Accessing which-path information in the absorption and emission of light by a quantum dot in a Ramsey sequence

Abstract

We quantify which-path information in the absorption and emission of light by a quantum dot along a Ramsey-like sequence. The quantum dot is excited by two successive classical $π/2$-pulses with tunable relative phase, yielding the spontaneous release of coherent superpositions of zero- and one-photon Fock states into two successive time bins. Along the sequence, the first time bin extracts information on the quantum dot energy state, behaving as a which-path detector for the Ramsey interferometer. The which-path information increases over time, and is accessed through the reduction of contrast of the Ramsey fringes. After the second pulse, the information still present in the first time bin controls the emission of coherent light into the second time bin, which is measurable through the reduction of the contrast of self-homodyne interference fringes in a Mach-Zehnder interferometer. Both measurements are in remarkable agreement with theoretical predictions. Our results quantitatively illustrate how which-path information and more generally quantum correlations impact light-matter energy exchanges in the quantum realm.

Figures (5)

• Figure 1: Which-Path information in a Ramsey-like sequence. (a) A quantum dot is driven by two classical $\pi/2$-pulses with relative phase $\varphi_R$, separated by a delay $\Delta t$. The photonic field $\phi^{-}_{g (e)}$ emitted in the first time bin $\tau_1$ carries which-path information about the quantum dot state, and alters the coherent emission $\phi^{+}_{g (e)}$ in the second time bin $\tau_2$. In our experiments, Which-path information is accessed immediately before ($\Delta t^-$) and after ($\Delta t^+$) the second Ramsey pulse. (b) Which-path information carried by the first time bin at $\Delta t^+$ is probed through the interference visibility in a path-unbalanced Mach-Zehnder interferometer. A delay line matched to the laser repetition period ($\tau_p$) overlaps successively emitted photonic states at the second beam splitter.
• Figure 2: (a) The absorption during the second excitation pulse at time $\Delta t$, in units of $\gamma^{-1}$, for a constructive (destructive) Ramsey phase $\varphi=0$$(\pi)$ in purple diamonds (blue circles), and the atomic dipole $\sigma^-_-$ (fringe visibility) in orange squares. Inset: The population of the qubit right before the second excitation pulse, $\Delta t^-$, as a function of delay. (b) WP information immediately before the second excitation pulse ($t=\Delta t^{-}$) as a function of the delay. Blue circles show the ideal WP information given by Eq. \ref{['eq:wp_ideal']} in the main text, while purple diamonds correspond to the WP information including dipole-induced damping.
• Figure 3: (a) Time-resolved total energy emission of the QD along the decay profile for various Ramsey phases, at a delay $\gamma\Delta t = 1.42 \pm 0.04$. (b) Time-resolved visibility of the MZI fringes with plateaus $v_{1}$ and $v_{2}$ for the same Ramsey phases and delay as in panel (a). The visibility $v_2$ is reduced due to the which-path information $w^{-}$ encoded in the first time bin (see text).
• Figure 4: (a,b) Modification of the which-path information encoded in the first time bin, as revealed through the coherent emission in the second time bin. Shown is the which-path information $1-w^+$, present in the second time bin $\Delta t^+$ as a function of the Ramsey phase for two different delays $\gamma\Delta t$. The values are obtained either directly from the temporally resolved plateaus (open circles), or inferred from the absorption data using Eq. \ref{['eq:w+w-']} assuming ideal $w^-$ (circles) or $w^-$ damped by the presence of a QD dipole (stars). The dashed curves correspond to the theoretical prediction of Eq. \ref{['eq:w+w-']}. The solid horizontal line indicates the measured WP $1-w^-$ in the first time bin.
• Figure S.1: The absorption during the second Ramsey pulse as a function of pulse delay with (solid line) and without (dashed line) spectral diffusion $\delta$ of the quantum dot transition frequency. The data shown corresponds to the data in the main text for two different Ramsey phases $\varphi_R$.