# Perspective on Some Recent and Future Developments in Casimir Interactions
## 4 Dynamical Casimir Effect  
The Dynamical Casimir effect (DCE) is another fluctuation-induced phenomenon, which has been studied extensively in the past. [PERSON] was the first to propose that quanta of the electromagnetic field from the vacuum can be generated from the vacuum in an ideal 1D cavity with moving boundaries [13]. Experimental demonstrations of this effect have been quite challenging since the number of generated quanta is tiny due to the small relative displacement of the wall with respect to the wavelength. In addition to using different cavity geometries to enhance this effect, the role of different materials has only recently started to be explored. It was clear from the very beginning that an observation of the DCE in the pure form can be extremely difficult due to the small velocities (in comparison with the speed of light \(c\)) of real boundaries that could be achieved in a laboratory. [PERSON] and [PERSON] [76] have calculated the rate of photon emission from an ideal mirror of area \(A\), oscillating with frequency \(\omega\)  
\[\frac{N}{\tau}=\frac{A\omega}{15\lambda^{2}}\left(\frac{v_{max}}{c}\right)^{2} \tag{11}\]  
where \(N\) is the number of photons generated during time \(\tau\gg 2\pi/\omega\), \(\lambda=2\pi c/\omega\), and \(v_{max}\) is the maximum velocity of the boundaries. For \(\frac{v_{max}}{c}\sim 10^{-7}\), \(\frac{\omega}{2\pi}\sim 10\) GHz, \(A\sim 10\) cm\({}^{2}\), and \(\lambda\sim 3\) cm we obtain \(\frac{N}{\tau}\sim 10^{-5}\) photons/s, or one photon pair every two days. However, the effect can be significantly amplified inside cavities with oscillating boundaries, provided the frequency of oscillations is close to the doubled eigenfrequency \(2\omega_{0}\) of some field mode when the conditions of parametric resonance are satisfied. The main result, obtained within quite different schemes [77; 78; 79; 80], is a simple formula for the number of quanta, created from the initial vacuum state during time \(t\),  
\[N(t)=\sinh^{2}(\epsilon\kappa\omega_{0}t), \tag{12}\]  
where \(\epsilon\) is the maximal relative displacement of the boundary with respect to the wavelength \(\lambda=\frac{2\pi c}{\omega_{0}}\) and \(\kappa<1\) is a number coefficient, which depends on the cavity geometry. The problem is that \(\epsilon\) cannot exceed the value of the order of \(10^{-8}\) for realistic boundaries. For this reason, the DCE in its pure form was not confirmed experimentally till now. In view of these difficulties, different ways to simulate the DCE were discussed for the past three decades by many authors, starting from reference [81]. Among the first proposals were ideas about possibilities of the DCE analogs in superconducting circuit devices [82; 83; 84], which were realized in experiments reported in [14; 85; 86]. The success of these experiments was related to the possibility of achieving the effective velocity of the boundary up to 25% of the light velocity in vacuum (although the analogy with the motion of real boundaries is not perfect). Many theoretical papers suggesting further improvements of the experimental schemes were published during the past decade: see more references in [87; 88; 89; 90]. Another idea was to use effective semiconductor mirrors [81; 91; 92; 93; 94], which can be created by strong periodic laser pulses. Unfortunately, attempts to implement this idea in practice [95] met severe difficulties due to high losses in semiconductor materials [96]. However, a new idea to use the resonance between the field mode and cyclotron transitions inside a semiconductor heterostructure in a strong and rapidly varying magnetic field was suggested recently in reference [97]. The main mechanism of the DCE is the amplification of vacuum fluctuations due to fast variations of instantaneous eigenfrequencies of the field modes. These variations can happen either due to change of real dimensions of the cavity confining the field or due to changes of the effective (optical) length when dielectric properties of the medium inside the cavity depend on time.