Photon bound state dynamics from a single artificial atom
Natasha Tomm, Sahand Mahmoodian, Nadia O. Antoniadis, Rüdiger Schott, Sascha R. Valentin, Andreas Dirk Wieck, Arne Ludwig, Alisa Javadi, Richard John Warburton
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.
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.
In recent years, the study of quantum electrodynamics (QED) in light-matter interactions has discovered various interesting phenomenons that orient many applications. However, due to the ambient entanglement among photons and atoms, few-particle dynamics remains challenging to analyze precisely and limits the progress in several fields. In few-particle systems, different number of atoms interacting with the light field generates drastically different results, even when there is only a single photon involved in the system. The interference between individual atom’s spontaneous emission wavefunctions can cooperatively alter the effective atom-light coupling strength. Depending on the spatial distance between individual of atoms and the involved cavities in the interaction progresses, the collective spontaneous emission rate can alter drastically from superradiance, where the emission rate is enhanced to a high value proportional to the atom number, to subradiance, where the excited atom ensemble stays in a dark state with the light trapped forever. Superradiance provides a promising mechanism to create an ultra-strong light-matter coupling environment, which is an important ingredient for the design of ultra-fast optical devices, frequency comb generation and quantum mirrors. The dark state of subradiance, on the other hand, is essential for the quantum memory implementation. Also, nontrivial phenomenons also occur when multiple photons interacting with a single atom simultaneously. When a finite number of photons incidents on an atom, their scattering through an atom is highly nonlinear, and one special eigenstate component of such nonlinear process, namely photonic bound states, exhibits many interesting properties in nonlinear quantum optical systems. The photons in such state are strongly bunched with each other, as if a virtual attractive force is in effect. Also, the frequency of photons are anti-correlated so that their total frequency remains a constant value, no matter how arbitrary the frequency of any individual is. Thesefeatures benefit certain nonlinear quantum processes for quantum computing and quantum imaging. Specially for two-photon excitation imaging, the same-parity two-level fluorophore molecules suffers from extremely low excitation efficiencies due to the far off-resonant intermediate states. However, by replacing the current commonly used ultrashort laser pulse illuminations with two photon bound state photon pairs, namely photonic dimers, the efficiency can be enhanced to orders of magnitude higher. Such exceptionally high excitation efficiency can potentially bring the current in vivo deep brain imaging depth from millimeter level to several centimeters. To obtain a stable source of such photonic dimers, it is found that a laser structure with gain medium of two-photon emission materials is capable of generating the coherent state of photonic dimer and can serve as a promising light source for nonlinear quantum optical devices.
We present a quantum dynamical study of pulsed few-photon scattering from a single artificial atom, consisting of a two-level system (TLS) or qubit, in a waveguide QED system, directly comparing and contrasting two different quantum theoretical simulation methods: (i) an input-output scattering approach that uses frequency-dependent scattering matrices, and (ii) a matrix product states (MPS) approach, which uses quantum noise operators in time bins and a tensor network technique to solve the time-dependent waveguide function for the entire system. Beginning with pulsed excitation using one-photon and two-photon Fock state pulses, we first show how to compute time-dependent observables with the scattering matrix approach, in terms of frequency integrals that encode the pulse spectrum, including how to extract the population dynamics of the excited quantum emitter, as well as the linear and nonlinear contributions. We present solutions for both symmetric and chiral TLS coupling. We then show how to compute the qubit and field observables in a more direct way using MPS, and obtain the characteristic bird-like shape for the two-photon correlation function at two times, which has been observed in recent experiments. We compare and contrast both of these methods, for one and two-photon excitation pulses, and show excellent agreement. We also present a study of the linear and nonlinear contributions, which can easily be calculated using scattering theory, and show the important role of pulse duration. Finally, we demonstrate the clear advantages of MPS by easily going to higher N-photon excitations, and show selected example population dynamics of up to eight-photon Fock-state pulses, manifesting in clear nonlinear population oscillations during the pulse interaction, similar to classical Rabi oscillations, but with quantum input fields that have a vanishing electric field expectation value.
Resonance fluorescence of natural or artificial atoms constitutes a prime method for generating non-classical light. While most efforts have focused on producing single photons, multi-photon emission is unavoidably present in the resonant driving of an atom. Here, we study the extent to which these processes occur: we quantify the multi-photon emission statistics in a resonantly driven two-level artificial atom—a semiconductor quantum dot in a micropillar cavity—when pumped by short optical pulses. By measuring auto-correlation functions up to the fourth order, we observe up to four photons emitted after a single pumping pulse and investigate the emission dynamics with finely resolved temporal measurements. Furthermore, we propose a method based on acquisition time gating to enhance the purity of a single-photon source while maintaining high efficiencies. Our results deepen the understanding of the photon emission processes in coherently driven atomic systems and suggest a simple but effective technique to reduce the multi-photon components of a single-photon source.
We theoretically study the few-and many-body dynamics of photons in chiral waveguides.In particular, we examine pulse propagation through an ensemble of N two-level systems chirally coupled to a waveguide.We show that the system supports correlated multiphoton bound states, which have a welldefined photon number n and propagate through the system with a group delay scaling as 1=n 2 .This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system.For sufficiently many photons and sufficiently short systems, we show that linear combinations of n-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency.Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition.Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons.Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters.Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.
The realization of nonlinear systems able to mediate strong interactions between light fields at the few photon level in an environment with minimal absorption represents a cornerstone for future developments of quantum information science and photonic quantum technologies.One approach to reach this goal is via strong coupling of single emitters to optical cavities as provided by cavity quantum electrodynamics (QED).The other one is via electromagnetically induced transparency (EIT) with single atoms or with atomic ensembles.This thesis reports on a system which merges both single-atom cavity QED in the strong coupling regime and EIT.First, we characterize this system theoretically and show that its energy eigenstates are very similar to the well known Jaynes-Cummings ladder of eigenstates.However, here, the eigenstates are optically controllable via the control field Rabi frequency provided by EIT.We show that increasing the control field Rabi frequency enhances the normalmode splitting, and therefore the effective light-matter coupling.Moreover, with this system we are able to observe photon blockade and a two-photon gateway for the same input probe field and to tune the behavior of the secondorder correlation function optically.Thanks to the long coherence times of EIT, photon blockade can be prolonged in time for longer times than the decay rates of the system.We refer to this effect as photon blockade with memory.Next, we verify our theoretical findings experimentally.By performing spectroscopy measurements on the single-atom cavity EIT system, we show an unprecedented EIT on/off contrast of about 80 % thanks to our strong atomcavity coupling rate.Later, we show experimentally, the ability to generate both, photon blockade and a two-photon gateway, for the same input field by just varying the control field Rabi frequency.Finally, by performing timedependent second-order correlations we observe strong oscillations in the correlations which are a result of the creation of a new light field in the cavity which beats with the impinging probe laser.We show experimentally that this new field has a coherence time longer than the decay rates of the system, confirming its EIT origin.In a final experiment, we take advantage of the strong atom-cavity coupling achieved to induce a group delay on probing pulses.Delays up to approximately 200 ns are measured.This is the first time a group delay is observed with a single atom as the delaying medium.iii
Controlling light photon-by-photon is central to quantum optics. At a fundamental level, photon interactions are mediated by their coupling to atoms, and ultimate control requires deterministic light-matter interfacing of single photons to single atoms. Extending this paradigm to radiatively couple multiple individual atoms in a deterministic and scalable manner opens the arena of many-body quantum optics. Here, we realize such a setting by coherently coupling solid-state artificial atoms to a nanophotonic waveguide and demonstrate higher-order photon correlations that are controlled by the number of quantum emitters. We study the scaling of nonlinear photonic transport induced by emitter-photon scattering and demonstrate that adding a quantum emitter generates higher-order photon correlations. Specifically, we experimentally observe genuine three-photon correlations from a pair of collectively coupled emitters, while contributions from lower photon numbers are suppressed. In addition, we scale to three resonant quantum emitters coupled to the waveguide. These advancements demonstrate the onset of many-body quantum optics in waveguide quantum electrodynamics, enabling new photonic quantum simulators, the creation of many-body entangled states, and the exploration of novel quantum phase transitions.