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Quantum Thermodynamics , Berlin, January 23 rd

Information thermodynamics in a quantum opto-mechanical hybrid system Alexia Auffèves Institut Néel, CNRS, France. Quantum Thermodynamics , Berlin, January 23 rd. Outline. Motivation All about Landauer Monitoring the battery Conclusion - Perspectives.

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Quantum Thermodynamics , Berlin, January 23 rd

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  1. Information thermodynamics in a quantum opto-mechanicalhybrid systemAlexia AuffèvesInstitut Néel, CNRS, France Quantum Thermodynamics, Berlin, January 23rd

  2. Outline Motivation All about Landauer Monitoring the battery Conclusion - Perspectives

  3. Context : information thermodynamics • Szilard (1921) + Landauer (1961) • « Information isphysical » • => Information has a physical support • Information canbeconvertedintoenergy • Energyallows to measure information • => Need for a reversible transformation Shannonentropy variation Energy

  4. Principle of a Szilard engine T Szilard engine(1921) Converts a bit of information into an elementarywork W0 Expansion V-> 2V Entropyincreases by 1 bit Extraction of a maximal work W0 = -kTln(2)

  5. Principle of Landauererasure T Landauererasure(1961) Erasing a bit requires an elementarywork W0 Compression 2V-> V Entropydecreases by 1 bit It costs a minimal work W0 = kTln(2)

  6. A Carnot engineworkingwitha single bit of information T2 T1 Efficiency of the engine Reached if the transformations are reversible

  7. Experimental state of the art Landauerworkmeasured on a colloidalparticle Ciliberto, Lutz, Nature (2011) Reversibilityreached Workprovided by a classicalexternaloperator Workdeducedfrom the observation of the bit

  8. Experimental state of the art Szilard enginerealizedwith a BrownianparticleUeda, Toyabe, Nature physics (2011) The workisstored in a microscopicdegree of freedom (nano-battery) Energydissipated in irreversiblemechanisms Information-to-work rate : 28%

  9. Wishlist Wewouldlike to monitor the full cycle of information to energy conversion => Reachreversibility in bothsteps • Wewouldlike to measure the elementarywork W0 in the batteryitself • => Large couplingwith the bit • High sensitivity to microscopicenergy changes • Doesitmean nano-battery? Is that compatible withreversibility?

  10. Hybridopto-mechanicalsystems An optically active quantum emittercoupled to a mechanicaloscillator (MO) Example : a single quantum dot embedded in a vibratingwire Yeo et al, Nature Nano (2014) The emitterfrequencydepends on the position of the MO

  11. Hybrid opto-mechanical systems Example : straininducedopto-mechanicalcoupling Energy of the QD as a function of the oscillation phase Yeo et al, Nature Nano (2014)

  12. A hybriddevice = a platform for information thermodynamics The battery (exchangingwork) The mechanicaloscillator The bit The quantum emitter The bath (exchangingheat) The light field

  13. Outline Motivation All about Landauer Monitoring the battery Conclusion - Perspectives

  14. Landauer in a nutshell E E<<kT Bit to erase The 2 states are equiprobable Hi = 1 0 0 1 Q Heat bath (T)

  15. Landauer in a nutshell E t = 0 : E<<kT Bit to erase B A T T E R Y The 2 states are equiprobable Hi=1 0 0 1 Q Heat bath (T)

  16. Landauer in a nutshell E Intermediate time E>kT Under progress B A T T E R Y If the operationisreversible : 0 0 1 Q Heat bath (T)

  17. Landauer in a nutshell E Intermediate time E>kT Under progress B A T T E R Y If the operationisreversible : 0 0 1 Q The batteryprovides a minimal work Heat bath (T)

  18. Landauer in a nutshell E t = tf : E>>>kT Complete B A T T E R Y The TLS has relaxedin state « 0 » Hf = 0 0 The battery has spent a minimal work 0 1 Q Heat bath (T)

  19. Landauer in a nutshell E Complete B A T T E R Y • The « reverse » transformation isSzilard engine • Extraction of W0 • The qubit ends up in a mixed state 0 0 1 Q Heat bath (T)

  20. Landauerprinciple in a hybrid system g : classical Rabi frequency γ : spontaneousemission rate |e> t = 0 : the laser isresonantwith the emitter Laser |g> g The laser saturates the emitter : the 2 states |e> and |g> are equiprobable. Hi = 1

  21. Landauerprinciple in a hybrid system Mech. Osc. t = tf : the laser is out of resonance |e> Laser The TLS has fullyrelaxedin state |g>. Hf = 0 |g> g => The laser+vacuummimicks a heat bath => The wholeoperationmimicksLandauer’serasure

  22. Landauerprinciple in a hybrid system A quasi-resonant laser Resonance with the laser During the oscillation, the qubitisbrought in and out of resonancewith the laser : successions of Landauer’serasures and Szilard’sengine

  23. Landauerprinciple in a hybrid system t = 0 : the laser isresonantwith the TLS Bit to erase L A S E R The 2 states |e> and |g> are equiprobable Hi = 1

  24. Landauerprinciple in a hybrid system t = 0 : the laser isresonantwith the emitter Bit to erase L A S E R M O The 2 states |e> and |g> are equiprobable Hi = 1

  25. Landauerprinciple in a hybrid system Intermediate time Under progress L A S E R M O If the operationis « slow enough » :

  26. Landauerprinciple in a hybrid system Intermediate time Under progress L A S E R M O If the operationis « slow enough » : Steady-state regime of optical Bloch equations Realized if Mimicksreversibility

  27. Landauerprinciple in a hybrid system Intermediate time Under progress L A S E R M O If the operationis « slow enough » : Level |e> depleted as soon as The Rabi frequency g plays the role of an effective temperature

  28. Landauerprinciple in a hybrid system Intermediate time Under progress L A S E R M O If the operationis slow enough: The mechanicaloscillatorprovides a minimal work

  29. Landauerprinciple in a hybrid system Complete t = tf : the laser is out of resonance L A S E R M O The TLS has relaxed in state |g> Hf = 0 The mechanicaloscillatorprovides a minimal work Optical equivalent of Landauerwork

  30. Comparisonbetween the two scenarii Thermal bath Optical bath d E 1/2 1/4 g kT

  31. Comparisonbetween the two scenarii Thermal bath Optical bath d E 1/2 1/4 g kT

  32. Comparisonbetween the two scenarii Thermal bath Optical bath d E 1/2 1/4 g kT In the optical bath : reversibility = adiabaticity Relaxation time = spontaneousemission time Negativedetuningscanhappen

  33. Evidencing Landauer principle in a quantum hybrid system A quasi-resonant laser Resonance with the laser Mechanicalfrequency <<< Spontaneousemission rate => reversibilityreachable

  34. EvidencingLandauerprinciple in a quantum hybrid system A quasi-resonant laser Resonance with the laser Mechanicalenergycanbemeasured Direct access to the state of the battery Direct observation of Landauer’swork

  35. Outline Motivation All about Landauer Monitoring the battery Conclusion - Perspectives

  36. Hamiltonian Emitter Couplingwith the laser Emitter-mechanicalcoupling MechanicalOscillator (MO)

  37. Describing the mechanical state Semi-classical description Complex amplitude Evolution : The TLS « pumps » the phonon mode Equivalent of radiation pressure Free evolution Rotation in the complex plane

  38. Optical Bloch equations Effective detuninginduced by the mechanical vibration In the adiabaticregime :

  39. Is the mechanicalresonatorabattery?YES Workprovided to the TLS Mechanicalenergy Measuring the mechanicalenergy= direct observation of the workexchanged

  40. Conditions to monitor information-energy conversions Elementaryworktakenfrom the MO Corresponds to a typical variation in the number of phonons Must overcome the shot noise+the thermal noise Ultra strongcouplingrequired Doablewith state of the art technologies

  41. Evolution of the mechanical state over a full oscillation

  42. Evolution of the mechanical state over a full oscillation When the TLS isout of resonancewith the laser : free evolution(rotation in the complex plane)

  43. Evolution of the mechanical state over a full oscillation Atresonance : Kinks = exchange of the elementarywork WL= conversion of a bit of information

  44. Complete thermodynamical cycle MO state β(t) Detuningδ(t) Shannon entropy WorkW(t)

  45. Complete thermodynamical cycle MO state β(t) Detuningδ(t) Shannon entropy WorkW(t) 1->3 : Landauererasure: work W0provided by the MO, qubiterased

  46. Complete thermodynamical cycle MO state β(t) Detuningδ(t) Shannon entropy WorkW(t) 3->5 : Szilard engine: work W0stored in the MO, qubit back in a mixed state

  47. Complete thermodynamical cycle MO state β(t) Detuningδ(t) Shannon entropy WorkW(t) 5->7 : inverse Landauererasure: work W0stored in the MO, qubiterased

  48. Complete thermodynamical cycle MO state β(t) Detuningδ(t) Shannon entropy WorkW(t) 7->1 : inverse Szilard engine: work W0provided by the MO, qubit back in a mixed state

  49. A quantum optical Carnot engine Work W0 = (π/4)ħgstored in /extractedfromthe MO

  50. A quantum optical Carnot engine => Enginebehaviorby modulating the laser Rabi frequency

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