Dynamical Casimir Effect Research Articles

Resource Letter CF-1: Casimir Force

This resource letter provides an introductory guide to the literature on the Casimir force. Journal articles and books are cited for the following topics: introductory articles and books, calculations, dynamical Casimir effect, mechanical analogs, applications, and experiments.

Dynamic Casimir Effect in Single Bubble Sonoluminescence

The bubble dynamics for the single bubble sonoluminescence (SBSL) has been coupled with the dynamic Casimir effect due to the quantum vacuum fluctuation. The numerical results show that the power radiated by the Casimir effect is on the order of 10-38 W and too weak to fit the experimental observation of SBSL although the spectrum of the radiation can be fitted well. It is impossible to take the quantum Casimir effect as a candidate for the origin of SBSL.

The “friction” of vacuum, and other fluctuation-induced forces

The static Casimir effect describes an attractive force between two conducting plates, due to quantum fluctuations of the electromagnetic (EM) field in the intervening space. Thermal fluctuations of correlated fluids (such as critical mixtures, super-fluids, liquid crystals, or electrolytes) are also modified by the boundaries, resulting in finite-size corrections at criticality, and additional forces that affect wetting and layering phenomena. Modified fluctuations of the EM field can also account for the ``van der Waals'' interaction between conducting spheres, and have analogs in the fluctuation-induced interactions between inclusions on a membrane. We employ a path integral formalism to study these phenomena for boundaries of arbitrary shape. This allows us to examine the many unexpected phenomena of the dynamic Casimir effect due to moving boundaries. With the inclusion of quantum fluctuations, the EM vacuum behaves essentially as a complex fluid, and modifies the motion of objects through it. In particular, from the mechanical response function of the EM vacuum, we extract a plethora of interesting results, the most notable being: (i) The effective mass of a plate depends on its shape, and becomes anisotropic. (ii) There is dissipation and damping of the motion, again dependent upon shape and direction of motion, due to emission of photons. (iii) There is a continuous spectrum of resonant cavity modes that can be excited by the motion of the (neutral) boundaries.

Dynamical Casimir effect in a nondegenerate cavity with losses and detuning

We analyze the possibility of creating photons from a vacuum due to the dynamical Casimir effect in a nondegenerate cavity with vibrating boundaries, taking into account losses and detuning from the exact resonance. Explicit analytical solutions of the equations for the quadrature variances of an equivalent field oscillator with a time-dependent frequency show that photon generation is possible provided the relative detuning and inverse quality factor do not exceed a critical value of the order of ${10}^{\ensuremath{-}8}.$ Under this condition, the field goes finally to a highly squeezed quantum state.

Path-integral approach to the dynamic Casimir effect with fluctuating boundaries

A path-integral formulation is developed for the dynamic Casimir effect. It allows us to study small deformations in space and time of the perfectly reflecting (conducting) boundaries of a cavity. The mechanical response of the intervening vacuum is calculated to linear order in the frequency\char21{}wave-vector plane, using which a plethora of interesting phenomena can be studied. For a single corrugated plate we find a correction to mass at low frequencies and an effective shear viscosity at high frequencies that are both anisotropic. The anisotropy is set by the wave vector of the corrugation. For two plates, the mass renormalization is modified by a function of the ratio between the separation of the plates and the wavelength of corrugations. The dissipation rate is not modified for frequencies below the lowest optical mode of the cavity and there is a resonant dissipation for all frequencies greater than that. In this regime, a divergence in the response function implies that such high-frequency deformation modes of the cavity cannot be excited by any macroscopic external forces. This phenomenon is intimately related to resonant particle creation. For particular examples of two corrugated plates that are stationary, or moving uniformly in the lateral directions, Josephson-like effects are observed. For capillary waves on the surface of mercury a renormalization to surface tension and sound velocity is obtained.

Observability of the bulk Casimir effect: Can the dynamical Casimir effect be relevant to sonoluminescence?

The experimental observation of intense light emission by acoustically driven, periodically collapsing bubbles of air in water (sonoluminescence) has yet to receive an adequate explanation. One of the most intriguing ideas is that the conversion of acoustic energy into photons occurs quantum mechanically, through a dynamical version of the Casimir effect. We have argued elsewhere that in the adiabatic approximation, which should be reliable here, Casimir or zero-point energies cannot possibly be large enough to be relevant. (About 10 MeV of energy is released per collapse.) However, there are sufficient subtleties involved that others have come to opposite conclusions. In particular, it has been suggested that bulk energy, that is, simply the naive sum of $\frac{1}{2}\ensuremath{\Elzxh}\ensuremath{\omega}$, which is proportional to the volume, could be relevant. We show that this cannot be the case, based on general principles as well as specific calculations. In the process we further illuminate some of the divergence difficulties that plague Casimir calculations, with an example relevant to the bag model of hadrons.

Trembling cavities in the canonical approach

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 boundaries. The method is applied to the configuration of moving mirror(s). Some properties as well as the relation to local Green function methods are discussed. PACS-numbers: 12.20; 42.50; 03.70.+k; 42.65.Vh Keywords: Dynamical Casimir effect; Moving mirrors; Cavity quantum field theory; Vibrating boundary;

Renormalization-group approach to the dynamical Casimir effect

In this paper we study the one dimensional dynamical Casimir effect. We consider a one dimensional cavity formed by two mirrors, one of which performs an oscillatory motion with a frequency resonant with the cavity. The naive solution, perturbative in powers of the amplitude, contains secular terms. Therefore it is valid only in the short time limit. Using a renormalization group technique to resum these terms, we obtain an improved analytical solution which is valid for longer times. We discuss the generation of peaks in the density energy profile and show that the total energy inside the cavity increases exponentially.

Observability of the bulk Casimir effect: Can the dynamical Casimir effect be relevant to sonoluminescence?

Observability of the bulk Casimir effect: Can the dynamical Casimir effect be relevant to sonoluminescence?

Production of photons by the parametric resonance in the dynamical Casimir effect

We calculate the number of photons produced by the parametric resonance in a cavity with vibrating walls. We consider the case that the frequency of vibrating wall is $n \omega_1 (n=1,2,3,...)$ which is a generalization of other works considering only $2 \omega_1$, where $\omega_1$ is the fundamental-mode frequency of the electromagnetic field in the cavity. For the calculation of time-evolution of quantum fields, we introduce a new method which is borrowed from the time-dependent perturbation theory of the usual quantum mechanics. This perturbation method makes it possible to calculate the photon number for any $n$ and to observe clearly the effect of the parametric resonance.

Hanbury-Brown-Twiss interferometry for sonoluminescence bubble

The two-photon correlation of the light pulse emitted from a sonoluminescence bubble is discussed. It is shown that several important information about the mechanism of light emission, such as the time-scale and the shape of the emission region could be obtained from the HBT interferometry. We also argue that such a measurement may serve to reject one of the two currently suggested emission mechanisms, i.e., thermal process versus dynamical Casimir effect.

Casimir effect in dielectrics: Bulk energy contribution

In a recent series of papers, Schwinger discussed a process that he called the dynamical Casimir effect. The key essence of this effect is the change in zero-point energy associated with any change in a dielectric medium. (In particular, if the change in the dielectric medium is taken to be the growth or collapse of a bubble, this effect may have relevance to sonoluminescence.) The kernel of Schwinger's result is that the change in Casimir energy is proportional to the change in the volume of the dielectric, plus finite-volume corrections. Other papers have called into question this result, claiming that the volume term should actually be discarded, and that the dominant term remaining is proportional to the surface area of the dielectric. In this paper, which is an expansion of an earlier Letter on the same topic, we present a careful and critical review of the relevant analyses. We find that the Casimir energy, defined as the change in zero-point energy due to a change in the medium, has at leading order a bulk volume dependence. This is in full agreement with Schwinger's result, once the correct physical question is asked. We have nothing new to say about sonoluminescence itself.

Mechanical Response of Vacuum

A path integral formulation is developed for the dynamic Casimir effect. It allows us to study arbitrary deformations in space and time of the perfectly reflecting (conducting) boundaries of a cavity. The mechanical response of the intervening vacuum is calculated to linear order in the frequency-wavevector plane. For a single corrugated plate we find a correction to mass at low frequencies, and an effective shear viscosity at high frequencies; both anisotropic. For two plates there is resonant dissipation for all frequencies greater than the lowest optical mode of the cavity.

Casimir energy for a spherical cavity in a dielectric: Applications to sonoluminescence

In a series of papers, Schwinger [Proc. Natl. Acad. Sci. U.S.A. 90, 958 (1993); 90, 2105 (1993); 90, 4505 (1993); 90, 7285 (1993); 91, 6473 (1994)] proposed that the ``dynamical Casimir effect'' might provide the driving force behind the puzzling phenomenon of sonoluminescence. Motivated by that exciting suggestion, we have computed the static Casimir energy of a spherical cavity in an otherwise uniform material. As expected, the result is divergent; yet a plausible finite answer is extracted, in the leading uniform asymptotic approximation. This result agrees with that found using \ensuremath{\zeta}-function regularization. Numerically, we find far too small an energy to account for the large burst of photons seen in sonoluminescence. If the divergent result is retained, it is of the wrong sign to drive the effect. Dispersion does not resolve this contradiction. In the static approximation, the Fresnel drag term is zero; on the other hand, the electrostriction could be comparable to the Casimir term. It is argued that this adiabatic approximation to the dynamical Casimir effect should be quite accurate.

Schwinger's dynamical Casimir effect: bulk energy contribution

Schwinger's Dynamical Casimir Effect is one of several candidate explanations for sonoluminescence. Recently, several papers have claimed that Schwinger's estimate of the Casimir energy involved is grossly inaccurate. In this letter, we show that these calculations omit the crucial volume term. When the missing term is correctly included one finds full agreement with Schwinger's result for the Dynamical Casimir Effect. We have nothing new to say about sonoluminescence itself except to affirm that the Casimir effect is energetically adequate as a candidate explanation.

The Dynamical Casimir Effect for an Oscillating Dielectric Model

Dynamical Casimir effects caused by a moving mirror and a varying dielectric medium are studied in the effective Hamiltonian approach. The explicit form of the effective Hamiltonian for the uniform, step-wise, and time-dependent dielectric model is derived in addition to that for the moving mirror model. The resonant properties of induced photons for both models are considered and it is found that in contrast to the moving mirror case, the inter-mode transition for the dielectric case is suppressed between the odd-odd levels and between the even-even levels. The effects of dissipation are also taken into account by the master equation. For numerical analyses, a convenient method to integrate the time evolution is proposed.

Sonoluminescence as quantum vacuum radiation.

Sonoluminescence is explained in terms of quantum vacuum radiation by moving interfaces between media of different polarizability. It can be considered as a dynamic Casimir effect, in the sense that it is a consequence of the imbalance of the zero-point fluctuations of the electromagnetic field during the noninertial motion of a boundary. The transition amplitude from the vacuum into a two-photon state is calculated in a Hamiltonian formalism and turns out to be governed by the transition matrix element of the radiation pressure. Expressions for the spectral density and the total radiated energy are given.

Photon Emission from a False Vacuum of Semiconductors

We consider photon creation through the dynamical Casimir effect in a semiconductor material. Unlike previous studies, we evaluate the number of created photons using a microscopic model in which polarization degree of freedom is included in the theory as a microscopic variable, under realistic situations in which material parameters vary by a finite magnitude within a finite time, in a material which exhibits strong dispersions in the dielectric constant. Our results differ strikingly from previous results.

Photon production by the dynamical Casimir effect.

In this paper we present some calculations regarding the average number of photons produced in the dynamical Casimir effect for the ideal case of two perfectly conducting uncharged parallel plates, using the zero-point energy summation method. We show that it is possible to create intense photon radiation when the two plates are modulated periodically.

On the origins of 1/f - noise & the dynamical Casimir effect

The dynamical Casimir effect in QED, which occurs for a frequency modulated electromagnetic oscillator, is described in terms of reflection backward in time of the oscillator mode. From an experimental point of view, backward in time reflections appear as radiated photons. We compute the frequency ( f) distribution of the emitted EM radiation due to a modulated pulse and show that it exhibits a 1/ f-singularity as f vanishes. We next consider other dynamical effects which arise due to (externally driven) periodic modulations of the frequency. This can lead to the production of sharply pulsed intense photon radiation. An example is given where radiation with frequencies considerably larger than the modulation frequency may develop and which may be detectable such as in sono-luminescence.