A proposal for the measurement of the non-stationary Casimir effect

Transcription

1 A proposal for the measurement of the non-stationary Casimir effect Giuseppe Ruoso INFN - Laboratori Nazionali di Legnaro - aim of the experiment - mechanical and effective motion - experimental set-up - discussion

2 The Project MIR proposal R & D financed by National Institute for Nuclear Physics (INFN) Two year budget Dino Zanello Caterina Braggio Gianni Carugno Carlo Del Noce Giacomo Bressi Augusto Lombardi Antonio Palmieri Giuseppe Ruoso Rome Ferrara Padova Pavia Legnaro Labs Recently added: Pavia Laser Group

3 Aim - I Set up an apparatus for the experimental verification of the dynamical casimir effect Single mirror motion Effect undetectable N ph ~ Ω T β 2 Quasi-realistic values Ω, v Ω ~ 10 GHz T ~ 1 s β = (v/c) = 10-8 N ph << 1 observation time

4 Aim - II Amplify the effect by means of a resonant cavity Moving wall on a high Q resonant cavity L Parametric resonance condition Ω m = 2 ν r ν r - cavity resonance frequency Ω m The effect of a single mirror is increased by the cavity quality factor Q N ph ~ Ω T β 2 Q Q ~ N ph >

5 Cavity In a realistic set-up a 3-dim cavity has an oscillating wall. Ω m ν r Cavity with dimensions ~ cm have resonance frequency varying from 30 GHz to 300 MHz. (microwave cavity) Large Q --> Superconducting cavity Great experimental challenge: motion of a surface at frequencies extremely large to match cavity resonance and with large velocity (β=v/c) Given the frequency ν r, the velocity v, hence the number of photons produced, is related to the maximum displacement achievable δx Points for discussion: i) cavity geometry ii) TE vs TM modes

6 Surface mechanical motion Strong limitation for a moving layer: INERTIA δx E = 1 2 ρvω 2 δx 2 ω / 2 π = 10 GHz δx > 1 nm Mechanical power P ~ kw - MW To be 10 GHz Very inefficient technique: to move the electrons giving the reflectivity one has to move also the nuclei with large waste of energy Also, problems with the mechanical design Instead of moving the complete layer one can produce oscillations on the surfaces. Maximum deformations before damage δ = ω a / v s, v s sound velocity Maximum boundary velocity ~ 50 m/s

7 How to produce high frequency motion i) Acoustic waves in solids In the 60 s Bömmel-Dransfeld produced GHz acoustic waves in quartz using piezo excitation, but exciting all modes. Motion of a single mode δx << 1 nm. Large microwave power necessary. ii) Acoustic microscopes Excitation of resonant modes in sapphire blocks (typical frequency 3 GHz) Use of high Q reduces power requests, in fact for sapphire Q f ~ 10 12, i.e. for f ~ 10 9 follows Q ~ Same amplitude with P/1000. But again δx ~ m and small area

8 Surface effective motion Van der Walls forces measured at µm distances on silicon sample change under illumination of the sample Parametric excitation of e.m. waves using a dense plasma layer in a cavity; the layer is created by irradiating a semiconductor film with femtosecond laser pulses Use of laser pulse on semiconductor to change very rapidly its index of refraction

9 Surface effective motion II Generate motion by placing the reflecting surface in two distinct positions alternatively Position 1 - metallic plate Position 2 - microwave mirror with driven reflectivity Metal plate Variable mirror Microwave USE P1 P2 Semiconductors under illumination can change their dielectric properties and become from completely transparent to completely reflective for microwaves. Light with photon energy hν > E band gap of semiconductor Enhances electron density in the conduction band Laser ON - OFF On semiconductor Time variable mirror

10 MIR - the experimental scheme A semiconductor layer (thickness ~ 1 mm) is placed on one end of a niobium superconducting cavity. Cavity resonance ν r. Using an amplitude modulated (at frequency f) laser light the semiconductor switches from transparency to reflection, thus producing an effective motion. when f = 2 ν r Photons will be produced in the vacuum and will be picked-up by the antenna With this set-up the amplitude of the motion in very large, thus providing a large effective velocity Discussion: i) is the effective motion equivalent to standard motion concerning the photon production? ii) what is the expected rate of vacuum photons?

11 Experimental issues Effective mirror the semiconductor when illuminated behaves as a metal timing of the generation and recombination processes quality factor of the cavity with inserted semiconductor possible noise coming from generation/recombination of carriers Detection system minimum detectable signal noise from blackbody radiation See Caterina Braggio s talk Laser system possibility of high frequency switching pulse energy > threshold for complete reflectivity number of consecutive pulses Pavia laser group: Positive answer! Create bursts with pulses Of appropriate wavelength and energy and pulse frequency up to 5 GHz Bursts can be repeated at low rate

12 Detailed set-up Working temperature 4-9 K Complete freeze out of carriers in semiconductor No background noise from thermal photons Cavity resonance in the range 2-3 GHz Semiconductor thickness ~ 1 mm

13 Detection scheme Steps 1. Find cavity frequency ν r 2. Wait for empty cavity 3. Set laser system to 2 ν r 4. Send burst with > 1000 pulses 5. Look for signal with τ ~ Q / 2πν r N pulses t p = 1/ 2 ν r Charged cavity. Will decay with its time constant Key points for discussion i) Motion of surface (change of cavity length) is given by laser pulse time (up) and semiconductor recombination time (down) ii) Power build up in vacuum (linear, exponential,..) iii)role of the blackbody radiation: is the total number of photons different for different working temperature

14 Multiple bursts To increase the signal to noise ratio multiple laser bursts (each with at least 1000 pulses) will be used. Averaging of each burst will be performed. Point for discussion: is the antenna field having the same phase at a given time from t0?

15 Check list Several things can be employed to disentangle a real signal from a spurious one Signal (a.u.) Change temperature of cavity Effect on black body photons Change laser pulse frequency Laser pulse frequency (a.u) Loading of cavity with real photons (is our system a microwave amplifier?) Power inside cavity at end of laser pulses (a.u.) Determine vacuum effect from several measurements with pre-loaded cavity Power inside cavity at t = t0 (a.u.) -change recombination time of semiconductor -change width of semiconductor layer

16 Summary of discussion points The experiment is feasible! There are points to be clarified to obtain a better design of the apparatus 1. Cavity shape/geometry 2. TE vs TM modes 3. Equivalence between real and effective motion 4. Precise number of expected photons 5. Power build up in the empty cavity (linear, exponential) 6. Effect of cavity temperature on final number of photons 7. Phase on the antenna field at a given time 8. Effect of pre-loading the cavity with microwave power