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Quantum fluctuations and the Casimir Effect in meso- and macro- systems Yoseph Imry

Quantum fluctuations and the Casimir Effect in meso- and macro- systems Yoseph Imry.

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Quantum fluctuations and the Casimir Effect in meso- and macro- systems Yoseph Imry

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  1. Quantum fluctuations and the Casimir Effect in meso- and macro- systems Yoseph Imry QUANTUM-NOISE-05

  2. I. Noise in the Quantum and Nonequilibrium Realm, What is Measured? Quantum Amplifier Noise. workwith:Uri Gavish, Weizmann (ENS)Yehoshua Levinson, Weizmann B. Yurke, LucentThanks: E. Conforti, C. Glattli, M. Heiblum, R. de Picciotto, M. Reznikov, U. Sivan ----------------------------- QUANTUM-NOISE-05

  3. II. Sensitivity of Quantum Fluctuations to the volume: Casimir Effect Y. Imry, Weizmann Inst. Thanks: M. Aizenman, A. Aharony, O. Entin, U. Gavish Y. Levinson, M. Milgrom, S. Rubin, A. Schwimmer, A. Stern, Z. Vager, W. Kohn. QUANTUM-NOISE-05

  4. Quantum, zero-point fluctuations Nothing comes out of a ground state system, but: Renormalization, Lamb shift, Casimir force, etc. No dephasing by zero-point fluctuations! How to observe the quantum-noise? (Must “tickle” the system). QUANTUM-NOISE-05

  5. Outline: • Quantum noise, Physics of Power Spectrum, dependence on full state of system • Fluctuation-Dissipation Theorem, in steady state • Application: Heisenberg Constraints on Quantum Amps’ • Casimir Forces. QUANTUM-NOISE-05

  6. Understanding The Physics of Noise-Correlators, and relationship to DISSIPATION: QUANTUM-NOISE-05

  7. x(t) t Classical measurement of time-dependent quantity, x(t), in a stationary state. C(t’-t)=<x(t) x(t’)> QUANTUM-NOISE-05

  8. x(t) t Classical measurement of a time-dependent quantity, x(t), in a stationary state. C(t’-t)=<x(t) x(t’)> Quantum measurement of the expectation value, <xop(t)>, in a stationary state. <x(t)> C(t)=? t QUANTUM-NOISE-05

  9. The crux of the matter: ------ From Landau and Lifshitz,Statistical Physics, ’59 (translated by Peierls and Peierls). QUANTUM-NOISE-05

  10. Van Hove (1954), EXACT: QUANTUM-NOISE-05

  11. QUANTUM-NOISE-05

  12. Emission = S(ω)≠S(-ω) = Absorption,(in general) From field with Nωphotons, net absorption (Lesovik-Loosen, Gavish et al): NωS(-ω) - (Nω+ 1) S(ω) For classical field (Nω>>> 1): CONDUCTANCE [S(-ω) - S(ω)] / ω QUANTUM-NOISE-05

  13. This is the Kubo formula (cf AA ’82)! Fluctuation-Dissipation Theorem (FDT) Valid in a nonequilibrium steady state!! Dynamical conductance - response to “tickling”ac field, (on top of whatever nonequilibrium state). Given by S(-ω) - S(ω) = F.T. of the commutator of the temporal current correlator QUANTUM-NOISE-05

  14. Nonequilibrium FDT • Need just a STEADY STATE SYSTEM: Density-matrix diagonal in the energy representation. “States |i> with probabilities Pi , no coherencies” • Pi -- not necessarily thermal, T does not appear in this version of the FDT (only ω)! QUANTUM-NOISE-05

  15. Partial Conclusions • The noise power is the ability of the system to emit/absorb (depending on sign of ω). FDT: NET absorption from classical field. (Valid also in steady nonequilibrium States) • Nothing is emitted from a T = 0 sample, but it may absorb… • Noise power depends on final state filling. • Exp confirmation: deBlock et al, Science 2003, (TLS with SIS detector). QUANTUM-NOISE-05

  16. A recent motivation How can we observe fractional charge (FQHE, superconductors) if current is collected in normal leads? Do we really measure current fluctuations in normal leads? ANSWER: NO!!! THE EM FIELDS ARE MEASURED. (i.e. the radiation produced by I(t)!) QUANTUM-NOISE-05

  17. Important Topic: Fundamental Limitations Imposed by the Heisenberg Principle on Noise and Back-Action in Nanoscopic Transistors. Will use our generalized FDT for this! QUANTUM-NOISE-05

  18. A Linear Amplifier Must Add Noise (E.g., C.M. Caves, 1979) Input (“signal”) Detector Amplifier Output xs , ps Xa , Pa Input (“signal”) Detector Amplifier Output xs , ps Xa , Pa Linear Amplifier: But then Heisenberg principle is violated. QUANTUM-NOISE-05

  19. A Linear Amplifier Must Add Noise (E.g., C.M. Caves) Input (“signal”) Detector Amplifier Output xs , ps Xa , Pa Linear Amplifier: But then Heisenberg principle is violated.  A Linear Amplifier does not exist ! QUANTUM-NOISE-05

  20. A Linear Amplifier Must Add Noise (E.g., C.M. Caves, 1979) Input (“signal”) Detector Amplifier Output xs , ps Xa , Pa In order to keep the linear input-output relation, with a large gain, the amplifier must add noise QUANTUM-NOISE-05

  21. A Linear Amplifier Must Add Noise (E.g., C.M. Caves, 1979) Input (“signal”) Detector Amplifier Output xs , ps Xa , Pa In order to keep the linear input-output relation, with a large gain, the amplifier must add noise choose then QUANTUM-NOISE-05

  22. Cosine and sine components of any currentfiltered with window-width QUANTUM-NOISE-05

  23. For phase insensitive linear amp: gL and gS are load and signal conductances (matched to those of the amplifier). G2 = power gain. QUANTUM-NOISE-05

  24. For Current Comm-s we Used Our Generalized Kubo: , where g is the differential conductance, leads to: QUANTUM-NOISE-05

  25. Average noise-power delivered to the load (one-half in one direction) QUANTUM-NOISE-05

  26. A molecular or a mesoscopic amplifier  B input siganl Cs Ls Resonant barrier coupled capacitively to an input signal Ia()= I0()+G Is() +back-action noise, In Is() QUANTUM-NOISE-05

  27. A new constraint on transistor-type amplifiers Coupling to signal = γ Noise is sum of original shot-noise I0~γ0 and “amplified back-action noise” In~ γ2 QUANTUM-NOISE-05

  28. General Conclusion: one should try and keep the ratio between old shot-noise and the amplified signal constant, and not much smaller than unity. In this way the new shot-noise, the one that appears due to the coupling with the signal, will be of the same order of the old shot-noise and the amplified signal and not much larger. QUANTUM-NOISE-05

  29. Amp noise summary • Mesoscopic or molecular linear amplifiers must add noise to the signal to comply with Heisenberg principle. • This noise is due to the original shot-noise, that is, before coupling to the signal, and the new one arising due to this coupling. • Full analysis shows how to optimize these noises. QUANTUM-NOISE-05

  30. The Casimir effect in meso- and macro- systems QUANTUM-NOISE-05

  31. Even at T=0, we are sorrounded by huge g.s. energy of various fields.No energy is given to us (& no dephasing!).But: various renormalizations, Lamb-shift…Casimir: If g.s. energy of sorrounding fields depends on system parameters (e.g. distances…) – a real force follows!This force was measured, It is interesting and important.Will explain & discuss some new features. QUANTUM-NOISE-05

  32. The Casimir Effect The attractive force between two surfaces in a vacuum - first predicted by Hendrik Casimir over 50 years ago - could affect everything from micromachines to unified theories of nature. (from Lambrecht, Physics Web, 2002) QUANTUM-NOISE-05

  33. Buks and Roukes, Nature 2002 (Effect relavant to micromechanical devices) From: QUANTUM-NOISE-05

  34. Why interesting? • (Changes of) HUGE vacuum energy—relevant • Intermolecular forces, electrolytes. • Changes of Newtonian gravitation at submicron scales? Due to high dimensions. • Cosmological constant. • “Vacuum friction”; Dynamic effect. • “Stiction” of nanomechanical devices… • Artificial phases, soft C-M Physics. QUANTUM-NOISE-05

  35. Casimir’s attractive force between conducting plates QUANTUM-NOISE-05

  36. QUANTUM-NOISE-05

  37. What is it (for volume V)? Milonni et al(kinetic theory): momentum delivered to the wall/unit time. Pressure || z in k state: QUANTUM-NOISE-05

  38. Total pressure: Replacing sum by integral, integrating over angles and changing from k to ω, with ω=: . Defining: QUANTUM-NOISE-05

  39. A “thermodynamic” calculation: D(ω) is photon DOS D(ω)extensiveand>0 P0issame order of magnitude, butNEGATIVE??? QUANTUM-NOISE-05

  40. Why kinetics and thermodynamics don’t agree?M. Milgrom: ‘Thermodynamic’ calculation valid for closed system. But states are added (below cutoff) with increasing V ! 1 cutoff Allowed k’s Increasing V QUANTUM-NOISE-05

  41. Result for P0 is non-universal QUANTUM-NOISE-05

  42. Effect of dielectric on one side“Macroscopic Casimir Effect” QUANTUM-NOISE-05

  43. Net Force on slab between different dielectrics QUANTUM-NOISE-05

  44. Effect of dielectric inside on the“Mesoscopic Casimir Effect” QUANTUM-NOISE-05

  45. Quasistationary (E. Lifshitz, 56) regime QUANTUM-NOISE-05

  46. Vacuum pressure on thin metal film Quasistationary: d<<c/ωp Surface plasmons on the two edges Even-odd combinations: d QUANTUM-NOISE-05

  47. Dispersion of thin-film plasmons For d<<c/ωp,light-line ω=ck is very steep-full EM effects don’t Matter-- quasi stationary appr. ω/ωp kd Note:opposite dependence of 2 branches on d QUANTUM-NOISE-05

  48. Casimir pressure on the film, from derivative of total zero-pt plasmon energy.: Large positive pressureson very thin metallic films, approaching eV/A3 scales for atomic thicknesses. QUANTUM-NOISE-05

  49. Conclusions • EM Vacuum pressure is positive, like kinetic calculation result. It is the Physical subtraction in Casimir’s calculation. Depends on properties of surface! • Effects due to dielectrics in both macro- and meso- regimes. Some sign control. • Large positive vacuum pressure due to surface plasmons, on thin metallic films. QUANTUM-NOISE-05

  50. END, Thanks for attention! QUANTUM-NOISE-05

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