Performance of shortcut-to-adiabaticity quantum engines Obinna Abah - - PowerPoint PPT Presentation

Performance of shortcut-to-adiabaticity quantum engines

Obinna Abah

Centre for Theoretical Atomic, Molecular and Optical Physics, Queen’s University Belfast, United Kingdom

Workshop on Quantum Science and Quantum Technologies ICTP, Trieste 2017

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 1 / 21

News..

Sales of inefficient vacuum cleaners banned By Euronews · last updated: 01/09/2017 Powerful vacuum cleaners are to be banned from today after the European Union introduced new rules which aim to improve energy efficiency across the continent.

'Widespread misconception’

The European Environment Bureau (EEB) said: "Power doesn't always equal performance, though the misconception has become widespread.” "Some efficient models maintained high standards of dust pick-up while using significantly less energy - due to design innovation." From BBC News 01/09/2017 Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 2 / 21

Outline

1

Motivation Introduction Downscaling engines

2

Four-stroke Otto engine

3

Shortcut-to-adiabaticity engine Fast and efficient engines Generic bounds on quantum machines

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 3 / 21

Introduction

Miniaturization: is about building smaller devices

Drexler 1981

• fundamental limit = atomic structure of matter

Transistor: 1947 Today

Introduction

Mobile phone: 1973/1983 Today

• weight 1.1kg, 30min talk time, 10h charge time, price 4000$

Introduction

”There is plenty of room at the bottom”:

Feynman 1959

”Consider any machine – for example, an automobile – and ask about the problems of making an infinitesimal machine like it” Two basic strategies: Follow engineers Follow nature

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 6 / 21

Macroscopic heat engine

→ convert thermal energy into mechanical work = motion Carnot efficiency: η = Work produced Heat absorbed ≤ 1−βh βc = 1−Tc Th (James Watt 1783: η ∼ 5 − 7 % ) → maximum efficiency Today’s gasoline engines: η ∼ 25 − 30 %

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 7 / 21

Downscaling of heat engines

Size

Car engine m mm µm nm Mini engine Colloidal engine Piezoresistive engine Nano heat engine (Classical or quantum)

Blickle-Bechinger, Nature Phys. (2011) Steeneken et al., Nat. Phys. 7 (2011)

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 8 / 21

Single atom heat engine

Rossnagel et al., Science 352, 325 (2016)

Reservoir engineering:

• Cold reservoir: laser (Doppler) cooling (always on)
• Hot reservoir: electrode noise (switched on/off)

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 9 / 21

Classical four-stroke heat engine

A B D C B D C A

( )

1

( )

4

( )

3

( )

2

Work

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 10 / 21

Quantum Otto heat engine

(2) Hot isochore Heat added

D B

(3) Isentropic expansion Work done

3

W

(4) Cold isochore Heat removed

A C

(1) Isentropic compression Work done

1

W

2

Q

4

Q

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 11 / 21

Quantum Otto heat engine: theory

A D B C

1 1 1 A

coth 2 2 H ω β ω =

     

ℏ ℏ

1 2 2 D

2 coth

2 2 H

Q

ω β ω

∗

=

     

ℏ ℏ

2 2 2 C

coth 2 2 H ω β ω =

     

ℏ ℏ

2 1 1 B

1 coth

2 2 H

Q

ω β ω

∗

=

     

ℏ ℏ

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 12 / 21

Quantum Otto heat engine

Abah et al, PRL 112, 030602 (2012)

A D B C

1 1 1 A

coth 2 2 H w b w =

æ ö ç ÷ è ø

h h

1 2 2 D

2 coth

2 2 H

Q

w b w

*

=

æ ö ç ÷ è ø

h h

2 2 2 C

coth 2 2 H w b w =

æ ö ç ÷ è ø

h h

2 1 1 B

1 coth

2 2 H

Q

w b w

*

=

æ ö ç ÷ è ø

h h

Question How can we speed up the heat engine? Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 13 / 21

National waiters day

gadgets – shoes, tray, ...

• ptimal protocol

Scientific Report 4 : 6208 (2014)

Waiters race, fast service is a priority!

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 14 / 21

Shortcut-to-adiabaticity (STA)

... inducing a ”fast motion video of the adiabatic dynamics.” Effective Hamiltonian: Heff(t) = H0(t) + Hi

STA(t)

Hi

STA(t) - STA driving Hamiltonian and i = (1, 3) - compression/expansion steps

fast and reduces irreversible losses ω(0) = ωi, ˙ ω(0) = 0, ¨ ω(0) = 0, ω(τ) = ωf , ˙ ω(τ) = 0, ¨ ω(τ) = 0,

Demirplak and Rice, JPC A 107, 9937 (2003) Berry, JPA 42, 365303 (2009) Chen et al, PRL 109, 100403 (2010) del Campo, PRL 111, 100502 (2013)

For harmonic oscillator: LCD technique HSTA = m 2

• Ω2

t − ω2 t

• x2

= m 2

• −3 ˙

ω2

t

4ω2

t

+ ¨ ωt 2ωt

• x2

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 15 / 21

Energetic cost of the shortcut driving

Elementary power analysis Pinst = 2 + 2 cos ωt

Pinst Pavg 2 4 6 8 10 12 1 2 3 4 Time Power

Pavg = (1/T) T

0 Pinstdt

Abah and Lutz, EPL 118, 40005 (2017)

5 10 15 20 2 4 6 8 10 Time τ Energetic cost

Cost of the driving:

• Hi

STA

• τ = (1/τ)

τ dt

• Hi

SA(t)

• Nonadiabatic work (friction):

WiNA = Wi − WiAD

• the actual and the adiabatic work

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 16 / 21

Performance of STA quantum engines

Efficiency: ηSTA = energy output energy input = −(W1STA + W3STA) Q2 +

• H1

STA

• τ +
• H3

STA

• τ

Power: PSTA = energy output Cycle time = −W1STA + W3STA τcycle .

NA STA QSL 5 10 15 20 25 0.50 0.55 0.60 0.65 0.70 Time τ Efficiency 16 20 24 0.67 0.68 0.67 STA NA QSL 5 10 15 20 25 0.0 0.5 1.0 1.5 2.0 Time, τ Power

Generic bounds: quantum speed limit (QSL)

Quantum: limits the speed of evolution of a system

Anandan and Aharonov, PRL (1990)

QSL time: τQSL = L(ρi,ρf )

HSTAτ ≤ τ

L(ρi , ρf ) - the Bures angle between density operators

Efficiency: ηSTA ≤ ηQSL

STA = − W1AD+W3AD Q2+(L1+L3)/τ

Power: PSTA ≤ PQSL

STA = − W1AD+W3AD τ 1

QSL+τ 3 QSL Abah and Lutz, EPL 118, 40005 (2017)

NA STA QSL 5 10 15 20 25 0.50 0.55 0.60 0.65 0.70 Time τ Efficiency 16 20 24 0.67 0.68 0.67 STA NA QSL 5 10 15 20 25 0.0 0.5 1.0 1.5 2.0 Time, τ Power

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 18 / 21

Fast and efficient quantum engines

Question: Is it true for every shortcut-to-adiabaticity protocol?

LCD CD IE 0.0 0.2 0.4 0.6 0.8 1.0 1.0 1.5 2.0 2.5 3.0 3.5 t/τ Q*

Abah and Lutz, arXiv. 1707.09963 (2017)

Q∗ - Adiabaticity parameter

LCD - local counterdiabatic driving CD - counterdiabatic driving IE - inverse engineering NA - nonadiabatic driving

NA LCD CD IE 5 10 15 20 0.50 0.55 0.60 0.65 0.70 Time τ Efficiency 16 20 24 0.67 0.68 LCD CD IE NA 0.50 0.55 0.60 0.65 0.70 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Efficiency Power

simultaneous increase of efficiency and power for fast cycles

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 19 / 21

Take-Home message

STA engine are energy efficient machines

• utperform their convention counterpart

Quantum speed limit impose bounds to performance

• fundamental limit for quantum machines
• tighter than the second law of thermodynamics

Power doesn’t always equal performance

• verall efficiency is important quantity

Obinna Abah (QUB) Energy efficient nanoscale machines September, 2017 20 / 21

References

⋆ Energy efficient quantum machines

• O. Abah and E. Lutz

EPL (Europhys. Lett.) 118, 40005 (2017)

⋆ Performance of shortcut-to-adiabaticity quantum engines

• O. Abah and E. Lutz

arxiv: 1707.09963 (2017)

⋆ Shortcut-to-adiabaticity quantum refrigerator

• O. Abah, M. Paternostro, and E. Lutz

(to appear soon)

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