1 / 50

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.

vivian
Télécharger la présentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related