Figure 1

Illustration of an afterglow experiment to search for chameleon particles. (a) Filling the vacuum tube by means of a laser beam with chameleons via photon-chameleon conversion in a magnetic field. (b) An isotropic chameleon gas forms. (c) Afterglow from chameleon-photon conversion in a magnetic field.Reuse & Permissions

Figure 2

Combined constraints on $n=1$ chameleon theories in terms of the potential parameters $\Lambda$, in units of the energy scale ${\rho }_{\Lambda }^{1/4}\simeq 0.002\mathrm{eV}\simeq (0.1\mathrm{mm}{)}^{-1}$ corresponding to the energy density of dark energy, versus the inverse coupling scale $1/M$, in units of $M_{\mathrm{Pl}}\simeq 1.2\times {10}^{19}\mathrm{GeV}$. Current constraints (blue solid line; from Ref. 8) arise from searches for violations of the weak equivalence principle (WEP), from searches for deviations from the $1/r^2$ law of the gravitational force (Irvine and Eöt-Wash), and from bounds on the strength of any fifth force from measurements of the Casimir force. Future space-based tests will improve the current limits to the one shown as a light-blue dotted dashed line. A search for an afterglow due to chameleon-photon reconversion at ALPS phase zero will be sensitive to the region indicated by the red solid line, corresponding to a loading and measurement time of $\Delta t=t=100\mathrm{s}$. The red dotted line corresponds to the academic case $\Delta t=1\mathrm{y}$ and $t=1\mathrm{h}$.Reuse & Permissions

Figure 3

Coherent evolution of the chameleon amplitude with number of cycles $N$. For illustration, we took $M=100\mathrm{GeV}$, $m=10\mu \mathrm{eV}$, $\ell =10\mathrm{m}$, $B=5\mathrm{T}$, and $\omega =1\mathrm{eV}$. The upper panel shows the case ${\delta }_1+{\delta }_2=0$ and a rapid oscillation. For the lower panel we chose $\delta =0$, such that the chameleon amplitudes add up resonantly. In this case the asymptotic amplitude is $|{\varphi }_{\infty }|\sim 1/P_{\gamma \to \varphi }$. Also shown is the envelope $|{\varphi }_{\infty }{|}^2·(1\pm e^{-t{\Gamma }_{\mathrm{load}}}{)}^2$ as a dotted line. After $N=100$ cycles the laser is switched off (marked as a dashed line) and the chameleon amplitude decays exponentially. Note that we use different ordinates in both panels.Reuse & Permissions

Figure 4

Coherent evolution of the photon amplitude with number of cycles $N$ for the benchmark points of Fig. 3. We show the intensity of the right-moving (left-moving) photons transmitted at $z=\ell$ ($z=0$) from the cavity as a thick green (thin red) line. In the resonant case (lower panel) the cavity acts as a mirror: The amplitude of right-moving photons is suppressed, whereas the left-moving photons reach the laser intensity. Again, after $N=100$ cycles the laser is switched off and photons are emitted with exponentially decaying intensities to both sides. In the resonant case the intensity of the beam reaches the laser intensity.Reuse & Permissions