Thermal effects of the Casimir forces Thermal effects of the Casimir - PowerPoint PPT Presentation

University of Trento University of Trento University of Trento University of Trento Thermal effects of the Casimir forces Thermal effects of the Casimir forces on ultra- -cold gases cold gases on ultra ������������� ������� ������ University of Trento, INFN and University of Trento, INFN and University of Trento, INFN and University of Trento, INFN and CNR- CNR CNR CNR - - -INFM BEC Center on Bose INFM BEC Center on Bose INFM BEC Center on Bose- INFM BEC Center on Bose - -Einstein Condensation, Trento, Italy - Einstein Condensation, Trento, Italy Einstein Condensation, Trento, Italy Einstein Condensation, Trento, Italy International Workshop on ‘’ADVANCES IN PRECISION TESTS AND EXPERIMENTAL GRAVITATION IN SPACE’’, Galileo Galilei Institute , Florence 28-30 Sept. 2006

The Team The Team ����������������������� ����������������������

����� ����������� ���������� ���� PV = nRT - Boyle and Gay-Lussac ideal gas lows could be explained by the kinetic theory of non-interacting point atoms (Joule, Kroning, Clausius,..), but are hardly exact a   ( ) - J.D. van der Waals (1873): eq. of state + − =  P  V b nRT v   2 - London (1930!): interaction potential between two atoms due to fluctuations of the atomic electric dipole moment d 1 ∝ − V VL r 6 → → α ≠ dispersion forces (it is necessary only that , 0 = ≠ = α d d d E 2 0 , 0 , i i the vacuum is a q.s. with observable physical consequences!) + orientation forces ( Keesom ,T, perm. dipoles) + induction forces ( Debye ,q-d) = 3 types vdW forces ≠ ∞ c - Casimir and Polder (1947): inclusion of retardation effect and at large >> λ distance r c 1 ∝ − V CP r 7

Lifshitz ������ ������ Lifshitz - by adding the vdW force between the atoms of the two plates and assuming a pairwise potential V=-B/r^n but this was experimentally wrong! - the vdW force is not additive: the force between two atoms depends of the presence of a third atom - Lifshitz (1955), Dzyaloshinskii and Pitaevskii (1961) developed a Macroscopic General Theory of the vdW Forces motivated by the experimental discrepancy with microscopic-additive theories I.E. Dzyaloshinskii, E.M. Lifshitz and L.P. Pitaevskii, Advances I.E. Dzyaloshinskii, E.M. Lifshitz and L.P. Pitaevskii, Advances in Physics 38, 165 (1961). in Physics 38, 165 (1961). Heroic Era! Heroic Era! - Lifshitz assumed the dielectrics characterized by randomly fluctuating sources as demanded by the FDT and solved the Maxwell equations using the Green function method - Ginzburg (1979): ''the calculations are so cumbersome that they were not even reproduced in the relevant Landau and Lifshitz volume where, as a rule, all important calculations are given'‘

Recent Measurements of Casimir Force Recent Measurements of Casimir Force Investigators Year Geometry Method Distance Materials Pressu Temp Accura Scale re (K) cy (nm) (mbar) (%) 10 -4 S. K. Lamoreaux 1997 Torsion 600 - Au(500nm) 300 5 pendulum 6000 5x10 -2 U. Mohideen & A. 1998 AFM 100 - 900 Al (300nm) + 300 2 Roy AuPd (20nm) 5x10 -2 A. Roy and U. 1999 AFM 100 - 900 Al (250nm)+ 300 2 Mohideen AuPd (8nm) 5x10 -2 G. L. Klimthitskaya, 1999 AFM 100 - 900 Al (300nm) + 300 1 A. Roy, U. Mohideen AuPd and V. M. (20nm) Mostepanenko T. Ederth 2000 Piezo-tube 20 - 100 50µm Au 1000 300 1 manipulator wires coated in thiol SAM H. B. Chan, V. A. 2001 MEMS 90 - 1000 Au (200nm) 1000 300 1 Aksyuk, R. N. torsion bar + Cr Kleiman, D. J. Bishop capacitance underlayer & F. Capasso 10 -5 G. Bressi, G. 2002 Interfero- 500 - Cr (50nm) 300 15 Carugno, R. Onofrio 3000 on Si metry & G. Ruoso 10 -4 R. S. Decca, D. 2003 MEMS 200 - Cu/Au 300 1 Lopez, E. Fischbach torsion bar 2000 & D. E. Krause capacitance 10 -11 NANOCASE 2005 AFM, MEMS 10 - 1000 Si, Au 20 - <1 - 1000

���������������������� ������������ �������������������� ��������� ����� ����� ��������������������� - Behaviour of Casimir-Polder force well explored experimentally at short distances (mainly forces between metallic bodies) Bressi et al. PRL 2002 (plate-plate configuration) - Behaviour at larger distances (few microns) less explored . In particular thermal effects of the force not yet measured - Cold atoms are natural candidates to explore thermal effects of the force at moderately large distances (5-10 microns).

Surface- -atom interaction atom interaction has been the Surface has been the object object of of systematic systematic experimental and and theoretical theoretical studies studies in in recent recent years years. . experimental Motivations : Motivations : - Open theoretical and experimental questions (ex: role of e.m. thermal fluctuations, usually masked ) - Perspectives for applications (atom chips, ..) - New constraints on hypothetical non-Newtonian forces at short distances

���������������� ���� ����� ���������� ����� ������������ - Shih and Parsegian (1975): deflection of atomic beam (VL) - Anderson (1988): deflection of atomic beam (VL), Rydberg atoms - Hinds (1993): deflection of atomic beam (CP) - Aspect (1997): reflection from atomic mirror - Shimizu (2001, 2005): reflection from solid surface - Vuletic (2004): BEC stability near surfaces - Ketterle (2004): BEC reflection from solid surface - Cornell (2005): BEC center of mass oscillation (CP) - Cornell (2006): BEC center of mass oscillation (Thermal)

Plan of the talk Plan of the talk • ������������ force at ������������������� • ������������ force �������������������������� • Recent �������������������� • ��������������� force ��������������������������

�������� ����������� ���������� ������� ����������������������� T ���������������������������� S ��������������� T ���������������������� E � � � � � � � � tot tot ind fl fl ind = ∇ ≈ ∇ + ∇ F r d t E r t d t E r t d t E r t ( ) ( ) ( , ) ( ) ( , ) ( ) ( , ) i i i i i i Force includes zero-point ( or vacuum ) fluctuations effects + thermal ( or radiation ) fluctuations effects ( crucial at large distance! )

Electric Field � � = ∫ � � � � ω ω • ω E r G r r P r [ ; ] [ ; , ' ] [ ] d V Fluctuations Dissipation Theorem   ε ω ω � � � � � � ' ' ( ) + fl fl   ω ω = δ ω − ω δ − δ P r P r r r [ ; ] [ ' , ' ] coth ( ' ) ( ' )   i j ij k T   S 2 2 B

������������������� ����!����"��� �# #� ��������� �������� ������������������� ����!����"�� [ ] ∞   ω � � � � ∫   eq = ω α ω ∂ ω F T z d G r r ( , ) coth Im ( ) [ ; , ]   � � � = = z ii r r r π k T 1 2   2 2 1 2 B 0   ω � 2   = + coth 1   ω k T − k T e � /   B 2 1 B Thermal fluctuations Vacuum fluctuations : T=0 eq = + eq F T z F z F T z ( , ) ( ) ( , ) th 0

���������������� ������ ������ �� �� $ ����!���� $ ����!���� ���������� ������ λ - Optical length fixed by optical properties of the substrate ( typically opt fractions of microns) - Thermal photon wavelength ( at room temperature) λ = � ≈ µ c k T m / 7 . 6 T B Casimir-Polder (Vacuum+retardation) van der Waals-London (Vacuum) Lifshitz (Thermal)