Fig. 1
From: An autonomous quantum machine to measure the thermodynamic arrow of time
a Situation under study: a qubit exchanging work W with a mechanical resonator and heat Q with a thermal bath at temperature T. The ensemble of the qubit and mechanics constitutes an autonomous machine. This figure includes the image “fire” (https://openclipart.org/detail/23803/fire) by Anonymous/CC0. b Evolution of the complex mechanical amplitude β if the qubit is in the \(\left| e \right\rangle\) (resp. \(\left| g \right\rangle\)) and the MO is initially prepared in the state \(\left| {{\mathrm{i}}\left| {\beta _0} \right|} \right\rangle\). The mechanics can be used as a meter to detect the qubit state if gm/Ω ≫ 1 (ultra-strong coupling regime). The mechanical fluctuations induced by the qubit state are small w.r.t. the free evolution if \(\left| {\beta _0} \right| \gg g_{\mathrm{m}}{\mathrm{/\Omega }}\) (semi-classical regime). These two regimes are compatible (see text). c Stochastic mechanical trajectories \(\vec \beta [\vec \epsilon {\kern 1pt} ]\) in the phase space defined by \((\tilde x,\tilde p)\) (see text). The MO is initially prepared in the coherent state \(\left| {{\mathrm{i}}\left| {\beta _0} \right|} \right\rangle\), and the qubit state is drawn from thermal equilibrium. Inset: Distribution of final states \(\left| {\beta _{\mathrm{\Sigma }}\left( {t_N} \right)} \right\rangle\) within an area of typical width gm/Ω. Parameters: T = 80 K, ħω0 = 1.2kBT, Ω/2π = 100 kHz, γ/Ω = 5, gm/Ω = 100, |β0| = 1000
