There has been rapid development of systems that yield strong interactions between freely propagating photons in one-dimension via controlled coupling to quantum emitters. This raises interesting possibilities such as quantum information processing with photons or quantum many-body states of light, but treating such systems generally remains a difficult task theoretically. Here, we describe a novel technique in which the dynamics and correlations of a few photons can be exactly calculated, based upon knowledge of the initial photonic state and the solution of the reduced effective dynamics of the quantum emitters alone. We show that this generalized 'input-output' formalism allows for a straightforward numerical implementation regardless of system details, such as emitter positions, external driving, and level structure. As a specific example, we apply our technique to show how atomic systems with infinite-range interactions and under conditions of electromagnetically induced transparency enable the selective transmission of correlated multi-photon states.from other emitters appears to be a difficult task. An exception is the weak excitation limit, in which atoms can be treated as linear scatterers and the powerful transfer matrix method of linear optics can be employed [18,19].The full quantum case has been solved exactly in a limited number of situations in which nonlinear systems are coupled to 1D waveguides [20][21][22][23][24][25][26][27][28][29][30]. The formalism employed in [21] is particularly elegant, because it establishes an input-output relation to determine the nonlinear scattering from a two-level atom. Here, we show that this technique can be efficiently generalized to many atoms, chiral or bi-directional waveguides, and arbitrary atomic configurations, providing a powerful tool to investigate nonlinear optical dynamics in all systems of interest.This paper is organized in the following way: first, we present a generalized input-output formalism to treat few-photon propagation in waveguides coupled to many atoms. We show that the infinite degrees of freedom associated with the photonic modes can be effectively integrated out, yielding an open, interacting 'spin' model that involves only the internal degrees of freedom of the atoms. This open system can be solved using a number of conventional, quantum optical techniques. Then, we show that the solution of the spin problem can be used to re-construct the optical fields. In particular, we provide a prescription to map spin correlations to S-matrix elements, which contain full information about the photon dynamics, and give explicit closed-form expressions for the one-and two-photon cases. Importantly, in analogy with the cavity QED case, our technique enables analytical solutions under some scenarios, but in general allows for simple numerical implementation under a wide variety of circumstances of interest, such as different level structures, external driving, atomic positions, atomic motion, etc. Finally, to illustrate the ease of usage, we apply ...

A powerful method to interface quantum light with matter is to propagate the light through an ensemble of atoms. Recently, a number of such interfaces have emerged, most prominently Rydberg ensembles, that enable strong nonlinear interactions between propagating photons. A largely open problem is whether these systems produce exotic many-body states of light and developing new tools to study propagation in the large photon number limit is highly desirable. Here we provide a method based on a “spin model” that maps quasi one-dimensional (1D) light propagation to the dynamics of an open 1D interacting spin system, where all photon correlations are obtained from those of the spins. The spin dynamics in turn are numerically solved using the toolbox of matrix product states. We apply this formalism to investigate vacuum induced transparency, wherein the different photon number components of a pulse propagate with number-dependent group velocity and separate at output.

Intense efforts have been made in recent years to realize nonlinear optical interactions at the singlephoton level. Much of this work has focused on achieving strong third-order nonlinearities, such as by using single atoms or other quantum emitters, while the possibility of achieving strong second-order nonlinearities remains unexplored. Here, we describe a novel technique to realize such nonlinearities using graphene, exploiting the strong per-photon fields associated with tightly confined graphene plasmons in combination with spatially nonlocal nonlinear optical interactions. We show that in properly designed graphene nanostructures, these conditions enable extremely strong internal downconversion between a single quantized plasmon and an entangled plasmon pair, or the reverse process of second harmonic generation. A separate issue is how such strong internal nonlinearities can be observed, given the nominally weak coupling between these plasmon resonances and free-space radiative fields. On one hand, by using the collective coupling to radiation of nanostructure arrays, we show that the internal nonlinearities can manifest themselves as efficient frequency conversion of radiative fields at extremely low input powers. On the other hand, the development of techniques to efficiently couple to single nanostructures would allow these nonlinear processes to occur at the level of single input photons.

A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell–Bloch equations. However, these equations are semi-phenomenological, as they treat emission of the atoms into other directions other than the mode of interest as being independent. On the other hand, in systems such as dense, ordered atomic arrays, atoms interact with each other strongly and spatial interference of the emitted light might be exploited to suppress emission into unwanted directions, thereby enabling improved error bounds. Here, we develop a general formalism that fully accounts for spatial interference, and which finds the maximum storage efficiency for a single photon with known spatial input mode into a collection of atoms with discrete, known positions. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number Na like ∼(logNnormalafalse)2∕Nnormala2, and that, remarkably, an array of just 4 × 4 atoms in principle allows for an error of less than 1%, which is comparable to a disordered ensemble with an optical depth of around 600.

Cold atoms coupled to photonic crystals constitute an exciting platform for exploring quantum many-body physics. For example, such systems offer the potential to realize strong photon-mediated forces between atoms, which depend on the atomic internal (spin) states, and where both the motional and spin degrees of freedom can exhibit long coherence times. An intriguing question then is whether exotic phases could arise, wherein crystalline or other spatial patterns and spin correlations are fundamentally tied together, an effect that is atypical in condensed matter systems. Here, we analyse one realistic model Hamiltonian in detail. We show that this previously unexplored system exhibits a rich phase diagram of emergent orders, including spatially dimerized spin-entangled pairs, a fluid of composite particles comprised of joint spin-phonon excitations, phonon-induced Néel ordering, and a fractional magnetization plateau associated with trimer formation.

We study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency. Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions.

We present a realistic scheme for how to construct a single-photon transistor where the presence or absence of a single microwave photon controls the propagation of a subsequent strong signal signal field. The proposal is designed to work with existing superconducting artificial atoms coupled to cavities. We study analytically and numerically the efficiency and the gain of our proposal and show that current transmon qubits allow for error probabilities ∼ 1% and gains of the order of hundreds.In analogy with electronic transistors, a single photon transistor is a device where the presence or absence of a single gate photon controls the propagation of a large number of signal photons [1,2]. Such devices would represent a milestone enabling a plethora of new approaches for processing light, but their realization is hampered by the absence of interactions between photons. A promising route towards strong interactions at the single photon level consists of coupling propagating photons to individual atom-like systems [3][4][5][6][7][8][9]. The best realization of such a coupling is achieved in the microwave regime where experiments have demonstrated an unprecedented control of the coupling between superconducting artificial atoms and microwave photons [10,11]. In this letter we describe how to realize a single photon transistor based on existing superconducting technology. The resulting devices can be directly employed to detect individual itinerant microwave photons, and may find a range of applications within quantum information processing.Various protocols for single photon non-linearities, quantum gates, and transistors using superconducting systems have been proposed [12][13][14][15], but have relied on unconventional qubit designs, multiple qubits and isolators, or temporal switching of parameters. A different method to construct the desired single photon transistors was described in Ref. [1], and realized in the optical regime in Ref. [2]. The atomic level structure used in that work is, however, not compatible with current superconducting artificial atoms (for convenience these will be referred to as atoms below). Here we show how to realize this proposal for a three level ladder (Ξ) system coupled to a superconducting cavity. This is the generic level scheme for the so-called transmon [16][17][18][19][20] and phase qubits [21] which essentially constitutes anharmonic ladders.We focus on the three lowest levels of the system. We assume that the Ξ-system is sufficiently anharmonic such that the cavity is resonant with the upper transition between states |g and |e , which has a coupling constant g, but off-resonant from the lower transition between |f and |g , see Fig. 1 (a). For now, we ignore the cavity coupling on the lower transition, deferring the discussion of this off-resonant cavity coupling to later. With this arrangement, we can be in a regime where there is a strong cavity enhancement of the decay of the upper level |e via the Purcell effect, such that it decays rapidly compared to the two lower level...

No abstract