On the Thermodynamic Costs of Pure Dephasing in Quantum Heat Engines
Institute of Theoretical�Physics Center for Quantum�BioSciences Ulm University
Martin B Plenio
Talk based on: Weber, Huelga, Plenio, ArXiv:2312.05375
Thermodynamics of Dephasing Assisted Heat Engines
Heat Engines
Quasistatic Operation versus the Real World
© actuateminds
Textbook heat engines
Very close to equilibrium which requires
quasistatic operation, i.e. vanishing power.
Carnot efficiency
Real world heat engines are different.
Lots of imperfections but also, we require them�to operate at finite power.
Thermodynamics of Dephasing Assisted Heat Engines
Sources of Inefficiencies
The Curzon-Ahlborn Bound for Carnot Cycle
In typical materials the heat flow is proportional to the temperature difference
Curzon, Ahlborn, Am. J. Phys. 1975�Novikov, J. Nuc. En. 1954; Chambadal 1957
Assuming adiabatic steps have duration proportional to sum of thermalization steps yields that at maximum power
the efficiency is
Thermodynamics of Dephasing Assisted Heat Engines
Quantum Heat Engines
The Otto-cycle
Adiabatic Compression
Adiabatic Expansion
Thermalisation
Thermalisation
Thermodynamics of Dephasing Assisted Heat Engines
Quantum Heat Engines
Definitions of Basic Quantitites
Following Alicki we chose to define work as
and heat as
Alicki. Physica A 1979
Thermodynamics of Dephasing Assisted Heat Engines
Sources of Inefficiencies I
Decoupling Work
Work medium is periodically coupled and decoupled from the
thermal baths.
Decoupling comes at work cost
This suggests that cost is proportional to engine-bath coupling strength & to system bath correlation
Is this cost unavoidable?
Thermodynamics of Dephasing Assisted Heat Engines
The Thermodynamic Cost of Dephasing in a Heat Engine
Full System-Bath Simulation
Prior, Chin, Huelga, Plenio, PRL 2010;
Chin, Rivas, Huelga, Plenio, J. Math. Phys. 2010;
Tamascelli, Smirne, Huelga, Plenio, PRL 2018
Tamascelli, Smirne, Lim, Huelga, Plenio, PRL 2019
Thermodynamics of Dephasing Assisted Heat Engines
The Thermodynamic Cost of Dephasing in a Heat Engine
Asymptotics of the Chain Mapping
Prior, Chin, Huelga, Plenio, PRL 2010;
Chin, Rivas, Huelga, Plenio, J. Math. Phys. 2010;
Tamascelli, Smirne, Huelga, Plenio, PRL 2018
Tamascelli, Smirne, Lim, Huelga, Plenio, PRL 2019
energies
coupling
Thermodynamics of Dephasing Assisted Heat Engines
The Thermodynamic Cost of Dephasing in a Heat Engine
Asymptotics of the Chain Mapping
Prior, Chin, Huelga, Plenio, PRL 2010;
Chin, Rivas, Huelga, Plenio, J. Math. Phys. 2010;
Tamascelli, Smirne, Huelga, Plenio, PRL 2018
Tamascelli, Smirne, Lim, Huelga, Plenio, PRL 2019
:
General proof follows from theory of orthogonal polynomials:
energies
coupling
Thermodynamics of Dephasing Assisted Heat Engines
Sources of Inefficiencies
Decoupling Work Can Be Made to Vanish
Consider harmonic oscillator coupled to a linear chain of harmonic oscillators in RWA
System thermalizes exponentially fast in time
decays exponentially in time
Perturbation travels away from system
Thermodynamics of Dephasing Assisted Heat Engines
Sources of Inefficiencies II
Quantum Friction
Expansion and compression steps change eigenstates
Finite rate operation, leads to coherences and then to �state transitions.
Introduce strong dephasing in the instantaneous �eigenbasis to suppress build up of coherences.
Simplest treatment uses time dependent Lindblad �operators (Feldmann & Kosloff, 2006)
Kosloff & Feldmann, PRE 2002
Feldmann & Kosloff, PRE 2006
Taken from Feldmann & Kosloff, PRE 2006
Question: Is such dephasing associated with a thermodynamical cost?
Thermodynamics of Dephasing Assisted Heat Engines
The Thermodynamic Cost of Dephasing in a Heat Engine
A Simplified Environment Model
Thermodynamics of Dephasing Assisted Heat Engines
The Thermodynamic Cost of Dephasing in a Heat Engine
A Simplified Environment Model
Strict equivalence proven in �Tamascelli Smirne, Huelga, Plenio PRL 2018
Thermodynamics of Dephasing Assisted Heat Engines
The Thermodynamic Cost of Dephasing in a Heat Engine
A Simplified Environment Model
Total exchanged energy with dephasing bath
Thermodynamics of Dephasing Assisted Heat Engines
The Thermodynamic Cost of Dephasing in a Heat Engine
A Specific Example
Thermodynamics of Dephasing Assisted Heat Engines
The Thermodynamic Cost of Dephasing in a Heat Engine
An Analytical Treatment
Heat transfer to dephasing bath during hot thermal strokes
Coupling to hot-bath
Duration of thermal stroke
Thermodynamics of Dephasing Assisted Heat Engines
The Thermodynamic Cost of Dephasing in a Heat Engine
An Analytical Treatment
For finite temperature dephasing bath we find
To keep power unchanged, fix
For any fixed power we can make vanishingly small the thermodynamic cost of the dephasing environment.
thermalization rates
peak location�width of dephasing bath spectral density �effective dephasing rate
Thermodynamics of Dephasing Assisted Heat Engines
Conclusions & Outlook
Yeah but no but yeah but …
Thermodynamics of Dephasing Assisted Heat Engines
Conclusions & Outlook
Yeah but no but yeah but …
Explore relation to�Pietzonka and Seifert. PRL 120, 190602 (2018)
Woods & Horodecki, PRX 13, 011016 (2023)
Thermodynamics of Dephasing Assisted Heat Engines
Conclusions & Outlook
Yeah but no but yeah but …
Explore relation to�Pietzonka and Seifert. PRL 120, 190602 (2018)
Woods & Horodecki, PRX 13, 011016 (2023)
Thermodynamics of Dephasing Assisted Heat Engines
Team & Sponsors
Martin Plenio
Susana Huelga
Koenraad Audenaert
Jaemin Lim
Professors & Staff
Postdocs
Dario Cilluffo
Thibaut Lacroix
Yu Liu
Julen Pedernales
Luciano Pettruzziello
Gabriela Wójtowicz
Dayou Yang
PhD students
Bachelor/Master students
Felix Ahnefeld
Lennart Bosch
Jonas Breustedt
Namgee Cho
Benjamin Desef
Giovanni Di Meglio
José Diogo Guimarães
Daniel Dulog
Kevin Kessing
Martin Korzeczek
Matthias Kost
Trinidad Lantaño-Pinto
Lea Lautenbacher
Nicola Lorenzoni
Daniel Siciliano
Giovanni Spaventa
Marit Steiner
Raphael Weber
Nicholas Schubel
Johanna Seitz
Synergy Grant:
Diamond Quantum Devices and Biology�(BioQ) �2013 -2019
QMED
PhoQuant
Spinning
GoCeQ
Synergy Grant: Quantum hyperpolarisation�for ultrasensitive NMR and MRI �(HyperQ) �2020 - 2026
ExtraQt
LemaQume
QuMicro�C-QuENS
SPINUS
@https://www.uni-ulm.de/nawi/institut-fuer-theoretische-physik-start-page/home/
Thermodynamics of Dephasing Assisted Heat Engines
The Team
Thermodynamics of Dephasing Assisted Heat Engines