Measurement Induced Subradiance

Abstract

Preparing subradiant steady states of collectively emitting quantum two-level emitters (TLEs) is hindered by their dark, weakly interacting nature. Existing approaches rely on patterned driving, local control, or structured environments. We propose a platform-independent protocol based on projective measurements on a single TLE. For permutation-symmetric ensembles, a single measurement yields appreciable occupation of single-excitation subradiant steady states. For generic arrays, repeated measurements on one emitter drive the unmeasured TLEs into a nearly pure state with large overlap with the subradiant Dicke subspace.

Figures (5)

• Figure 1: (a) Schematic of $N$ two-level emitters undergoing collective spontaneous emission and subject to single emitter (local) measurements. Top panel depicts a permutation symmetric ensemble (PSE) subjected to a projective measurement of $\hat{\sigma}_i^{\mu=(x,z)}$ (shown in green) and bottom panel shows a generic array where repeated measurements of $\hat{\sigma}_i^{x}$ are applied. (b) Population dynamics in the Dicke basis $\vert J,M\rangle$: In a PSE, collective decay (red curly arrows) redistributes population across Dicke ladders with the same total spin $J$ but local measurements (dashed green arrows) provide an irreversible way to redistribute population across different $J$ ladders, steering the system away from superradiant to subradiant states (blue).
• Figure 2: Steady state probability $P_{\mathrm{sub}}^{\mathrm{ss},\mu}$ to be in a subradiant Dicke state due to a single measurement of (a) $\hat{\sigma}^z$ or (b) $\hat{\sigma}^x$ of a single emitter at $t_\mathrm{m}$ for a permutation symmetric ensemble of $N$ TLEs. Solid lines are from exact analytical expressions and symbols are from numerical solution of Eq. \ref{['eq:SpMe']}.
• Figure 3: Estimated life-time $t_\mathrm{sub}$ for an $N$ TLE array with separation $d = 0.1\lambda_0$ interacting with a waveguide as a function of $t_\mathrm{m}$ at which a single measurement of (a) $\hat{\sigma}^z$ or (b) $\hat{\sigma}^x$ is performed. Results calculated by direct numerical solution of Eq. \ref{['eq:SpMe']} are presented in units of the lifetime without measurements $t^{\mathrm{um}}_\mathrm{sub}$.
• Figure 4: Subradiant population of the unmeasured emitters of an array of $N=7$ TLEs placed with separation $d =0.34\lambda_0$ inside a waveguide. The $\hat{\sigma}_x^i$ of the emitter at location $i=3$ is measured repeatedly at the rate $r_\mathrm{m}$ starting from $t_{\mathrm{in}} = 0.25\Gamma_0^{-1}$. Dashed lines represents the results from the Zeno limit effective master equation Eq. \ref{['eq:ZenoME']}.
• Figure 5: Time evolution of the purity $\mathcal{P}$ of the state of unmeasured qubits averaged over $2000$ MCWF trajectories for different measurement rates $r_\mathrm{m}$ of the $i=3^\mathrm{rd}$ TLE. Dashed line depicts the result for driving of the $i^\mathrm{th}$ TLE with the Rabi frequency $\Omega_i = 10\Gamma_0$. Other parameters are same as in Fig. \ref{['fig:Psub_Nm1']}.