibrium state, the discrete time-translation symmetry in periodically driven (Floquet) systems is allowed to be spontaneously broken, resulting in the so-called Floquet or discrete time crystals. While most works so far searching for time crystals focus on the symmetry breaking process and the possible stabilising mechanisms, the many-body physics from the interplay of symmetry-broken states, which we call the condensed matter physics in time crystals, is not fully explored yet. This review aims to summarise the very preliminary results in this new research field with an analogous structure of condensed matter theory in solids. The whole theory is built on a hidden symmetry in time crystals, i.e., the phase space lattice symmetry, which allows us to develop the band theory, topology and strongly correlated models in phase space lattice. In the end, we outline the possible topics and directions for the future research. arXiv:2005.03138v2 [cond-mat.quant-gas] 23 May 2020 Contents 1 Brief introduction to time crystals3 1.1 Wilczek's time crystal . .3 1.2 No-go theorem . .3 1.3 Discrete time-translation symmetry breaking . -
Creating Big Time Crystals with Ultracold Atoms
New J. Phys. 22 (2020) 085004 https://doi.org/10.1088/1367-2630/aba3e6 PAPER Creating big time crystals with ultracold atoms OPEN ACCESS Krzysztof Giergiel1,TienTran2, Ali Zaheer2,ArpanaSingh2,AndreiSidorov2,Krzysztof RECEIVED 1 2 1 April 2020 Sacha and Peter Hannaford 1 Instytut Fizyki Teoretycznej, Universytet Jagiellonski, ulica Profesora Stanislawa Lojasiewicza 11, PL-30-348 Krakow, Poland REVISED 2 23 June 2020 Optical Sciences Centre, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia ACCEPTED FOR PUBLICATION E-mail: [email protected] and [email protected] 8 July 2020 PUBLISHED Keywords: time crystals, Bose–Einstein condensate, ultracold atoms 17 August 2020 Original content from Abstract this work may be used under the terms of the We investigate the size of discrete time crystals s (ratio of response period to driving period) that Creative Commons Attribution 4.0 licence. can be created for a Bose–Einstein condensate (BEC) bouncing resonantly on an oscillating Any further distribution mirror. We find that time crystals can be created with sizes in the range s ≈ 20–100 and that such of this work must maintain attribution to big time crystals are easier to realize experimentally than a period-doubling (s=2) time crystal the author(s) and the because they require either a larger drop height or a smaller number of bounces on the mirror. We title of the work, journal citation and DOI. also investigate the effects of having a realistic soft Gaussian potential mirror for the bouncing BEC, such as that produced by a repulsive light-sheet, which is found to make the experiment easier to implement than a hard-wall potential mirror. -
Prelab 5 – Wave Interference
Musical Acoustics Lab, C. Bertulani PreLab 5 – Wave Interference Consider two waves that are in phase, sharing the same frequency and with amplitudes A1 and A2. Their troughs and peaks line up and the resultant wave will have amplitude A = A1 + A2. This is known as constructive interference (figure on the left). If the two waves are π radians, or 180°, out of phase, then one wave's crests will coincide with another waves' troughs and so will tend to cancel itself out. The resultant amplitude is A = |A1 − A2|. If A1 = A2, the resultant amplitude will be zero. This is known as destructive interference (figure on the right). When two sinusoidal waves superimpose, the resulting waveform depends on the frequency (or wavelength) amplitude and relative phase of the two waves. If the two waves have the same amplitude A and wavelength the resultant waveform will have an amplitude between 0 and 2A depending on whether the two waves are in phase or out of phase. The principle of superposition of waves states that the resultant displacement at a point is equal to the vector sum of the displacements of different waves at that point. If a crest of a wave meets a crest of another wave at the same point then the crests interfere constructively and the resultant crest wave amplitude is increased; similarly two troughs make a trough of increased amplitude. If a crest of a wave meets a trough of another wave then they interfere destructively, and the overall amplitude is decreased. This form of interference can occur whenever a wave can propagate from a source to a destination by two or more paths of different lengths. -
Lecture 9, P 1 Lecture 9: Introduction to QM: Review and Examples
Lecture 9, p 1 Lecture 9: Introduction to QM: Review and Examples S1 S2 Lecture 9, p 2 Photoelectric Effect Binding KE=⋅ eV = hf −Φ energy max stop Φ The work function: 3.5 Φ is the minimum energy needed to strip 3 an electron from the metal. 2.5 2 (v) Φ is defined as positive . 1.5 stop 1 Not all electrons will leave with the maximum V f0 kinetic energy (due to losses). 0.5 0 0 5 10 15 Conclusions: f (x10 14 Hz) • Light arrives in “packets” of energy (photons ). • Ephoton = hf • Increasing the intensity increases # photons, not the photon energy. Each photon ejects (at most) one electron from the metal. Recall: For EM waves, frequency and wavelength are related by f = c/ λ. Therefore: Ephoton = hc/ λ = 1240 eV-nm/ λ Lecture 9, p 3 Photoelectric Effect Example 1. When light of wavelength λ = 400 nm shines on lithium, the stopping voltage of the electrons is Vstop = 0.21 V . What is the work function of lithium? Lecture 9, p 4 Photoelectric Effect: Solution 1. When light of wavelength λ = 400 nm shines on lithium, the stopping voltage of the electrons is Vstop = 0.21 V . What is the work function of lithium? Φ = hf - eV stop Instead of hf, use hc/ λ: 1240/400 = 3.1 eV = 3.1eV - 0.21eV For Vstop = 0.21 V, eV stop = 0.21 eV = 2.89 eV Lecture 9, p 5 Act 1 3 1. If the workfunction of the material increased, (v) 2 how would the graph change? stop a. -
Waves: Interference Instructions: Read Through the Information Below
Pre-AP Physics Week 2: Day 1 Notes Waves: Interference Instructions: Read through the information below. Then answer the questions below. When two or more waves meet, they interact with each other. The interaction of waves with other waves is called wave interference. Wave interference may occur when two waves that are traveling in opposite directions meet. The two waves pass through each other, and this affects their amplitude. Amplitude is the maximum distance the particles of the medium move from their resting positions when a wave passes through. How amplitude is affected by wave interference depends on the type of interference. Interference can be constructive or destructive. Constructive Interference Destructive Interference Constructive interference occurs when crests of one Destructive interference occurs when the crests of one wave overlap the crests of the other wave. The figure wave overlap the troughs, or lowest points, of another above shows what happens. As the waves pass through wave. The figure above shows what happens. As the each other, the crests combine to produce a wave with waves pass through each other, the crests and troughs greater amplitude. The same can happen with two cancel each other out to produce a wave with zero troughs interacting. amplitude. (NOTE: They don’t always have to fully cancel out. Destructive interference can be partial cancellation.) TRUE or FALSE: Identify the following statements as being either true (T) or false (F). 1. When two pulses meet up with each other while moving through the same medium, they tend to bounce off each other and return back to their origin. -
Arxiv:2007.08348V3
Dynamical transitions and critical behavior between discrete time crystal phases 1 1,2, Xiaoqin Yang and Zi Cai ∗ 1Wilczek Quantum Center and Key Laboratory of Artificial Structures and Quantum Control, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China 2Shanghai Research Center for Quantum Sciences, Shanghai 201315, China In equilibrium physics, spontaneous symmetry breaking and elementary excitation are two con- cepts closely related with each other: the symmetry and its spontaneous breaking not only control the dynamics and spectrum of elementary excitations, but also determine their underlying struc- tures. In this paper, based on an exactly solvable model, we propose a phase ramping protocol to study an excitation-like behavior of a non-equilibrium quantum matter: a discrete time crystal phase with spontaneous temporal translational symmetry breaking. It is shown that slow ramp- ing could induce a dynamical transition between two Z2 symmetry breaking time crystal phases in time domain, which can be considered as a temporal analogue of the soliton excitation spacially sandwiched by two degenerate charge density wave states in polyacetylene. By tuning the ramping rate, we observe a critical value at which point the transition duration diverges, resembling the critical slowing down phenomenon in nonequilibrium statistic physics. We also discuss the effect of stochastic sequences of such phase ramping processes and its implication to the stability of the discrete time crystal phase against noisy perturbations. Usually, the ground state energy of an equilibrium sys- question is how to generalize such an idea into the non- tem does not have much to do with its observable behav- equilibirum quantum matters with intriguing SSB absent ior. -
Physical Quantum States and the Meaning of Probability Michel Paty
Physical quantum states and the meaning of probability Michel Paty To cite this version: Michel Paty. Physical quantum states and the meaning of probability. Galavotti, Maria Carla, Suppes, Patrick and Costantini, Domenico. Stochastic Causality, CSLI Publications (Center for Studies on Language and Information), Stanford (Ca, USA), p. 235-255, 2001. halshs-00187887 HAL Id: halshs-00187887 https://halshs.archives-ouvertes.fr/halshs-00187887 Submitted on 15 Nov 2007 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. as Chapter 14, in Galavotti, Maria Carla, Suppes, Patrick and Costantini, Domenico, (eds.), Stochastic Causality, CSLI Publications (Center for Studies on Language and Information), Stanford (Ca, USA), 2001, p. 235-255. Physical quantum states and the meaning of probability* Michel Paty Ëquipe REHSEIS (UMR 7596), CNRS & Université Paris 7-Denis Diderot, 37 rue Jacob, F-75006 Paris, France. E-mail : [email protected] Abstract. We investigate epistemologically the meaning of probability as implied in quantum physics in connection with a proposed direct interpretation of the state function and of the related quantum theoretical quantities in terms of physical systems having physical properties, through an extension of meaning of the notion of physical quantity to complex mathematical expressions not reductible to simple numerical values. -
Magnetic Manipulation of Polymeric Nanostructures
Magnetic Manipulation of Polymeric Nanostructures R.S.M. Rikken 1,2, H. Engelkamp 1, R.J.M. Nolte 2, J.C. Maan 1, J.C.M. van Hest 2, D.A. Wilson 2, P.C.M. Christianen 1* 1 High Field Magnet Laboratory (HFML-EMFL), Radboud University, Toernooiveld 7, 6525 ED Nijmegen, The Netherlands 2 Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands *corresponding author: [email protected] Polymersomes are bilayer vesicles self-assembled from amphiphilic block copolymers. They are ideal and versatile nano-objects since they have many adjustable properties such as their flexibility, permeability and functionality, which can be used as nano-containers and nanomotors for nanochemistry and drug delivery [1, 2]. We have recently developed a polymersome system using poly(ethylene glycol)-polystyrene (PEG-PS) block copolymers. PEG-PS polymersomes have the advantage that their flexibility can be controlled by the contents of organic solvents like THF and dioxane, which act as a plasticizer on the polystyrene membrane. It also allows flexible polymersomes to be fixated by adding an excess of water. For many applications, the shape of a polymersome is very important since shape and functionality are closely related. In this talk an overview will be given of our efforts to control the shape of polymersomes by application of osmotic and/or magnetic forces. It will be shown that high magnetic fields can be used in two different ways: either to probe the polymersome shape using magnetic alignment or to modify the shape by magnetic deformation. We have investigated two different methods in which an osmotic pressure is used to change the polymersome shape. -
When the Uncertainty Principle Goes to 11... Or How to Explain Quantum Physics with Heavy Metal
Ronald E. Hatcher Science on Saturday Lecture Series 12 January 2019 When The Uncertainty Principle goes to 11... or How to Explain Quantum Physics with Heavy Metal Philip Moriarty Professor, University of Nottingham, United Kingdom ABSTRACT: There are deep and fundamental linKs between quantum physics and heavy metal. No, really. There are. Far from being music for Neanderthals, as it’s too often construed, metal can be harmonically and rhythmically complex. That complexity is the source of many connections to the quantum world. You’ll discover how the Heisenberg uncertainty principle comes into play with every chugging guitar riff, what wave interference has to do with Iron Maiden, and why metalheads in mosh pits behave just liKe molecules in a gas. BIOGRAPHY: Philip Moriarty is a professor of physics, a heavy metal fan, a Keen air-drummer, and author of “When The Uncertainty Principle Goes To 11 (or How To Explain Quantum Physics With Heavy Metal” (Ben Bella 2018). His research at the University of Nottingham focuses on prodding, pushing, and poKing single atoms and molecules; in this nanoscopic world, quantum physics is all. Moriarty has taught physics for twenty years and has always been strucK by the number of students in his classes who profess a love of metal music, and by the deep connections between heavy metal and quantum mechanics. A frequent contributor to the Sixty Symbols YouTube channel, which won the Institute of Physics’ Kelvin Award in 2016 for “for innovative and effective promotion of the public understanding of physics”, he has a Keen interest in public engagement, outreach, and bridging the arts-science divide. -
Rethinking a Delayed Choice Quantum Eraser Experiment: a Simple Baseball Model Jeffrey H
PHYSICS ESSAYS 26, 1 (2013) Rethinking a delayed choice quantum eraser experiment: A simple baseball model Jeffrey H. Boyda) 57 Woods Road, Bethany, Connecticut 06524, USA (Received 10 June 2012; accepted 26 December 2012; published online 26 February 2013) Abstract: In a double slit experiment, you can see an interference fringe pattern or you can know which slit the photon came through, but not both. There are two diametrically opposite theories about why this happens. One is complementarity. The other is the proposal made in this article. An experiment, published in 2000 [Y.-H. Kim et al., Phys. Rev. Lett. 8, 1 (2000)] allegedly supports the idea of complementarity. With different starting assumptions, we arrive at opposite conclusions: complementarity is irrelevant to this experiment. Our assumptions come from the Theory of Elementary Waves. Waves are assumed to travel in the opposite direction: from the detector to the laser. All wave interference is located at the laser. All decisions of importance are located at the laser, not at the detectors. The “decisions” concern which of several elementary rays a photon chooses to follow (this is a probabilistic decision). If a photon is emitted in response to one such impinging ray, all wave interference is then complete. The photon will follow backwards that ray alone, with a probability of one, back to the pair of detectors from which that ray originated. Based on these assumptions, the experiment has nothing to do with complementarity. There is also no delayed choice and no quantum eraser. Conclusion: complementarity is not the only way to understand this experiment.