Casimir forces: from Au to time crystals

New developments in the Casimir effect

The subject of this book is the Casimir effect, i.e., a manifestation of zero-point oscillations of the quantum vacuum in the form of forces acting between closely spaced bodies. It is a purely quantum effect. There is no force acting between neutral bodies in classical electrodynamics. The Casimir effect has become an interdisciplinary subject. It plays an important role in various fields of physics such as condensed matter physics, quantum field theory, atomic and molecular physics, gravitation and cosmology, and mathematical physics. Most recently, the Casimir effect has been applied to nanotechnology and for obtaining constraints on the predictions of unification theories beyond the Standard Model. The book assembles together the field-theoretical foundations of this phenomenon, the application of the general theory to real materials, and a comprehensive description of all recently performed measurements of the Casimir force, including the comparison between experiment and theory. There is increasing interest in forces of vacuum origin. Numerous new results have been obtained during the last few years which are not reflected in the literature, but are very promising for fundamental science and nanotechnology. The book provides a source of information which presents a critical assessment of all of the main results and approaches contained in published journal papers. It also proposes new ideas which are not yet universally accepted but are finding increasing support from experiment.

The Casimir effect, a key observable realization of vacuum fluctuations, is usually taught in graduate courses on quantum field theory. The growing importance of Casimir forces in microelectromechanical systems motivates this subject as a topic for graduate many-body physics courses. To this end, we revisit the Casimir effect using methods common in condensed matter physics. We recover previously derived results and explore the implications of the analogies implicit in this treatment.

Quantum field theory on toroidal topology: Algebraic structure and applications

It is becoming increasingly clear that ideas from quantum information theory, particularly the notion of quantum entanglement, play a fundamental role in some of the deepest aspects of our modern theories of quantum fields and gravity. The aim of this research was to explore the role that quantum entanglement plays in quantum field theories and in the nature of space-time and gravity. Building on a variety of earlier results obtained in these regards at the University of Illinois, we explored the constraints on the dynamical content of quantum field theories that follow from their entanglement properties. Topological field theories are important examples of particularly simple quantum field theories whose patterns of entanglement make connections between high energy physics, condensed matter physics and mathematics. These theories are directly relevant to low energy properties of certain materials. The study of such theories allowed us to investigate ideas that are relevant to quantum information research, such as new notions of entanglement between multiple parties and the quantum properties of interfaces between different phases of such materials. In addition, we employed new results in mathematics which strengthen monotonicity constraints on relative entropy to study their ramifications in quantum field theories, and we used quantum information methods to study the emergence of quantum gravity and string theory in holographic quantum field theories.

The Casimir force provides a striking example of the effects of quantum fluctuations in a mesoscopic system. Because it arises from the objects’ electromagnetic response, the necessary calculations in quantum field theory are most naturally expressed in terms of electromagnetic scattering from each object. In this review, we illustrate a variety of such techniques, with a focus on those that can be expressed in terms of surface effects, including both idealized boundary conditions and their physical realization in terms of material properties.

It is proposed that the contribution of vacuum fluctuations to spontaneous emission and the Casimir force can be attributed to the creation of single photons at the positions of charged particles as in relativistic quantum field theory. Thus the change from normal to symmetric order in the particle-field interaction Hamiltonian and the preservation of the equal-time commutation relations need not imply vacuum fluctuations in the absence of matter.

The distinction between vacuum-field and source-radiation effects in phenomena such as the Lamb shift, Casimir forces, and spontaneous emission relies on additional assumptions at the theoretical level, and an experimental approach was never considered feasible. Fermi's two-atom problem, a Gedankenexperiment on how atoms interact with the electromagnetic field via vacuum and source radiation, provides key theoretical insight. Advances in ultrafast optics now enable experimental analogues using two laser pulses in a nonlinear crystal. Here we demonstrate the detection of vacuum- and source-radiation-induced correlations between two pulses, separated by their causal properties. Specifically, vacuum fluctuations and source radiation are shown to correlate distinct quadratures of near-infrared pulses, enabling individual probing via phase-sensitive detection. Our results experimentally verify the time-domain fluctuation-dissipation theorem at the quantum level and open avenues for studying quantum radiation effects in time-dependent media, including entanglement harvesting from the vacuum and quantum field detection in curved-space analogues.

This paper discusses recent developments on quantum electrodynamical (QED) phenomena, such as the Casimir effect, and their use in nanomechanics and nanotechnology in general. Casimir forces and torques arise from quantum fluctuations of vacuum or, more generally, from the zero-point energy of materials and their dependence on the boundary conditions of the electromagnetic fields. Because the latter can be tailored, this raises the interesting possibility of designing QED forces for specific applications. After a concise review of the field in an historical perspective, high precision measurements of the Casimir force using microelectromechanical systems (MEMS) technology and applications of the latter to nonlinear oscillators are presented, along with a discussion of its use in nanoscale position sensors. Then, experiments that have demonstrated the role of the skin-depth effect in reducing the Casimir force are presented. The dielectric response of materials enters in a nonintuitive way in the modification of the Casimir-Lifshitz force between dielectrics through the dielectric function at imaginary frequencies epsiv(ixi). The latter is illustrated in a dramatic way by experiments on materials that can be switched between a reflective and a transparent state (hydrogen switchable mirrors). Repulsive Casimir forces between solids separated by a fluid with epsiv(ixi) intermediate between those of the solids over a large frequency range is discussed, including ongoing experiments aimed at its observation. Such repulsive forces can be used to achieve quantum floatation in a virtually frictionless environment, a phenomenon that could be exploited in innovative applications to nanomechanics. The last part of the paper deals with the elusive QED torque between birefringent materials and efforts to observe it. We conclude by highlighting future important directions

John Stuart Dowker was born in Sheffield, Yorkshire, on 18 March 1937. His life, therefore, was very much influenced by the Second World War. This is evident as his father died on active service in 1945, after being called up in 1941. His grandfather also died shortly afterwards, so he did not know either of them very well. Nevertheless, it seems that he picked up a positive attitude towards natural sciences as both were technically minded. His mother later provided, often from borrowed money, all the necessary intellectual food in forms of chemistry sets, slide rules and other things that a boy needed to develop his interests. Stuart scored excellently in the 11-plus exam, which was used to decide the type of school a pupil should attend after primary school. Although Stuart was generally allowed to do what he wanted, his mother insisted that he chose King Edward VII Grammar School (KES), the top school in Sheffield at the time. KES allowed Stuart to fully develop his intellectual abilities, and after the S-level exam he received a prestigious state scholarship which allowed him to study at any university in the country.

According to quantum field theory, empty space—the ground state with all real excitations removed—is not empty, but filled with quantum-vacuum fluctuations. Their presence can manifest itself through phenomena such as the Casimir force, spontaneous emission, or dispersion forces. These fluctuating fields possess correlations between space-time points outside the light cone, i.e. points causally disconnected according to special relativity. As a consequence, two initially uncorrelated quantum objects in empty space which are located in causally disconnected space-time regions, and therefore unable to exchange information, can become correlated. Here, we have experimentally demonstrated the existence of correlations of the vacuum fields for non-causally connected space-time points by using electro-optic sampling. This result is obtained by detecting vacuum-induced correlations between two 195 fs laser pulses separated by a time of flight of 470 fs. This work marks a first step in analyzing the space-time structure of vacuum correlations in quantum field theory.

In this paper, I propose a quantization of gravity that leads to photons mediated gravitation. The quantization of general relativity depends now on the modified special relativity [A. Almosallami, e-print viXra:1111.0001v1 (2011); e-print viXra:1401.0043 [High Energy Particle Physics](2014)], which introduces a new interpretation of the Lorentz transformation equations depending on quantum theory (Copenhagen school) [A. AlMosallami, IJSER 5, 128 (2014); Int. J. Mod. Theor. Phys. 3, 44 (2014); e-print viXra:1111.0001v1 [Relativity and Cosmology] (2011); e-printviXra:1401.0043 [High Energy Particle Physics] (2014); IJSER 5, 451 (2014)]. In these new transformations, I propose there is no space-time continuum, as in special relativity; it is only time, and space is invariant. This new interpretation of the Lorentz transformations leads to thetransformation being vacuum energy dependent instead of relative velocity dependent as in Einstein's interpretation of the Lorentz transformation equations of the theory of special relativity. Furthermore, the Lorentz factor is equivalent to the refractive index in optics. In this new interpretationof the Lorentz transformations, I refuse the reciprocity principle adopted by Einstein in the theory of special relativity. Refusing the reciprocity principle in this theory leads to the disappearance of all the paradoxes of the theory of special relativity: The Twin paradox, Ehrenfest paradox,the Ladder paradox, and Bell's spaceship paradox. Furthermore, according to my interpretation, one could explain the experimental results of quantum tunneling and entanglement (spooky action), Casimir effect, and Hartman effect. The new interpretation of the Lorentz transformation equationsleads also to the wave-particle duality as in the quantum theory, and thus agrees with Heisenberg uncertainty principle. The generalization of the transformation leads also to the concept of acceleration or deceleration as vacuum fluctuations as in the quantum field theory. In the proposedquantized force, the force is given as a function of frequency, where in this paper I defined the relativistic momentum as a function of frequency equivalent to the relativistic kinetic energy held by a body and time, and then the quantized force is given as the first derivative of the momentumwith respect to time. Subsequently, I introduce Newton's second law as its relativistic quantized force. Further, I introduce the relativistic quantized inertial force, and then, by my equivalence principle, which agrees completely with the experimental results of quantum field theory, I introducethe relativistic quantized gravitational force, and the quantized time dilation.

Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this 2008 book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts are applied to research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. This self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics. It has been reissued as an Open Access publication on Cambridge Core.

Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts and methodology are applied to current research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. Divided into five parts, with each part addressing a particular stage in the conceptual and technical development of the subject, this self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics.

In this work we axe interested in dephasing or decoherence in the zero-temperature limit. The only source of decoherence are then provided by vacuum (zero-point) fluctuations. Concern with vacuum fluctuations has a long history [1] starting with theories of black-body radiation and the Planck spectrum and important effects like the Lamb shift, the Casimir effect and the Debye-Waller factor. More recently, the role of vacuum fluctuations was discussed in theories of macroscopic quantum tunneling and even more closely related to our subject in theories of macroscopic quantum coherence [2, 3]. In mesoscopic physics, we deal with systems that are so small and are cooled to such low temperatures that the wave nature of electrons becomes important and interference effects become measurable. Dephasing processes are therefore also of central importance in mesoscopic physics. Ultimately in the zero-temperature limit only vacuum fluctuations remain and it is clearly very interesting and fascinating to inquire about a possible role of such fluctuations.