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arXiv:1210.0389 · Optics Letters

Direct measurement of the Wigner time delay for the scattering of light by a single atom

Ronan Bourgain, J. Pellegrino, Stephan Jennewein, Yvan R. P. Sortais, Antoine Browaeys

Published May 28, 2013• 34 citations
arXivHTMLPDF

Abstract

We have implemented the Gedanken experiment of an individual atom scattering a wave packet of near-resonant light, and measured the associated Wigner time delay as a function of the frequency of the light. In our apparatus, the atom behaves as a two-level system and we have found delays as large as 42 ns at resonance, limited by the lifetime of the excited state. This delay is an important parameter in the problem of collective near-resonant scattering by an ensemble of interacting particles, which is encountered in many areas of physics.

DOI
10.1364/ol.38.001963

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We have implemented the Gedanken experiment of an individual atom scattering a wave packet of near-resonant light, and measured the associated Wigner time delay as a function of the frequency of the light. In our apparatus, the atom behaves as a two-level system and we have found delays as large as 42 ns at resonance, limited by the lifetime of the excited state. This delay is an important parameter in the problem of collective near-resonant scattering by an ensemble of interacting particles, which is encountered in many areas of physics.
Resonant scattering of weak coherent laser pulses on a single two-level system realized in a semiconductor quantum dot is investigated with respect to a time delay between incoming and scattered light. This type of time delay was predicted by Wigner in 1955 for purely coherent scattering and was confirmed for an atomic system in 2013 [R. Bourgain et al., Opt. Lett. 38, 1963 (2013)OPLEDP0146-959210.1364/OL.38.001963]. In the presence of electron-phonon interaction, we observe deviations from Wigner's theory related to incoherent and strongly non-Markovian scattering processes which are hard to quantify via a detuning-independent pure dephasing time. We observe detuning-dependent Wigner delays of up to 530 ps in our experiments which are supported quantitatively by microscopic theory allowing for pure dephasing times of up to 950 ps.
We study light scattering of atomic wave packets in free space and discuss the results in terms of atom-photon entanglement and which-way information. Using ultracold atoms released from an optical lattice, we realize a Gedanken experiment which interferes single photons scattering off of Heisenberg uncertainty-limited wave packets. We unify the free-space and trapped-atom pictures by measuring the light scattered before and during wave packet expansion and show the coherence properties of the scattered light are independent of the presence of the trap. Therefore, recoilless scattering in a trap (Mössbauer effect), the different frequency of sidebands, and the excitation of an excited harmonic oscillator state are not essential to the question of which fraction of light scattering is coherent or incoherent. Our experiment demonstrates the potential of using atomic Mott insulators to create single-atom wave packets for fundamental studies.
The interaction between photons and a single two-level atom constitutes a fundamental paradigm in quantum physics. The nonlinearity provided by the atom leads to a strong dependence of the light-matter interface on the number of photons interacting with the two-level system within its emission lifetime. This nonlinearity unveils strongly correlated quasiparticles known as photon bound states, giving rise to key physical processes such as stimulated emission and soliton propagation. Although signatures consistent with the existence of photon bound states have been measured in strongly interacting Rydberg gases, their hallmark excitation-number-dependent dispersion and propagation velocity have not yet been observed. Here we report the direct observation of a photon-number-dependent time delay in the scattering off a single artificial atom-a semiconductor quantum dot coupled to an optical cavity. By scattering a weak coherent pulse off the cavity-quantum electrodynamics system and measuring the time-dependent output power and correlation functions, we show that single photons and two- and three-photon bound states incur different time delays, becoming shorter for higher photon numbers. This reduced time delay is a fingerprint of stimulated emission, where the arrival of two photons within the lifetime of an emitter causes one photon to stimulate the emission of another.
We study theoretically the scattering of light by an ensemble of N resonant atoms in a subwavelength volume. We consider the low intensity regime so that each atom responds linearly to the field. While N noninteracting atoms would scatter N^{2} more than a single atom, we find that N interacting atoms scatter less than a single atom near resonance. In addition, the scattered power presents strong fluctuations, either from one realization to another or when varying the excitation frequency. We analyze this counterintuitive behavior in terms of collective modes resulting from the light-induced dipole-dipole interactions. We find that for small samples and sufficiently large atom number, their properties are governed only by their volume.
When a single photon propagates through a cloud of two-level atoms, part of its energy is temporarily stored as a collective atomic excitation. This raises a fundamental question: is it possible to meaningfully quantify how long the photon spends in the form of an atomic excitation? If so, does this duration depend on whether the photon is ultimately transmitted through the cloud or scattered by the atoms? These questions motivated recent experimental work by some of us [Sinclair et al., PRX Quantum 3, 010314 (2022)], but until now there has been no theoretical prediction for these conditional durations. We answer these questions by extending the concept of a dwell time from quantum tunneling to light–matter interactions, introducing an experimentally measurable “atomic excitation time.” Using the weak-value formalism combined with quantum trajectory theory, we derive analytical expressions for this time conditioned on the photon being transmitted through the cloud or scattered into a side mode. We show that, for transmitted photons, this time is equal to the (spectrally averaged) group delay, even in regimes where the group delay is negative. For scattered photons, the time is given by the sum of an ensemble-averaged group delay and an always-positive Wigner time delay, well known in elastic scattering theory. Finally, we present a toy model that explains how such negative dwell times can arise as a result of quantum interference. This work provides new insight into the complex and surprising histories of photons traveling through absorptive media.
Quantum weak measurements, wavepacket shifts and optical vortices are universal wave phenomena, which originate from fine interference of multiple plane waves. These effects have attracted considerable attention in both classical and quantum wave systems. Here we report on a phenomenon that brings together all the above topics in a simple one-dimensional scalar wave system. We consider inelastic scattering of Gaussian wave packets with parameters close to a zero of the complex scattering coefficient. We demonstrate that the scattered wave packets experience anomalously large time and frequency shifts in such near-zero scattering. These shifts reveal close analogies with the Goos-Hänchen beam shifts and quantum weak measurements of the momentum in a vortex wavefunction. We verify our general theory by an optical experiment using the near-zero transmission (near-critical coupling) of Gaussian pulses propagating through a nano-fibre with a side-coupled toroidal micro-resonator. Measurements demonstrate the amplification of the time delays from the typical inverse-resonator-linewidth scale to the pulse-duration scale.