We investigate Coherent Population Trapping in a strongly interacting ultracold Rydberg gas. Despite the strong van der Waals interactions and interparticle correlations, we observe the persistence of a resonance with subnatural linewidth at the single-particle resonance frequency as we tune the interaction strength. This narrow resonance cannot be understood within a meanfield description of the strong Rydberg-Rydberg interactions. Instead, a many-body density matrix approach, accounting for the dynamics of interparticle correlations, is shown to reproduce the observed spectral features.PACS numbers: 42.50. Gy,42.50.Ct,32.80.Ee Coherent population trapping (CPT), i.e. the population of a quantum state decoupled from a resonant light field, serves as a paradigm for a quantum interference effect [1]. First observed in 1976 [2], CPT with its related phenomena electromagnetically induced transparency (EIT) [3,4] and stimulated Raman adiabatic passage (STIRAP) [5] has provided the basis for a large variety of effects and applications in many areas of physics, such as high-resolution spectroscopy, coherent control, metrology, quantum information and quantum gases. While CPT, EIT and STIRAP are generally described in terms of isolated single-atom interactions with coherent light fields, the situation becomes more involved when interactions between the particles need to be considered.To gain initial insights into the effects of interactions on the quantum interference in CPT, consider two atoms with a three-level ladder structure with states |1 , |2 and |3 as shown in Fig. 1(a). The atoms are exposed to two resonant coherent light fields and interact only if both of them are in the highly excited atomic state |3 . In the case of non-interacting atoms the population accumulates in the two-body product state of the single-particle dark state |d which is a coherent superposition of |1 and |3 [1]. This state is defined as the eigenstate of the total Hamiltonian with vanishing coupling to the coherent light field. When turning on the interparticle interaction this state is no longer a dark state as it is no longer an eigenstate of the total Hamiltonian. As pointed out in [6], the two interacting atoms, nevertheless, possess two dark states |d ± . These states are dissipative due to the admixture of the intermediate, decaying state |2 , but are significantly populated by optical pumping. While these states have dissipative character, they do not contain the state |33 and are, thus, immune to interactions.In a first approach to a many-particle system one could apply a meanfield model by replacing many-body opera- PSfrag replacementsFIG. 1: (a) Excitation scheme ( 87 Rb). Ω1 and Ω2 are the Rabi frequencies at 780 and 480 nm, respectively, δ is the detuning of the upper transition; (b) calculated Rydberg state population, produced by the two-step sequence described in the text. The upper panel shows the result of a meanfield calculation, which predicts a strong shift and broadening of the resonance line. On the contrary, the...

Ultrafast electron diffractive imaging of nanoscale objects such as biological molecules 1,2 and defects in solid-state devices 3 provides crucial information on structure and dynamic processes: for example, determination of the form and function of membrane proteins, vital for many key goals in modern biological science, including rational drug design 4 . High brightness and high coherence are required to achieve the necessary spatial and temporal resolution, but have been limited by the thermal nature of conventional electron sources and by divergence due to repulsive interactions between the electrons, known as the Coulomb explosion. It has been shown that, if the electrons are shaped into ellipsoidal bunches with uniform density 5 , the Coulomb explosion can be reversed using conventional optics, to deliver the maximum possible brightness at the target 6,7 . Here we demonstrate arbitrary and real-time control of the shape of cold electron bunches extracted from laser-cooled atoms. The ability to dynamically shape the electron source itself and to observe this shape in the propagated electron bunch provides a remarkable experimental demonstration of the intrinsically high spatial coherence of a cold-atom electron source, and the potential for alleviation of electron-source brightness limitations due to Coulomb explosion 6 . Carbon nanotube field emitters are at present the brightest available electron sources but must operate at low currents to avoid Coulomb expansion and are therefore not suitable for ultrafast imaging. Limited bunch shaping has been demonstrated with photoemission sources 7,8 , which use high-energy laser pulses to generate electrons at high current. Combined with longitudinal bunch compression, sub-100 fs pulses have been obtained with sufficient brightness for diffraction studies of gold 8,9 . However, large increases in brightness are needed for single-shot imaging of weakly scattering materials such as biological molecules, and further increases in the brightness of intrinsically hot photoemission sources will be difficult.Recent simulations 10,11 and experiments 12 show that photoionization of a cold atom cloud can produce cold electron bunches with high coherence and current. Electrons are extracted by nearthreshold photoionization of atoms that have been laser-cooled to microKelvin temperature 13 . We demonstrate here that the extracted electron bunches have extremely small transverse momentum, and show that the source has quasi-homogeneous rather than thermal coherence properties; that is, unlike conventional photocathode sources, the transverse locations of the cold electrons remain strongly correlated to their original location at the source.In addition, the internal structure of the atoms that form the underlying electron source provides a unique tool for three-dimensional control of the electron bunch shape 5 . We show that it is possible to engineer the spatial profiles of the incident excitation and photoionization laser beams to control the shape ARC Centre of Excellence in C...

The linewidth of external cavity diode lasers (ECDLs) is an increasingly important characteristic for experiments in coherent optical communications and atomic physics. The Schawlow-Townes and time-averaged linewidths depend on free parameters of the design, such as cavity length, power, and grating characteristics. We show that the linewidth is also sensitive to the focus, set by the distance between the laser and the collimating lens, due to the effect on the external cavity backcoupling efficiency. By considering these factors, a simple ECDL can readily achieve linewidths below 100 kHz.