John Goold

8/12/2019 John Goold

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Directions in quantum thermodynamicsof non equilibrium systems

NMR QIPRio 2013

ohn !oold "I#$P% $rieste&


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'(ailable ener)y is the main ob*ect at sta+e

in the stru))le for e,istence and thee(olution of the -orld.

/ud-i) oltmann
http://strangewondrous.net/browse/author/b/boltzmann+ludwighttp://strangewondrous.net/browse/author/b/boltzmann+ludwig


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Far from equilibrium statisticalmechanics

Explorations in QuantumSystems


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NMR?

ee tal+ of Roberto erra on riday 4...............


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Introduction

asic notions and introduction to fluctuation relations

5,6lorin) quantum thermodynamics notion of quantum -or+

'n e,6erimental 6ro6osal

'66lications "Mainly in manybody 6hysics&


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Thermodynamics !

#onsider the familiar )as 7 6iston setu6

No ree /unch

$his inequality is certainly notmandated by the underlyin) microsco6ic dynamics


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Thermodynamics !

's -e a66ly thermodynamics to smallerand smallersystems the second la-becomes 8blurred8 and statistical fluctuations about the a(era)e becomeim6ortant9

No ree /unch on '(era)e


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Clausius inequality - no free lunch on average

Out of equilibrium Work becomes stochastic

#. aryns+i% 'nnu. Re(. #ondens. Matter Phys. 2% 32: "2011&


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Fluctuation Relations

Remar+able relations e,ist bet-een the fluctuationsin the -or+ done in a non;equilibriumtransformation and the equilibrium6ro6erties of the system.

$asa+i;#roo+s Relation

aryns+i equality

#am6isi et al% Re(. Mod. Phys.


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The "nd #a$

aryns+i equality

ensen8s inequality

#laussius inequality

7

>

5ncodes the 2nd la-

No ree /unch9 "?n a(era)e&


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%hat do fluctuation relations tell you??

$a+e some @amiltonian% classical or quantum and dri(e bet-een

I can e,tract information on equillibrium 6rocess inde6endentof the 6ath I ta+e9


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Experiments &'lassical()

5,6erimental (alidation of free;ener)y landsca6e reconstructionfrom non;equillibrium sin)le force s6ectrosco6y measurements!u6ta et al% Nature Physics =% A31% une "2011&

#roo+s relation

!. #roo+s% Phys. Re(. /ett. ::% 100A02 "200=&


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Experiments

Berification of the #roo+s luctuation theorem and reco(ery of RN' foldin) free ener)ies#olin et al% Nature% C3=%231 une "200&

5qual -hen


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$urnin) to-ards quantum systems

Q t % * d + t d fi iti d - i t ti - t f ti


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Quantum %or* and +eat , definitions under -quasi.static- transformation

heat -or+

Quantum Systems / thermodynamics in finite time?


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Quantum Systems / thermodynamics in finite time?

5ner)y

$ime

Measure 5En-ith 6robabiliy6En

Measure 58Em-ith 6robaility6"mFn&

1. Pre6are G2. Measure G3. 5(ol(e GC. Measure . uild statistics1. Pre6are G2. Measure G3. 5(ol(e GC. Measure . uild statistics

0 b bilit di t ib ti f i t l h


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0robability distribution of internal ener1y chan1es

Probability of chan)in) internal ener)y in a sin)le run

1. Pre6are G2. Measure G3. 5(ol(e GC. Measure . uild statistics1. Pre6are G2. Measure G3. 5(ol(e GC. Measure . uild statistics

2eri ation of fl ct ation relation


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2eri3ation of fluctuation relation

Its not o6erational ohn9'nd thats my 6oint

or closed systems

%or* 2istribution for closed quantum systems &4nitary)


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%or* 2istribution for closed quantum systems &4nitary)

Hor+ Distribution

5ner)y

$ime

@ei)hts of delta 6ea+s

%or* 2istribution


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%or* 2istribution

Hor+ Distribution

@ei)hts of delta 6ea+s

Phys. Re(. 5. =% 00102% "200=&$al+ner% /ut% @an))i


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#roo+s relation

Emer1ent Irre3ersibility


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Emer1ent Irre3ersibility

econd la- by Jlien8s inequality

Relati3e Entropybet-een for-ard and bac+-ard distributions

'roo*s Relation

Entropy Production and the arrow of time

Parrondo et al% NP "200:&.

Irre(ersible entro6y chan)e

Irre3ersibility/ Emer1ence of a time arro$


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y 1

. Deffner and 5. /ut% Phys. Re(. /ett. 10% 1=0C02 "2010&

!eneralised #laussius Inequality

Kse mathematical6ro6erties of relati(eentro6y to loo+ at bounds onentro6y 6roduction


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Hhat about e,6erimentsL


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%or* 2istribution


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Hor+ Distribution

5ner)y

$ime

$ry to measure directly.........

%or* 2istribution


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Hor+ Distribution

5ner)y

$ime

$ry to measure directly.........


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Different '66roach

The papers


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0robe the characteristic function of $or*


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Probe system -ith ancilla

Hould li+e to mani6ulate qubit so -or+ is done on the system o(er some time inter(al

Simple Ramsey Interferometry $ith ancilla


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"2& 't t>0% a @adamard o6eration isa66lied to the qubit

"3& 6in de6endent cou6lin)s areInde6endently (aried accordin)

to a 6re;defined 6rotocol that)enerates unitary e(olution

"1& or tO0 the qubit and systemare thermalised in the 6roduct state

"C& ' second @adamard !ate is a66lied

#onditional unitarys are )i(enby

Reconstruct the characteristic function usin1 Ramsey Si1nal


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'ncilla is measured

A judicious choice of the couplings establishes a direct relationship betweencharacteristic function corresponding to the desired quench protocal on thesystem

Implementation usin1 a sin1le trapped ion


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Kse )round state eeman suble(els

Motional tate as system to 6robe

Kse far detuned lasers to createa s6in de6endentdi6ole 6otential

ollo-in) rotatin) -a(e a66ro,imation and usualadiabatic elimination of the far detuned e,cited states!et interaction hamiltonian

#ontrol Rabi frequencys by (aryin) laser intensity for each 6olarisatoin


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Hor+ in /amb;Dic+e re)ime the e,tent of the ion8s motion is smallcom6ared to the s6atial (ariation of the o6tical di6ole 6otential.

y choosin) the a66ro6riate relati(e 6hase% the o6tical di6ole 6otential causes

the oscillator to be dis6laced

!reat do -or+ -ith time de6endent dis6lacment te,t boo+ e,am6le

Implementation usin1 a sin1le trapped ion


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ourier $ransform

"a& "b&C0#a7

'roo*s Relation


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#an e,tract initial tem6eraturefrom cur(e fit 9

'ncilla thermometry fromfluctuations L

Dis6laced oscillator

!oold% /o !ullo et al. in)le qubit thermometry of a many body system "In 6re6eration&


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'66lications for quench 6roblems

in many body 6hysics

Moti3ation


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Collapse and revival of the matter wave field of a BoseEinstein condensate

Greiner et al. Nature 419, 51-54 (2002).

Kltra;cold atoms

/on) coherence times% controllable

' 6lay)round for quantum dynamics far from equilibrium

Moti3ation


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A quantum Newton's cradle

Kinoshita et al. Nature 440, 900 (2006).

Moti3ation


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Lightconeli!e spreading of correlations in a quantum man"#od" s"stem

Cheneauet al. Nature 481, 484 (2012).

Irre3ersibility/ Emer1ence of a time arro$


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Interpretation for sudden quench


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Mani6ulate first moment

Irre(ersible entro6y chan)eor small quench

/atency in 6ure state thermodynamics of quantum 6hase transition ari(130=.CC

5. Mascarenhas% @. ra)anca% R. Dorner% M. ranca antos% B. Bedral%J. Modi% . !oold

Sudden quench of the trans3erse field in the quantum Isin1 model
http://arxiv.org/find/quant-ph/1/au:+Mascarenhas_E/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Braganca_H/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Dorner_R/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Santos_M/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Vedral_V/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Vedral_V/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Modi_K/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Goold_J/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Goold_J/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Modi_K/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Vedral_V/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Santos_M/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Dorner_R/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Braganca_H/0/1/0/all/0/1http://arxiv.org/find/quant-ph/1/au:+Mascarenhas_E/0/1/0/all/0/1


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>> 1c = 1


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Emergent Thermodynamics in a quenched manybody systemR. Dorner, J. Goold, M. Paternostro, C. Cormick and V. VedralPhys. Rev. Lett. 109, 1001 !"01"#


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%hat is a Fermi 5as ? The non.interactin1 case at least


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Non;interactin) case build the many6article -a(efunction from the sin)le 6article ei)enstates ofthe confinin) )eometry

'"-&

5

6nderson-s 7rtho1onality 'atastrophe


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6ndersons 7rtho1onality 'atastrophe


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#onsider the o(erla6 bet-een the un6erturbed and 6erturbed states

tates become ortho)onal as a function of N and the scatterin) interaction "characterisedby a 6hase shift&

6nderson-s 7rtho1onality 'atastrophe , time dependence


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$he dynamical theory of the ?# -as de(elo6ed by Noieres and De Dominicis -hosubsequently calculated the transient res6onse of a ermi sea after the s-itchin) on ofa core;hole in a metal (ia ;ray absorbtion 6rocess.

Recall definition of -or+ characteristic function999999999999999999

6ndersons 7rtho1onality 'atastrophe , 2ynamical Theory


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Hhile 'nderson8s ori)inal -or+ in(ol(ed stationary states% the creation of a 6erturbedmany;body state is% in )eneral% a time;de6endent 6rocess.


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6iS2

5quillibrium branch

Perturbed branch

?ff dia)onals of the reduced density matri, e,actly de6end on o(erla6

5,actly equi(alent to the calculation for ray absorbtion in a metal999

6pplication in En1ine 2esi1n


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More Bang for your buck:Towards super-adiabatic quantum engines

'dolfo Del #am6o% ohn !oold and Mauro Paternostroar,i(.or)1333223 "2013&

Idea in a nutshell

inite time stochastic en)ine

5fficency Po-er

Kse su6er adiabatic 6rotocals on adiabats in order to su6ress friction -hile notcom6rimisin) efficency

'onclusions and further directions


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Quantum fluctuation theorems e,ist and are a consequence of second la-

tatistics of -or+ can be e,tracted (ia sin)le qubit 6robe under realistic conditions

'66lications in $hermodynamics of quenched manybody systems and quantum5n)ine Desi)n "inite time&

?6en systems% heat% correlations% thermodynamics of informaiton 6rocessin) "-ithfinite time&

!o raibh mile maith a)aibh9


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"$han+ you all9&

!o raibh mile maith a)aibh9

'old'old atomic 1ases as en3ironments


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Mesoscopic Molecular Ions in ose-!insteinCon"ensates#$ C%t&' ($ )harchenko' an" M$ *$ +ukin

,hys$ #e$ +ett$ ./' 0/001 230034

5 trappe" sin6le ion insi"e a ose !insteinCon"ensateC$ 7ipkes' 8$ ,al9er' C$ 8ias an" M$ )ohl:ature$ ;;' .. 230104

Ion in"uce" "ensity bubble in a stron6ly correlate" one"imensional 6as

$ ool"' ?$ *oerk' 7' I"9iasek' @$ Calarco' @h$ usch,hys$ #e$ 5$2#4 ./' 0;101 230104

'old'old atomic 1ases as en3iroments in open quantum systems theory


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Polaron Problem

C.H. Wu, A. Sommer, and A.W. Zwierlien

PRL. 464, 102 230402 (2011)

John Goold

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