Limits on nonstandard forces in the submicrometer range

Dark Matter Axions, Non-Newtonian Gravity and Constraints on Them from Recent Measurements of the Casimir Force in the Micrometer Separation Range

We consider axionlike particles as the most probable constituents of dark matter, the Yukawa-type corrections to Newton’s gravitational law and constraints on their parameters following from astrophysics and different laboratory experiments. After a brief discussion of the results by Prof. Yu. N. Gnedin in this field, we turn our attention to the recent experiment on measuring the differential Casimir force between Au-coated surfaces of a sphere and the top and bottom of rectangular trenches. In this experiment, the Casimir force was measured over an unusually wide separation region from 0.2 to 8μm and compared with the exact theory based on first principles of quantum electrodynamics at nonzero temperature. We use the measure of agreement between experiment and theory to obtain the constraints on the coupling constant of axionlike particles to nucleons and on the interaction strength of a Yukawa-type interaction. The constraints obtained on the axion-to-nucleon coupling constant and on the strength of a Yukawa interaction are stronger by factors of 4 and 24, respectively, than those found previously from gravitational experiments and measurements of the Casimir force but weaker than the constraints following from a differential measurement where the Casimir force was nullified. Some other already performed and planned experiments aimed at searching for axions and non-Newtonian gravity are discussed, and their prospects are evaluated.

Combined Test of the Gravitational Inverse-Square Law at the Centimeter Range

Experiments measuring the Newtonian gravitational constant G can offer uniquely sensitive probes of the test of the gravitational inverse-square law. An analysis of the non-Newtonian effect in two independent experiments measuring G is presented, which permits a test of the 1/r^{2} law at the centimeter range. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 5-500 mm and improves the previous bounds by up to a factor of 7 at the length range of 60-100 mm.

Constraints on Theoretical Predictions beyond the Standard Model from the Casimir Effect and Some Other Tabletop Physics

We review the hypothetical interactions predicted beyond the Standard Model which could be constrained by using the results of tabletop laboratory experiments. These interactions are described by the power-type potentials with different powers, Yukawa potential, other spin-independent potentials, and by the spin-dependent potentials of different kinds. In all these cases the current constraints on respective hypothetical interactions are considered which follow from the Casimir effect and some other tabletop physics. The exotic particles and constraints on them are discussed in the context of problems of the quantum vacuum, dark energy, and the cosmological constant.

The State of the Art in Constraining Axion-to-Nucleon Coupling and Non-Newtonian Gravity from Laboratory Experiments

Constraints on the Yukawa-type corrections to Newton’s gravitational law and on the coupling constant of axionlike particles to nucleons obtained from different laboratory experiments are reviewed and compared. The constraints on non-Newtonian gravity under discussion cover the wide interaction range from nanometers to millimeters and follow from the experiments on neutron scattering, measuring the Casimir force and Cavendish-type experiments. The constraints on the axion-to-nucleon coupling constant following from the magnetometer measurements, Cavendish-type experiments, Casimir physics, and experiments with beams of molecular hydrogen are considered, which refer to the region of axion masses from 10−10 to 200 eV. Particular attention is given to the recent constraints obtained from measuring the Casimir force at nanometer separation distance between the test bodies. Several proposed experiments focussed on constraining the non-Newtonian gravity, axionlike particles and other hypothetical weakly interacting particles, such as chameleons and symmetrons, are discussed.

Improvement for Testing the Gravitational Inverse-Square Law at the Submillimeter Range

We improve the test of the gravitational inverse-square law at the submillimeter range by suppressing the vibration of the electrostatic shielding membrane to reduce the disturbance coupled from the residual surface potential. The result shows that, at a 95% confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=48  μm. This work establishes the strongest bound on the magnitude α of the Yukawa violation in the range of 40-350  μm, and improves the previous bounds by up to a factor of 3 at the length scale λ≈70  μm. Furthermore, the constraints on the power-law potentials are improved by about a factor of 2 for k=4 and 5.

Weakly bound molecules as sensors of new gravitylike forces

Several extensions to the Standard Model of particle physics, including light dark matter candidates and unification theories predict deviations from Newton's law of gravitation. For macroscopic distances, the inverse-square law of gravitation is well confirmed by astrophysical observations and laboratory experiments. At micrometer and shorter length scales, however, even the state-of-the-art constraints on deviations from gravitational interaction, whether provided by neutron scattering or precise measurements of forces between macroscopic bodies, are currently many orders of magnitude larger than gravity itself. Here we show that precision spectroscopy of weakly bound molecules can be used to constrain non-Newtonian interactions between atoms. A proof-of-principle demonstration using recent data from photoassociation spectroscopy of weakly bound Yb2 molecules yields constraints on these new interactions that are already close to state-of-the-art neutron scattering experiments. At the same time, with the development of the recently proposed optical molecular clocks, the neutron scattering constraints could be surpassed by at least two orders of magnitude.

Prospects for Searching Thermal Effects, Non-Newtonian Gravity and Axion-Like Particles: Cannex Test of the Quantum Vacuum

We consider the Cannex (Casimir And Non-Newtonian force EXperiment) test of the quantum vacuum intended for measuring the gradient of the Casimir pressure between two flat parallel plates at large separations and constraining parameters of the chameleon model of dark energy in cosmology. A modification of the measurement scheme is proposed that allows simultaneous measurements of both the Casimir pressure and its gradient in one experiment. It is shown that with several improvements the Cannex test will be capable to strengthen the constraints on the parameters of the Yukawa-type interaction by up to an order of magnitude over a wide interaction range. The constraints on the coupling constants between nucleons and axion-like particles, which are considered as the most probable constituents of dark matter, could also be strengthened over a region of axion masses from 1 to 100 meV.

MICROSCOPE Mission: First Constraints on the Violation of the Weak Equivalence Principle by a Light Scalar Dilaton

The existence of a light or massive scalar field with a coupling to matter weaker than gravitational strength is a possible source of violation of the weak equivalence principle. We use the first results on the Eötvös parameter by the MICROSCOPE experiment to set new constraints on such scalar fields. For a massive scalar field of mass smaller than 10^{-12}  eV (i.e., range larger than a few 10^{5}  m), we improve existing constraints by one order of magnitude to |α|<10^{-11} if the scalar field couples to the baryon number and to |α|<10^{-12} if the scalar field couples to the difference between the baryon and the lepton numbers. We also consider a model describing the coupling of a generic dilaton to the standard matter fields with five parameters, for a light field: We find that, for masses smaller than 10^{-12}  eV, the constraints on the dilaton coupling parameters are improved by one order of magnitude compared to previous equivalence principle tests.

Testing General Relativity with Stellar Orbits around the Supermassive Black Hole in Our Galactic Center

We demonstrate that short-period stars orbiting around the supermassive black hole in our Galactic center can successfully be used to probe the gravitational theory in a strong regime. We use 19 years of observations of the two best measured short-period stars orbiting our Galactic center to constrain a hypothetical fifth force that arises in various scenarios motivated by the development of a unification theory or in some models of dark matter and dark energy. No deviation from general relativity is reported and the fifth force strength is restricted to an upper 95% confidence limit of |α|<0.016 at a length scale of λ=150 astronomical units. We also derive a 95% confidence upper limit on a linear drift of the argument of periastron of the short-period star S0-2 of |ω[over ˙]_{S0-2}|<1.6×10^{-3}  rad/yr, which can be used to constrain various gravitational and astrophysical theories. This analysis provides the first fully self-consistent test of the gravitational theory using orbital dynamic in a strong gravitational regime, that of a supermassive black hole. A sensitivity analysis for future measurements is also presented.

New Test of the Gravitational Inverse-Square Law at the Submillimeter Range with Dual Modulation and Compensation

By using a torsion pendulum and a rotating eightfold symmetric attractor with dual modulation of both the interested signal and the gravitational calibration signal, a new test of the gravitational inverse-square law at separations down to 295  μm is presented. A dual-compensation design by adding masses on both the pendulum and the attractor was adopted to realize a null experiment. The experimental result shows that, at a 95% confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=59  μm. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 70-300  μm, and improves the previous bounds by up to a factor of 2 at the length scale λ≈160  μm.

High-precision tilt sensor using a folded Mach-Zehnder geometry in-phase and quadrature interferometer

A new high-sensitivity homodyne in-phase and quadrature (I/Q) -interferometer scheme for measuring the tilt change of a target is presented. The new tilt sensor is a Mach-Zehnder interferometer folded by the target, in which the phase change is induced by the in-plane tilt change of the target but is not sensitive to any other motions. The interferometer is specially designed to minimize interferences caused by environmental perturbations. The induced phase is directly measured by using the I/Q-demodulation scheme. The tilt sensor exhibits an excellent sensitivity 10  prad/Hz^1/2 at a frequency slightly above 1 Hz and a 0.4  prad/Hz^1/2 at a frequency higher than 30 Hz.

Disentangling geometric and dissipative origins of negative Casimir entropies

Dissipative electromagnetic response and scattering geometry are potential sources for the appearance of a negative Casimir entropy. We show that the dissipative contribution familiar from the plane-plane geometry appears also in the plane-sphere and the sphere-sphere geometries and adds to the negative Casimir entropy known to exist in these geometries even for perfectly reflecting objects. Taking the sphere-sphere geometry as an example, we carry out a scattering-channel analysis, which allows us to distinguish between the contributions of different polarizations. We demonstrate that dissipation and geometry share a common feature making possible negative values of the Casimir entropy. In both cases there exists a scattering channel whose contribution to the Casimir free energy vanishes in the high-temperature limit. While the mode-mixing channel is associated with the geometric origin, the transverse electric channel is associated with the dissipative origin of the negative Casimir entropy. By going beyond the Rayleigh limit, we find even for large distances that negative Casimir entropies can occur also for Drude-type metals provided the dissipation strength is sufficiently small.

Constraints on new gravitylike forces in the nanometer range

We report on a new constraint on gravitylike short-range forces, in which the interaction charge is mass, obtained by measuring the angular distribution of 5 Å neutrons scattering off atomic xenon gas. Around 10^{7} scattering events were collected at the 40 m small angle neutron scattering beam line located at the HANARO research reactor of the Korean Atomic Energy Research Institute. The extracted coupling strengths of new forces in the Yukawa-type parametrization are g[over ^]^{2}=(0.2±6.8±2.0)×10^{-15}  GeV^{-2} and g[over ^]^{2}=(-5.3±9.0_{-2.8}^{+2.7})×10^{-17}  GeV^{-2} for interaction ranges of 0.1 and 1.0 nm, respectively. These strengths correspond to 95% confidence level limits of g^{2}<(1.4±0.2)×10^{-14}  GeV^{-2} and g^{2}<(1.3±0.2)×10^{-16}  GeV^{-2}, improving the current limits for interaction ranges between 4 and 0.04 nm by a factor of up to 10.

Variable-temperature device for precision Casimir-force-gradient measurement

We present the design and use of an instrument that is based on a microcantilever to perform precision force gradient measurements. We demonstrate its performance through measurements of the Casimir pressure at various temperatures. The instrument can operate in high vacuum environments and temperatures between 5 K and 300 K. It uses an all-fiber optical interferometer to detect the resonant-frequency shift of a customized microcantilever due to the presence of a force gradient. To measure this shift we use both, a technique of frequency-modulation atomic force microscopy and the direct recording of the thermomechanical resonant frequency.

How to modify the van der Waals and Casimir forces without change of the dielectric permittivity

We propose a new experiment on the measurement of the Casimir force and its gradient between a Au-coated sphere and two different plates made of doped semiconductors. The concentrations of charge carriers in the plates are chosen slightly below and above the critical density at which the Mott-Anderson insulator-metal transition occurs. We calculate changes in the Casimir force and the Casimir pressure due to the insulator-metal transition using the standard Lifshitz theory and the phenomenological approach neglecting the contribution of free charge carriers in the dielectric permittivity of insulator materials (this approach was recently supported by the measurement data of several experiments). It is demonstrated that for the special selection of semiconductor materials (S- or Se-doped Si, B-doped diamond) the calculation results using the two theoretical approaches differ significantly and the predicted effects are easily detectable using the existing laboratory setups. In the case that the prediction of the phenomenological approach is confirmed, this would open opportunities to modify the van der Waals and Casimir forces with almost no change of room temperature dielectric permittivity.

Test of the gravitational inverse square law at millimeter ranges

We report a new test of the gravitational inverse square law at millimeter ranges by using a dual-modulation torsion pendulum. An I-shaped symmetric pendulum and I-shaped symmetric attractors were adopted to realize a null experimental design. The non-Newtonian force between two macroscopic tungsten plates is measured at separations ranging down to 0.4 mm, and the validity of the null experimental design was checked by non-null Newtonian gravity measurements. We find no deviations from the Newtonian inverse square law with 95% confidence level, and this work establishes the most stringent constraints on non-Newtonian interaction in the ranges from 0.7 to 5.0 mm, and a factor of 8 improvement is achieved at the length scale of several millimeters.

New experimental limits on non-Newtonian forces in the micrometer range

We report measurements of the short-range forces between two macroscopic gold-coated plates using a torsion pendulum. The force is measured for separations between 0.7 and 7 μm and is well described by a combination of the Casimir force, including the finite-temperature correction, and an electrostatic force due to patch potentials on the plate surfaces. We use our data to place constraints on the Yukawa-type "new" forces predicted by theories with extra dimensions. We establish a new best bound for force ranges 0.4-4 μm and, for forces mediated by gauge bosons propagating in (4+n) dimensions and coupling to the baryon number, extract a (4+n)-dimensional Planck scale lower limit of M(*)>70 TeV.

Short-range force detection using optically cooled levitated microspheres

We propose an experiment using optically trapped and cooled dielectric micro-spheres for the detection of short-range forces. The center-of-mass motion of a microsphere trapped in vacuum can experience extremely low dissipation and quality factors of 10(12), leading to yoctonewton force sensitivity. Trapping the sphere in an optical field enables positioning at less than 1 μm from a surface, a regime where exotic new forces may exist. We expect that the proposed system could advance the search for non-Newtonian gravity forces via an enhanced sensitivity of 10(5)-10(7) over current experiments at the 1 μm length scale. Moreover, our system may be useful for characterizing other short-range physics such as Casimir forces.

Thermal Casimir effect in the plane-sphere geometry

The thermal Casimir force between two metallic plates is known to depend on the description of material properties. For large separations the dissipative Drude model leads to a force a factor of 2 smaller than the lossless plasma model. Here we show that the plane-sphere geometry, in which current experiments are performed, decreases this ratio to a factor of 3/2, as revealed by exact numerical and large-distance analytical calculations. For perfect reflectors, we find a repulsive contribution of thermal photons to the force and negative entropy values at intermediate distances.

Quantum dissipative Brownian motion and the Casimir effect

We explore an analogy between the thermodynamics of a free dissipative quantum particle in one dimension and that of an electromagnetic field between two mirrors of finite conductivity. While a free particle isolated from its environment will effectively be in the high-temperature limit for any nonvanishing temperature, a finite coupling to the environment leads to quantum effects ensuring the correct low-temperature behavior. Even then, it is found that under appropriate circumstances the entropy can be a nonmonotonic function of the temperature. Such a scenario with its specific dependence on the ratio of temperature and damping constant also appears for the transverse electric mode in the Casimir effect. The limits of vanishing dissipation for the quantum particle and of infinite conductivity of the mirrors in the Casimir effect both turn out to be noncontinuous.