An experimental set-up for the measurement of the Casimir effect at separations larger than a few microns is presented. The apparatus is based on a mechanical resonator and uses a homodyne detection technique to sense the Casimir force in the plane-parallel configuration. First measurements in the 3-10 micrometer range show an unexpected large force probably due to patch effects.
We describe an isoelectronic differential apparatus designed to observe the influence on the Casimir force of the Mott-Anderson metal-insulator transition in doped semiconductors. Alternative theories of dispersion forces lead to different predictions for this effect. The investigation of this problem by standard apparatus, based on absolute measurements of the Casimir force, is very difficult because the effect is small in the region of sub-micron separations, where the Casimir force can be measured precisely. The differential apparatus described here is immune by design to several sources of…
State of a $d$-dimensional quantum system can only be inferred by performing an informationally complete measurement with $m\geqslant d^2$ outcomes. However, an experimentally accessible measurement can be informationally incomplete. Here we show that a single informationally incomplete measuring apparatus is still able to provide all the information about the quantum system if applied several times in a row. We derive a necessary and sufficient condition for such a measuring apparatus and give illustrative examples for qubits, qutrits, general $d$-level systems, and composite systems of $n$ q…
We propose a new method to measure Casimir-Polder force in an optical cavity by means of atomic excitations. We utilize a framework in which Unruh-DeWitt Hamiltonian mimics the full matter-field interaction and find a connection between the excitation rate of the two-level atom and the Casimir-Polder energy, allowing to map one onto the other. We argue that such a realization opens a route to study Casimir-Polder potentials through measurement of excited state's population in large, spatially compact ensembles of atoms.
In this study, we investigate quantum nonseparability between an observed system and a measuring apparatus, or multiple measuring apparatuses. We show that the physical meaning of the outcome of the measuring apparatus obtained by weak measurement with a post-selection differs critically from that without any post-selection. In this study, the nonseparability plays the essential role, which is shown to be the same in a simultaneous conventional von Neumann-type measurement of multiple observables. From this viewpoint, we suggest a new concept, known as {\it simultaneous readability}, which is …
We study the influence of stationary axisymmetric spacetimes on Casimir energy. We consider a massive scalar field and analyze its dependence on the apparatus orientation with respect to the dragging direction associated with such spaces. We show that, for an apparatus orientation not considered before in the literature, the Casimir energy can change its sign, producing a repulsive force. As applications, we analyze two specific metrics: one associated with a linear motion of a cylinder and a circular equatorial motion around a gravitational source described by Kerr geometry.
In this work, we consider a Casimir apparatus that is put into free fall (e.g., falling into a black hole). Working in 1+1D, we find that two main effects occur: First, the Casimir energy density experiences a tidal effect where negative energy is pushed toward the plates and the resulting force experienced by the plates is increased. Second, the process of falling is inherently nonequilibrium and we treat it as such, demonstrating that the Casimir energy density moves back and forth between the plates after being "dropped,'' with the force modulating in synchrony. In this way, the Casimir ene…
We consider experiments on measuring the Casimir interaction which have been performed in the last four years. The emphasis is made on measuring differences in the Casimir pressures under a transition of the plate metal from normal to superconducting state and on the Casimir metrology platform using a commercial micromechanical sensor. In both cases several problems in the comparison between experiment and theory are discussed.
Two types of quantum measurements, measuring the spins of an entangled pair and attempting to measure a spin at either of two positions, are analysed dynamically by apparatuses of the Curie-Weiss type. The outcomes comply with the standard postulates.
We study the dynamics of a quantum system $Γ$ with an environment $Ξ$ made of $N$ elementary quantum components. We aim at answering the following questions: can the evolution of $Γ$ be characterized by some general features when $N$ becomes very large, regardless of the specific form of its interaction with each and every component of $Ξ$? In other terms: should we expect all quantum systems with a macroscopic environment to undergo a somehow similar evolution? And if yes, of what type? In order to answer these questions we use well established results from large-$N$ quantum field theories, p…
Work is an observable quantity associated with a process, however there is no Hermitian operator associated with its measurement. We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian via two von-Neumann measurements of the system's energy carried out by a measuring apparatus modeled as a free particle of finite localization and interaction time with the system. We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality an…
Thermal noise limitations to force measurements with torsion pendulums: Applications to the measurement of the Casimir force and its thermal correction
A recent experiment [R. A. Norte et al. Phys. Rev. Lett. {\bf 121}, 030405 (2018)] probed the variation of the Casimir force between two closely spaced thin Al films, as they transition into a superconducting state, observing a null result. We present here computations of the Casimir effect for superconductors, based on the Mattis-Bardeen formula for their optical response. We show that for the Al cavity used in the experiment the effect of the transition is over two hundred and fifty times smaller than the experimental sensitivity, in agreement with the observed null result. We demonstrate th…
A quantum measuring instrument is constructed that utilises symmetry breaking to enhance a microscopic signal. The entire quantum system consists of a system-apparatus-environment triad that is composed of a small set of spin-1/2 particles. The apparatus is a ferromagnet that measures the $z$-component of a single spin. A full quantum many-body calculation allows for a careful examination of the loss of phase coherence, the formation and amplification of system-apparatus correlations, the irreversibility of registration, the fault tolerance, and the bias of the device.
We propose an experiment for measuring the effective Casimir pressure between two parallel SiC plates with aligned nuclear spins. The prospective constraints on an axion-neutron coupling constant for both hadronic and GUT axions are calculated using the process of one-axion exchange. For this purpose, a general expression for the additional pressure arising between two polarized plates due to the exchange of one axion between their constituent fermions is derived. We demonstrate that only the polarization component perpendicular to the plates contribute to the pressure. The obtained pressure c…
We consider the out-of-thermal-equilibrium Casimir-Polder interaction between atoms of He$^*$, Na, Cs, and Rb and a cavity wall made of sapphire coated with a vanadium dioxide film which undergoes the dielectric-to-metal phase transition with increasing wall temperature. Numerical computations of the Casimir-Polder force and its gradient as the functions of atom-wall separation and wall temperature are made when the latter exceeds the temperature of the environment. The obtained results are compared with those in experiment on measuring the gradient of the Casimir-Polder force between $^{87}$R…
It is well known that residual electrostatic forces create significant difficulties to precise measurements of the Casimir force and to wide use of Casimir-operated microdevices. We experimentally demonstrate that with the help of Ar-ion cleaning of the surfaces it is possible to make electrostatic effects negligibly small as compared to the Casimir interaction. Our experimental setup consists of the dynamic atomic force microscope supplemented with an Ar-ion gun and argon reservoir. The residual potential difference between the Au-coated surfaces of a sphere and a plate was measured both befo…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run into difficulties of one sort or another. One of the first detailed descriptions was given by Sudarshan and his collaborators who, motivated by the measurement problem in quantum mechanics, proposed a Hilbert space formulation of classical-quantum interactions which made use of the Koopman-von Neumann description of classical systems. Here we use the approach …
The possibility of performing simultaneous measurements in quantum mechanics is investigated in the context of the Curie-Weiss model for a projective measurement. Concretely, we consider a spin-$\frac{1}{2}$ system simultaneously interacting with two magnets, which act as measuring apparatuses of two different spin components. We work out the dynamics of this process and determine the final state of the measuring apparatuses, from which we can find the probabilities of the four possible outcomes of the measurements. The measurement is found to be non-ideal, as (i) the joint statistics do not c…
