Recent advances in nanotechnology and atomic physics may allow for a demonstration of the dynamical Casimir effect. An array of film bulk acoustic resonators (FBARs) coherently driven at twice the resonant frequency of a high-quality electromagnetic cavity can generate a stationary state of Casimir photons. These are detected using an alkali atom beam prepared in an inverted population of hyperfine states, with an induced superradiant burst producing a detectable radio-frequency signal. We describe here the results of the simulations of the dynamics of superradiance and superfluorescence, with the aim to optimize the parameters for the detectability of Casimir photons. When the superradiant lifetime is shorter than the dissipation time, we find superradiant evolution to be similar in character but dramatically slower than in the usual lossy case.
This is a review of publications on classical and quantum electrodynamics in cavities with moving boundaries (in the quantum case this subject is labeled frequently as "nonstationary Casimir effect" or "dynamical Casimir effect"), from 1921 to October of 2000, with an emphasis on analytical results related to cavities with resonantly oscillating boundaries.
Superradiance occurs when a collection of atoms exhibits cooperative, spontaneous emission of photons at a rate that exceeds that of its component parts. Here, we reveal a similar phenomenon in a hydrodynamic system consisting of a pair of vibrationally-excited cavities, coupled through their common wavefield, that spontaneously emit droplets via interfacial fracture. We show that the droplet emission rate of two coupled cavities is higher than the emission rate of two isolated cavities. We further show that the amplified emission rate varies sinusoidally with distance between the cavities, th…
We study the creation of photons in resonant cylindrical cavities with time dependent length. The physical degrees of freedom of the electromagnetic field are described using Hertz potentials. We describe the general formalism for cavities with arbitrary section. Then we compute explicitly the number of TE and TM motion-induced photons for cylindrical cavities with rectangular and circular sections. We also discuss the creation of TEM photons in non-simply connected cylindrical cavities.
We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose-Einstein condensate in an optomechanical cavity. The system is studied using both classical and quantized mirror motions. The cavity frequency is harmonically modulated in time for both the cases. The main quantity of interest is the number of intracavity scattered photons. The system has been investigated under the weak and strong modulation. It has been observed that the amplitude of the scattered photons is more for the classical mirror motion than the quantized mirror motion. Also, initially, th…
There is the possibility in principle that the noncompensated Casimir force exists in open nanosized metal cavities arranged in the form of periodic structures. It is found that when trapezoid cavities are strictly periodic all the Casimir expulsion forces are completely compensated. However, when the distance of the gap is formed between the cavities, in the periodic configuration a noncompensated expulsion force proportional to the number of cavities appears. There are such effective parameters of the periodic configuration (the angles of the opening of cavities, their lengths and the relati…
We report on preliminary results on the measurement of variations of the Casimir energy in rigid cavities through its influence on the superconducting transition of in-cavity aluminium (Al) thin films. After a description of the experimental apparatus we report on a measurement made with thermal photons, discussing its implications for the zero-point photons case. Finally we show the preliminary results for the zero-point case.
The possibility in principle is shown that the noncompensated Casimir force can exist in nanosized open metal cavities. The force shows up as time-constant expulsion of open cavities toward their least opening. The optimal parameters of the angles of the opening, of "generating lines" of cavities and their lengths are found at which the expulsive force is maximal. The theory is created for trapezoid configurations, in particular for parallel mirrors which experience both the transverse Casimir pressure and longitudinal compression at zero general expulsive force.
We consider the interaction pressure acting on the surface of a dielectric sphere enclosed within a magnetodielectric cavity. We determine the sign of this quantity regardless of the geometry of the cavity for systems at thermal equilibrium, extending the Dzyaloshinskii-Lifshitz-Pitaevskii result for homogeneous slabs. As in previous theorems regarding Casimir-Lifshitz forces, the result is based on the scattering formalism. In this case the proof follows from the variable phase approach of electromagnetic scattering. With this, we present configurations in which both the interaction and the s…
We study the peculiarities of the nonstationary Casimir effect (creation of photons in cavities with moving boundaries) in the special case of two resonantly coupled modes with frequencies $ω_0$ and $(3Δ)ω_0$, parametrically excited due to small amplitude oscillations of the ideal cavity wall at the frequency $2ω_0(1δ)$ (with $|δ|,|Δ|\ll 1$). The effects of thermally induced oscillations in time dependences of the mean numbers of created photons and the exchange of quantum purities between the modes are discovered. Squeezing and photon distributions in each modes are calculated for initial vac…
We obtain expressions for the Casimir energy and force following an approach which may be applied to cavities made up of arbitrary materials. In the case of planar cavities we obtain the well known Lifshitz formula. The approach is easily generalizable to other geometries.
We present a new derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are in general lossy and characterized by frequency dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the C…
We calculate the Casimir energy at spherical cavities within a host made up of an arbitrary material described by a possibly dispersive and lossy dielectric response. To that end, we add to the coherent optical response a contribution that takes account of the incoherent radiation emitted by the host in order to guarantee the detailed balance required to keep the system at thermodynamic equilibrium in the presence of dissipation. The resulting boundary conditions allow a conventional quantum mechanical treatment of the radiation within the cavity from which we obtain the contribution of the ca…
Cavities with periodically oscillating mirrors have been predicted to excite photon pairs out of the quantum vacuum in a process known as the Dynamical Casimir effect. Here we propose and analyse an experimental layout that can provide an efficient modulation of the effective optical length of a cavity mode in the near-infrared spectral region. An analytical model of the dynamical Casimir emission is developed and compared to the predictions of a direct numerical solution of Maxwell's equations in real time. A sizeable intensity of dynamical Casimir emission is anticipated for realistic operat…
Nonclassical Many-Body Superradiant States with Interparticle and Spin-Momentum Entanglement
JILA and Department of Physics, University of Colorado（科罗拉多大学物理系与JILA）；Theoretische Physik, Universität des Saarlandes（萨尔兰州立大学理论物理学）；Physikalisches Institut, University of Bonn（波恩大学物理研究所）
We perform a theoretical analysis of a setup intended to measure the repulsive (outward) Casimir forces predicted to exist inside of perfectly conducting rectangular cavities. We consider the roles of the conductivity of the real metals, of the temperature and surface roughness. The use of this repulsive force to reduce friction and wear in micro and nanoelectromechanical systems (MEMS and NEMS) is also considered.
In this paper we study the Casimir energy of a sample made by N cavities, with N >> 1, across the transition from the metallic to the superconducting phase of the constituting plates. After having characterized the energy for the configuration in which the layers constituting the cavities are made by dielectric and for the configuration in which the layers are made by plasma sheets, we concentrate our analysis on the latter. It represents the final step towards the macroscopic characterization of a "multi cavity" (with N large) necessary to fully understand the behaviour of the Casimir energy …
Casimir-type forces, such as those between two neutral conducting plates, or between a sphere, atom or molecule and a plate have been widely studied and are becoming of increasing significance, for example, in nanotechnology. A key challenge is to better understand, from a fundamental microscopic approach, why the Casimir force is in some circumstances attractive and in others repulsive. Here, we study the Casimir-Polder forces experienced by small quantum systems such as atoms or molecules in an optical cavity. In order to make the problem more tractable, we work in a 1+1 dimensional setting,…
The Casimir force due to {\it thermal} fluctuations (or pseudo-Casimir force) was previously calculated for the perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to {\it quantum} fluctuations in a weakly-interacting dilute Bose-Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic …
The existence of quantum tricriticality and exotic phases are found in a Dicke triangle (TDT) where three cavities, each one containing an ensemble of three-level atoms, are connected to each other through the action of an artificial magnetic field. The conventional superradiant phase (SR) is connected to the normal phase through first- and second-order boundaries, with tricritical points located at the intersection of such boundaries. Apart from the SR phase, a chiral superradiant (CSR) phase is found by tuning the artificial magnetic field. This phase is characterized by a nonzero photon cur…
We report on measurements of the Casimir force in a sphere-plane geometry using a cryogenic force microscope to move the force probe in situ over different materials. We show how the electrostatic environment of the interacting surfaces plays an important role in weak force measurements and can overcome the Casimir force at large distance. After minimizing these parasitic forces, we measure the Casimir force between a gold-coated sphere and either a gold-coated or a heavily doped silicon surface in the 100-400 nm distance range. We compare the experimental data with theoretical predictions and…
Nonlinear terms in the equations of motion can induce secularly growing loop corrections to correlation functions. Recently such corrections were shown to affect the particle production by a nonuniformly moving ideal mirror. We extend this conclusion to the cases of ideal vibrating cavity and single semitransparent mirror. These models provide natural IR and UV scales and allow a more accurate study of the loop behavior. In both cases we confirm that two-loop correction to the Keldysh propagator quadratically grows with time. This growth indicates a breakdown of the semiclassical approximation…
We consider the Casimir-Polder potential of particles placed inside a metallic cylindrical cavity at finite temperatures, taking account of thermal non-equilibrium effects. In particular, we study how the resonant (thermal non-equilibrium) potential and transition rates can be enhanced by fine-tuning the radius of the cavity to match the transition wavelength of the dominant transition of the particle. Numerical calculations show that the CP potential acting atoms prepared in low-lying Rydberg states can be enhanced beyond 30 kHz, which is within the range of observability of modern experiment…
We study the influence of fluctuations in periodic motion of boundaries of an ideal three-dimensional cavity on the rate of photon generation from vacuum due to the nonstationary Casimir effect.
We present a canonical formalism facilitating investigations of the dynamical Casimir effect by means of a response theory approach. We consider a massless scalar field confined inside of an arbitaray domain $G(t)$, which undergoes small displacements for a certain period of time. Under rather general conditions a formula for the number of created particles per mode is derived. The pertubative approach reveals the occurance of two generic processes contributing to the particle production: the squeezing of the vacuum by changing the shape and an acceleration effect due to motion af the boundari…
In this paper we study the behavior of the Casimir energy of a "multi-cavity" across the transition from the metallic to the superconducting phase of the constituting plates. Our analysis is carried out in the framework of the ARCHIMEDES experiment, aiming at measuring the interaction of the electromagnetic vacuum energy with a gravitational field. For this purpose it is foreseen to modulate the Casimir energy of a layered structure composing a multi-cavity coupled system by inducing a transition from the metallic to the superconducting phase. This implies a thorough study of the behavior of t…
We consider the problem of motion-induced photon creation from quantum vacuum inside closed, perfectly conducting cavities with time-dependent geometries. These include one dimensional Fabry-Perrot resonators with Dirichlet or Neumann boundary conditions, three dimensional cylindrical waveguides, and a spherical shell. The number of Casimir TE, TM and TEM photons is computed. We also present a classical mechanical analogue of the one dimensional dynamical Casimir effect.
Motivated by the experimental realization of Dicke model in optical cavities, we model an optomechanical system consisting of a two level BEC with transverse pumping. We investigate the transition from normal and inverted state to the superradiant phase through a detailed study of the phase portrait of the system. The rich phase portrait generated by analytic arguments displays two types of superradiant phases, regions of coexistence and some portion determining the persistent oscillations. We study the time evolution of the system from any phase and discuss the role of mirror frequency in ach…
We report on a new force that acts on cavities (literally empty regions of space) when they are immersed in a background of non-interacting fermionic matter fields. The interaction follows from the obstructions to the (quantum mechanical) motions of the fermions caused by the presence of bubbles or other (heavy) particles in the Fermi sea, as, for example, nuclei in the neutron sea in the inner crust of a neutron star or superfluid grains in a normal Fermi liquid. The effect resembles the traditional Casimir interaction between metallic mirrors in the vacuum. However, the fluctuating electroma…
In this article we explore the dynamics of many-body atomic systems symmetrically coupled to a single Lorentzian photonic cavity. Our study reveals interesting dynamical characteristics including non-zero steady states, superradiant decay, enhanced energy transfer and the ability to modulate oscillations in the atomic system by tuning environmental degrees of freedom. We also analyse a configuration consisting of a three-atom chain embedded in a photonic cavity. Similarly, we find a strong enhancement of the energy transfer rate between the two ends of the chain and identified specific initial…
We study the entanglement dynamics between two cavities when one of them is harmonically shaken in the context of quantum information theory. We find four different regimes depending on the frequency of the motion and the spectrum of the moving cavity. If the moving cavity is three dimensional only two modes inside get coupled and the entanglement can either degrade asymptotically with time or oscillate depending on the driving. On the other hand, if the cavity has an equidistant spectrum the entanglement can either vanish asymptotically if it is driven with its fundamental frequency or have a…
We study the dynamical Casimir effect in a double superconducting cavity in a circuit quantum electrodynamics architecture. Parameters in the quantum circuit are chosen in such a way the superconducting cavity can mimic a double cavity, formed by two perfectly conducting outer walls and a dielectric one, with arbitrary permittivity separating both halves. We undertake a spectral analysis of the cavity, showing that the spectrum varies significantly depending on the values of the susceptibility of the dielectric mirror and the relative lengths of both cavities. We study the creation of photons …
In the context of ultracold atoms in multimode optical cavities, the appearance of a quantum-critical glass phase of atomic spins has been predicted recently. Due to the long-range nature of the cavity-mediated interactions, but also the presence of a driving laser and dissipative processes such as cavity photon loss, the quantum optical realization of glassy physics has no analog in condensed matter, and could evolve into a "cavity glass microscope" for frustrated quantum systems out-of-equilibrium. Here we develop the non-equilibrium theory of the multimode Dicke model with quenched disorder…
Recent studies of strongly interacting atoms and photons in optical cavities have rekindled interest in the Dicke model of atomic qubits coupled to discrete photon cavity modes. We study the multimode Dicke model with variable atom-photon couplings. We argue that a quantum spin glass phase can appear, with a random linear combination of the cavity modes superradiant. We compute atomic and photon spectral response functions across this quantum phase transition, both of which should be accessible in experiment.
Despite tremendous progress in the research on self-assembled nanotechnological building blocks such as macromolecules, nanowires, and two-dimensional materials, synthetic self-assembly methods bridging nanoscopic to macroscopic dimensions remain unscalable and inferior to biological self-assembly. In contrast, planar semiconductor technology has had an immense technological impact owing to its inherent scalability, yet it appears unable to reach the atomic dimensions enabled by self-assembly. Here we use surface forces including Casimir-van der Waals interactions to deterministically self-ass…
We consider various approaches to the creation of a high-stability active optical frequency standard, where the atomic ensemble itself produces a highly stable and accurate frequency signal. The short-time frequency stability of such standards may overcome the stability of lasers stabilized to macroscopic cavities which are used as local oscillators in the modern optical frequency standard systems. The main idea is to create a "superradiant" laser operating deep in the bad cavity regime, where the decay rate of the cavity field significantly exceeds the decoherence rate of the lasing transitio…
Optical cavity QED provides a platform with which to explore quantum many-body physics in driven-dissipative systems. Single-mode cavities provide strong, infinite-range photon-mediated interactions among intracavity atoms. However, these global all-to-all couplings are limiting from the perspective of exploring quantum many-body physics beyond the mean-field approximation. The present work demonstrates that local couplings can be created using multimode cavity QED. This is established through measurements of the threshold of a superradiant, self-organization phase transition versus atomic pos…
