Casimir effect and the MIR experiment D. Zanello INFN Roma 1 G. Carugno INFN Padova

Summary The quantum vacuum and its microscopic consequences The static Casimir effect: theory and experiments Friction effects of the vacuum and the dynamical Casimir effect The MIR experiment proposal

The quantum vacuum Quantum vacuum is not empty but is defined as the minimun of the energy of any field Its effects are several at microscopic level: –Lamb shift –Landè factor (g-2) –Mean life of an isolated atom

The static Casimir effect This is a macroscopic effect of the quantum vacuum, connected to vacuum geometrical confinement HBG Casimir 1948: the force between two conducting parallel plates of area S spaced by d

Experimental verifications The first significant experiments were carried on in a sphere-plane configuration. The relevant formula is Investigators R Range (  m) Precision (%) Van Blokland and Overbeek (1978) 1 m at small distances 50 average Lamoreaux (1997)12.5 cm at very small distance, larger elsewhere Mohideen et al (1998) 200  m Chan et al (2001) 100  m R is the sphere radius

Results of the Padova experiment (2002) First measurement of the Casimir effect between parallel metallic surfaces

Friction effects of the vacuum Fulling and Davies (1976): effects of the vacuum on a moving mirror –Steady motion (Lorentz invariance) –Uniformly accelerated motion (Free falling lift) –Non uniform acceleration (Friction!): too weak to be detectable N ph ~  T  v/c  2

Amplification using an RF cavity GT Moore (1970): proposes the use of an RF EM cavity for photon production Dodonov et al (1989), Law (1994), Jaeckel et al (1992): pointed out the importance of parametric resonance condition in order to multiply the effect  m = 2  0  m = excitation frequency  0 = cavity resonance frequency

Parametric resonance The parametric resonance is a known concept both in mathematics and physics In mathematics it comes from the Mathieu equations In physics it is known in mechanics (variable length swing) and in electronics (oscillating circuit with variable capacitor)

Theoretical predictions A.Lambrecht, M.-T. Jaekel, and S. Reynaud, Phys. Rev. Lett. 77, 615 (1996) 1.Linear growth 2. Exponential growth V. Dodonov, et al Phys. Lett. A 317, 378 (2003); M. Crocce, et al Phys. Rev. A 70, (2004); M. Uhlmann et al Phys. Rev. Lett. 93, 19 (2004) t is the excitation time

Is energy conserved? t E E in E out t E E in E out Srivastava (2005):

Resonant RF Cavity Great experimental challenge: motion of a surface at frequencies extremely large to match cavity resonance and with large velocity (  =v/c) mm In a realistic set-up a 3-dim cavity has an oscillating wall. Cavity with dimensions ~ cm have resonance frequency varying from 30 GHz to 300 MHz. (microwave cavity)

Surface motion Mechanical motion. Strong limitation for a moving layer: INERTIA Very inefficient technique: to move the electrons giving the reflectivity one has to move also the nuclei with large waste of energy Maximum displacement obtained up to date of the order of 1 nm Effective motion. Realize a time variable mirror with driven reflectivity (Yablonovitch (1989) and Lozovik (1995)

Resonant cavity with time variable mirror Time variable mirror MIR Experiment

The Project Dino ZanelloRome Caterina BraggioPadova Gianni Carugno Giuseppe Messineo Trieste Federico Della Valle Giacomo BressiPavia Antonio Agnesi Federico Pirzio Alessandra Tomaselli Giancarlo Reali Giuseppe Galeazzi Legnaro Labs Giuseppe Ruoso MIR – RD R & D financed by National Institute for Nuclear Physics (INFN) MIR 2006 APPROVED AS Experiment.

Our approach Taking inspiration from proposals by Lozovik (1995) and Yablonovitch (1989) we produce the boundary change by light illumination of a semiconductor slab placed on a cavity wall Time variable mirror Semiconductors under illumination can change their dielectric properties and become from completely transparent to completely reflective for selected wavelentgh. A train of laser pulses will produce a frequency controlled variable mirror and thus if the change of the boundary conditions fulfill the parametric resonance condition this will result in the Dynamical Casimir effect with the combined presence of high frequency, large Q and large velocity

Expected results Complete characterization of the experimental apparatus has been done by V. Dodonov et al (see talk in QFEXT07). V V Dodonov and A V Dodonov “QED effects in a cavity with time-dependent thin semiconductor slab excited by laser pulses” J Phys B 39 (2006) 1-18 Calculation based on realistic experimental conditions,  semiconductor recombination time,   ps  semiconductor mobility,   1 m 2 / (V s)  ( ) semiconductor light absorption coefficient t semiconductor thickness, t  1 mm laser: 1 ps pulse duration, 200 ps periodicity, 10-4 J/pulse (a, b, L) cavity dimensions Expected photons N > 10 3 per train of shots

 (ps) Z 2  3  F ( )10 -4 N (n=10 5 pulses) N (n=10 4 pulses) A 0 = 10 D = 2 mm  = b = cm 2 /Vs = 2.5 GHz = 12 cm (b = 7 cm, L = 11.6) Photon generation plus damping

Measurement set-up The complete set-up is divided into Laser system Resonant cavity with semiconductor Receiver chain Data acquisition and general timing Cryostat wall

Experimental issues Effective mirror the semiconductor when illuminated behaves as a metal (in the microwave band) 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 Laser system possibility of high frequency switching pulse energy for complete reflectivity number of consecutive pulses

Semiconductor as a reflector Results: Perfect reflectivity for microwave Si, GaAs: R=1; Light energy to make a good mirror ≈ 1  J/cm 2 Experimental set-up Reflection curves for Si and Cu Time (  s) Light pulse

Semiconductor I The search for the right semiconductor was very long and stressful, but we managed to find the right material Requests:  ~ 10 ps,  ~ 1 m 2 / (V s) Neutron Irradiated GaAs Irradiation is done with fast neutrons (MeV) with a dose ~ neutrons/cm 2 (performed by a group at ENEA - ROMA). These process while keeping a high mobility decreases the recombination time in the semiconductor High sensitivity measurements of the recombination time performed on our samples with the THz pump and probe technique by the group of Prof. Krotkus in Vilnius (Lithuania)

Semiconductor II: recombination time Results obtained from the Vilnius group on Neutron Irradiated GaAs Different doses and at different temperatures The technique allows to measure the reflectivity from which one calculate the recombination time 1. Same temperature T = 85 K2. Same dose (7.5E14 N/cm 2 ) Estimated  = 18 ps

Semiconductor III: mobility Mobility can be roughly estimated for comparison with a known sample from the previous measurements and from values of non irradiated samples. From literature one finds that little change is expected between irradiated and non irradiated samples at our dose We are setting up an apparatus for measuring the product  using the Hall effect.  ~ 1 m 2 / (V s)

Cavity with semiconductor wall Fundamental mode TE 101 : the electric field E 600  m thick slab of GaAs Computer model of a cavity with a semiconductor wafer on a wall a = 7.2 cm b = 2.2 cm l = 11.2 cm Q L =  measured ≈ 3 · 10 6

Superconducting cavity Cryostats old new Cavity geometry and size optimized after Dodonov’s calculations Q value ~ 10 7 for the TE 101 mode 2.5 GHz No changes in Q due to the presence of the semiconductor Niobium: 8 x 9 x 1 cm 3 The new one has a 50 l LHe vessel Working temperature K Antenna hole Semiconductor holding top

Electronics I Final goal is to measure about GHz (Cryogenic) Use a very low noise cryogenic amplifier and then a superheterodyne detection chain at room temperature CAPA The cryogenic amplifier CA has 37 dB gain allowing to neglect noise coming from the rest of the detector chain Special care has to be taken in the cooling of the amplifier CA and of the cable connecting the cavity antenna to it Picture of the room temperature chain

Electronics II: measurements Cryogenic amplifier ~ 10 cm Motorized control of the pick-up antenna Superconducting cavity

Electronics III: noise measurement Using a heated 50  resistor it is possible to obtain noise temperature of the first amplifier and the total gain of the receiver chain 1. Amplifier + PostAmplifier 2. Complete chain

Sensitivity The power P measured by the FFT is: k B - Boltmann’s constant G - total gain B - bandwidth T N - amplifier noise temperature T R - 50  real temperature The noise temperature T N = 7.2 K corresponds to J For a photon energy = J sensitivity ~ 100 photons Results: T N1 = T N2 No extra noise added in the room temperature chain G 1 = 72 dB = G tot = 128 dB =

Black Body Photons in Cavity at Resonance Noise 50 Ohm Resistor at R.T. Noise Signal from TE101 Cavity at R.T. Cavity Noise vs Temperature

Laser system I Laser master oscillator 5 GHz, low power Pulse picker Optical amplifier Pulsed laser with rep rate ~ 5 GHz, pulse energy ~100  J, train of pulses, slightly frequency tunable ~ 800 nm Total number of pulses limited by the energy available in the optical amplifier Each train repeated every few seconds Optics Express 13, 5302 (2005)

Laser system II Master oscillator Pulse picker Diode preamplifier Flash lamp final amplifier Current working frequency: 4.73 GHz Pulse picker: ~ 2500 pulses, adjustable Diode preamplifier gain: 60 dB Final amplifier gain: > 20 dB Total energy of the final bunch: > 100 mJ

Detection scheme Steps 1.Find cavity frequency r 2.Wait for empty cavity 3.Set laser system to 2 r 4.Send burst with > 1000 pulses 5.Look for signal with  ~ Q / 2  r Expected number of photons: Niobium cavity with TE 101 r = 2.5 GHz (22 x 71 x 110 mm 3 ) Semiconductor GaAs with thickness  x = 1 mm Single run with ~ 5000 pulses N ≥ 10 3 photons

Check list -change recombination time of semiconductor -change width of semiconductor layer Several things can be employed to disentangle a real signal from a spurious one Change temperature of cavity Effect on black body photons Loading of cavity with real photons (is our system a microwave amplifier?) Change laser pulse rep. frequency

Conclusions We expect to complete assembly Spring this year. First measure is to test the amplification process with preloaded cavity, then vacuum measurements Loading of cavity with real photons and measure Gain Change laser pulse rep. frequency - change recombination time of semiconductor - change thickness of semiconductor Several things can be employed to disentangle a real signal from a spurious one Carry on measurements at different temperatures and extrapolate to T = 0 Kelvin

D -L G 0 Problem: derivation of a formula for the shift of resonance in the MIR em cavity and compare it with numerical calculations and experimental data. Result: a thin film is an ideal mirror (freq shift) even if G   s complex dielectric function transparent background MIR experiment: 800 nm light impinging on GaAs + 1  m abs. Length = plasma thickness + mobility 10 4 cm 2 /Vs    m  cm  A>1 Frequency shift

N ph = sinh 2 (n  ) = sinh 2 (  T 0 ) ideal case unphysically large number of photons dissipation effects (instability removed) T  0 non zero temperature experiment? N ph = sinh 2 (n  )(1+2 0 ) thermal photons are amplified as well n =  T/2  N b =

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