Storage and control of optical photons using Rydberg polaritons

Rydberg atom electric field sensing for metrology, communication and hybrid quantum systems

Rydberg atoms-based electric field sensing has developed rapidly over the past decade. A variety of theoretical proposals and experiment configurations are suggested and realized to improve the measurement metrics, such as intensity sensitivity, bandwidth, phase, and accuracy. The Stark effect and electromagnetically induced transparency (EIT) or electromagnetically induced absorption (EIA) are fundamental physics principles behind the stage. Furthermore, various techniques such as amplitude- or frequency-modulation, optical homodyne read-out, microwave superheterodyne and frequency conversion based on multi-wave mixing in atoms are utilized to push the metrics into higher levels. In this review, different technologies and the corresponding metrics they had achieved were presented, hoping to inspire more possibilities in the improvement of metrics of Rydberg atom-based electric field sensing and broadness of application scenarios.

Strongly Nonlinear Interaction between Nonclassical Light and a Blockaded Rydberg Atomic Ensemble

We investigate the interaction between nonclassical light with a tunable multiphoton component and a highly nonlinear medium based on cold Rydberg atoms. The nonclassical field emitted by a DLCZ quantum memory is stored using Rydberg electromagnetically induced transparency, experiencing strong nonlinear response due to the dipole blockade. We show that the storage efficiency in the Rydberg ensemble decreases as a function of the multiphoton strength of the input field, as a result of the nonlinearity. We also show that the autocorrelation function g^{(2)}(0) of the retrieved field after storage in the Rydberg state is considerably reduced, leading to the first demonstration of single photon filtering with nonclassical input light. Finally, we develop a simple simulation that allows us to model the effect of our medium on the input state. This work is a step towards matter-mediated photon-photon interactions with nonclassical light.

Three-dimensional solitons in Rydberg-dressed cold atomic gases with spin-orbit coupling

We present numerical results for three-dimensional (3D) solitons with symmetries of the semi-vortex (SV) and mixed-mode (MM) types, which can be created in spinor Bose-Einstein condensates of Rydberg atoms under the action of the spin-orbit coupling (SOC). By means of systematic numerical computations, we demonstrate that the interplay of SOC and long-range spherically symmetric Rydberg interactions stabilize the 3D solitons, improving their resistance to collapse. We find how the stability range depends on the strengths of the SOC and Rydberg interactions and the soft-core atomic radius.

Manipulation of single stored-photon with microwave field based on Rydberg polariton

We demonstrate a coherent microwave manipulation of a single optical photon based on a single Rydberg excitation in an atomic ensemble. Due to the strong nonlinearities in a Rydberg blockade region, a single photon can be stored in the formation of Rydberg polariton using electromagnetically induced transparency (EIT). The manipulation of the stored single photon is performed by applying a microwave field that resonantly couples the nS_1/2 and nP_3/2, while the coherent readout is performed by mapping the excitation into a single photon. We achieve a single photon source with g⁽²⁾(0) = 0.29 ± 0.08 at 80S_1/2 without applying microwave fields. By implementing the microwave field during the storage time and retrieval process, we show the Rabi oscillation and modulation of stored photons that can be controlled to retrieve early or late. Rapid modulation frequencies up to 50 MHz can be obtained. Our experimental observations can be well explained via numerical simulations based on an improved superatom model accounting for the dipole-dipole interactions in a Rydberg EIT medium. Our work provides a way to manipulate the stored photons by employing the microwave field, which is significant for developing quantum technologies.

Demonstration of a Quantum Gate Using Electromagnetically Induced Transparency

We demonstrate a native CNOT gate between two individually addressed neutral atoms based on electromagnetically induced transparency. This protocol utilizes the strong long-range interactions of Rydberg states to enable conditional state transfer on the target qubit when operated in the blockade regime. An advantage of this scheme is it enables implementation of multiqubit CNOT^{k} gates using a pulse sequence independent of qubit number, providing a simple gate for efficient implementation of digital quantum algorithms and stabilizer measurements for quantum error correction. We achieve a loss corrected gate fidelity of F_{CNOT}^{cor}=0.82(6), and prepare an entangled Bell state with F_{Bell}^{cor}=0.66(5), limited at present by laser power. We present a number of technical improvements to advance this to a level required for fault-tolerant scaling.

High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source

Compared to other types of qubits, photon is one of a kind due to its unparalleled advantages in long-distance quantum information exchange. Therefore, photon is a natural candidate for building a large-scale, modular optical quantum computer operating at room temperature. However, low-fidelity two-photon quantum logic gates and their probabilistic nature result in a large resource overhead for fault tolerant quantum computation. While the probabilistic problem can, in principle, be solved by employing multiplexing and error correction, the fidelity of linear-optical quantum logic gate is limited by the imperfections of single photons. Here, we report the demonstration of a linear-optical quantum logic gate with truth table fidelity of 99.84(3)% and entangling gate fidelity of 99.69(4)% post-selected upon the detection of photons. The achieved high gate fidelities are made possible by our near-optimal Rydberg single-photon source. Our work paves the way for scalable photonic quantum applications based on near-optimal single-photon qubits and photon-photon gates.

The current main source of errors for photonic quantum logic gates is the imperfections of the single photons. Here, by using high-quality photons from Rydberg atoms, the authors are able to reach 99.7% entangling gate fidelity in a photonic CNOT gate.

Dynamical Collective Excitations and Entanglement of Two Strongly Correlated Rydberg Superatoms

Based on the dipole blockade effect and with the aid of the superatom (SA) model, we propose a scheme to investigate the correlated evolution of two Rydberg sub-superatoms (SSAs), formed by two spatially separated atomic Rydberg sub-ensembles but in the same blockade region. Starting from the pure separable states, we investigate the in-phase or anti-phase correlated dynamics and explore how two Rydberg SSAs entangle with each other mediated by a single Rydberg excitation. Starting from the entangled states, we discuss the robustness of the system against decoherence induced by the dephasing rate. Our results show that both the correlated evolution of two Rydberg SSAs and their collective-state entanglement are usually sensitive to the number of each Rydberg SSA. This allows us to coherently manipulate the Rydberg ensemble over long distances from the single-quantum level to the mesoscopic level by changing the number of atoms. Furthermore, the method for dividing an SA into two SSAs and obtaining their spin operators without any approximation can be readily generalized to the case of many SSAs. It may have potential promising applications in quantum information processing and provide an attractive platform to study the quantum-classical correspondence, many-body physics and so on.

Collective Resonance of D States in Rubidium Atoms Probed by Optical Two-Dimensional Coherent Spectroscopy

Collective resonance of interacting particles has important implications in many-body quantum systems and their applications. Strong interactions can lead to a blockade that prohibits the excitation of a collective resonance of two or more nearby atoms. However, a collective resonance can be excited with the presence of weak interaction and has been observed for atoms in the first excited state (P state). Here, we report the observation of collective resonance of rubidium atoms in a higher excited state (D state) in addition to the first excited state. The collective resonance is excited by a double-quantum four-pulse excitation sequence. The resulting double-quantum two-dimensional (2D) spectrum displays well-isolated peaks that can be attributed to collective resonances of atoms in P and D states. The experimental one-quantum and double-quantum 2D spectra can be reproduced by a simulation based on the perturbative solutions to the optical Bloch equations, confirming collective resonances as the origin of the measured spectra. The experimental technique provides a new approach for preparing and probing collective resonances of atoms in highly excited states.

Unraveling Two-Photon Entanglement via the Squeezing Spectrum of Light Traveling through Nanofiber-Coupled Atoms

We observe that a weak guided light field transmitted through an ensemble of atoms coupled to an optical nanofiber exhibits quadrature squeezing. From the measured squeezing spectrum we gain direct access to the phase and amplitude of the energy-time entangled part of the two-photon wave function which arises from the strongly correlated transport of photons through the ensemble. For small atomic ensembles we observe a spectrum close to the line shape of the atomic transition, while sidebands are observed for sufficiently large ensembles, in agreement with our theoretical predictions. Furthermore, we vary the detuning of the probe light with respect to the atomic resonance and infer the phase of the entangled two-photon wave function. From the amplitude and the phase of the spectrum, we reconstruct the real and imaginary part of the time-domain wave function. Our characterization of the entangled two-photon component constitutes a diagnostic tool for quantum optics devices.

Collectively Encoded Rydberg Qubit

We demonstrate a collectively encoded qubit based on a single Rydberg excitation stored in an ensemble of N entangled atoms. Qubit rotations are performed by applying microwave fields that drive excitations between Rydberg states. Coherent readout is performed by mapping the excitation into a single photon. Ramsey interferometry is used to probe the coherence of the qubit, as well as to test the robustness to external perturbations. We show that qubit coherence is preserved even as we lose atoms from the polariton mode, preserving Ramsey fringe visibility. We show that dephasing due to electric field noise scales as the fourth power of field amplitude. These results show that robust quantum information processing can be achieved via collective encoding using Rydberg polaritons, and hence this system could provide an attractive alternative coding strategy for quantum computation and networking.

Tunable Three-Body Loss in a Nonlinear Rydberg Medium

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential for generating novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. Our numerical simulations of the full three-body wave function and analytical estimates based on Fermi's golden rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

Photon storage and routing in quantum dots with spin-orbit coupling

As an essential element for quantum information processing and quantum communication, efficient quantum memory based on solid-state platforms is imperative for practical applications but remains a challenge. Here we propose a scheme to realize a highly efficient and controllable storage and routing of single photons based on quantum dots (QDs) with a Rashba spin-orbit coupling (SOC). We show that the SOC in the QDs can provide a flexible built-up of electromagnetically induced transparency (EIT) for single-photon propagation, and storage, retrieval, as well as routing of single-photon wavepackets can also be implemented through the EIT. Moreover, we demonstrate that the propagation loss of the single-photon wavepackets in the QDs may be largely suppressed by means of a weak microwave field, by which the storage and routing of the single photons can be made to have high efficiency and fidelity. Our research opens a route for designs of advanced solid-state devices promising for applications in photonic quantum-information processing and transmission based on the QDs with SOC.

Self-Induced Transparency in Warm and Strongly Interacting Rydberg Gases

We study dispersive optical nonlinearities of short pulses propagating in high number density, warm atomic vapors where the laser resonantly excites atoms to Rydberg P states via a single-photon transition. Three different regimes of the light-atom interaction, dominated by either Doppler broadening, Rydberg atom interactions, or decay due to thermal collisions between ground state and Rydberg atoms, are found. We show that using fast Rabi flopping and strong Rydberg atom interactions, both in the order of gigahertz, can overcome the Doppler effect as well as collisional decay, leading to a sizable dispersive optical nonlinearity on nanosecond timescales. In this regime, self-induced transparency (SIT) emerges when areas of the nanosecond pulse are determined primarily by the Rydberg atom interaction, rather than the area theorem of interaction-free SIT. We identify, both numerically and analytically, the condition to realize Rydberg SIT. Our study contributes to efforts in achieving quantum information processing using glass cell technologies.

Storage and retrieval of ultraslow soliton at optical nanofiber interface via electromagnetically induced transparency

We theoretically investigate the optical memory in a nanofiber system via electromagnetically induced transparency (EIT) in a nonlinear region. Because of the tight transverse confinement, the light-atom interaction is significantly enhanced and thus, the EIT effect is enhanced. The inhomogeneous mode field distribution contributes spatially to the EIT dispersion. We develop a systematic analysis method to study the nonlinearity of the system and prove that the optical soliton is available in the system and can be stored and retrieved with high efficiency and stability. We also study a strategy to optimize the soliton optical memory. The results obtained in this study are promising for practical applications of all-optical information processing.

Pulsed-pump phosphorus-doped fiber Raman amplifier around 1260 nm for applications in quantum non-linear optics

We describe a fiber Raman amplifier for nanosecond and sub-nanosecond pulses centered around 1260 nm. The amplification takes place inside a 4.5-m-long polarization-maintaining phosphorus-doped fiber, pumped at 1080 nm by 3-ns-long pulses with a repetition rate of 200 kHz and up to 1.75 kW peak power. The input seed pulses are of sub-mW peak-power and minimal duration of 0.25 ns, carved out of a continuous-wave laser with sub-MHz linewidth. We obtain linearly polarized output pulses with peak powers of up to 1.4 kW, corresponding to peak-power conversion efficiency of over 80%. An ultrahigh small signal gain of 90 dB is achieved, and the signal-to-noise ratio 3 dB below the saturation power is above 20 dB. No significant temporal and spectral broadening is observed for output pulses up to 400 W peak power, and broadening at higher powers can be reduced by phase modulation of the seed pulse. Thus, nearly-transform-limited pulses with peak power up to 1 kW are obtained. Finally, we demonstrate the generation of pulses with controllable frequency chirp, pulses with variable width, and double pulses. This amplifier is thus suitable for coherent control of narrow atomic resonances, especially for the fast and coherent excitation of rubidium atoms to Rydberg states. These abilities open the way towards several important applications in quantum non-linear optics.

Cavity-enhanced and long-lived optical memories for two orthogonal polarizations in cold atoms

The storage and retrieval efficiency (SRE) and lifetime of optical quantum memories are two key performance indicators for scaling up quantum information processing. Here, we experimentally demonstrate a cavity-enhanced long-lived optical memory for two polarizations in a cold atomic ensemble. Using electromagnetically induced-transparency (EIT) dynamics, we demonstrate the storages of left-circularly and right-circularly polarized signal light pulses in the atoms, respectively. By making the signal and control beams collinearly pass through the atoms and storing the two polarizations of the signal light as two magnetic-field-insensitive spin waves, we achieve a long-lived (3.5 ms) memory. By placing a low-finesse optical ring cavity around the cold atoms, the coupling between the signal light and the atoms is enhanced, which leads to an increase in SRE. The presented cavity-enhanced storage shows that the SRE is ∼30%, corresponding to an intrinsic SRE of ∼45%.

Photon propagation through dissipative Rydberg media at large input rates

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.

Hanbury Brown-Twiss Correlations for a Driven Superatom

Hanbury Brown-Twiss interference and stimulated emission, two fundamental processes in atomic physics, have been studied in a wide range of applications in science and technology. We study interference effects that occur when a weak probe is sent through a gas of two-level atoms that are prepared in a singly excited collective (Dicke or "superatom") state and for atoms prepared in a factorized state. We measure the time-integrated second-order correlation function g^{(2)} of the output field as a function of the delay τ between the input probe field and radiation emitted by the atoms and find that, for the Dicke state, g^{(2)} is twice as large for τ=0 as it is for γ_{e}τ≫1 (γ_{e} is an excited state decay rate), while for the product state, this ratio is equal to 3/2. The results agree with those of a theoretical model in which any effects related to stimulated emission are totally neglected-the coincidence counts measured in our experiment arise from Hanbury Brown-Twiss interference between the input field and the field radiated by the atoms.

Single-Shot Nondestructive Detection of Rydberg-Atom Ensembles by Transmission Measurement of a Microwave Cavity

We present an experimental realization of single-shot nondestructive detection of ensembles of helium Rydberg atoms. We use the dispersive frequency shift of a superconducting microwave cavity interacting with the ensemble. By probing the transmission of the cavity, we determine the number of Rydberg atoms or the populations of Rydberg quantum states when the ensemble is prepared in a superposition. At the optimal microwave probe power, determined by the critical photon number, we reach single-shot detection of the atom number with 13% relative precision for ensembles of about 500 Rydberg atoms with a measurement backaction characterized by approximately 2% population transfer.

Extended Range of Dipole-Dipole Interactions in Periodically Structured Photonic Media

The interaction between quantum two-level systems is typically short range in free space and in most photonic environments. We show that diminishing momentum isosurfaces with equal frequencies can create a significantly extended range of interaction between distant quantum systems. The extended range is robust and does not rely on a specific location or orientation of the transition dipoles. A general relation between the interaction range and properties of the isosurface is described for structured photonic media. It provides a new way to mediate long-range quantum behavior.

Semideterministic Entanglement between a Single Photon and an Atomic Ensemble

Entanglement between a single photon and a matter qubit is an indispensable resource for quantum repeater and quantum networks. With atomic ensembles, the entanglement creation probability is typically very low to inhibit high-order events. In this paper, we propose and experimentally realize a scheme that creates atom-photon entanglement with an intrinsic efficiency of 50%. We make use of Rydberg blockade to generate two collective excitations, lying in separate internal states. By introducing the momentum degree of freedom for the excitations, and interfering them via Raman coupling, we entangle the two excitations. Via retrieving one excitation, we create the entanglement between the polarization of a single photon and the momentum of the remaining atomic excitation, with a measured fidelity of 0.901(8). The retrieved optical field is verified to be genuine single photons. The realized entanglement may be employed to create entanglement between two distant nodes in a fully heralded way and with a much higher efficiency.

Polariton Exchange Interactions in Multichannel Optical Networks

We examine the dynamics of Rydberg polaritons with dipolar interactions that propagate in multiple spatial modes. The dipolar excitation exchange between different Rydberg states mediates an effective exchange between polaritons that enables photons to hop across different spatial channels. Remarkably, the efficiency of this photon exchange process can increase with the channel distance and becomes optimal at a finite rail separation. Based on this mechanism, we design a simple photonic network that realizes a two photon quantum gate with a robust π phase, protected by the symmetries of the underlying photon interaction and the geometry of the network. These capabilities expand the scope of Rydberg electromagnetically induced transparency towards multidimensional geometries for nonlinear optical networks and explorations of photonic many-body physics.

Electron-nuclear correlated multiphoton-route to Rydberg fragments of molecules

Atoms and molecules exposed to strong laser fields can be excited to the Rydberg states with very high principal quantum numbers and large orbitals. It allows acceleration of neutral particles, generate near-threshold harmonics, and reveal multiphoton Rabi oscillations and rich photoelectron spectra. However, the physical mechanism of Rydberg state excitation in strong laser fields is yet a puzzle. Here, we identify the electron-nuclear correlated multiphoton excitation as the general mechanism by coincidently measuring all charged and neutral fragments ejected from a H₂ molecule. Ruled by the ac-Stark effect, the internuclear separation for resonant multiphoton excitation varies with the laser intensity. It alters the photon energy partition between the ejected electrons and nuclei and thus leads to distinct kinetic energy spectra of the nuclear fragments. The electron-nuclear correlation offers an alternative visual angle to capture rich ultrafast processes of complex molecules.

Strongly Correlated Photon Transport in Waveguide Quantum Electrodynamics with Weakly Coupled Emitters

We show that strongly correlated photon transport can be observed in waveguides containing optically dense ensembles of emitters. Remarkably, this occurs even for weak coupling efficiencies. Specifically, we compute the photon transport properties through a chirally coupled system of N two-level systems driven by a weak coherent field, where each emitter can also scatter photons out of the waveguide. The photon correlations arise due to an interplay of nonlinearity and coupling to a loss reservoir, which creates a strong effective interaction between transmitted photons. The highly correlated photon states are less susceptible to losses than uncorrelated photons and have a power-law decay with N. This is described using a simple universal asymptotic solution governed by a single scaling parameter which describes photon bunching and power transmission. We show numerically that, for randomly placed emitters, these results hold even in systems without chirality. The effect can be observed in existing tapered fiber setups with trapped atoms.

Ultracold Rydberg molecules

Ultracold molecules formed from association of a single Rydberg atom with surrounding atoms or molecules and those from double Rydberg excitations are discussed in this review. Ultralong-range Rydberg molecules possess a novel molecular bond resulting from scattering of the Rydberg electron from the perturber atoms or molecules. The strong interactions between Rydberg atoms in ultracold gases may lead to formation of macroscopic Rydberg macrodimers. The exquisite control over the properties of the Rydberg electron means that interesting and unusual few-body and quantum many-body features can be realized in such systems.

Rydberg molecules have been extensively studied both theoretically and experimentally. Here the authors review the recent developments in the study of various types of Rydberg molecules and their potential for future applications in spectroscopy, sensing and quantum information.

Rydberg-Dressed Magneto-optical Trap

We propose and demonstrate the laser cooling and trapping of Rydberg-dressed Sr atoms. By off-resonantly coupling the excited state of a narrow (7 kHz) cooling transition to a high-lying Rydberg state, we transfer Rydberg properties such as enhanced electric polarizability to a stable magneto-optical trap operating at <1  μK. Simulations show that it is possible to reach a regime where the long-range interaction between Rydberg-dressed atoms becomes comparable to the kinetic energy, opening a route to combining laser cooling with tunable long-range interactions.

Observation of three-photon bound states in a quantum nonlinear medium

Bound states of massive particles, such as nuclei, atoms, or molecules, constitute the bulk of the visible world around us. By contrast, photons typically only interact weakly. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. Photon correlation and conditional phase measurements reveal the distinct bunching and phase features associated with three-photon and two-photon bound states. Such photonic trimers and dimers possess shape-preserving wave functions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are described by an effective field theory of Rydberg-induced photon-photon interactions. These observations demonstrate the ability to realize and control strongly interacting quantum many-body states of light.

Optimization of photon storage fidelity in ordered atomic arrays

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 N a like ∼ ( log N a ) 2 ∕ N a 2 , 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.

Two Step Excitation in Hot Atomic Sodium Vapor

A two step excitation scheme in hot atomic sodium vapor is experimentally investigated. The observed effects reflect a coupling between the 3²S, 3²P and the 3²D states. We present the relative dependence on detuning of the two utilized lasers around λ = 589 nm and 819 nm. Unlike expected, we achieve a higher detuning dependence of the probe and the coupling laser by a factor of approximately three. The presented work aimed for a Rydberg excitation and quantum light storage. Such schemes are usually implemented with a red laser on the D-line transition and a coupling laser of shorter (typically blue) wavelength. Due to the fact that higher P-Rydberg states are approximately two times higher in energy than the 3²D state, a two photon transition from the atomic excited 3²P state to a Rydberg P state is feasible. This might circumvent laser frequency doubling whereby only two lasers might mediate a three photon process. The scheme of adding three k-vectors allows for electromagnetically induced transparency experiments in which the resulting k-vector can be effectively reduced to zero. By measurements utilizing electric fields and an analysis of the emission spectrum of the atomic vapor, we can exclude the excitation of the P-P two photon transition.

Enhanced spectral profile in the study of Doppler-broadened Rydberg ensembles

Combination of the electromagnetically-induced-transparency (EIT) effect and Rydberg-state atoms has attracted great attention recently due to its potential application in the photon-photon interaction or qubit operation. In this work, we studied the Rydberg-EIT spectra with room-temperature 87Rb atoms. Spectroscopic data under various experimental parameters all showed that the contrast of EIT transparency as a function of the probe field intensity is initially enhanced, reaches a maximum value and then decays gradually. The contrast of spectral profile at the optimum probe field intensity is enhanced by 2-4 times as compared with that at weakest intensity. Moreover, the signal-to-noise ratio of the spectrum can potentially be improved by 1 to 2 orders of magnitude. We provided a theoretical model to explain this behavior and clarified its underlying mechanism. Our work overcomes the obstacle of weak signal in the Rydberg-EIT spectrum caused by an apparent relaxation rate of the Rydberg polariton and weak coupling transition strength, and provides the useful knowledge for the Rydberg-EIT study.

Correlated Photon Dynamics in Dissipative Rydberg Media

Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging many-body problem in the limit of a large optical depth per blockade radius. In our approach, we separate the single-polariton EIT physics from Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of nonperturbative dissipative interactions relevant to current experiments. Our model is able to capture the many-body dynamics of bright, coherent pulses through these strongly interacting media. We compare our model with available experimental data in this regime and find good agreement. We also analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the presence of imperfect single-photon EIT.

Symmetry-protected collisions between strongly interacting photons

Realizing robust quantum phenomena in strongly interacting systems is one of the central challenges in modern physical science. Approaches ranging from topological protection to quantum error correction are currently being explored across many different experimental platforms, including electrons in condensed-matter systems, trapped atoms and photons. Although photon-photon interactions are typically negligible in conventional optical media, strong interactions between individual photons have recently been engineered in several systems. Here, using coherent coupling between light and Rydberg excitations in an ultracold atomic gas, we demonstrate a controlled and coherent exchange collision between two photons that is accompanied by a π/2 phase shift. The effect is robust in that the value of the phase shift is determined by the interaction symmetry rather than the precise experimental parameters, and in that it occurs under conditions where photon absorption is minimal. The measured phase shift of 0.48(3)π is in excellent agreement with a theoretical model. These observations open a route to realizing robust single-photon switches and all-optical quantum logic gates, and to exploring novel quantum many-body phenomena with strongly interacting photons.

Storing single photons emitted by a quantum memory on a highly excited Rydberg state

Strong interaction between two single photons is a long standing and important goal in quantum photonics. This would enable a new regime of nonlinear optics and unlock several applications in quantum information science, including photonic quantum gates and deterministic Bell-state measurements. In the context of quantum networks, it would be important to achieve interactions between single photons from independent photon pairs storable in quantum memories. So far, most experiments showing nonlinearities at the single-photon level have used weak classical input light. Here we demonstrate the storage and retrieval of a paired single photon emitted by an ensemble quantum memory in a strongly nonlinear medium based on highly excited Rydberg atoms. We show that nonclassical correlations between the two photons persist after retrieval from the Rydberg ensemble. Our result is an important step towards deterministic photon-photon interactions, and may enable deterministic Bell-state measurements with multimode quantum memories.

Quantum simulations and many-body physics with light

In this review we discuss the works in the area of quantum simulation and many-body physics with light, from the early proposals on equilibrium models to the more recent works in driven dissipative platforms. We start by describing the founding works on Jaynes-Cummings-Hubbard model and the corresponding photon-blockade induced Mott transitions and continue by discussing the proposals to simulate effective spin models and fractional quantum Hall states in coupled resonator arrays (CRAs). We also analyse the recent efforts to study out-of-equilibrium many-body effects using driven CRAs, including the predictions for photon fermionisation and crystallisation in driven rings of CRAs as well as other dynamical and transient phenomena. We try to summarise some of the relatively recent results predicting exotic phases such as super-solidity and Majorana like modes and then shift our attention to developments involving 1D nonlinear slow light setups. There the simulation of strongly correlated phases characterising Tonks-Girardeau gases, Luttinger liquids, and interacting relativistic fermionic models is described. We review the major theory results and also briefly outline recent developments in ongoing experimental efforts involving different platforms in circuit QED, photonic crystals and nanophotonic fibres interfaced with cold atoms.

Inelastic Photon Scattering via the Intracavity Rydberg Blockade

Electromagnetically induced transparency (EIT) in a ladder system involving a Rydberg level is known to yield giant optical nonlinearities for the probe field, even in the few-photon regime. This enhancement is due to the strong dipole-dipole interactions between Rydberg atoms and the resulting excitation blockade phenomenon. In order to study such highly correlated media, ad hoc models or low-excitation assumptions are generally used to tackle their dynamical response to optical fields. Here, we study the behavior of a cavity Rydberg-EIT setup in the nonequilibrium quantum field formalism, and we obtain analytic expressions for elastic and inelastic components of the cavity transmission spectrum, valid up to higher excitation numbers than previously achieved. This allows us to identify and interpret a polaritonic resonance structure, to our knowledge unreported so far.

Quantum memory with strong and controllable Rydberg-level interactions

Realization of distributed quantum systems requires fast generation and long-term storage of quantum states. Ground atomic states enable memories with storage times in the range of a minute, however their relatively weak interactions do not allow fast creation of non-classical collective states. Rydberg atomic systems feature fast preparation of singly excited collective states and their efficient mapping into light, but storage times in these approaches have not yet exceeded a few microseconds. Here we demonstrate a system that combines fast quantum state generation and long-term storage. An initially prepared coherent state of an atomic memory is transformed into a non-classical collective atomic state by Rydberg-level interactions in less than a microsecond. By sheltering the quantum state in the ground atomic levels, the storage time is increased by almost two orders of magnitude. This advance opens a door to a number of quantum protocols for scalable generation and distribution of entanglement.

Quantum information processing requires long-storage time of quantum states, but this typically comes at the expense of their addressability. Here the authors developed a method that exploits interaction between Rydberg and ground states of an atom reporting fast state generation and long-term storage.

Storage Enhanced Nonlinearities in a Cold Atomic Rydberg Ensemble

The combination of electromagnetically induced transparency with the nonlinear interaction between Rydberg atoms provides an effective interaction between photons. In this Letter, we investigate the storage of optical pulses as collective Rydberg atomic excitations in a cold atomic ensemble. By measuring the dynamics of the stored Rydberg polaritons, we experimentally demonstrate that storing a probe pulse as Rydberg polaritons strongly enhances the Rydberg mediated interaction compared to the slow propagation case. We show that the process is characterized by two time scales. At short storage times, we observe a strong enhancement of the interaction due to the reduction of the Rydberg polariton group velocity down to 0. For longer storage times, we observe a further, weaker enhancement dominated by Rydberg induced dephasing of the multiparticle components of the state. In this regime, we observe a nonlinear dependence of the Rydberg polariton coherence time with the input photon number. Our results have direct consequences in Rydberg quantum optics and may enable the test of new theories of strongly interacting Rydberg systems.

Effective Field Theory for Rydberg Polaritons

We develop an effective field theory (EFT) to describe the few- and many-body propagation of one-dimensional Rydberg polaritons. We show that the photonic transmission through the Rydberg medium can be found by mapping the propagation problem to a nonequilibrium quench, where the role of time and space are reversed. We include effective range corrections in the EFT and show that they dominate the dynamics near scattering resonances in the presence of deep bound states. Finally, we show how the long-range nature of the Rydberg-Rydberg interactions induces strong effective N-body interactions between Rydberg polaritons. These results pave the way towards studying nonperturbative effects in quantum field theories using Rydberg polaritons.

Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Förster resonances

Mapping the strong interaction between Rydberg atoms onto single photons via electromagnetically induced transparency enables manipulation of light at the single-photon level and few-photon devices such as all-optical switches and transistors operated by individual photons. Here we demonstrate experimentally that Stark-tuned Förster resonances can substantially increase this effective interaction between individual photons. This technique boosts the gain of a single-photon transistor to over 100, enhances the non-destructive detection of single Rydberg atoms to a fidelity beyond 0.8, and enables high-precision spectroscopy on Rydberg pair states. On top, we achieve a gain larger than 2 with gate photon read-out after the transistor operation. Theory models for Rydberg polariton propagation on Förster resonance and for the projection of the stored spin-wave yield excellent agreement to our data and successfully identify the main decoherence mechanism of the Rydberg transistor, paving the way towards photonic quantum gates.

Single photon level of light control is possible by using the effective interaction between single photons and Rydberg atoms. Here the authors utilized such interaction of Stark-tuned Forster resonances to boost the gain of a Rydberg single-photon transistor and perform high precision spectroscopy.

Three-Body Interaction of Rydberg Slow-Light Polaritons

We study a system of three photons in an atomic medium coupled to Rydberg states near the conditions of electromagnetically induced transparency. Based on the analytical analysis of the microscopic set of equations in the far-detuned regime, the effective three-body interaction for these Rydberg polaritons is derived. For slow light polaritons, we find a strong three-body repulsion with the remarkable property that three polaritons can become essentially noninteracting at short distances. This analysis allows us to derive the influence of the three-body repulsion on bound states and correlation functions of photons propagating through a one-dimensional atomic cloud.

Broadband photon-photon interactions mediated by cold atoms in a photonic crystal fiber

We demonstrate theoretically that photon-photon attraction can be engineered in the continuum of scattering states for pairs of photons propagating in a hollow-core photonic crystal fiber filled with cold atoms. The atoms are regularly spaced in an optical lattice configuration and the photons are resonantly tuned to an internal atomic transition. We show that the hard-core repulsion resulting from saturation of the atomic transitions induces bunching in the photonic component of the collective atom-photon modes (polaritons). Bunching is obtained in a frequency range as large as tens of GHz, and can be controlled by the inter-atomic separation. We provide a fully analytical explanation for this phenomenon by proving that correlations result from a mismatch of the quantization volumes for atomic excitations and photons in the continuum. Even stronger correlations can be observed for in-gap two-polariton bound states. Our theoretical results use parameters relevant for current experiments and suggest a simple and feasible way to induce interactions between photons.

Enhanced third-order and fifth-order Kerr nonlinearities in a cold atomic system via Rydberg-Rydberg interaction

We investigate the optical Kerr nonlinearities of an ensemble of cold Rydberg atoms under the condition of electromagnetically induced transparency (EIT). By using an approach beyond mean-field theory, we show that the system possesses not only enhanced third-order nonlinear optical susceptibility, but also giant fifth-order nonlinear optical susceptibility, which has a cubic dependence on atomic density. Our results demonstrate that both the third-order and the fifth-order nonlinear optical susceptibilities consist of two parts, contributed respectively by photon-atom interaction and Rydberg-Rydberg interaction. The Kerr nonlinearity induced by the Rydberg-Rydberg interaction plays a leading role at high atomic density. We find that the fifth-order nonlinear optical susceptibility in the Rydberg-EIT system may be five orders of magnitude larger than that obtained in traditional EIT systems. The results obtained may have promising applications in light and quantum information processing and transmission at weak-light level.

Pulsed Rydberg four-wave mixing with motion-induced dephasing in a thermal vapor

We report on time-resolved pulsed four-wave mixing (FWM) signals in a thermal Rubidium vapor involving a Rydberg state. We observe FWM signals with dephasing times up to 7 ns, strongly dependent on the excitation bandwidth to the Rydberg state. The excitation to the Rydberg state is driven by a pulsed two-photon transition on ns timescales. Combined with a cw de-excitation laser, a strongly directional and collective emission is generated according to a combination of the phase matching effect and averaging over Doppler classes. In contrast to a previous report (Huber et al. in Phys Rev A 90: 053806, 2014) using off-resonant FWM, at a resonant FWM scheme we observe additional revivals of the signal shortly after the incident pulse has ended. We infer that this is a revival of motion-induced constructive interference between the coherent emissions of the thermal atoms. The resonant FWM scheme reveals a richer temporal structure of the signals, compared to similar, but off-resonant excitation schemes. A simple explanation lies in the selectivity of Doppler classes. Our numerical simulations based on a four-level model including a whole Doppler ensemble can qualitatively describe the data.

Many-body decoherence dynamics and optimized operation of a single-photon switch

We develop a theoretical framework to characterize the decoherence dynamics due to multi-photon scattering in an all-optical switch based on Rydberg atom induced nonlinearities. By incorporating the knowledge of this decoherence process into optimal photon storage and retrieval strategies, we establish optimized switching protocols for experimentally relevant conditions, and evaluate the corresponding limits in the achievable fidelities. Based on these results we work out a simplified description that reproduces recent experiments (Nat. Commun. 7 12480) and provides a new interpretation in terms of many-body decoherence involving multiple incident photons and multiple gate excitations forming the switch. Aside from offering insights into the operational capacity of realistic photon switching capabilities, our work provides a complete description of spin wave decoherence in a Rydberg quantum optics setting, and has immediate relevance to a number of further applications employing photon storage in Rydberg media.

Observation of interference effects via four-photon excitation of highly excited Rydberg states in thermal cesium vapor

We report on the observation of electromagnetically induced transparency (EIT) and absorption (EIA) of highly excited Rydberg states in thermal Cs vapor using a four-step excitation scheme. The advantage of this four-step scheme is that the final transition to the Rydberg state has a large dipole moment and one can achieve similar Rabi frequencies to two- or three-step excitation schemes using two orders of magnitude less laser power. This scheme enables new applications such as dephasing free Rydberg excitation. The observed lineshapes are in good agreement with simulations based on multilevel optical Bloch equations.

Monodisperse cluster crystals: Classical and quantum dynamics

We study the phases and dynamics of a gas of monodisperse particles interacting via soft-core potentials in two spatial dimensions, which is of interest for soft-matter colloidal systems and quantum atomic gases. Using exact theoretical methods, we demonstrate that the equilibrium low-temperature classical phase simultaneously breaks continuous translational symmetry and dynamic space-time homogeneity, whose absence is usually associated with out-of-equilibrium glassy phenomena. This results in an exotic self-assembled cluster crystal with coexisting liquidlike long-time dynamical properties, which corresponds to a classical analog of supersolid behavior. We demonstrate that the effects of quantum fluctuations and bosonic statistics on cluster-glassy crystals are separate and competing: Zero-point motion tends to destabilize crystalline order, which can be restored by bosonic statistics.

Coulomb Bound States of Strongly Interacting Photons

We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasibound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wave function resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms.

Coherence and Rydberg Blockade of Atomic Ensemble Qubits

We demonstrate |W⟩ state encoding of multiatom ensemble qubits. Using optically trapped Rb atoms, the T_{2} coherence time is 2.6(3) ms for N[over ¯]=7.6 atoms and scales approximately inversely with the number of atoms. Strong Rydberg blockade between two ensemble qubits is demonstrated with a fidelity of 0.89(1), and with a fidelity of ∼1.0 when postselected on a control ensemble excitation. These results are a significant step towards deterministic entanglement of atomic ensembles.

Dipolar Dephasing of Rydberg D-State Polaritons

We experimentally study the effects of the anisotropic Rydberg interaction on D-state Rydberg polaritons slowly propagating through a cold atomic sample. We observe the interaction-induced dephasing of Rydberg polaritons at very low photon input rates into the medium. We develop a model combining the propagation of the two-photon wave function through our system with nonperturbative calculations of the anisotropic Rydberg interaction to show that the observed effect can be attributed to pairwise interaction of individual Rydberg polaritons at distances larger than the Rydberg blockade.

Microwaves Probe Dipole Blockade and van der Waals Forces in a Cold Rydberg Gas

We show that microwave spectroscopy of a dense Rydberg gas trapped on a superconducting atom chip in the dipole blockade regime reveals directly the dipole-dipole many-body interaction energy spectrum. We use this method to investigate the expansion of the Rydberg cloud under the effect of repulsive van der Waals forces and the breakdown of the frozen gas approximation. This study opens a promising route for quantum simulation of many-body systems and quantum information transport in chains of strongly interacting Rydberg atoms.