1. New constraints on Yukawa-type interactions from the Casimir effect V. M. Mostepanenko Noncommercial Partnership “Scientific Instruments”, Moscow, Russia QFEXT11, Benasque, Spain, 2011

2. CONTENT 1.Introduction 2. Constraints from gravitational experiments 3. Constraints from the normal Casimir force between test bodies with smooth surfaces 4. Constraints from the normal Casimir force between test bodies with corrugated surfaces 5. Constraints from the lateral Casimir force 6.Constraints from the thermal Casimir-Polder force 7. Possibilities to strengthen constraints from the Casimir force 8. Conclusions QFEXT11, Benasque, Spain, 2011

3. 1. INTRODUCTION Yukawa-type corrections to Newton’s law: Power-type corrections to Newton’s law: QFEXT11, Benasque, Spain, 2011

4. Yukawa- and power-type potentials originate from: 1) Exchange of light and massless elementary particles, such as: --- arion; --- scalar axion; --- graviphoton; --- dilaton; --- goldstino; --- moduli. These particles may contribute to the dark matter and dark energy. QFEXT11, Benasque, Spain, 2011

5. 2) Extra-dimensional theories with low-energy compactification scale Arkani-Hamed, Dimopoulos, Dvali, PRD, 1999 cm QFEXT11, Benasque, Spain, 2011

6. The Yukawa-type force between two macrobodies QFEXT11, Benasque, Spain, 2011

7. 2. CONSTRAINTS FROM GRAVITATIONAL EXPERIMENTS The strongest constraints on Yukawa-type corrections to Newton's gravitational law following from various gravitational experiments (lines 1-5) and measurements of the Casimir force (line 6). QFEXT11, Benasque, Spain, 2011

8. 3. CONSTRAINTS FROM THE NORMAL CASIMIR FORCE BETWEEN TEST BODIES WITH SMOOTH SURFACES Measured quantities are the Casimir force or its gradient: Obtaining constraints on Yukawa forces: QFEXT11, Benasque, Spain, 2011

9. Opinion: one and the same experiment cannot be used for the two purposes (a) to exclude or confirm some theory of the Casimir force; (b) to place constraints on the Yukawa force (Lambrecht, Reynaud, arXiv:1106.3848) This opinion would be worthwhile only if the difference between the excluded and confirmed theories for the Casimir force can be modeled by the Yukawa force. QFEXT11, Benasque, Spain, 2011

10. Measurements of the Casimir force using an atomic force microscope Force sensitivity 10 -17 N possible We achieve 10 -13 N Mohideen et al, 1998-2000 QFEXT11, Benasque, Spain, 2011

11. Shematic setup Schematic setup with a micromachined oscillator for measurements of the Casimir force gradient Decca et al, 2003-2007 QFEXT11, Benasque, Spain, 2011

12. The strongest constraints on Yukawa-type corrections to Newton's gravitational law obtained from the measurement of the Casimir force using an atomic force microscope (red line), from the measurement of the Casimir pressure by means of a micromachined oscillator (green line), and from the Casimir-less experiment (blue line), from the torsion pendulum experiment of 1997 (grey line) and from the torsion balance experiment 2009 (black line). QFEXT11, Benasque, Spain, 2011

13. Constraints from recent torsion pendulum experiment (Sushkov, Kim, Dalvit, Lamoreaux, Nature Phys. 2011; arXiv:1108.2547) Problems with this experiment: (a) The original data are not available; (b) the measured force of nonestablished origin is up to a factor of 10 larger than the Casimir force; (c) at separations above 3 micrometers the Casimir force obtained after subtraction much better agrees not with the Drude, but with the plasma model (Klimchitskaya, Bordag, Fischbach, Krause, Mostepanenko, Int. J. Mod. Phys. A, 2011) QFEXT11, Benasque, Spain, 2011

14. Constraints on Yukawa-type interaction obtained from the Casimir-less experiment (blue line), Lamoreaux, 1997 experiment [Bordag, Geyer, Klimchitskaya, Mostepanenko, PRD, 1998] (grey line), Lamoreaux, 2011 experiment (pink line), gravitational experiment [Geraci et al.,PRD 2008] (dashed line). QFEXT11, Benasque, Spain, 2011 Problems arising from using large spherical lenses cast doubts on all constraints obtained from Lamoreaux’s and Masuda&Sasaki experiments.

15. 4. CONSTRAINTS FROM THE NORMAL CASIMIR FORCE BETWEEN TEST BODIES WITH CORRUGATED SURFACES (Bao, Guerout, Lussange, Lambrecht, Cirelli, Klemens, Mansfield, Pai, Chan, PRL, 2010) QFEXT11, Benasque, Spain, 2011

16. Constraints on the parameters of Yukawa-type interaction which are obtained from the experiments performed by means of a micromechanical torsional oscillator with a corrugated Si plate (pink line) and with a flat Au-coated plate (green line), from the Casimir-less experiment (blue line), and from the experiments using a torsion pendulum (grey and black lines). Bezerra, Klimchitskaya, Mostepanenko, Romero, PRD, 2011 QFEXT11, Benasque, Spain, 2011

17. 5. CONSTRAINTS FROM THE LATERAL CASIMIR FORCE Golestanian, Kardar, PRL 1997; Chen, Mohideen, Klimchitskaya, Mostepanenko, PRL 2002, PRA 2002; Chiu, Klimchitskaya, Marachevsky, Mostepanenko, Mohideen, PRB 2009, PRB 2010. QFEXT11, Benasque, Spain, 2011

18. Experimental scheme x-piezo introduces phase change z-piezo changes separation distance QFEXT11, Benasque, Spain, 2011

19. Constraints on the parameters of Yukawa-type interaction from measurements of the lateral Casimir force between corrugated surfaces (red line), and from measurements of the normal Casimir force by means of an atomic force microscope (red dashed line), and a micromachined oscillator (green line). Bezerra, Klimchitskaya, Mostepanenko, Romero, PRD, 2010 QFEXT11, Benasque, Spain, 2011

20. 6. CONSTRAINTS FROM THE THERMAL CASIMIR-POLDER FORCE Obrecht, Wild, Antezza, Pitaevskii, Stringari, Cornell, PRL (2007) Experiment on measuring the Casimir-Polder force between a glass plate and Rb atoms belonging to the Bose-Einstein condensate. QFEXT11, Benasque, Spain, 2011

21. Obrecht, Wild, Antezza, Pitaevskii, Stringari, Cornell, PRL (2007); Klimchitskaya, Mostepanenko, JPA (2008). Frequency shift of center-of-mass oscillations of Bose-Einstein condensate of Rb atoms QFEXT11, Benasque, Spain, 2011

22. Constraints from measurements of the Casimir-Polder force (brown line), from the experiment using a torsion balance (black line), from the measurement of the Casimir force by means of a torsion pendulum (grey line), and from the gravitational experiment (short-dashed line). ( Bezerra, Klimchitskaya, Mostepanenko, Romero, PRD 2010) QFEXT11, Benasque, Spain, 2011

23. 7. POSSIBILITIES TO STRENGTHEN CONSTRAINTS FROM THE CASIMIR FORCE 1. Using normal Casimir force with a smooth sphere and a corrugated plate. 2. Using normal Casimir force in cylinder-plate configuration. QFEXT11, Benasque, Spain, 2011

24. Plate with rectangular corrugations Bezerra, Klimchitskaya, Mostepanenko, Romero, PRD, 2011 The dashed line shows the prospective constraints that can be obtained from the experiment with a corrugated Au plate instead of Si plate. QFEXT11, Benasque, Spain, 2011

25. Constraints on the parameters of Yukawa-type interaction from proposed measurements of the normal Casimir force between a smooth sphere and a corrugated plate of micromachined oscallator (dashed green line), from measurements of the lateral Casimir force between corrugated surfaces (red line), and from measurements of the normal Casimir force using a smooth plate of micromachined oscillator (green line). Bezerra, Klimchitskaya, Mostepanenko, Romero, PRD 2010 QFEXT11, Benasque, Spain, 2011

26. Cylinder-plate configuration Decca, Fischbach, Klimchitskaya, Krause, Lopez, Mostepanenko, PRA 2010 QFEXT11, Benasque, Spain, 2011

27. The dashed line shows the prospective constraints that can be obtained from measuring the gradient of the Casimir force between a plate and a microfabricated cylinder. Klimchitskaya, Romero, PRD 2010 QFEXT11, Benasque, Spain, 2011

28. 8. CONCLUSIONS 1.Experiments on the Casimir force lead to stronger constraints at shorter interaction range where gravitational experiments do not work. 2. Recent measurements of the normal Casimir force between a sphere and rectangular corrugated plate confirmed constraints obtained from several different experiments. 3. Precise measurements of the lateral Casimir force strengthen previously known constraints up to two and a half million times. 4. In near future further strengthening of constraints is expected from measuring the normal Casimir force between a smooth sphere and a corrugated plate. QFEXT11, Benasque, Spain, 2011