You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


---
abstract: 'We propose an experiment for generating and detecting vacuum-induced dissipative motion. A high frequency mechanical resonator driven in resonance is expected to dissipate mechanical energy in quantum vacuum via photon emission. The photons are stored in a high quality electromagnetic cavity and detected through their interaction with ultracold alkali-metal atoms prepared in an inverted population of hyperfine states. Superradiant amplification of the generated photons results in a detectable radio-frequency signal temporally distinguishable from the expected background.'
author:
- 'Woo-Joong Kim'
- James Hayden Brownell
- Roberto Onofrio
title: Detectability of dissipative motion in quantum vacuum via superradiance
---

- Macroscopic quantum effects are suitable to bridge the gap between quantum theory and general relativity. In this context, observable effects due to the change in the boundary conditions of quantum fields, like the creation of particles in an expanding universe [@Schroedinger] or the Casimir force [@Casimir], may provide crucial information. So far the attention has been mainly focused on [*conservative*]{} Casimir forces, with measurements performed in a variety of geometries ranging from the original parallel plane [@Sparnaay; @Bressi] to the sphere-plane [@vanBlokland; @Lamoreaux; @Mohideen; @Chan; @Decca] and crossed-cylinders [@Ederth]. Meanwhile, there have been several theoretical attempts at studying the [*dissipative*]{} contribution of vacuum fluctuations to understand their interplay with the relativity of motion [@Moore; @Fulling; @Jaekel]. In principle, dissipative Casimir forces should be evidenced as a further damping source in the non-uniformly accelerated motion of micromechanical resonators already implemented for measuring the conservative component of the force. However, given the level of dissipations coming from more technical sources, a direct detection of the dissipative Casimir force seems out of experimental reach. Instead of focusing the attention on deviations from conservative motion, the dissipation induced in vacuum could be more easily detected by looking at the radiated photons that are less contaminated from other sources of noise [@Lambrecht]. This phenomenon, also known as dynamical Casimir effect (see [@Barton] for an updated review), can be understood both as the creation of particles under nonadiabatic changes in the boundary conditions of quantum fields, or as classical parametric amplification where the zero point energy of a vacuum field mode is exponentially amplified in time. Theoretical analysis indicates that under parametric amplification in an electromagnetic cavity an initial state of $N_0$ photons with frequency within the resonance bandwidth of the fundamental mode of the cavity $\omega$ is transformed into a squeezed state with an average number of photons growing in time as [@Dodonov; @Plunien; @Crocce] $$\label{eq:photonnumber}
N_{\mathrm{Cas}}(t)=N_0 \sinh^{2}(\Omega \epsilon t),$$ assuming that the parametric resonance condition with a mechanical driving at a frequency $\Omega=2 \omega$ is fulfilled. The product $\Omega \epsilon$ represents the squeezing parameter, with the modulation depth $\epsilon=v/c$, where $v$ is the velocity of the resonator and $c$ the speed of light. This exponential growth is eventually limited by the photon leakage of the cavity expressed through the optical quality factor $Q_{\mathrm{opt}}$, which saturates at the hold time $\tau=Q_{\mathrm{opt}}/\omega$, reaching a maximum photon population $$\label{eq:sat}
N_{\mathrm{Cas}}^{\mathrm{max}}=N_{\mathrm{Cas}}(\tau)=N_0 \sinh^{2}(2 Q_{\mathrm{opt}} \epsilon).$$

In this Letter, we discuss a generation mechanism for Casimir photons and a nearly quantum-limited photodetection scheme in the radio-frequency range based on the interaction of the generated photons with an excited population of atoms. This proposed experiment, initially sketched in [@Onofrio], exploits in addition the high gain of superradiant emission to boost the expected signal to detectable levels, and a schematic outline of its components is shown in Fig. \[fig1\]. An extremely weak signal of Casimir photons will trigger the emission of an intense, time-compressed, superradiant pulse whose characteristic delay time will provide the signature of mechanically induced vacuum radiation.

[*Generation of Casimir photons*]{} - Current thin film technology makes feasible mechanical motions in the GHz range, with the highest frequency reported to date $\Omega/2\pi=$3.0 GHz and a modulation depth of $\epsilon=10^{-8}$ [@Zhang]. This has been obtained through a film bulk acoustic resonator (FBAR) [@Ruby; @Cleland; @Gabl], consisting of a vibrating aluminum nitride (AlN) film of thickness corresponding to one half of the acoustic wavelength, sandwiched between two electrodes. The average number of photons at saturation, Eq. (\[eq:sat\]), depends on the product of two parameters, $Q_{\mathrm {opt}}$ and $\epsilon$, which can be on the order of $10^8$ and $10^{-8}$ respectively. The average number of photons in the cavity is very sensitive to this product, with $N_{\mathrm{Cas}}^{\mathrm{max}} = 1.4, 13, 740$ for values of $Q_{\mathrm {opt}} \epsilon = 0.5, 1, 2$ for a vacuum state with $N_0=1$, respectively. The expected saturated power initiated by Casimir emission is $$\label{eq:phpower}
P_{\mathrm{Cas}}=
N_{\mathrm{Cas}}^{\mathrm{max}} \frac{\hbar \omega}{\tau}.$$ For a 3.0 GHz FBAR resonator and a benchmark value of $Q_{\mathrm {opt}} \epsilon \simeq 1$ at the edge of current technology, the saturated power $3 \times 10^{-22}$ W is too low to be directly detectable. This demands the use of an efficient, nearly quantum-limited, photon detector in the radio-frequency range.

![Generation and detection of photons irradiated through vacuum-induced damping of motion. The two-level atoms are optically pumped to the maximum angular momentum state of the spin-orbit manifold which only allows for a single, downward, circularly polarized, magnetic dipole transition. The atoms are then sent through the cavity (a). The Casimir photons are generated through mechanical modulation of one FBAR resonator (b). An amplified superradiant pulse is triggered by a weak Casimir signal and detected by radio-frequency electronics or atomic fluorescence (c). []{data-label="fig1"}](dycasandy.fig1.eps){width="0.80\columnwidth"}

[*Detection of Casimir photons*]{} - Ultra-sensitive atomic detection schemes can be exploited for detecting Casimir photons by preparing an ensemble of population-inverted atoms in a hyperfine state whose transition frequency corresponds to the cavity resonance. An additional amplification process is available in which the weak Casimir signal triggers the stimulated emission of the ensemble of atoms. This effect is a form of superradiance [@Benedict; @Gross]. One favorable feature to be exploited for the proposed scheme is that the hyperfine splitting of the ground states for alkali atoms ranges from 0.2 GHz for Li to 9 GHz for Cs, conveniently matching the operating frequencies of FBAR resonators achieved or achievable in the near future [@Note1]. The hyperfine transition in the ground state occurs through a magnetic dipole interaction, and its natural lifetime in free space is approximately $$\label{eq:T1}
T_1 \approx \frac{3 \pi \epsilon_0 \hbar c^5}{\mu_{B}^2 \omega^3},$$ where $\mu_{B}$ is the Bohr magneton and $\epsilon_0$ the electric permittivity in vacuum. This natural lifetime in free space is favorably reduced inside a resonant cavity due to the modification of density of states [@Purcell; @Goy] $$\label{eq:Tcav} T_1^\mathrm{cav} = \frac{4\pi^2}{3Q_\mathrm{opt}}
\frac{V}{\lambda^3} T_1,$$ where $V$ is the cavity volume. For a few GHz cavity with 1 cm$^2$ cross-sectional area and $Q_{\mathrm {opt}}=10^8$, the natural lifetime is reduced by a factor of $10^{10}$. In spite of this cavity-enhanced spontaneous rate, the typical hyperfine transition lifetime for the alkali-metal atoms is still impractically long, on the order of $10^3-10^{5}$ s. The superradiant lifetime - the characteristic time scale for superradiant evolution when $N_{\mathrm{at}}$ atoms are enclosed within the cavity - is $T_{\mathrm{SR}} = T_1^{\mathrm{cav}}/N_{\mathrm{at}}$. Hence the emission time scale for the experiment is further reduced in the millisecond range for $N_{\mathrm {at}} \approx 10^8$ or less. The peak power of the superradiant pulse is $$\label{eq:atpower}
P_{\mathrm {SR}} = N_{\mathrm{at}} \frac{\hbar \omega}{T_{\mathrm {SR}}},$$ increasing quadratically with the number of atoms. Considering as before a few GHz resonator with $10^8$ atoms and $T_{\mathrm {SR}}=10^{-3}$ s, yields $P_{\mathrm{SR}} = 10^{-13}$ W, a billionfold improvement over the initial power estimated in Eq. \[eq:phpower\].

The superradiant emission can be detected in either of two ways. First, a power or field detector can be coupled to the cavity. The detector should be fast enough to resolve one superradiant lifetime. Such direct measurement would be preferred although the coupling mechanism itself is likely to reduce the quality factor of the cavity significantly in order to attain sufficient coupling efficiency. Micro-bolometers mounted on etched “spiderwebs” have an ultimate sensitivity of $10^{-16}\,\mathrm{W}/\sqrt{{\mathrm{Hz}}}$ in the GHz range [@Turner]. Spectrum analyzers are sensitive to sub-fW RF power of kHz bandwidth [@Agilent], and the temporal profile of the burst can be reconstructed through vector analysis. Second, the exiting atoms can be interrogated resonantly with the lower hyperfine state to ascertain the lower state population and therefore the energy released into the cavity. Either D-line fluorescence or ionization current can be monitored at the thousand atom level sensitivity [@Chen]. The average delay time can be inferred by varying the time the atoms stay within the cavity. Coherent D-line excitation may also generate free-induction decay, due to the coherent magnetic moment developed on the hyperfine transition as a consequence of the amplification process, that would have a clearer signature. The two detection techniques are complementary to each other, and could be used in coincidence to further reject spurious signals.

[*Background rejection*]{} - Casimir-generated photons are not the only seed to trigger the stimulated amplification process. In particular, any atom decaying spontaneously will also trigger a superradiant burst. In this case, the process is more commonly known as superfluorescence. The temporal envelope of the photon burst allows for discrimination among the triggering sources. Indeed, the average delay between the initial stimulation of the atomic population depends on the number of atoms and resonant photons $N_{\mathrm{ph}}$ initially present [@Haroche]: $$\label{eq:delay}
T_{\mathrm {D}}=T_{\mathrm {SR}} \ {\ln} \biggl[
\frac{N_{\mathrm {at}}}{1+N_{\mathrm {ph}}}\biggr].$$ The delay is typically around ten superradiant lifetimes but with an inherent uncertainty due to quantum fluctuations. Both the delay and its uncertainty shrink as the number of initial photons increases. Measuring the delay can then indicate the number of initial Casimir photons. Tailoring the atomic number can further distinguish the Casimir signal from superfluorescent pulses. In order for the superradiant pulse to develop fully, the growth rate must exceed any decay process, which is primarily Doppler dephasing in the atomic cloud, and the atoms must remain in the interaction region for a time longer than the delay time. Then superfluorescence will be suppressed relative to Casimir superradiance provided that the atoms will be removed from the cavity after the expected Casimir delay time but prior to the superfluorescence delay $T_{\mathrm {D}}^{(0)}$ \[obtained with $N_{\mathrm{ph}}=0$ in Eq. \[eq:delay\]\].

[*Experimental approach*]{} - The Casimir photon population is allowed to reach saturation before introducing the prepared atoms. The atoms can be trapped and cooled with standard magneto-optical techniques, optically pumped and then transported into the cavity via optical tweezers. The existing photons then trigger a coherent pulse so long as the superradiant delay time is less than the cavity hold time. The direct use of an atomic beam is prevented by the short interaction time available in this configuration. While, based on Eq. \[eq:atpower\], it looks advantageous to increase the number of atoms, an upper bound is imposed by the necessity to resolve the delay time as in Eq. 7. A major advantage of the proposed scheme is that outside the cavity the atoms are effectively inert due to the long hyperfine lifetime. Furthermore, the atoms are not resonant with the direct emission of photons at frequency $\Omega$ originating from antenna dipole irradiation due to the mechanical oscillation.

[|c|c|c|c|c|]{}

------------------------------------------------------------------------

& $^6$Li & $^{23}$Na & $^{87}$Rb & $^{133}$Cs\

------------------------------------------------------------------------

$\nu$(GHz) & 0.228 & 1.77 & 6.83 & 9.19\

------------------------------------------------------------------------

$L$(mm) & 657 & 84.6 & 21.9 & 16.3\

------------------------------------------------------------------------

$T_1$(s) & $8.4 \times 10^{16}$ & $1.8 \times 10^{14}$ & $3.1 \times 10^{12}$ &$1.3 \times 10^{12}$\

------------------------------------------------------------------------

$T_{1}^{\mathrm {cav}}$(s) & $3.2 \times 10^{5}$ & $4.1 \times 10^{4}$ &$1.1 \times 10^4$ & $8.0 \times 10^3$\

------------------------------------------------------------------------

$N_{\mathrm{at}}^{\mathrm {max}}$ & $6.4 \times 10^8$ & $8.2 \times 10^7$ & $2.2 \times 10^7$ & $1.6 \times 10^7$\

------------------------------------------------------------------------

$T_{\mathrm {D}}^{(0)}$(ms) & $10.1 $ & $9.1$ & $8.5$ & $8.3$\

------------------------------------------------------------------------

$T_{\mathrm {D}}$ (ms) & $8.8$ &$7.8$ & $7.1$ & $7.0$\

------------------------------------------------------------------------

$P_{\mathrm {Cas}}$(W) & $2.8 \times 10^{-23}$ & $1.7 \times 10^{-21}$ & $2.5 \times 10^{-20}$ &$4.6 \times 10^{-20}$\

------------------------------------------------------------------------

$P_{\mathrm {SR}}$(W) & $\,1.9 \times 10^{-13}\,$ & $\,1.9 \times 10^{-13}\,$ & $\,2.0 \times 10^{-13}\,$ & $\,1.9 \times 10^{-13}\,$\

The atom number, $N_{\mathrm{at}}$, and the interaction time are the primary adjustable parameters. The maximum sensitivity is obtained when the former is adjusted so that the superradiant lifetime is comparable to the detector speed (or the transfer speed for the interrogation technique) and the latter is slightly less than the superfluorescent delay time. In Table 1, we summarize the various time scales and photon production rates involved in our proposed scheme for hyperfine transitions of different alkali-metal species. Lithium is not a practical candidate due to the large cavity size, whereas cesium and rubidium require mechanical frequencies not presently available. In this regard, sodium looks promising instead, with many individual steps of our proposed experiment already demonstrated. Sodium atoms in the maximum amount of $10^8$ have been trapped at a temperature of $T=100\, n$K in a Bose condensed state [@Na], radio-frequency transitions between hyperfine states have been intentionally driven [@Gorlitz], and superradiance phenomena have been observed [@Inouye]. Concerning the detection speed, both micro-bolometers and heterodyne receivers are fast enough to resolve the shortest achievable pulse. The difference in delay times is a few $T_{\mathrm{SR}}$ and so to suppress the superfluorescence, the atom transfer time out of the cavity should be at most $T_{\mathrm{SR}}$. Given that the transfer rate with optical tweezers is limited by the mechanical drive moving the focusing lens to roughly 10 cm/s, corresponding to a transfer time of 100 ms in and out of the cavity [@Gustavson], the number of atoms required is $N_{\mathrm{at}}=6 \times 10^5$, corresponding to a peak power of $2 \times 10^{-15}$ W.

The key parameter in our scheme is the optical quality factor. Assuming a relative error in the determination of the delay time of 10$\%$, a situation with $Q_{\mathrm {opt}} \epsilon=1$ determines the borderline for the temporal discrimination between superradiance induced by Casimir photons and superfluorescence, with a significantly improved signal for $Q_{\mathrm {opt}} \epsilon$ larger than unity. Quality factors of $10^8$ [@Raimond] and $10^{10}$ [@Rempe] have been reported for open, Gaussian, superconducting cavities. While, as already mentioned, the transient decrease of the cavity transmission occurs on a timescale longer than the superradiant pulse, care must be taken to minimize the losses introduced by the FBAR resonator as well as ports to admit the atoms and monitor the RF power.

Scaling the size of existing resonators and dissipation of heat are other issues to be carefully addressed. Given a typical size of current FBARs of $\simeq 500 \mu$m${}^2$, increasing the FBAR to 1 cm${}^2$ could adversely introduce additional acoustic modes as well as enhance the risk of a pinhole breakdown through the AlN film. The power required to drive the FBAR is obtained by considering the kinetic energy of a vibrating material whose energy is dissipated in the timescale of $Q_{\mathrm{m}}/\Omega$, where $Q_{\mathrm{m}}$ is the mechanical quality factor, which gives $P=\rho V \Omega^3 \delta x^2/4
Q_{\mathrm{m}}$. Expressing the volume of the vibrating body [*V*]{} in terms of the cross sectional area [*A*]{} and the thickness of the material, one half of the acoustic wavelength $2 \pi v_a/ \Omega
$, we obtain $P_{\mathrm{FBAR}}=\rho A v_a \pi^3 \epsilon^2
c^2/Q_{\mathrm{m}}$, independent of frequency. For a cross sectional area of 1 $\mathrm{cm}^2$, $\epsilon=10^{-9}$, $\rho=10^3~$ kg/m${}^3$ and $v_a=10,400$ m/s for aluminum nitride with a typical mechanical quality factor $Q_{\mathrm{m}}=10^3$, the dissipated power is about 3 W [@Note2], smaller than the maximum threshold power of $\simeq$ 10 W applicable to a FBAR resonator without damaging it [@Ballou]. In principle, the mechanical quality factor can be increased up to 4,000 at room temperature, even larger at cryogenic temperatures, by a careful design of the multiple reflection layer and the refinement of an annealing process [@Multilayer]. To minimize the moving boundary area to reduce heat load and fabrication difficulty, the cavity could be a hollow, coaxial waveguide terminated with length equal to half the resonant wavelength. Finally, the thermal contribution to the initial photon population $N_0$ at 10 mK is $N_{\mathrm{therm}}=6 \times 10^{-4}$, negligible with respect to the Casimir contribution [@Lambrechthermal].

[*Conclusions*]{} - We have proposed an experiment involving superradiant amplification to detect the dynamical Casimir photons generated by a vibrating wall in an electromagnetic cavity. Although the observation of radiated photons is limited by the current technology, the use of superradiant atoms should overcome the technical limits and make their unambiguous detection possible. The technology currently available for mechanical resonators, the analysis of various alkali atoms, and the interplay of the timescales indicate that a detection scheme based upon use of Sodium atoms should have realistic chances to detect photons radiated by non-uniformly accelerating bodies in quantum vacuum.

We thank D. A. R. Dalvit, E. S. Kim, P. W. Milonni, and G. Ruoso for useful discussions.

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