A microwave-cavity parametric amplifier for studying the Dynamical Casimir effect MIR experiment GR – Les Houches 2014

Summary Dynamical Casimir Effect with microwave cavities Parametric amplification: degenerate case Parametric amplification: 1) RF or 2) Laser Excitation Study of the thermal background - time evolution of thermal distribution Current status – perspectives/Conclusion GR – Les Houches 2014

Dynamical Casimir effect A boundary moving with non-uniform acceleration, allows to study dissipative effects connected with quantum vacuum Moore 1970, J. Math. Phys. 11, 2679; Fulling and Davies 1976, Proc. R. Soc. Lond. A 348, 393 Emission of real photons related to the frequency of the moving boundary Single mirror performing periodic motion Quasi-realistic values Nph ~ W T b2 W ~ 10 GHz T ~ 1 s observation time b = (v/c) = 10-8 Lambrecht, Jaeckel, and Reynaud 1996, Phys. Rev. Lett. 77, 615 Effect undetectable Nph << 1 W, v Use cavity resonators to increase signal GR – Les Houches 2014

Dynamical Casimir effect Geometry variable resonant cavity L Parametric resonance condition If Wm = 2 Wr Q, Wr Nph ~ Q Wr T b2 >> 1 Wm Length modulation Modulation of resonance frequency Suitable resonant cavity: microwave regime nr Cavity with dimensions ~ 1 - 10 cm have resonance frequency varying from 30 GHz to 3 GHz. (microwave cavity) Wm GR – Les Houches 2014

Experimental realization Use a cylindrical reentrant geometry and mount the variable wall on top of the reentrant nose Mounting Hole for laser illumination 650 micron GaAs Cavity resonance frequency = 2.5 GHz Laser amplitude modulation = 5 GHz Our best effort was unable to reach sufficient gain for the parametric process. With a train of ~ 2000 pulses maximum amplification was smaller than 1 due to very large unexpected losses in the illuminated semiconductor GR – Les Houches 2014

A microwave cavity set-up – variable mirror A semiconductor layer (thickness ~ 1 mm) is placed on one end of a niobium super-conducting cavity. Cavity resonance nr. Using an amplitude modulated (at frequency f) laser light the semiconductor switches from transparency to reflection, thus producing an effective motion. when f = 2 nr (Parametric resonance) Photons will be produced in the vacuum and will be picked-up by the antenna Single pulse Plas ~ 10 mJ With this set-up the amplitude of the motion is very large, thus providing a large effective velocity Number of pulses n ~ 2000 GR – Les Houches 2014

Microwave cavity with varicap A cylindrical reentrant copper cavity is equipped with a variable capacitance diode (varicap) mounted in front of the reentrant post Variable diode MACOM 46470 0V capacity ~ 1.5 pF Varicap 42 mm GR – PIERS2014

AC driving Quality factor Q=pncav/g Resonance frequency ncav Let’s now suppose to modulate harmonically the resonance frequency, by using the varicap, at some frequency nvar . To study this process we model the microwave resonator with an LRC circuit with a variable capacitance in parallel Quality factor Q=pncav/g Resonance frequency ncav For t >0 Degenerate parametric amplifier: For f = 2 ncav the electromagnetic field in the resonant circuit, i.e. inside the microwave cavity, will exhibit an exponential growth of type exp(st), with s = p h ncav The effect is phase sensitive. j is the phase of the input field For t >> tp In case of dissipation GR – Les Houches 2014

The way to the Dynamical Casimir effect To detect the DCE we have to realize an amplification of the vacuum, i.e. one has to work with an initial state having average thermal photon number smaller than 1. Moreover there must be no external contribution to the energy stored in the cavity. To realize this situation one has to check that the energy measured in the cavity corresponds to the average thermal photon bath energy for the corresponding thermodinamical temperature T. A reliable measurement of this is to determine the noise temperature of the parametric amplifier as a function of the cavity temperature: Absolute determination of the parametric gain Variable resistor Variable input level (amplified noise source) GR – PIERS2014

Measurement with noise source In order to have an input with large dynamics we use an amplified noise source coupled to the cavity via a weakly coupled port. We perform pulsed parametric amplification. Microwave cavity Data acquisition on fast scope Port P1 Port P2 Noise Source Tns = 10 000 K k1 Coupling c1 very weak Coupling c2 critical or weak Port P3 Varicap Effective temperature loaded into the cavity from port P1 RF Signal generator Pulser G(t) - gain of the parametric amplifier; B – measurement bandwidth; kB – Boltzmann constant GR – PIERS2014

New setup - Resonant cavity pumping In order to avoid varicap coupling changes when cooling, a new setup has been designed Varicap is fed trough a resonant cavity (Pump cavity) Coupling is fixed and well defined Only degenerate parametric amplification is possible Resonance frequency ratio between pump and signal cavity exactly 2 Fine tuning performed with a sapphire rod A small wire connection provides varicap biasing GR – PIERS2014

Room temperature Double cavity Degenerate amplifier Noise temperature determination for two different index of modulation on the varicap Signal cavity nr = 1488 MHz Dnr = 700 kHz Q ~ 2000 tc = 400 ns Gain coefficients tp(1) = 160 ns tp(2) = 140 ns GR – PIERS2014

Comparison of data with thermal input We generated a set of times tT assuming the initial energy is given by a random value extracted by the Bose Einstein distribution and having a random phase in the interval [0, 2p] The only free parameter is a common time t0 added to all generated values, in order to match the measured average time This is not the case for the single-mode photon distribution, described by (1), since when selecting a very narrow frequency band the number of photons is reduced below detectability. On the other hand, enlarging the measurement band will soon spoil the single mode, reducing its variance as (1n)2 = ¯n (1 + ¯n/μ), with μ the number of modes. These are the reasons why only a few measurements of the Bose–Einstein distribution have been made [5, 6], but with an average number of photons ¯n 1 and with apparatuses that can work only in a very limited temperature Data: 11000 samples of tT measured at room temperature with tp = 84 ns, in a cavity with Q ~ 100 , resonance frequency ~ 1.5 GHz. Initial average thermal photon number ~ 4200. GR – PIERS2014

Cryogenic set-up Main characteristic: Cryostat allowing LN2 and LHe operation Two stage isolator for critically coupled antenna to avoid power leak from RT cabling and devices Varicap driving with resonant cavity tuned to 2 ncav Very weakly coupled second antenna for calibration Double chamber for better temperature isolation GR – PIERS2014

The current experimental apparatus The cavities with antennas and varicap biasing Varicap biasing Signal cavity Antennas Pump cavity Thermal and electromagnetic isolation stages and filtering GR – PIERS 2014

Noise level @ cryogenic temperature Liquid Nitrogen Thermodynamic temperature Tcavity = 78 K Liquid Helium Tcavity ~ 8 K Si puo’ dire che uno ha due manici per verificare, cioè vede anche la forma dello spettro che deve essere termico T noise = 90 ± 5 K T noise = 13 ± 2 K GR – PIERS2014

Heating of the system Tnoise ~ 12 K We have monitored the heating of the system measuring the average energy content of the cavity Gain parameter for the parametric amplification stable up to 33 K Cavity energy, i.e. temperature, follows thermometer from about 18-20 K Floor temperature is Tnoise ~ 12 K We suspect that the cavity temperature is not uniform. For example higher floor temperature measured with sapphire rod more inside cavity. GR – PIERS2014

LASER INDUCED NON LINER OPTICS APPROACH Laser Induced Optical Kerr Effect to change dielectric constant within the cavity Laser Frequency Rate twice the Cavity Frequency RF Signal Present in the Cavity Probably noise induced GR – PIERS2014

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N fotoni medio =100 Conclusioni Parametric amplification Work at 8-10 Kelvin At 10 Kelvin @ 1,5 GHz ( 10-5 eV ) N fotoni medio =100 Energia E.M. Misurata = 10-3 eV Nuovo set up Criogenico @ Kelvin Richiesta 7 Keuro Sotto Dotazione GR – PIERS2014

Saturation The exponential growth for the parametric process cannot last forever, and it is normally stopped due to saturation in the system that changes the properties of the semiconductor. Typical temporal behaviour: Antenna signal t=0 In saturation many non-linear phenomena appears, not relevant for us time We have to define a measurement procedure which uses the non saturated part of the signal GR – PIERS2014

Measurement scheme – Pulse mode In order to avoid saturation the system is used in pulsed mode For each pulse in the varicap pump we measure the time tT needed to reach an arbitrary value of power at the critically coupled antenna This allows to have fixed SNR at the measurement point and avoid large errors on small input values Enabling signal for varicap driving Reference level VT RF signal from Critically Coupled antenna (No amplification) tT DARE UN PO’ DI NUMERI PER DARE UN’IDEA Repeated measurements of several times tT will give information on the system GR – PIERS2014