An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near-and long-term perspectives of this fascinating and rapidly expanding field.hybrid quantum systems | quantum technologies | quantum information During the last several decades, quantum physics has evolved from being primarily the conceptual framework for the description of microscopic phenomena to providing inspiration for new technological applications. A range of ideas for quantum information processing (1) and secure communication (2, 3), quantum enhanced sensing (4-8), and the simulation of complex dynamics (9-14) has given rise to expectations that society may before long benefit from such quantum technologies. These developments are driven by our rapidly evolving abilities to experimentally manipulate and control quantum dynamics in diverse systems, ranging from single photons (2, 13), atoms and ions (11,12), and individual electron and nuclear spins (15-17), to mesoscopic superconducting (14, 18) and nanomechanical devices (19,20). As a rule, each of these systems can execute one or a few specific tasks, but no single system can be universally suitable for all envisioned applications. Thus, photons are best suited for transmitting quantum information, weakly interacting spins may serve as long-lived quantum memories, and the dynamics of electronic states of atoms or electric charges in semiconductors and superconducting elements may realize rapid processing of information encoded in their quantum states. The implementation of devices that can simultaneously perform several or all of these tasks, e.g., reliably store, process, and transmit quantum states, calls for a new paradigm: that of hybrid quantum systems (HQSs) (15, 21-24). HQSs attain their multitasking capabilities by combining different physical components wit...

We present a theory of electromagnetically induced transparency in a cold ensemble of strongly interacting Rydberg atoms. Long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our model is computationally very efficient and is in quantitative agreement with the results of recent experiment of Pritchard et al. [Phys. Rev. Lett. 105, 193603 (2010) Recently, several experiments on EIT [18][19][20][21], and the closely related CPT (coherent population trapping) [22], with Rydberg atoms were performed. Strong VdW interactions between the atomic Rydberg states were prominently manifest in Ref. [21]: Increasing the probe field amplitude led to reduction of its transmission within the EIT window, which, quite surprisingly, was accompanied by negligible broadening and indiscernible shift of the EIT line. Here we develop a theoretical model for EIT with Rydberg atoms, whose predictions fully reproduce the experimental observations [21]. The crux of our approach is the coarse-grained treatment of the atomic medium composed of effective superatoms (SAs), with each SA represented by collective states of atoms in the blockade volume that can accommodate only one Rydberg excitation. A weak probe field propagates through the EIT medium with little attenuation, but for a stronger field with more than one photon per SA, the excess photons are subject to enhanced-essentially twolevel atom-absorption. This leads to the field attenuation with the simultaneous buildup of an avoided volume between the probe photons [17]. The inclusion of twophoton correlations is the key feature of our work, not present in the numerical simulations of [21] and recent theoretical studies [23] which agreed with the experiment at weak probe fields but had significant discrepancies for stronger fields. Our theory is not limited to weak probe fields and/or low atomic densities, yet, despite intrinsic nonlinearity, it is intuitive and numerically efficient, amounting to the solution of a pair of coupled differential equations for the probe field intensity and its secondorder correlation, in the spirit of the BBGKY hierarchy.Consider an ensemble of N = V d 3 r ρ(r) cold atoms of density ρ(r) in the (quantization) volume V interacting with two optical fields. The quantized probe fieldÊ p of frequency ω p acts on the atomic transition between the ground |g and excited |e states, and the control field of frequency ω c drives the transition |e → |r with Rabi frequency Ω c [see Fig. 1(a)]. A pair of atoms i and j at positions r i and r j excited to the Rydberg states |r interact with each other via a VdW potentialh∆(r i − r j ) =hC 6 /|r i − r j | 6 [24]. In the frame rotating with frequencies ω p,c , the system Hamiltonian H = H a + V af + V VdW co...

We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle states, which can be classified as (i) scattering states of asymptotically free particles, and (ii) interaction-bound dimer states. Our results provide a very transparent framework to understand the properties of interacting pairs of particles in a lattice.