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

2. 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

3. 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

4. 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 ~ cm have resonance frequency varying from 30 GHz to 3 GHz. (microwave cavity) Wm
GR – Les Houches 2014

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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 = 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

11. 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

12. 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

13. 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: 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

14. 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

15. 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

16. 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

17. 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 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

18. 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

19. GR – PIERS2014

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

21. 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

22. 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