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

Quantum thermodynamics: 1 Mauro Paternostro Queen’s University Belfast Advanced School on Quantum Science and Quantum T echnologies (ICTP , T rieste, 4 September 2017)

Non-equilibrium thermodynamics of quantum processes: 1 or an invitation to study stochastic thermodynamics of quantum processes Mauro Paternostro Queen’s University Belfast Advanced School on Quantum Science and Quantum T echnologies (ICTP , T rieste, 4 September 2017)

Belfast

Queen’s University Belfast Joseph Larmor John Stuart Bell Harrie Massey David Bates, FRS

On the shoulders of Belfast’s giants 4 November: John Bell day

On the shoulders of Belfast’s giants Lord Kelvin Born in Belfast in 1824 Belfast, Botanic Gardens

Thermodynamics…

…and (one of) its evolution(s) Framework for non-equilibrium quantum processes Hot Heat Re-definition of work, heat, entropy… Q Work in non-equilibrium quantum contexts Heat Cold Thermodynamics-inspired arena for the study/use of quantum resources

My take of it Fundamental viewpoint T echnological viewpoint Using quantumness Thermodynamics is a theory to optimise machine of inherently complex systems performance

Content & structure n Non-equilibrium definition of thermodynamic work: fluctuation theorems Landauer principle & quantum (open-system)dynamics Irreversibility & entropy production in closed q-systems Quantum correlations, coherences and thermodynamics

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

Setting the context In quantum contexts: work is not an observable n m p 0 p 0 n p τ m | n δ n [ i H f ] all instan n,m and ˆ ˆ H f ith H i simplifie characte X p 0 Work Distribution m | n δ ( W − ( E 0 P F ( W ) = m − E n )) n p τ n,m P . T alkner, E. Lutz, and P . Haenggi, Phys. Rev. E 75, 050102 (2007)

Fluctuation theorems Work Distribution Characteristic function of Work Distribution Z dWe ıuW P F ( W ) X p 0 χ F ( u ) = m | n δ ( W − ( E 0 P F ( W ) = n p τ m − E n )) n,m h i U † ( τ , 0) e ıuH ( λ τ ) U ( τ , 0) e − ıuH ( λ 0 ) ρ G ( λ 0 ) χ F ( u ) = = Tr ρ G ( λ 0 ) = e − β H ( λ 0 ) Z ( λ 0 )

Fluctuation theorems Work Distribution Characteristic function of Work Distribution Z dWe ıuW P F ( W ) X p 0 χ F ( u ) = m | n δ ( W − ( E 0 P F ( W ) = n p τ m − E n )) n,m h e − β W i = e − β ∆ F Jarzynski sky equality Jarzynski, PRL 78 2690 (1997) free-energy change T asaki-Crooks G. E. Crooks, PRE 60, 2721 (1999) relation H. T asaki, cond-mat/0009244 (2000)

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 SET a b ne ne C L C L C j C j C R C R ~ d V g V g c

What’s wrong with it “The major obstacle for the experimental verification of the work fluctuation relation is posed by the necessity of performing quantum projective measurements of energy”

Measuring work A h h S H f u ˆ U τ e − i ˆ H i u ⊗ | 0 ⟩⟨ 0 | A + e − i ˆ G ( u , τ ) = ˆ ˆ U τ ⊗ | 1 ⟩⟨ 1 | A R. Dorner, et al., Phys. Rev.Lett. 110, 230601 (2013) L. Mazzola, G. De Chiara, and MP , Phys. Rev. Lett. 110, 230602 (2013) L. Mazzola, G. De Chiara, and MP , Int. J. Quant. Inf. (2014)

The experiment week ending P H Y S I C A L R E V I E W L E T T E R S PRL 113, 140601 (2014) 3 OCTOBER 2014 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. Serra 1 1 Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, R. Santa Adélia 166, 09210-170 Santo André, x sin π t y cos π t ✓ ◆ ˆ H F ( t ) = 2 π ~ ν ( t ) σ C σ C ˆ 2 τ + ˆ , 2 τ

The experiment G 1 ⌘ | 0 i h 0 | H ⌦ e � iu ˆ C H α (0) + | 1 i h 1 | H ⌦ ˆ ˆ 1 1 C + | 1 i h 1 | H ⌦ e � iu ˆ H α ( τ ) . G 2 ⌘ | 0 i h 0 | H ⌦ ˆ ˆ 1 1 produce rotations by the displayed interaction ˆ σ H σ C H J = 2 π J ˆ z ˆ z time) are represented e � β ˆ H α (0) / Z 0 to ρ 0 HC = | 0 i h 0 | H ⌦ equilibrium state of 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)

Other experimental studies Experimental test of the quantum Jarzynski equality with a trapped-ion system Shuoming An 1 , Jing-Ning Zhang 1 , Mark Um 1 , Dingshun Lv 1 , Yao Lu 1 , Junhua Zhang 1 , Zhang-Qi Yin 1 , H. T. Quan 2,3 * and Kihwan Kim 1 * Raman2 a c b Adiabatic process ω ω ν ω ω ν 171 Yb + L + X − and L − X + F = 1 2 P 1/2 F = 0 V RF Detection ∆ GND d V d.c. V d.c. Instantaneous process σ σ − + Raman2 ω GND ∆ k L V RF X ⏐↑〉 F = 1 2 S 1/2 ω B ω Raman1 Y HF Raman1 X F = 0 ⏐↓〉 Z ω ω L + HF S. An, et al., Nature Phys. 11, 193 (2015)

Other experimental studies Experimental study of quantum thermodynamics using optical vortices ujo, 1 T. H¨ affner, 1 R. Bernardi, 1 D. S. Tasca, 2 M. P. J. R. Medeiros de Ara´ Lavery, 3 M. J. Padgett, 4 A. Kanaan, 1 L. C. C´ eleri, 5, ∗ and P. H. Souto Ribeiro 1, † 1 Departamento de F´ ısica, Universidade Federal de Santa Catarina, Florian´ opolis, SC, Brazil R. Medeiros de Araujo, et al. arXiv: 1705.02990

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 Folman 3 1 (a) Free Free Entangling Entangling Imaging Fall Fall Operation Operation (Motion) Driving (Electronic state) Atom chip (b) (c) Initial state preparation Probability - RF - Entangling - ∂B / ∂z - g Driving - RF - Entangling - ∂B / ∂z - Imaging z F . Cerisola et al., arXiv:1706.07866

The Belfast crew