Aladin2: First Demonstration of Phase Transition Influenced by Vacuum Fluctuation

1. Aladin2: an experiment for the first demonstration of a phase transition influenced by vacuum fluctuation E. Calloni Dip. Scienze Fisiche Federico II NapoliINFN sezione di Napoli

2. SCIENTIFIC MOTIVATIONS • First demonstration of a phase transition influenced by vacuum fluctuations • First direct measurement of variation of Casimir energy in rigid bodies: possibility to open the way to measure the debated dependence of Casimir energy by geometry • Long-term R&D on verification of equivalence principle applied to vacuum fluctuations INSTITUTES PARTICIPATING • INFN sez. Naples -Italy • IPHT (Institute for Physical High Technology) - Jena – Germany • Federico II University – Naples – Italy • Seconda Università di Napoli – Aversa - Italy G. Bimonte, D. Born, E. Calloni, G. Esposito, U. Hubner, E. Il’Ichev, L. Milano, L. Rosa, D. Stornaiuolo, F. Tafuri, R. Vaglio

3. z L a y x The Casimir effect is a macroscopic manifestation of vacuum fluctuations. It is derived considering the zero point e.m. energy contained in a Casimir cavity, i.e. in the volume defined by two perfectly reflecting parallel plates • Spiegare lo scopo globale della strategia • Indicare l'obiettivo specifico da raggiungere • Se necessario, utilizzare più punti If the plates are perfectly reflecting the modes that can oscillate must have discrete wavenumbers on vertical axes kz = np/a while all values are allowed for kx e ky 3

4. The regularization is made by determing the Casimir Energy as the change in energy (in the same volume) when the plates are at distance “a” with respect to the plates having ainfinity Ereg = E(a) – E( ) a • Casimir Energy =1.3x10-7 N • Casimir Force Perfectly reflecting mirrors: long wavelengths are “expelled”from the cavity, so that the internal energy is:

5. History and some open questions Theory of Casimir effect : 1948 First measurement Sparnay 1954 with 100% error (Force ) Presently tested (Force) with 0.5% error (?!) Theoretical disagreement on renormalization procedure in case of different cavity geometries - no agreement on sign of expected energies Application to MEMS and NEMS Theoretical debats on zero frequency mode contribution in case of real material “Dynamic Casimir effect” (G. Carugno esperimento MIR) Cosmological constant problem: interaction of vacuum energy with gravitational field 4 S. K. Lamoreaux Rep. Prog. Phys. 68:201-236 (2005)

6. Cosmological Constant Problem Problem: “the universe exhibits a vacuum energy density much smaller than the one resulting from application of quantum mechanics and equivalence principle” Cosmological costant problem120 orders of magnitude Weinberg Rev. Mod. Phys. 61 (1989) First calculation Pauli (1930) Radius of the Universe = 31 Km! “This universe would not even reach to the moon” In spite of enormous theoretical work on different and deep hypothesis (not solving the problem even at theoretical level) there is not even an experiment to study (confirming or disproving) the application of equivalence principle for vacuum energy.

7. z L a y x Rigid Casimir Cavity in weak gravitational fieldThe component of stress-energy tensor in Minkowsky space-time: • can be written in a covariant form: is the 4-vector space-like orthogonal to the plates L.S. Brown, G.J. Maclay, Phys. Rev. 184 (1969) 5

8. So that, by substituting the metric tensor hmn with gnm of the laboratory system fixed on the earth, it can be easily calculated the force (density) exterted by the gravitational field on the Casimir cavity The force is positive (directed upward) : taking into account a system as big as GW detectors’ mirrors made of 106 layers with Separation of 5 nm (oxide) the total force is about 10-14 N d 6

9. The experiment could not be performed as a “sum of weight” of the components: it must be carried in AC, modulating the vacuum energy contained into the cavities. This in principle could be done by modulating the plates reflectivities (i.e.the h factor, which takes into account that real materials are not perfect reflectors) X ifh= 0.5 F Comparison with Virgo sensitivity Visible also With torsion Pendulum experiment Experimental problem: modulate Casimir energy without exchanging too much energy with the system (to not destroy the possibility of measurement and control) and measure it. Phys Letters A, 297, 328-333, (2002)

10. ALADIN2 Experiment for the direct measurement of vacuum energy variation in a rigid Casimir cavity via the modulation of the reflectivity of one plate, obtained by the normal/superconducting phase transition S = 100 nm Au,Ag a = 10 nm Al2O3 D = 10 nm Al Since the optical properties of the film (in the microwave region) change when it becomes superconducting, and since the Casimir free energy Fc stored in the cavity depends on the reflectivity of the film, we expect a variation of energy from the normal (n) to superconducting (s) states: Indeed DFc is expected to be positive, because, in the superconducting state, the film should be closer to an ideal mirror than in the normal state, and so Fc (s) should be more negative than Fc (n)

11. The change in energy can be calculated following the Casimir energy calculation in case of real plates with complex conductivity s : modulation factor with respect perfect reflectivity N metal Re(s) Diel N/S Plot of real part of conducibility s normalized to zero frequency Drude conducibilty s0 for different temperatures: T = Tc (Drude) T/Tc = 0.9 T/Tc = 00.3 The conducibility changes only in the very low frequency region (microwave) so the modulation depth (if Tc is of the order of 1 K) is expected to be small for small Tc…

12. ..but also the energy exchanged with the system, besides the vacuum energy, is expected to be small being linked to the condensation energy which is (roughly) proportional to Tc2 . Better to use low Tc superconductors. If the two energy variations are comparable then it is expected that vacuum fluctuations modifies the transition Is there a way to measure DFc? The proposed way to measure DFc consists in placing the cavity in a parallel magnetic field and measuring the critical field that destroys the superconductivity of the film.

13. Critical field of superconductors The critical fielddepends on the shape of the sample and on the direction of the field. For a thick flat slab in a paralle field, it is called thermodynamical field and is denoted as Hc. The value of Hc is obtained by equating the magnetic energy (per unit volume) required to expel the magnetic field with the condensation energy (density) of the superconductor. • Superconductivity is destroyed by a critical magnetic field. f n/S (T) : density of free energy at zero field inthe n/s state Hc(T) follows an approximate Parabolic law

14. Superconducting film as a plate of a Casimir cavity When the superconducting film is a plate of the cavity, the condensation energy Econd of the film is augmented by the difference DFc among the Casimir free energies DFc causes a shift of critical field dHc: Expected signal The ratio DFc/Econd diverges TTc No theory Phys. Rev. Lett. 94-180402 (2005) Nucl. Phys. B 726, 441 (2005)

15. EXPECTED SIGNAL TE Zero mode contribution & Long mean free path DT 50 mK No TE Zero mode contribution & Conservative free path DT 10 mK • Different theories: TE zero mode contribution ? • Uncertainties on parameters (Au mean free path-Plasma Frequency) 150 stand-alone film in-cavity film 100 TC0-T (mk) 10 < DT < 50 mK D T 50 - NO Theory 0 2 4 6 8 10 Applied Field (mT)

16. Based on commercial Oxford Heliox 3He cryostat: base temperature 300 mK Experimental apparatus Detlef Born The home-made uniform-field coil is placed Under vacuum to allow external magnetic screening

17. F The measurement consists in placing under vacuum a sample cointaining a couple of 2 layer structures (Al film + oxide) and a couple of 3 layer structure (Al film + oxide + metal)The couples have different areas (like in figure) to verify that the effect does not depend on area C C c F Area of 100x100 mm2 And 20x20 mm2 C F F ALIGNMENT The constraint is that the angles formed by cavities and films on the same sample do not differ with the magnetic field do not differ more than 10-3 rad We estimate that in the same sample Dq < 10-4

18. Typical standard measurement on a cavity: the applied magnetic field is fixed and the transition is obtained by varying the temperature: the shift in transition temperature is defined by averaging the temperatures in the linear region The transition width is about 50 mK The applied field are of the order of 10 mT

19. All the samples are deposited in the same chip and worked in the same way until the last metal covering 1K plate (T~1.5K) 5 cm In the scheme is reported the lay out of A single sample: the distance between The various structures (2 and 3 layers) Are about 2.5 mm 3He pot (Tmin= 250mK) Cavities are covered With Au or Ag; the difference is expected to be small

20. Measurement with radiation @ 300 K Preliminary measurement: no isolation from infrared and Microwave radiation The Casimir energy variation is roughtly proportional to the density of photons of frequency n few times 2KTc/h v = 10KTc/h (Tc = 1.5 K) In a 300K bath the system is expected to behave in a similar way with respect to zero point case except for a Magnification factor:

21. Measurement with real EM @300K • As expected it mimics the “Casimir signal” • DT is 300 mK

22. Zoom for low applied fields The difference derives from the linear behaviour of film due to EM noise radiation carried from outside by the cables Conclusion from this measurement: we expect the Casimir Signal DT on the conservative side of range DT 10 mK

23. Zoom Sensitivity to Casimir effect EM screened Tc = 1.52 K 50 mK are a “big” effect

24. Expected parabolic behaviour recovered with dt 6 mK 2 points Measured at 3 days of Distance: they Differ for about 3 mK FILM T0- T (mK) The parabola it is not a fit on these points: it is the parabola estimated with High fields measurements (with a single copper-powder Filter the high field region is not Influenced by EM noise)

25. After a first analysis on cavity The uncertainties on cavity are higher: 10 mK T0- T (mK) The cavity points are a first measurement and are to be Intended as a first preliminar set

26. Next experimental steps • Repeat the measurement on variuos cavities • Repeat the measurement with cavities having different parameters (lower gap to increase the signal)

27. Current studies for future developments 1) The measurement on rigid cavities could open the way to test the debated possibility of positive energy configurations  positive force  real nano-motors 2) Verification of equivalence principle of vacuum energy 3) Contribution in studying gravity effects on vacuum fluctuations and discriminate between local/global explanation of Casimir effect: theoretical results Trace Anomaly (see L. Rosa talk) Phys. Rev. D 74, 085011 (2006) 4) Upgrade to test the region where presently the theory lacks (?) – useful for cosmology (?)

28. CONCLUSIONS • Sensitivity seems encouraging for the first measurement of variation of Casimir energy in rigid bodies • Demonstrate a phase transition influenced by vacuum fluctuations • Long Term R&D of effects of gravitational field on vacuum energy