Superradiance and Superabsorption Engine of $N$ Two-Level Systems: $N^{2}$-Power Scaling at Near-Unity Efficiency

TL;DR

The paper tackles the challenge of creating scalable quantum heat engines by exploiting cooperative effects in ensembles of $N$ two-level systems. It introduces a unified mean-field approach that describes both superradiant emission and superabsorption as unitary strokes with $\mathrm{sech}^2$-shaped pulses, yielding a quadratic power scaling $P \propto N^{2}$ while achieving efficiencies approaching unity. Through analytic mean-field results and exact numerical simulations up to $N=500$, the work shows that the cycle—comprising a pumping stroke to invert population and a subsequent emission stroke—operates with minimal heat exchange during the pulses and rapid convergence to a stable limit cycle under repeated operation. These findings suggest a practical route to scalable, high-performance quantum heat engines based on collective phenomena in engineered reservoirs and provide guidance on parameter regimes for near-term experimental realization.

Abstract

We present a thermal engine that exploits the \emph{cooperative superradiance} and \emph{superabsorption} of a sample of \(N\) two-level atoms. This engine operates using a single cold reservoir via cycles of collective pumping followed by decay. Using an effective mean-field Hamiltonian to describe the many-body dynamics, we design optimized drive pulses that preserve adiabaticity and achieve an average power output scaling quadratically with the system size, \(P \propto N^2\). An experimentally measurable figure of merit demonstrates that the efficiency of this superengine can approach unity. The resulting analytical model, which yields a representative Hamiltonian for the sample within the mean-field formalism, is validated by numerical simulations. Our results pave the way for scalable and highly efficient quantum heat engines based on collective effects.

Figures (7)

• Figure 1: Superabsorption. Comparison of the analytical pulse $I_0\,\mathop{\mathrm{sech}}\nolimits^2\!\bigl(\tfrac{t - t_d}{\tau}\bigr)$ (dashed-black line) and the simulated (exact) absorbed intensity (solid-blue line), obtained from an initial thermal states undergoing collective decay. Input parameters: $N=300$, $\gamma_{\mathrm{up}}=0.01$, $T=0.5$. Derived parameters: $t_d=28.9559$, $r = 0.7616$, $\theta_0 = 0.7050$ rad, and $\tau=0.8754$. The inset shows the polarization dynamics $\langle J_z(t)\rangle$ versus. $t$. Time is given in units of $1/\omega_0$.
• Figure 2: Superradiance. Comparison of the analytical pulse $I_0\,\mathop{\mathrm{sech}}\nolimits^2\!\bigl(\tfrac{t - t_d}{\tau}\bigr)$ (dashed black line with diamond markers) and the simulated radiated intensity (solid blue line with circle markers) starting from an initial thermal state undergoing collective absorption. Input parameters: $N=300$, $\omega_0=1.0$, $\gamma_{\mathrm{down}}=0.01$, $T = -0.5$. Since the population is inverted due to the collective pumping, we performed this simulation using a Gibbs state with effective negative temperature. Derived parameters: $t_d = 0.8754$, $r = 0.7616$, $\theta_0 = 0.7050$ rad, and $\tau = 0.8754$. The inset shows the polarization dynamics $\langle J_z(t) \rangle$ versus $t$. Time is given in units of $1/\omega_0$.
• Figure 3: Superengine Cycle: The atomic sample begins in a thermal state with disordered dipole moments. It then undergoes multimodal pumping, triggering a superabsorption effect that inverts its population and orders the dipoles. This is followed by a superradiance emission, after which the sample re-thermalizes with the reservoir.
• Figure 4: Superpulses across $k=5$ cycles. Dotted (green) curve: pumping on; dashed (yellow) curve: natural decay with pumping off; solid (blue) curve: resultant intensity during both superabsorption and superradiance strokes. Input parameters (in units of $\omega_0$): $N=80$, $T_c=0.5$, $\gamma_{\mathrm{down}}=0.01$, $\gamma_{\mathrm{up}} = 3.5\,\gamma_{\mathrm{down}}$.
• Figure 5: Efficiency $\eta$ versus number of cycles $k$. The high efficiency is a hallmark of the superengine. Input parameters (in units of $\omega_0$): $N=80$, $T_c =0.5$, $\gamma_{\mathrm{down}}=0.01$, $\gamma_{\mathrm{up}} = 3.5\,\gamma_{\mathrm{down}}$.