Quantum thermodynamics: 1 Mauro Paternostro Queens University - - PowerPoint PPT Presentation

Mauro Paternostro Queen’s University Belfast

Quantum thermodynamics: 1

Advanced School on Quantum Science and Quantum T echnologies (ICTP , T rieste, 4 September 2017)

Mauro Paternostro Queen’s University Belfast

Non-equilibrium thermodynamics

• f quantum processes: 1

Advanced School on Quantum Science and Quantum T echnologies (ICTP , T rieste, 4 September 2017)

• r an invitation to study stochastic

thermodynamics of quantum processes

Belfast

Queen’s University Belfast

John Stuart Bell

Joseph Larmor David Bates, FRS Harrie Massey

4 November: John Bell day

On the shoulders

• f Belfast’s giants

On the shoulders

• f Belfast’s giants

Lord Kelvin Belfast, Botanic Gardens

Born in Belfast in 1824

Thermodynamics…

Framework for non-equilibrium quantum processes Thermodynamics-inspired arena for the study/use of quantum resources

…and (one of) its evolution(s)

Re-definition of work, heat, entropy… in non-equilibrium quantum contexts

Work Hot Cold Heat Heat

Q

My take of it

Fundamental viewpoint

Thermodynamics is a theory

• f inherently complex systems

T echnological viewpoint

Using quantumness to optimise machine performance

Content & structure

Landauer principle & quantum (open-system)dynamics

Quantum correlations, coherences and thermodynamics

Non-equilibrium definition of thermodynamic work: fluctuation theorems

n

Irreversibility & entropy production in closed q-systems

Work and quantum

T alkner, Lutz, and Haenggi, Phys. Rev. E 75, 050102 (2007)

Setting the context

P . T alkner, E. Lutz, and P . Haenggi, Phys. Rev. E 75, 050102 (2007)

n

n,m

p0

n

p0

npτ m|nδ

PF (W) = X

n,m

p0

npτ m|nδ (W − (E0 m − En))

Work Distribution

all instan ith ˆ Hi characte

m

[

i H f]

and ˆ H f simplifie

In quantum contexts: work is not an observable

Fluctuation theorems

PF (W) = X

n,m

p0

npτ m|nδ (W − (E0 m − En))

Work Distribution

Characteristic function of Work Distribution

χF (u) = Z dWeıuW PF (W)

= Tr h U †(τ, 0)eıuH(λτ )U(τ, 0)e−ıuH(λ0)ρG(λ0) i

ρG(λ0) = e−βH(λ0) Z(λ0)

χF (u) =

Fluctuation theorems

PF (W) = X

n,m

p0

npτ m|nδ (W − (E0 m − En))

Work Distribution

Characteristic function of Work Distribution

χF (u) = Z dWeıuW PF (W)

• H. T

asaki, cond-mat/0009244 (2000)

• G. E. Crooks, PRE 60, 2721 (1999)

T asaki-Crooks relation

he−βW i = e−β∆F sky equality

free-energy change

Jarzynski, PRL 78 2690 (1997)

Jarzynski

Classical fluctuation relations

• J. Liphardt, S. Dumont, S. B. Smith, I. Jr Tinoco, and C. Bustamante,

Science, 296, 1832 (2002)

• D. Collin, F

. Ritort, C. Jarzynski, S. B. Smith, I. Tinoco Jr, and C. Bustamante, Nature 437, 231 (2005)

First proposal (as far as I know)

Ingenious filtering scheme for energy measurements

Other proposals and implementations

a c d Vg Vg

CL CL Cj Cj CR CR

ne ne

~

b SET

“The major obstacle for the experimental verification of the work fluctuation relation is posed by the necessity of performing quantum projective measurements of energy”

What’s wrong with it

S A

h h

Measuring work

• L. Mazzola, G. De Chiara, and MP

, Phys. Rev. Lett. 110, 230602 (2013)

• R. Dorner, et al., Phys. Rev.Lett. 110, 230601 (2013)
• L. Mazzola, G. De Chiara, and MP

, Int. J. Quant. Inf. (2014)

ˆ G(u, τ) = ˆ Uτe−i ˆ

Hiu ⊗ |0⟩⟨0|A + e−i ˆ Hf u ˆ

Uτ ⊗ |1⟩⟨1|A

The experiment

ˆ H F(t) = 2π~ν (t) ✓ ˆ σC

x sin πt

2τ + ˆ σC

y cos πt

2τ ◆ ,

Experimental Reconstruction of Work Distribution and Study of Fluctuation Relations in a Closed Quantum System

Tiago B. Batalhão,1 Alexandre M. Souza,2 Laura Mazzola,3 Ruben Auccaise,2 Roberto S. Sarthour,2 Ivan S. Oliveira,2 John Goold,4 Gabriele De Chiara,3 Mauro Paternostro,3,5 and Roberto M. Serra1

1Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, R. Santa Adélia 166, 09210-170 Santo André,

PRL 113, 140601 (2014) P H Y S I C A L R E V I E W L E T T E R S

week ending 3 OCTOBER 2014

The experiment

ˆ G1 ⌘ |0i h0|H ⌦ eiu ˆ

Hα(0) + |1i h1|H ⌦ ˆ

1

1

C

ˆ G2 ⌘ |0i h0|H ⌦ ˆ

1

1

C + |1i h1|H ⌦ eiu ˆ Hα(τ).

produce rotations by the displayed interaction ˆ HJ = 2πJ ˆ σH

z ˆ

σC

z

time) are represented

to ρ0

HC = |0i h0|H ⌦

equilibrium state of

eβ ˆ

Hα(0)/Z0

T . B. Batalhao, et al. Phys. Rev. Lett. 113, 140601 (2014)

The experiment

Backward process

T . B. Batalhao, et al. Phys. Rev. Lett. 113, 140601 (2014)

The experiment

T asaki-Crooks relation

T . B. Batalhao, et al. Phys. Rev. Lett. 113, 140601 (2014)

The experiment

Jarzynski equality

T . B. Batalhao, et al. Phys. Rev. Lett. 113, 140601 (2014)

c d

Adiabatic process Instantaneous process

2P1/2 2S1/2 171Yb+

F = 0 F = 1 F = 0 F = 1 Raman2 Raman1

b

Detection ⏐↑〉 ⏐↓〉 Raman2 Vd.c.

a

VRF VRF GND GND Raman1 B X Y Z

L + X − and L − X +

ω ω ν ν ∆ ω ω

L + HF

ω ω

L

ω

HF

ω

X

ω

+

σ

−

σ Vd.c. ∆k

Other experimental studies

Experimental test of the quantum Jarzynski equality with a trapped-ion system

Shuoming An1, Jing-Ning Zhang1, Mark Um1, Dingshun Lv1, Yao Lu1, Junhua Zhang1, Zhang-Qi Yin1,

• H. T. Quan2,3* and Kihwan Kim1*
• S. An, et al., Nature Phys. 11, 193 (2015)

Other experimental studies

Experimental study of quantum thermodynamics using optical vortices

• R. Medeiros de Ara´

ujo,1 T. H¨ affner,1 R. Bernardi,1 D. S. Tasca,2 M. P. J. Lavery,3 M. J. Padgett,4 A. Kanaan,1 L. C. C´ eleri,5, ∗ and P. H. Souto Ribeiro1, †

1Departamento de F´

ısica, Universidade Federal de Santa Catarina, Florian´

• polis, SC, Brazil
• R. Medeiros de Araujo, et al. arXiv: 1705.02990

Entangling Operation Entangling Operation Driving

Free Fall Free Fall

Imaging

(Motion) (Electronic state)

(a) (b)

Probability

(c) g

Atom chip

Imaging Driving

• RF -

Entangling

• ∂B/∂z -

Initial state preparation

• RF -

z

Entangling

• ∂B/∂z -

Other experimental studies

Using a quantum work meter to test non-equilibrium fluctuation theorems

Federico Cerisola,1, 2 Yair Margalit,3 Shimon Machluf,4 Augusto J. Roncaglia,1, 2 Juan Pablo Paz,1, 2 and Ron Folman3

1

F . Cerisola et al., arXiv:1706.07866

The Belfast crew