Atomic-superfluid heat engines controlled by twisted light

TL;DR

This work introduces a quantum heat engine built from a ring-trapped Bose-Einstein condensate inside a Fabry–Pérot cavity driven by light carrying orbital angular momentum. The core idea is to harness polaritonic modes arising from strong light–matter coupling, and to realize an Otto cycle by detuning sweeps that interchange the lower polariton between photonlike and phononlike character, enabling work extraction between photon and phonon reservoirs. The authors derive analytical expressions for work and efficiency, showing η = 1 − Ω_f/Ω_i and a finite-time robust performance enabled by shortcuts to adiabaticity, with the OAM index $\ell$ acting as a tunable control parameter. They also present a tractable two-mode reduction via adiabatic elimination for lower $\ell$, preserving the essential physics while simplifying analysis. Overall, the proposal demonstrates a feasible pathway to programmable quantum heat engines in cavity QED with ring BECs, where detuning and OAM provide versatile knobs to optimize performance.

Abstract

We theoretically propose a quantum heat engine using a setup consisting of a ring-trapped Bose-Einstein condensate placed in a Fabry--Pérot cavity where the optical fields carry orbital angular momentum. We first show that the cavity-enhanced light-atom coupling leads to the emergence of polaritonic modes, whose character can be reversibly switched between photonlike and phononlike by detuning sweeps allowing work extraction governed by distinct reservoirs. We investigate the dependence of the engine efficiency on the orbital angular momentum. Beyond ideality, we discuss finite-time scenarios based on shortcuts to adiabaticity such that the efficiency retains its ideal-operation value, despite finite-time challenges. Finally, for lower values of the orbital angular momentum, we describe an alternate scheme for operating quantum heat engines based on the adiabatic elimination of a mechanical mode. Our analysis identifies orbital angular momentum as an experimentally-accessible control knob that can reconfigure the performance of such quantum heat engines as desired.

Figures (6)

• Figure 1: Schematic setup showing the BEC rotating in a ring trap inside a cavity driven by the control and signal fields, which are in coherent superpositions of Laguerre-Gaussian modes carrying OAM $\pm \ell \hbar$.
• Figure 2: Polaritonic frequencies (in units of $\gamma_0$) and with $\tilde{G} = 4\gamma_0$, along with the bare modes $(\tilde{G}=0)$ for physical choices of the parameters Kalita_2023 conforming to $L_p = 20$, $\ell = 130$, $m = 23$ amu, and $R = 10 ~ \mu m$. This leads to $\omega_c \approx 173.27\gamma_0$ and $\omega_d \approx 126.56 \gamma_0$.
• Figure 3: Variation of the efficiency of the Otto cycle as a function of the detuning $-\bar{\Delta}_f$ (in units of $\gamma_0$) along with the light-matter coupling constant $\tilde{G}$ (in units of $\gamma_0$; left panel) and the orbital angular momentum $\ell$ (right panel). We have taken $|\bar{\Delta}_i| = 10 \omega_c$. The left panel corresponds to $\ell = 130$ while the right panel corresponds to $\tilde{G} = 4\gamma_0$.
• Figure 4: Finite-time detuning protocols for the isentropes $(a) \rightarrow (b)$ (main figure) and $(c) \rightarrow (d)$ (inset). Here, $-\bar{\Delta}_{1}(t)$ and $-\bar{\Delta}_{2}(t)$ represent the detuning protocols corresponding to the frequency protocols $\Omega_1(t)$ and $\Omega_2(t)$ evaluated using $\rho_1(t)$ given in Eq. \ref{['eq:rho_1']} and $\rho_2(t)$ given in Eq. \ref{['eq:rho_2']}, respectively. The dashed lines represent the detunings $|\bar{\Delta}_i| = 250\gamma_0$ and $|\bar{\Delta}_f| = 2\gamma_0$.
• Figure 5: Two-mode polaritonic frequencies (in units of $\gamma_0$) and with $\tilde{G} = 0.2\gamma_0$ for physical choices of the parameters conforming to $L_p = 20$, $\ell = 19$, $m = 23$ amu, and $R = 10 ~ \mu$m. This leads to $\omega_c \approx 7.392\gamma_0$ and $\omega_d \approx 0.712 \gamma_0$.