Quantum thermodynamics and irreversibility
|
|
- Vernon Dawson
- 5 years ago
- Views:
Transcription
1 Seminário para a Universidade Federal de Minas Gerais Quantum thermodynamics and irreversibility Gabriel Teixeira Landi FMT - IFUSP
2 Summary Quantum Thermodynamics? Motivation from Quantum Information Sciences. Recent progress and general trends in the field. Our contribution: quantifying irreversibility at the quantum level.
3 We live in the age of quantum technologies Since its conception, quantum mechanics has already provided us with remarkable technologies: Lasers. Semiconductors: solar panels, LEDs, computers, smartphones. Nuclear magnetic resonance, electron microscopy, etc. These are now called Quantum Technologies 1.0 (UK Defence Science and Technology Laboratory)
4 But quantum mechanics also predicts other properties, such as coherence and entanglement, which are not usually employed in these applications.
5 Coherence In QM we learn that a superposition of states is also a valid state: i = a 1i + b 2i But when we construct the periodic table, we don t care about this: we just put the electrons in each state. That s not very quantum: Its quantum because the energy levels are discrete. But other than that, its classical. 1
6 Interaction with the environment Consider a 2-level system in an arbitrary state. For a pure state we have i = a 0i + b 1i =) = ih = a 2 a b ab b 2 More generally, we have = p0 q q p 1 The interaction with the environment does two things: 1. Changes the populations in a certain basis. 2. Destroys coherences. p0 q q p 1! p p 0 1
7 Isolate, experiment, understand And so began a long quest to isolate, experiment and understand with these more exotic quantum resources: Superconducting qubits Coherence, entanglement, squeezing, asymmetry, purity, discord, &c. We now have are many platforms where we can have impressive control over individual quantum systems: Quantum optics, trapped ions, superconducting qubits, NMR, NV centers in diamond, Bose-Einstein condensates, ultra-cold atoms in optical lattices, &c.
8 Quantum Technologies 2.0 Together with these experimental advances, it also became clear that we could harness these quantum resources to produce new technologies: Secure communications with quantum cryptography. Exponentially faster algorithms with quantum computers. Higher sensitivity with quantum metrology. Will any of these ever see the light of day? Based on the history of physics, we will definitely see some applications. But even if no direct applications appear: What we learned so far in this field is already helping in many other areas, such as e.g. strongly correlated systems (in this context correlation = entanglement).
9 Quantum Thermodynamics It is now straightforward to define what is the goal of Quantum Thermodynamics : To understand the role of quantum resources in thermodynamic quantities such as heat and work. Topics of current interest include: The role of measurements in thermodynamic processes. Thermal transformations under the presence of quantum fluctuations. How coherence, entanglement and squeezing affect the operation of heat engines. Irreversibility at the quantum level.
10 Review of the recent literature
11 Quantum measurement
12 Thermal operations
13 Rényi entropy S = 1 1 log tr von Neumann entropy S 1 = tr( ln ) A transition is allowed when: F (, ) F ( 0, ) Generalizes the second law. For macroscopic systems all Rényi entropies converge to von Neumann.
14 More general heat engines
15
16 Coherence producing engine
17 Measures of Irreversibility
18 Entropy production The energy of a system satisfies a continuity equation: dhhi dt For the entropy that is not true: = E ds dt = Π represents the entropy production rate due to the irreversible dynamics: 0 and = 0 only in equilibrium Dinâmica estocástica e irreversibilidade, T. Tomé e M. J. de Oliveira
19 Example: RL circuit E 2 /RT 4 2 / Φ Π t E Steady-state ds dt =0 ss = ss = E 2 RT
20 Example: two inductively coupled RL circuits ss = E 2 1 R 1 T 1 + E 2 2 R 2 T 2 + m 2 R 1 R 2 (L 1 L 2 m 2 )(L 2 R 1 + L 1 R 2 ) (T 1 T 2 ) 2 T 1 T 2 GTL, T. Tomé and M. J. de Oliveira, J. Phys A. 46 (2013)
21 Traditional formulation The traditional theory of entropy production, for both quantum and classical systems, is based on the following formulas: Entropy flux ds dt = Entropy production = E T ds = de T = d dt S( eq) S( eq )=tr( ln ln eq ) (Relative entropy) J. Schnakenberg, Rev. Mod. Phys. 48, 571 (1976). H. Spohn, J. Math. Phys., 19, 1227 (1978) T. Tomé and M. J. de Oliveira, Phys. Rev. Lett, 108, (2012)
22 J. P. Santos, L. C. Céleri, GTL, M. Paternostro, arxiv: Entropy production and loss of coherence The environment selects a preferred basis for the system. = When the system interacts with an environment, two things happen simultaneously: p0 q q p 1 The populations adjust to the levels imposed by the bath: The system looses coherence. p n = hn ni We may write the relative entropy as S( eq )=S(p p eq )+C( ) S(p p eq )= X n C( ) =S(p) p n ln p n /p eq n S( ) ) = d + coh Entropy is produced due to the classical transitions between energy levels and also due to the loss of coherence
23 Problems with the standard formulation ds dt = = d dt S( eq) = E T Difficult to extend to systems connected to multiple reservoirs. Cannot be extended to non-equilibrium reservoirs: Squeezed baths, dephasing baths, engineered baths, &c. Breaks down at T = 0.
24 Spontaneous emission is at T = 0 Every system is nature is connected to a bath: Vacuum fluctuations act as a zero-temperature bath. Explains why atoms emit photons and relax to the ground-state. The theory of open quantum systems accounts for this type of process quite naturally. Everything is well behaved. But Π and Φ diverge when T 0.
25 Example: evolution of a coherent state Consider the evolution of a harmonic oscillator starting from a coherent state: (0) = µihµ The evolution remains as a (pure) coherent state: (α) (t) = µ t ihµ t - µ t = µe (i!+ /2)t (α) The entropy is zero throughout, but Π and Φ would both be infinite. This is clearly an inconsistency of the theory.
26 Dynamics of open quantum systems
27 Lindblad dynamics Most widely used tool to describe experiments in Quantum Information setups. d dt = D( ) = X i[h, ]+D( ) L L 1 2 {L L, } Idea: the most general evolution of a closed system is a Unitary. The most general evolution of an open system is a Kraus map:! X M k M k, X M k M k =1 k k Lindblad s theorem: if such a map is also Markovian (forms a semigroup), then it can be expressed as a Lindblad master equation.
28 Open quantum harmonic oscillator We revisit this problem using the simplest model in quantum mechanics: the harmonic oscillator: H =!(a a +1/2) The dissipator describing the contact with a thermal bath is apple apple D( ) = ( n + 1) a a 1 2 {a a, } + n a 1 a 2 {aa, } n = 1 e! 1 Classical dynamics describes emission and absorption of quanta. But also captures quantum features. ( )
29
30 Phase space Instead of using wavefunctions or density matrices, we work in phase space using the Wigner function: W (, )= 1 Z 2 d 2 e + tr e a a Phase space is now the complex plane, with: x = p 2Re( ), p = p 2Im( ) Thermal equilibrium is a Gaussian 1 W eq = ( n +1/2) exp 2 n +1/2 For T = 0 this gives the vacuum state, which still has a non-zero width: quantum fluctuations.
31 Rényi-2 and Wigner entropy The authors of this paper showed that for quantum systems all Rényi entropies have thermodynamic significance. S = 1 1 ln tr The simplest one to use is the Rényi-2 entropy: S 2 = ln tr 2 In PRL 109, (2012) the authors showed that for Gaussian states, this actually coincides with the Wigner entropy Z S = d 2 W (, )lnw(, )
32 Quantum Fokker-Planck equation d dt = i[h, ]+D( ) In terms of the Wigner function, the Lindblad equation becomes a quantum Fokker-Planck equation: t W = ( W ( W ) + D(W ) D(W )=@ J(W )+@ J (W ) J(W )= 2 apple W +( n +1/2)@ W This is a continuity equation and J(W) is the irreversible component of the probability current. J(W eq )=0 U. Seifert, Rep. Prog. Phys. 75, (2012)
33 Wigner entropy production and flux We use 3 different methods to show that the Wigner entropy production for a harmonic oscillator will be: Z = d 2 4 ( n +1/2) The entropy flux rate then becomes J(W ) 2 W = n +1/2 appleha ai n = E!( n +1/2) At high temperatures!( n +1/2) ' T so we get ' E T Now both Π and Φ remain finite at T = 0.
34 Stochastic trajectories and fluctuation theorems We can also arrive at the same result using a completely different method. We analyze the stochastic trajectories in the complex plane. The quantum Fokker-Planck equation is equivalent to a Langevin equation in the complex plane: da dt = i!a 2 A + p ( n +1/2) (t) h (t) (t 0 )i =0, h (t) (t 0 )i = (t t 0 )
35 We can now define the entropy produced in a trajectory as a functional of the path probabilities for the forward and reversed trajectories: [ (t)] = ln P[ (t)] P R [ ( t)] This quantity satisfies a fluctuation theorem he i =1 We show that we can obtain exactly the same formula for the entropy production rate if we define it as = hd [A(t)]i dt
36 M. Brunelli, et. al. arxiv: Experiments Optomechanical system (Vienna) BEC in a highfinesse cavity (ETH)
37 Generalizations
38 J. P. Santos, L. C. Céleri, GTL, M. Paternostro, arxiv: Spins and qubits We would like to have a similar framework for spin systems. Spin coherent states: i = e J z e J y J, Ji Husimi-Q function: Wehrl entropy: Q( ) =h i Z = d Q( )lnq( ) The Quantum Fokker-Planck equation is now written in terms of orbital angular momentum operators. i[j z, ]! J z (Q) Q
39 J. P. Santos, L. C. Céleri, GTL, M. Paternostro, arxiv: Dephasing and amplitude damping The dephasing bath induces no population changes, only decoherence: D( ) = 2 [J z, [J z, ]] It leads to no entropy flux, only an entropy production: Z = d J z(q) 2 2 Q We compare this with the amplitude damping: D( ) = ( n + 1) apple J J {J +J, } + n apple J + J 1 2 {J J +, } We now see the separation of a contribution from population changes and a contribution from decoherence. = 2 Z d Q ( [2JQ sin + (cos (2 n + 1))@ Q] 2 (2 n + 1) cos apple ) + J z (Q) 2 (2 n + 1) cos 1 cos sin 2
40 Squeezed baths Example of a non-equilibrium reservoir. apple D z ( ) = (N + 1) + N M apple a a a a 1 2 {a a, } 1 2 {aa, } apple a a 1 2 {a a, } M applea a 1 {aa, } 2 J E = dha ai dt J S = dhaai dt = (N ha ai) = (M haai) N +1/2 =( n +1/2) cosh 2r M = ( n +1/2)e i sinh(2r)
41 For the squeezed bath we find that the entropy production rate is given by = 4 ( n +1/2) Z d 2 W J z cosh r + J z e i( 2! st) sinh r 2 J z (W )= 2 apple W +(N +1/2)@ W + M W The entropy flux rate is given by = n +1/2 apple cosh(2r)ha ai n +sinh 2 (r) Re[M t haai] n +1/2
42 Onsager theory for squeezing Our formalism allows us to cast this problem within the same thermodynamic framework of Onsager s transport theory: Joint transport of energy and squeezing. We can even define a Squeezing Peltier and Squeezing Seebeck effect. J E = T 1,1 n + T 1,2 r J S = T 2,1 n + T 2,2 r Entropy production and flux can be written like in standard thermodynamics: = f E J E + f S J S + f SJ S =( f E f E )J E +( f S f S )J S +( f S f S)J S
43 Conclusions Quantum Information Sciences: understand and exploit the role of quantum resources, such as coherence and entanglement. Quantum thermodynamics: understand how these resources affect properties such as heat, work and entropy production. Theory of irreversibility for open quantum systems is incomplete. We proposed an alternative for Gaussian states using the Wigner entropy. This approach solves the T = 0 problem and is also useful to study engineered reservoirs.
44 Collaborators: Jader. P. Santos (post-doc) Mauro Paternostro (Queen Belfast) Lucas Céleri (UFG) Dragi Karevski and Malte Henkel (Uni Nancy) André Timpanaro and Fernando Semião (UFABC) Sascha Wald Trieste) Cecilia Cormick Cordoba) Giovanna Morigi (Särbrucken) Thank you. Students: Wellington Ribeiro: dephasing in fermionic systems. William Malouf: entropy production and mutual information. Heitor Casagrande: DMRG simulations of open quantum systems. Pedro Portugal: backflow of information in Non-Markovian dynamics. Franklin Luis: transport of squeezing in opto-mechanical systems. Bruno Goes: dynamics of dissipative quantum phase transitions. Mariana Cipolla: entropy production and entanglement in the spin-boson model.
45 Squeezed baths and gravitational waves
46 Most used approaches Keldysh Green s functions (discussed in Altland s book on Cond. Mat. Field Theory). Quantum Fokker-Planck-Kramers equation. M. J. de Oliveira, PRE, 94, (2016) Quantum Brownian motion: A. Caldeira and A. Leggett, Physica A, 121, 587 (1983). L. Pucci, M. Esposito and L. Peliti, J. Stat. Mech. 13, P04005 (2013).
Measures of irreversibility in quantum phase space
SISSA, Trieste Measures of irreversibility in quantum phase space Gabriel Teixeira Landi University of São Paulo In collaboration with Jader P. Santos (USP), Raphael Drummond (UFMG) and Mauro Paternostro
More informationC.W. Gardiner. P. Zoller. Quantum Nois e. A Handbook of Markovian and Non-Markovia n Quantum Stochastic Method s with Applications to Quantum Optics
C.W. Gardiner P. Zoller Quantum Nois e A Handbook of Markovian and Non-Markovia n Quantum Stochastic Method s with Applications to Quantum Optics 1. A Historical Introduction 1 1.1 Heisenberg's Uncertainty
More informationdensity operator and related quantities A. Isar Department of Theoretical Physics, Institute of Atomic Physics POB MG-6, Bucharest-Magurele, Romania
IFA-FT-396-994 Damped quantum harmonic oscillator: density operator and related quantities A. Isar Department of Theoretical Physics, Institute of Atomic Physics POB MG-6, Bucharest-Magurele, Romania Internet:
More informationQuantum control of dissipative systems. 1 Density operators and mixed quantum states
Quantum control of dissipative systems S. G. Schirmer and A. I. Solomon Quantum Processes Group, The Open University Milton Keynes, MK7 6AA, United Kingdom S.G.Schirmer@open.ac.uk, A.I.Solomon@open.ac.uk
More informationMESOSCOPIC QUANTUM OPTICS
MESOSCOPIC QUANTUM OPTICS by Yoshihisa Yamamoto Ata Imamoglu A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim Brisbane Toronto Singapore Preface xi 1 Basic Concepts
More informationCooperative Phenomena
Cooperative Phenomena Frankfurt am Main Kaiserslautern Mainz B1, B2, B4, B6, B13N A7, A9, A12 A10, B5, B8 Materials Design - Synthesis & Modelling A3, A8, B1, B2, B4, B6, B9, B11, B13N A5, A7, A9, A12,
More informationOpen Quantum Systems. Sabrina Maniscalco. Turku Centre for Quantum Physics, University of Turku Centre for Quantum Engineering, Aalto University
Open Quantum Systems Sabrina Maniscalco Turku Centre for Quantum Physics, University of Turku Centre for Quantum Engineering, Aalto University Turku Quantum Technologies GOAL at least 3 useful concepts
More informationFrom trapped ions to macroscopic quantum systems
7th International Summer School of the SFB/TRR21 "Control of Quantum Correlations in Tailored Matter 21-13 July 2014 From trapped ions to macroscopic quantum systems Peter Rabl Yesterday... Trapped ions:
More informationQuantum correlations and decoherence in systems of interest for the quantum information processing
Universita' degli Studi di Milano Physics, Astrophysics and Applied Physics PhD School: 1 st Year-Student Mini-Workshop Quantum correlations and decoherence in systems of interest for the quantum information
More informationClassical and quantum simulation of dissipative quantum many-body systems
0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 0 20 32 Classical and quantum simulation of dissipative quantum many-body systems
More informationEmergent Fluctuation Theorem for Pure Quantum States
Emergent Fluctuation Theorem for Pure Quantum States Takahiro Sagawa Department of Applied Physics, The University of Tokyo 16 June 2016, YITP, Kyoto YKIS2016: Quantum Matter, Spacetime and Information
More informationLecture 2: Open quantum systems
Phys 769 Selected Topics in Condensed Matter Physics Summer 21 Lecture 2: Open quantum systems Lecturer: Anthony J. Leggett TA: Bill Coish 1. No (micro- or macro-) system is ever truly isolated U = S +
More informationQuantum optics. Marian O. Scully Texas A&M University and Max-Planck-Institut für Quantenoptik. M. Suhail Zubairy Quaid-i-Azam University
Quantum optics Marian O. Scully Texas A&M University and Max-Planck-Institut für Quantenoptik M. Suhail Zubairy Quaid-i-Azam University 1 CAMBRIDGE UNIVERSITY PRESS Preface xix 1 Quantum theory of radiation
More informationElements of Quantum Optics
Pierre Meystre Murray Sargent III Elements of Quantum Optics Fourth Edition With 124 Figures fya Springer Contents 1 Classical Electromagnetic Fields 1 1.1 Maxwell's Equations in a Vacuum 2 1.2 Maxwell's
More informationSusana F. Huelga. Dephasing Assisted Transport: Quantum Networks and Biomolecules. University of Hertfordshire. Collaboration: Imperial College London
IQIS2008, Camerino (Italy), October 26th 2008 Dephasing Assisted Transport: Quantum Networks and Biomolecules Susana F. Huelga University of Hertfordshire Collaboration: Imperial College London Work supported
More informationMEASUREMENT THEORY QUANTUM AND ITS APPLICATIONS KURT JACOBS. University of Massachusetts at Boston. fg Cambridge WW UNIVERSITY PRESS
QUANTUM MEASUREMENT THEORY AND ITS APPLICATIONS KURT JACOBS University of Massachusetts at Boston fg Cambridge WW UNIVERSITY PRESS Contents Preface page xi 1 Quantum measurement theory 1 1.1 Introduction
More informationIrreversibility and the arrow of time in a quenched quantum system. Eric Lutz Department of Physics University of Erlangen-Nuremberg
Irreversibility and the arrow of time in a quenched quantum system Eric Lutz Department of Physics University of Erlangen-Nuremberg Outline 1 Physics far from equilibrium Entropy production Fluctuation
More informationThermalisation and vortex formation in a mechanically perturbed condensate. Vortex Lattice Formation. This Talk. R.J. Ballagh and Tod Wright
Thermalisation and vortex formation in a mechanically perturbed condensate Jack Dodd Centre ACQAO R.J. Ballagh and Tod Wright Jack Dodd centre for Photonics and Ultra-cold Atoms Department of Physics University
More informationQuantum structures of photons and atoms
Quantum structures of photons and atoms Giovanna Morigi Universität des Saarlandes Why quantum structures The goal: creation of mesoscopic quantum structures robust against noise and dissipation Why quantum
More informationSpin-Boson Model. A simple Open Quantum System. M. Miller F. Tschirsich. Quantum Mechanics on Macroscopic Scales Theory of Condensed Matter July 2012
Spin-Boson Model A simple Open Quantum System M. Miller F. Tschirsich Quantum Mechanics on Macroscopic Scales Theory of Condensed Matter July 2012 Outline 1 Bloch-Equations 2 Classical Dissipations 3 Spin-Boson
More informationThe phases of matter familiar for us from everyday life are: solid, liquid, gas and plasma (e.f. flames of fire). There are, however, many other
1 The phases of matter familiar for us from everyday life are: solid, liquid, gas and plasma (e.f. flames of fire). There are, however, many other phases of matter that have been experimentally observed,
More informationExperimental Rectification of Entropy Production by Maxwell s Demon in a Quantum System
Experimental Rectification of Entropy Production by Maxwell s Demon in a Quantum System Tiago Barbin Batalhão SUTD, Singapore Work done while at UFABC, Santo André, Brazil Singapore, January 11th, 2017
More informationThermodynamics for small devices: From fluctuation relations to stochastic efficiencies. Massimiliano Esposito
Thermodynamics for small devices: From fluctuation relations to stochastic efficiencies Massimiliano Esposito Beijing, August 15, 2016 Introduction Thermodynamics in the 19th century: Thermodynamics in
More informationLight-Matter Correlations in Polariton Condensates
Light-Matter Correlations in Polariton Condensates 1) Alexey Kavokin University of Southampton, UK SPIN, CNR, Rome, Italy Alexandra Sheremet Russian Quantum Center, Moscow, Russia Yuriy Rubo Universidad
More informationA tutorial on non-markovian quantum processes. Kavan Modi Monash University Melbourne, Australia
A tutorial on non-markovian quantum processes Kavan Modi Monash University Melbourne, Australia Quantum Information Science http://monqis.physics.monash.edu Postdoc Felix Pollock PhD Students Francesco
More informationQUANTUM DECOHERENCE IN THE THEORY OF OPEN SYSTEMS
Ó³ Ÿ. 007.. 4, º 38.. 3Ä36 Š Œ œ ƒˆˆ ˆ ˆŠˆ QUANTUM DECOHERENCE IN THE THEORY OF OPEN SYSTEMS A. Isar Department of Theoretical Physics, Institute of Physics and Nuclear Engineering, Bucharest-Magurele,
More informationFrom cavity optomechanics to the Dicke quantum phase transition
From cavity optomechanics to the Dicke quantum phase transition (~k; ~k)! p Rafael Mottl Esslinger Group, ETH Zurich Cavity Optomechanics Conference 2013, Innsbruck Motivation & Overview Engineer optomechanical
More informationUniversal Post-quench Dynamics at a Quantum Critical Point
Universal Post-quench Dynamics at a Quantum Critical Point Peter P. Orth University of Minnesota, Minneapolis, USA Rutgers University, 10 March 2016 References: P. Gagel, P. P. Orth, J. Schmalian Phys.
More informationWigner function description of a qubit-oscillator system
Low Temperature Physics/Fizika Nizkikh Temperatur, 013, v. 39, No. 3, pp. 37 377 James Allen and A.M. Zagoskin Loughborough University, Loughborough, Leics LE11 3TU, UK E-mail: A.Zagoskin@eboro.ac.uk Received
More informationPreface. Preface to the Third Edition. Preface to the Second Edition. Preface to the First Edition. 1 Introduction 1
xi Contents Preface Preface to the Third Edition Preface to the Second Edition Preface to the First Edition v vii viii ix 1 Introduction 1 I GENERAL THEORY OF OPEN QUANTUM SYSTEMS 5 Diverse limited approaches:
More informationExperimental Quantum Computing: A technology overview
Experimental Quantum Computing: A technology overview Dr. Suzanne Gildert Condensed Matter Physics Research (Quantum Devices Group) University of Birmingham, UK 15/02/10 Models of quantum computation Implementations
More informationQuantum decoherence: From the self-induced approach to Schrödinger-cat experiments
Quantum decoherence: From the self-induced approach to Schrödinger-cat experiments Maximilian Schlosshauer Department of Physics University of Washington Seattle, Washington Very short biography Born in
More informationOpen quantum systems
Chapter 4 Open quantum systems 4. Quantum operations Let s go back for a second to the basic postulates of quantum mechanics. Recall that when we first establish the theory, we begin by postulating that
More information1.0 Introduction to Quantum Systems for Information Technology 1.1 Motivation
QSIT09.V01 Page 1 1.0 Introduction to Quantum Systems for Information Technology 1.1 Motivation What is quantum mechanics good for? traditional historical perspective: beginning of 20th century: classical
More informationIntroduction to Modern Quantum Optics
Introduction to Modern Quantum Optics Jin-Sheng Peng Gao-Xiang Li Huazhong Normal University, China Vfe World Scientific» Singapore* * NewJerseyL Jersey* London* Hong Kong IX CONTENTS Preface PART I. Theory
More informationQuantum Reservoir Engineering
Departments of Physics and Applied Physics, Yale University Quantum Reservoir Engineering Towards Quantum Simulators with Superconducting Qubits SMG Claudia De Grandi (Yale University) Siddiqi Group (Berkeley)
More informationCluster mean-field approach to the steady-state phase diagram of dissipative spin systems. Davide Rossini. Scuola Normale Superiore, Pisa (Italy)
Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems Davide Rossini Scuola Normale Superiore, Pisa (Italy) Quantum simulations and many-body physics with light Orthodox
More informationEE 223 Applied Quantum Mechanics 2 Winter 2016
EE 223 Applied Quantum Mechanics 2 Winter 2016 Syllabus and Textbook references Version as of 12/29/15 subject to revisions and changes All the in-class sessions, paper problem sets and assignments, and
More informationGerardo Adesso. Davide Girolami. Alessio Serafini. University of Nottingham. University of Nottingham. University College London
Gerardo Adesso University of Nottingham Davide Girolami University of Nottingham Alessio Serafini University College London arxiv:1203.5116; Phys. Rev. Lett. (in press) A family of useful additive entropies
More informationquantum mechanics is a hugely successful theory... QSIT08.V01 Page 1
1.0 Introduction to Quantum Systems for Information Technology 1.1 Motivation What is quantum mechanics good for? traditional historical perspective: beginning of 20th century: classical physics fails
More informationTHE FIRST JOINT COQUS AND IMPRS-QST VIENNA ON COMPLEX QUANTUM SYSTEMS TU WIEN, ATOMINSTITUT, VIENNA 18TH - 22ND SEPTEMBER 2017
THE FIRST JOINT COQUS AND IMPRS-QST VIENNA ON COMPLEX QUANTUM SYSTEMS TU WIEN, ATOMINSTITUT, VIENNA 18TH - 22ND SEPTEMBER 2017 1 1705-1730 Eli s a W i l l C o Q u S, T U W i e n Quantum optical circulator
More informationA path integral approach to the Langevin equation
A path integral approach to the Langevin equation - Ashok Das Reference: A path integral approach to the Langevin equation, A. Das, S. Panda and J. R. L. Santos, arxiv:1411.0256 (to be published in Int.
More informationQuantum Mechanical Foundations of Causal Entropic Forces
Quantum Mechanical Foundations of Causal Entropic Forces Swapnil Shah North Carolina State University, USA snshah4@ncsu.edu Abstract. The theory of Causal Entropic Forces was introduced to explain the
More informationTowards Quantum Gravity Measurement by Cold Atoms
Towards Quantum Gravity Measurement by Cold Atoms SUPA, RAL, Sonangol, IMechE, IOP Quantum Gravity and Gauge Group University of Aberdeen University of Nottingham Quantum Fields, Gravity & Information
More informationMeasuring entanglement in synthetic quantum systems
Measuring entanglement in synthetic quantum systems ψ?? ψ K. Rajibul Islam Institute for Quantum Computing and Department of Physics and Astronomy University of Waterloo research.iqc.uwaterloo.ca/qiti/
More informationQuantum theory has opened to us the microscopic world of particles, atoms and photons..and has given us the keys of modern technologies
Power and strangeness of the quantum Quantum theory has opened to us the microscopic world of particles, atoms and photons.and has given us the keys of modern technologies This is a theory whose logics
More informationQuantum computation and quantum information
Quantum computation and quantum information Chapter 7 - Physical Realizations - Part 2 First: sign up for the lab! do hand-ins and project! Ch. 7 Physical Realizations Deviate from the book 2 lectures,
More informationSimulating Quantum Simulators. Rosario Fazio
Simulating Quantum Simulators Rosario Fazio Critical Phenomena in Open Many-Body systems Rosario Fazio In collaboration with J. Jin A. Biella D. Rossini J. Keeling Dalian Univ. SNS - Pisa St. Andrews J.
More informationQuantification of Gaussian quantum steering. Gerardo Adesso
Quantification of Gaussian quantum steering Gerardo Adesso Outline Quantum steering Continuous variable systems Gaussian entanglement Gaussian steering Applications Steering timeline EPR paradox (1935)
More informationThermodynamical cost of accuracy and stability of information processing
Thermodynamical cost of accuracy and stability of information processing Robert Alicki Instytut Fizyki Teoretycznej i Astrofizyki Uniwersytet Gdański, Poland e-mail: fizra@univ.gda.pl Fields Institute,
More informationStatistical Mechanics
Franz Schwabl Statistical Mechanics Translated by William Brewer Second Edition With 202 Figures, 26 Tables, and 195 Problems 4u Springer Table of Contents 1. Basic Principles 1 1.1 Introduction 1 1.2
More informationLecture2: Quantum Decoherence and Maxwell Angels L. J. Sham, University of California San Diego
Michigan Quantum Summer School Ann Arbor, June 16-27, 2008. Lecture2: Quantum Decoherence and Maxwell Angels L. J. Sham, University of California San Diego 1. Motivation: Quantum superiority in superposition
More informationShort Course in Quantum Information Lecture 2
Short Course in Quantum Information Lecture Formal Structure of Quantum Mechanics Course Info All materials downloadable @ website http://info.phys.unm.edu/~deutschgroup/deutschclasses.html Syllabus Lecture
More informationQuântica Oscilador Paramétrico
Luz e Átomos como ferramentas para Informação Quântica Oscilador Paramétrico Ótico Inst. de Física Marcelo Martinelli Lab. de Manipulação Coerente de Átomos e Luz Parametric Down Conversion Energy and
More informationEmergence of the classical world from quantum physics: Schrödinger cats, entanglement, and decoherence
Emergence of the classical world from quantum physics: Schrödinger cats, entanglement, and decoherence Luiz Davidovich Instituto de Física Universidade Federal do Rio de Janeiro Outline of the talk! Decoherence
More informationFluctuation theorem in systems in contact with different heath baths: theory and experiments.
Fluctuation theorem in systems in contact with different heath baths: theory and experiments. Alberto Imparato Institut for Fysik og Astronomi Aarhus Universitet Denmark Workshop Advances in Nonequilibrium
More information5.74 Introductory Quantum Mechanics II
MIT OpenCourseWare http://ocw.mit.edu 5.74 Introductory Quantum Mechanics II Spring 009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Andrei Tokmakoff,
More informationFundamentals. Statistical. and. thermal physics. McGRAW-HILL BOOK COMPANY. F. REIF Professor of Physics Universüy of California, Berkeley
Fundamentals of and Statistical thermal physics F. REIF Professor of Physics Universüy of California, Berkeley McGRAW-HILL BOOK COMPANY Auckland Bogota Guatemala Hamburg Lisbon London Madrid Mexico New
More informationEntanglement in Many-Body Fermion Systems
Entanglement in Many-Body Fermion Systems Michelle Storms 1, 2 1 Department of Physics, University of California Davis, CA 95616, USA 2 Department of Physics and Astronomy, Ohio Wesleyan University, Delaware,
More informationMany-Body Localization. Geoffrey Ji
Many-Body Localization Geoffrey Ji Outline Aside: Quantum thermalization; ETH Single-particle (Anderson) localization Many-body localization Some phenomenology (l-bit model) Numerics & Experiments Thermalization
More informationMath Questions for the 2011 PhD Qualifier Exam 1. Evaluate the following definite integral 3" 4 where! ( x) is the Dirac! - function. # " 4 [ ( )] dx x 2! cos x 2. Consider the differential equation dx
More informationList of Comprehensive Exams Topics
List of Comprehensive Exams Topics Mechanics 1. Basic Mechanics Newton s laws and conservation laws, the virial theorem 2. The Lagrangian and Hamiltonian Formalism The Lagrange formalism and the principle
More informationDynamical Collapse in Quantum Theory
Dynamical Collapse in Quantum Theory Lajos Diósi HAS Wigner Research Center for Physics Budapest August 2, 2012 Dynamical Collapse in Quantum Theory August 2, 2012 1 / 28 Outline 1 Statistical Interpretation:
More informationAnderson Localization Looking Forward
Anderson Localization Looking Forward Boris Altshuler Physics Department, Columbia University Collaborations: Also Igor Aleiner Denis Basko, Gora Shlyapnikov, Vincent Michal, Vladimir Kravtsov, Lecture2
More informationINTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition
INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition Kerson Huang CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group an Informa
More informationRef: Bikash Padhi, and SG, Phys. Rev. Lett, 111, (2013) HRI, Allahabad,Cold Atom Workshop, February, 2014
Cavity Optomechanics with synthetic Landau Levels of ultra cold atoms: Sankalpa Ghosh, Physics Department, IIT Delhi Ref: Bikash Padhi, and SG, Phys. Rev. Lett, 111, 043603 (2013)! HRI, Allahabad,Cold
More informationDissipative nuclear dynamics
Dissipative nuclear dynamics Curso de Reacciones Nucleares Programa Inter universitario de Fisica Nuclear Universidad de Santiago de Compostela March 2009 Karl Heinz Schmidt Collective dynamical properties
More informationDEPHASING CHANNELS FOR OVERCOMPLETE BASES
DEPHASING CHANNELS FOR OVERCOMPLETE BASES C. Jess Riedel IBM Research Quantum Lunch LANL 24 July 2014 Pointer states Pointer states are a fundamental concept in decoherence and quantum-classical transition
More informationEntropy of a Two-Level Atom Driven by a Detuned Monochromatic Laser. Field and Damped by a Squeezed Vacuum
Applied Mathematics & Information Sciences 2(1) (28), 21 29 An International Journal c 28 Dixie W Publishing Corporation, U. S. A. Entropy of a Two-Level Atom Driven by a Detuned Monochromatic Laser Field
More informationEntanglement and Correlation of Quantum Fields in an Expanding Universe
Entanglement and Correlation of Quantum Fields in an Expanding Universe Yasusada Nambu (Nagoya University, Japan) International Workshop on Strings, Black Holes and Quantum Information @ Tohoku Univ 2015/9/9
More informationand R (GM) 1/ (r GM) 1/. (6) Dividing (5) by (6), he obtains after considering that β = 1/T, the expression for the Hawking temperature, namely T = 1/
A NOTE ON BLACK HOLE TEMPERATURE AND ENTROPY P. R. SILVA Departamento de Física Instituto de Ciências Exatas Universidade Federal de Minas Gerais C. P. 70 3013-970 Belo Horizonte Minas Gerais BRAZIL e-mail:
More informationQUANTUM TECHNOLOGIES: THE SECOND QUANTUM REVOLUTION* Jonathan P. Dowling
QUANTUM TECHNOLOGIES: THE SECOND QUANTUM REVOLUTION* Jonathan P. Dowling Quantum Science & Technologies Group Hearne Institute for Theoretical Physics Louisiana State University http://quantum.phys.lsu.edu
More informationOnsager theory: overview
Onsager theory: overview Pearu Peterson December 18, 2006 1 Introduction Our aim is to study matter that consists of large number of molecules. A complete mechanical description of such a system is practically
More informationSplitting of a Cooper pair by a pair of Majorana bound states
Chapter 7 Splitting of a Cooper pair by a pair of Majorana bound states 7.1 Introduction Majorana bound states are coherent superpositions of electron and hole excitations of zero energy, trapped in the
More informationNon-Equilibrium Physics with Quantum Gases
Non-Equilibrium Physics with Quantum Gases David Weiss Yang Wang Laura Adams Cheng Tang Lin Xia Aishwarya Kumar Josh Wilson Teng Zhang Tsung-Yao Wu Neel Malvania NSF, ARO, DARPA, Outline Intro: cold atoms
More informationPositive Tensor Network approach for simulating open quantum many-body systems
Positive Tensor Network approach for simulating open quantum many-body systems 19 / 9 / 2016 A. Werner, D. Jaschke, P. Silvi, M. Kliesch, T. Calarco, J. Eisert and S. Montangero PRL 116, 237201 (2016)
More informationQuantum Neural Network
Quantum Neural Network - Optical Neural Networks operating at the Quantum Limit - Preface We describe the basic concepts, operational principles and expected performance of a novel computing machine, quantum
More informationExploring quantum magnetism in a Chromium Bose-Einstein Condensate
CLEO Europe - IQEC Munich May 14th 013 Olivier GORCEIX Exploring quantum magnetism in a Chromium Bose-Einstein Condensate Laboratoire de Physique des Lasers Université Paris 13, SPC Villetaneuse - France
More informationTransmitting and Hiding Quantum Information
2018/12/20 @ 4th KIAS WORKSHOP on Quantum Information and Thermodynamics Transmitting and Hiding Quantum Information Seung-Woo Lee Quantum Universe Center Korea Institute for Advanced Study (KIAS) Contents
More informationComparative analysis of non-equilibrium quantum Landauer bounds
Comparative analysis of non-equilibrium quantum Landauer bounds Steve Campbell in collaboration with: Giacomo Guarnieri, Mauro Paternostro, and Bassano Vacchini To Appear July(ish) 2017 Landauer s Principle
More informationCoherence and optical electron spin rotation in a quantum dot. Sophia Economou NRL. L. J. Sham, UCSD R-B Liu, CUHK Duncan Steel + students, U Michigan
Coherence and optical electron spin rotation in a quantum dot Sophia Economou Collaborators: NRL L. J. Sham, UCSD R-B Liu, CUHK Duncan Steel + students, U Michigan T. L. Reinecke, Naval Research Lab Outline
More informationForum for Electromagnetic Research Methods and Application Technologies (FERMAT)
Forum for Electromagnetic Research Methods and Application Technologies (FERMAT) Entanglement of two-level atoms above graphene Andrei Nemilentsau, Seyyed Ali Hassani, George Hanson Department of Electrical
More informationDISSIPATIVE TRANSPORT APERIODIC SOLIDS KUBO S FORMULA. and. Jean BELLISSARD 1 2. Collaborations:
Vienna February 1st 2005 1 DISSIPATIVE TRANSPORT and KUBO S FORMULA in APERIODIC SOLIDS Jean BELLISSARD 1 2 Georgia Institute of Technology, Atlanta, & Institut Universitaire de France Collaborations:
More informationSpin chain model for correlated quantum channels
Spin chain model for correlated quantum channels Davide Rossini Scuola Internazionale Superiore di Studi Avanzati SISSA Trieste, Italy in collaboration with: Vittorio Giovannetti (Pisa) Simone Montangero
More information31st Jerusalem Winter School in Theoretical Physics: Problem Set 2
31st Jerusalem Winter School in Theoretical Physics: Problem Set Contents Frank Verstraete: Quantum Information and Quantum Matter : 3 : Solution to Problem 9 7 Daniel Harlow: Black Holes and Quantum Information
More informationMinimum Bias Events at ATLAS
Camille Bélanger-Champagne Lehman McGill College University City University of New York Thermodynamics Charged Particle and Correlations Statistical Mechanics in Minimum Bias Events at ATLAS Statistical
More informationThermodynamics and Phase Coexistence in Nonequilibrium Steady States
Thermodynamics and Phase Coexistence in Nonequilibrium Steady States Ronald Dickman Universidade Federal de Minas Gerais R.D. & R. Motai, Phys Rev E 89, 032134 (2014) R.D., Phys Rev E 90, 062123 (2014)
More informationNon-Markovian Quantum Dynamics of Open Systems
Non-Markovian Quantum Dynamics of Open Systems Heinz-Peter Breuer Physikalisches Institut, Albert-Ludwigs-Universität Freiburg 640. WE-Heraeus-Seminar Non-Markovianity and Strong Coupling Effects in Thermodynamics
More informationQuantum Memory with Atomic Ensembles
Lecture Note 5 Quantum Memory with Atomic Ensembles 04.06.2008 Difficulties in Long-distance Quantum Communication Problems leads Solutions Absorption (exponentially) Decoherence Photon loss Degrading
More informationStochastic equations for thermodynamics
J. Chem. Soc., Faraday Trans. 93 (1997) 1751-1753 [arxiv 1503.09171] Stochastic equations for thermodynamics Roumen Tsekov Department of Physical Chemistry, University of Sofia, 1164 Sofia, ulgaria The
More informationNo Fine theorem for macroscopic realism
No Fine theorem for macroscopic realism Johannes Kofler Max Planck Institute of Quantum Optics (MPQ) Garching/Munich, Germany 2nd International Conference on Quantum Foundations Patna, India 17 Oct. 2016
More informationPairing properties, pseudogap phase and dynamics of vortices in a unitary Fermi gas
Pairing properties, pseudogap phase and dynamics of vortices in a unitary Fermi gas Piotr Magierski (Warsaw University of Technology/ University of Washington, Seattle) Collaborators: Aurel Bulgac (Seattle)
More informationAtom assisted cavity cooling of a micromechanical oscillator in the unresolved sideband regime
Atom assisted cavity cooling of a micromechanical oscillator in the unresolved sideband regime Bijita Sarma and Amarendra K Sarma Department of Physics, Indian Institute of Technology Guwahati, Guwahati-781039,
More informationTowards quantum metrology with N00N states enabled by ensemble-cavity interaction. Massachusetts Institute of Technology
Towards quantum metrology with N00N states enabled by ensemble-cavity interaction Hao Zhang Monika Schleier-Smith Robert McConnell Jiazhong Hu Vladan Vuletic Massachusetts Institute of Technology MIT-Harvard
More informationLecture 21: Lasers, Schrödinger s Cat, Atoms, Molecules, Solids, etc. Review and Examples. Lecture 21, p 1
Lecture 21: Lasers, Schrödinger s Cat, Atoms, Molecules, Solids, etc. Review and Examples Lecture 21, p 1 Act 1 The Pauli exclusion principle applies to all fermions in all situations (not just to electrons
More informationS.K. Saikin May 22, Lecture 13
S.K. Saikin May, 007 13 Decoherence I Lecture 13 A physical qubit is never isolated from its environment completely. As a trivial example, as in the case of a solid state qubit implementation, the physical
More informationMASTER OF SCIENCE IN PHYSICS
MASTER OF SCIENCE IN PHYSICS The Master of Science in Physics program aims to develop competent manpower to fill the demands of industry and academe. At the end of the program, the students should have
More informationPhysics & Astronomy UBC Vancouver Pacific Institute for Theoretical Physics
PCE STAMP DECOHERENCE in REAL SYSTEMS: MECHANISMS of DECOHERENCE (7 PINES, May 08, 2010) Physics & Astronomy UBC Vancouver Pacific Institute for Theoretical Physics SOME HISTORICAL PERSPECTIVE 1: OLD-STYLE
More information4.5 Open quantum harmonic oscillator
are still in the interaction picture, so we may want to go bac to the Shcrödinger picture. For practical purposes it is also convenient to open the commutators and rearrange this as follows: d S dt = ds
More informationQuantum Optics. Manipulation of «simple» quantum systems
Quantum Optics Manipulation of «simple» quantum systems Antoine Browaeys Institut d Optique, Palaiseau, France Quantum optics = interaction atom + quantum field e g ~ 1960: R. Glauber (P. Nobel. 2005),
More information