Purcell-enhanced quantum adsorption

TL;DR

The work investigates how phonon damping and finite adsorbent size alter the quantum adsorption rate of cold atoms in a regime where single-phonon emission dominates. By modeling adsorption with a multimode quantum Rabi Hamiltonian and solving time-dependent dynamics via a Dirac–Frenkel variational ansatz, the authors derive a closed-form, cavity-like expression for the acoustic Purcell effect on adsorption. They show that a mesoscopic adsorbent acts as an acoustic cavity whose mode spacing Δω and damping η can either enhance or suppress adsorption relative to the Fermi golden rule, with enhancement possible when the effective spectral parameter Ns is an integer. The results provide a route to control phonon-assisted processes using mechanical metamaterials and suggest experimental tests and applications in solid-state quantum devices where adsorption is detrimental or advantageous.

Abstract

Cold atoms can adsorb to a surface with the emission of a single phonon when the binding energy is sufficiently small. The effects of phonon damping and adsorbent size on the adsorption rate in this quantum regime are studied using the multimode Rabi model. It is demonstrated that the adsorption rate can be either enhanced or suppressed relative to the Fermi golden rule rate, in analogy to cavity effects in the spontaneous emission rate in QED. A mesoscopic-sized adsorbent behaves as an acoustic cavity that enhances the adsorption rate when tuned to the adsorption transition frequency and suppresses the rate when detuned. This acoustic cavity effect occurs in the regime where the frequency spacing between vibrational modes exceeds the phonon linewidth.

Figures (4)

• Figure 1: Relative adsorption rate $R/R_0$ versus coupling strength $\frac{\eta}{\Delta\omega}$ for on-resonance cases $N=4$ and $N_s=1$ (green); $N=60$ and $N_s=15$ (blue). The leading asymptotic behavior $R/R_0$ for $\frac{\eta}{\Delta\omega}\to 0$ given in Eq. \ref{['asymp']} is plotted (magneta, dot-dashed). Fermi golden rule result (horizontal, red) is displayed for comparison. The rate is enhanced relative to $R_0$ for low $\frac{\eta}{\Delta\omega}$.
• Figure 2: Relative adsorption rate $R/R_0$ versus coupling strength $\frac{\eta}{\Delta\omega}$ for off-resonance cases $N=60$ with $N_s=14.25$ (blue); $N=5$ with $N_s=1.25$ (green). The leading asymptotic behavior $R/R_0$ for $\frac{\eta}{\Delta\omega}\to 0$ is plotted (magneta, dot-dashed). Purcell suppression is manifest for all $\frac{\eta}{\Delta\omega}$.
• Figure 3: Relative adsorption rate $R/R_0$ versus coupling strength $\frac{\eta}{\Delta\omega}$ for a near-resonance case $N=40$ with $N_s=9.89$ (green). The leading asymptotic behavior $R/R_0$ for $\frac{\eta}{\Delta\omega}\to 0$ is plotted (magneta, dot-dashed). Purcell enhancement is evident for $\frac{\eta}{\Delta\omega}\gtrsim 0.04$, while suppression occurs below this threshold.
• Figure 4: Relative adsorption rate $R/R_0$ displays oscillations with adsorbate energy $E_c$ for a finite-size adsorbent [$\frac{\eta}{\Delta\omega}=0.15$ (green); $\frac{\eta}{\Delta\omega}=0.3$ (blue, dashed), $\frac{\eta}{\Delta\omega}=1$ (magenta, dot-dashed)]. For nonlinear dispersion, the frequency spacing between successive modes is not constant, but it may be nearly so over a sufficiently small energy interval.