Electromagnetically induced transparency with Rydberg atoms

Measurement of relative transition strengths of 133Cs Rydberg D states using electromagnetically induced transparency

Transition strengths between states are fundamental physical properties of atomic spectra. The differences in fine structure splitting of certain states are mainly attributed to the angular momentum parts of transition dipole matrix elements. These can be calculated by integrating the wave-functions theoretically and can be accessed by selecting corresponding polarizations of the exciting lasers experimentally. We measured the transition strengths ratios of nD5 / 2 /nD3 / 2 via Rydberg electromagnetically induced transparency (EIT) by changing the powers and polarizations of probing and coupling lasers in a room temperature cesium vapor cell. The variation of the ratios on the principal quantum number n which ranges from 40 to 62 is also investigated. Theoretical and experimental results agreed with each other.

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.

Biphoton generation enhanced by nonlocal nonlinearity via Rydberg interactions

Strongly correlated Stokes and anti-Stokes photon pairs (biphotons) exhibiting very large generation rates and spectral brightnesses could be attained at extremely low pump powers and optical depths. This is realized via spontaneous four-wave mixing in cold atoms with enhanced nonlocal (Rydberg) optical nonlinearities and prepared into a dark state with a large population imbalance. The scheme works with all light fields on resonance yet with negligible linear absorption and Raman gain.

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.

Optimal optical Ferris wheel solitons in a nonlocal Rydberg medium

We propose a scheme for the creation of stable optical Ferris wheel (OFW) solitons in a nonlocal Rydberg electromagnetically induced transparency (EIT) medium. Depending on a careful optimization of both the atomic density and the one-photon detuning, we obtain an appropriate nonlocal potential provided by the strong interatomic interaction in Rydberg states that can perfectly compensate for the diffraction of the probe OFW field. Numerical results show that the fidelity remains larger than 0.96, while the propagation distance has exceeded 160 diffraction lengths. Higher-order OFW solitons with arbitrary winding numbers are also discussed. Our study provides a straightforward route to generate spatial optical solitons in the nonlocal response region of cold Rydberg gases.

Experimental Realization of Reconfigurable Photonic Lattices in Coherent Rydberg Atomic Vapors

We experimentally demonstrated the formation of a one-dimensional electromagnetically induced optical lattice in coherently prepared three-level 85Rb Rydberg atomic vapors with electromagnetically induced transparency (EIT). The one-dimensional photonic lattice was optically induced by a coupling field with a spatially periodical intensity distribution deriving from the interference of two strong Gaussian beams from the same laser source (~480 nm). Under the Rydberg-EIT condition, the incident weak probe beam can feel a tunable spatially modulated susceptibility, which is verified by the controllable discrete diffraction pattern observed at the output plane of the vapor cell. This investigation not only opens the door for experimentally introducing the strong interaction between Rydberg atoms to govern the beam dynamics in photonic lattices based on atomic coherence but also provides an easily accessible periodic environment for exploring Rydberg-atom physics and related applications.

Polarization Spectroscopy Applied to Electromagnetically Induced Transparency in Hot Rydberg Atoms Using a Laguerre–Gaussian Beam

In this work, we have applied polarization spectroscopy to study electromagnetically induced transparency involving hot Rb85 Rydberg state in a vapor cell using a Laguerre–Gaussian mode beam. Such spectroscopy technique generates a dispersive signal, which allows a direct measurement of the transition linewidth. Our results show that the measured transition linewidth for a Laguerre–Gaussian mode control beam is narrower than for a Gaussian mode. Besides, it can be well reproduced by a simplified Lindblad master equation model.

Sensitivity Improvement and Determination of Rydberg Atom-Based Microwave Sensor

We present a theoretical and experimental investigation of the improvement and determination of the sensitivity of Rydberg atom-based microwave RF sensor. An optical Bloch equation has been set up based on the configuration that two-color cascading lasers exciting atom to highly Rydberg state and a microwave RF coupling this Rydberg state to its adjacent neighbor. The numerical simulation shows that the sensitivity of the atomic RF sensor is correlated with the amplitude strengths of the applied two lasers and the RF itself. It also depends on the frequency detuning of the coupling laser, which induces an asymmetrically optical splitting. The coupling laser frequency fixing at the shoulder of the stronger one is more favorable for a higher sensitivity. Accordingly, we perform an experimental demonstration for the optimization of all these parameters and the sensitivity is improved to 12.50(04) nVcm−1·Hz−1/2.

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.

Ferris wheel patterning of Rydberg atoms using electromagnetically induced transparency with optical vortex fields

We study the formation of spatially dependent electromagnetically induced transparency (EIT) patterns from pairs of Laguerre-Gauss (LG) modes in an ensemble of cold interacting Rydberg atoms. The EIT patterns can be generated when two-photon detuning does not compensate for the Rydberg level energy shift induced by van der Waals interaction. Depending on the topological numbers of each LG mode, we can pattern dark and bright Ferris-wheel-like structures in the absorption profile with tunable barriers between sites, providing confinement of Rydberg atoms in transverse direction while rendering them transparent to light at specific angular positions. We also show how the atomic density may affect the azimuthal modulation of the absorption profile.

Light propagation in a three-dimensional Rydberg gas with a nonlocal optical response

We theoretically investigate the linear susceptibility and propagation of light in a three-dimensional (3-D) Rydberg gas under conditions of electromagnetically induced transparency. Rydberg atoms with two relevant S states are coupled via exchange interactions. When the gas is initially prepared in an entangled spin-wave state, this coupling induces a strong, nonlocal susceptibility whereby the photon field at one point of the medium acts as a source at a distant position. The nonlocal propagation occurs not only in the propagation direction but also in the paraxial direction. We discuss the absorption features and numerically simulate the 3-D propagation of probe laser light. Combined with the long-range exchange interaction, we show that the 3-D Rydberg gas is an ideal medium for studying nonlocal wave phenomena, in which the strength, range, and sign of the nonlocal interaction kernel can be widely tuned.

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.

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.

Stochastic switching in the Rydberg atomic ensemble

We demonstrated stochastic switching in a bistable system implemented with the Rydberg atomic ensemble, which is realized by cascaded Rydberg excitation in a cesium vapor cell. Measurement of Rydberg state's population by means of the electromagnetically induced transparency allows us to investigate the nonlinear behavior in Rydberg atomic ensemble experimentally. The transition between the two states of the bistable system is driven by the intensity noise of the laser beams. Rydberg atomic ensemble accumulates energy in an equilibrium situation and brings the nonlinear system across the threshold, where stochastic switching occurs between the two states.

Mean field theory of weakly-interacting Rydberg polaritons in the EIT system based on the nearest-neighbor distribution

The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weakly-interacting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt with the strongly-interacting cases. Here, we consider the weakly-interacting regime and develop a mean field model based on the nearest-neighbor distribution. Using the mean field model, we further derive the analytical formulas for the attenuation coefficient and phase shift of the output probe field. The predictions from the formulas are consistent with the experimental data in the weakly-interacting regime, verifying the validity of our model. As the DDI-induced phase shift and attenuation can be seen as the consequences of elastic and inelastic collisions among particles, this work provides a very useful tool for conceiving ideas relevant to the EIT system of weakly-interacting Rydberg polaritons and for evaluating experimental feasibility.

Exotic Photonic Molecules via Lennard-Jones-like Potentials

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a Förster resonance with other Rydberg states. We consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters ("molecules") of photons. We demonstrate that for a few-body problem, the multibody interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in two dimensions preferentially arrange themselves in a line configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

Electromagnetically induced transparency of interacting Rydberg atoms with two-body dephasing

We study electromagnetically induced transparency in a three-level ladder type configuration in ultracold atomic gases, where the upper level is an electronically highly excited Rydberg state. An effective distance dependent two-body dephasing can be induced in a regime where dipole-dipoles interaction couple nearly degenerate Rydberg pair states. We show that strong two-body dephasing can enhance the excitation blockade of neighboring Rydberg atoms. Due to the dissipative blockade, transmission of the probe light is reduced drastically by the two-body dephasing in the transparent window. The reduction of transmission is accompanied by a strong photon-photon anti-bunching. Around the Autler-Townes doublets, the photon bunching is amplified by the two-body dephasing, while transmission is largely unaffected. Besides relevant to the ongoing Rydberg atom studies, our study moreover provides a setting to explore and understand two-body dephasing dynamics in many-body systems.

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.

Rydberg-atom-based digital communication using a continuously tunable radio-frequency carrier

Up to now, the measurement of radio-frequency (RF) electric field achieved using the electromagnetically-induced transparency (EIT) of Rydberg atoms has proved to be of high-sensitivity and shows a potential to produce a promising atomic RF receiver at resonance between two chosen Rydberg states. In this paper, we study the extension of the feasibility of digital communication via this quantum-based antenna over a continuously tunable RF-carrier at off-resonance. Our experiment shows that the digital communication at a rate of 500 kbps can be performed reliably within a tunable bandwidth of 200 MHz near a 10.22 GHz carrier. Outside of this range, the bit error rate (BER) increases, rising to, for example, 15% at an RF-detuning of ±150 MHz. In the measurement, the time-varying RF field is retrieved by detecting the optical power of the probe laser at the center frequency of RF-induced symmetric or asymmetric Autler-Townes splitting in EIT. Prior to the digital test, we studied the RF-reception quality as a function of various parameters including the RF detuning and found that a choice of linear gain response to the RF-amplitude can suppress the signal distortion. The modulating signal can be decoded at speeds up to 500 kHz in the tunable bandwidth. Our test consolidates the physical basis for reliable communication and spectral sensing over a wider broadband RF-carrier, which paves a way for the concurrent multi-channel communications founded on the same pair of Rydberg states.

The effect of oscillator and dipole-dipole interaction on multiple optomechanically induced transparency in cavity optomechanical system

We theoretically investigate the optomechanically induced transparency (OMIT) phenomenon in a N-cavity optomechanical system doped with a pair of Rydberg atoms with the presence of a strong control field and a weak probe field applied to the Nth cavity. It is found that 2N - 1 (N < 10) numbers of OMIT windows can be observed in the output field when N cavities couple with N mechanical oscillators and the mechanical oscillators coupled with different even- or odd-labelled cavities can lead to diverse effects on OMIT. Furthermore, the ATS effect appears with the increase of the effective optomechanical coupling rate. On the other hand, two additional transparent windows (extra resonances) occur, when two Rydberg atoms are coupled with the cavity field. With DDI strength increasing, the extra resonances move to the far off-resonant regime but the left one moves slowly than the right one due to the positive detuning effect of DDI. During this process, Fano resonance also emerges in the absorption profile of output field.

Electromagnetically induced transparency in a spin-orbit coupled Bose-Einstein condensate

The artificial field can be generated by properly arranging pulsed magnetic fields interacting with a Bose-Einstein condensate (BEC), which can be widely used to simulate the phenomena of traditional condensed matter physics, such as spin-orbit (SO) coupling and the neutral atom spin Hall effect. The introduction of SO coupling in a BEC will alter its optical properties. Eletromagnetically induced transparency (EIT) is a powerful tool that can change and detect the properties of an atomic medium in a nondestructive way. It is important and interesting to study EIT properties and to investigate the effects of SO coupling on EIT. In this paper, we investigate EIT in a SO-coupled BEC. Not only is the transparency existing, but the real and imaginary parts of the susceptibility have an additional red frequency shift, which is linearly proportional to the strength of the SO coupling. By using this unconventional, sensitive EIT spectrum, SO coupling can be detected and its strength can be accurately measured according to the frequency shift.

Enhancement of Goos-Hänchen shift due to a Rydberg state

This paper hints at the Goos-Hänchen shift properties of a cavity containing an ensemble of atoms using a four-level atomic system involving a Rydberg state. By means of the stationary phase theory and density matrix formalism in quantum optics, we study theoretically the Goos-Hänchen shifts in both reflected and transmitted light beams. It is realized that as a result of the interaction between Rydberg and excited states in such a four-level atom-light coupling scheme the maximum positive and negative Goos-Hänchen shifts can be obtained in reflected and transmitted light beams owning to the effect of the Rydberg electromagnetically induced transparency (EIT) or Rydberg electromagnetically induced absorption. In particular, when the switching field is absent and the Rydberg EIT is dominant in the medium, a giant Goos-Hänchen shift can be achieved for both reflected and transmitted light beams.

Photon Subtraction by Many-Body Decoherence

We experimentally and theoretically investigate the scattering of a photonic quantum field from another stored in a strongly interacting atomic Rydberg ensemble. Considering the many-body limit of this problem, we derive an exact solution to the scattering-induced spatial decoherence of multiple stored photons, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis reveals a correlated coherence-protection process in which the scattering from one excitation can shield all others from spatial decoherence. We discuss how this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability.

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.

Electromagnetically induced polarization grating

Based on electromagnetically induced transparency (EIT), we investigate an all-optical grating structure to realize polarization-dependent multiple beam splitting in the Raman-Nath limit. To optimize the grating performance, higher excited state [e.g., nS_1/2 (n ≥ 6)] of ultracold ⁸⁷Rb atoms is employed to construct a five-level Ξ-Λ system sharing one common populated ground state. A principal advantage of our proposed scheme is that the σ^± components of a linearly polarized weak probe field can be decoupled and thus be independently diffracted with high efficiency in both one and two dimensions by exploiting different quasi-standing waves as the two strong coupling fields in the Ξ and Λ configurations. Such an all-optical polarization-sensitive operation could greatly enhance the tunability and capacity of all-optical multiplexing, interconnecting, and networking in free space for both classical and quantum applications.

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.

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.

A photon counting and a squeezing measurement method by the exact absorption and dispersion spectrum of Λ-type Atoms

Recently, the master equations for the interaction of two-mode photons with a three-level Λ-type atom are exactly solved for the coherence terms. In this paper the exact absorption spectrum is applied for the presentation of a non-demolition photon counting method, for a few number of coupling photons, and its benefits are discussed. The exact scheme is also applied where the coupling photons are squeezed and the photon counting method is also developed for the measurement of the squeezing parameter of the coupling photons.

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.

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.

Cooperative nonlinear grating sensitive to light intensity and photon correlation

Utilizing dipole blockade of Rydberg excitations, we study an ensemble of stationary atoms driven into the four-level N configuration for achieving a new kind of electromagnetically induced grating in the presence of a traveling-wave and a standing-wave classical control fields. This grating shows cooperative optical nonlinearities as manifested by the sensitivity of output diffraction patterns to input light intensities (photon correlations) of a quantum probe field, promising then an essential opportunity for distinguishing weaker and stronger (bunched and anti-bunched) light fields.

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.

Nonequilibrium many-body steady states via Keldysh formalism

Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under nonequilibrium dynamics. While these states and their phase transitions have been studied extensively with mean-field theory, the validity of the mean-field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean-field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class.

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.

Correlated Exciton Transport in Rydberg-Dressed-Atom Spin Chains

We investigate the transport of excitations through a chain of atoms with nonlocal dissipation introduced through coupling to additional short-lived states. The system is described by an effective spin-1/2 model where the ratio of the exchange interaction strength to the reservoir coupling strength determines the type of transport, including coherent exciton motion, incoherent hopping, and a regime in which an emergent length scale leads to a preferred hopping distance far beyond nearest neighbors. For multiple impurities, the dissipation gives rise to strong nearest-neighbor correlations and entanglement. These results highlight the importance of nontrivial dissipation, correlations, and many-body effects in recent experiments on the dipole-mediated transport of Rydberg excitations.

Eight-wave mixing process in a Rydberg-dressing atomic ensemble

We investigate the eight-wave mixing (EWM) process involving highly excited Rydberg states with the assistance of coexisting electromagnetically induced transparency (EIT) windows in a thermal ⁸⁵Rb vapor both theoretically and experimentally. By use of a disturbance-free optical detection method, the Rydberg EWM characterized by multiple sets of spin coherence is presented via the interplay and competition between the dressing-state effects and excitation blockade caused by strong Rydberg-Rydberg interaction. Such interplay and competition can be demonstrated by the intensity evolutions of multi-wave mixing (MWM) signals via controlling the atomic density, the frequency detuning and Rabi frequencies of corresponding laser fields. The observed Rydberg EWM tailored by EIT windows can possess of much narrower linewidth <30MHz and provide a new way for the study of Rydberg effect in the atomic ensemble above room temperature.

Quantum phase gate for optical qubits with cavity quantum optomechanics

We show that a cavity optomechanical system formed by a mechanical resonator simultaneously coupled to two modes of an optical cavity can be used for the implementation of a deterministic quantum phase gate between optical qubits associated with the two intracavity modes. The scheme is realizable for sufficiently strong single-photon optomechanical coupling in the resolved sideband regime, and is robust against cavity losses.

Collective excitation of Rydberg-atom ensembles beyond the superatom model

In an ensemble of laser-driven atoms involving strongly interacting Rydberg states, the steady-state excitation probability is usually substantially suppressed. In contrast, here we identify a regime in which the Rydberg excited fraction is enhanced by the interaction. This effect is associated with the buildup of many-body coherences induced by coherent multiphoton excitations between collective states. The excitation enhancement should be observable under currently existing experimental conditions and may serve as a direct probe for the presence of coherent multiphoton dynamics involving collective quantum states.

Tuning ultracold chemical reactions via Rydberg-dressed interactions

We show that ultracold chemical reactions with an activation barrier can be tuned using Rydberg-dressed interactions. Scattering in the ultracold regime is sensitive to long-range interactions, especially when weakly bound (or quasibound) states exist near the collision threshold. We investigate how, by Rydberg dressing a reactant, one enhances its polarizability and modifies the long-range van der Waals collision complex, which can alter chemical reaction rates by shifting the position of near-threshold bound states. We carry out a full quantum mechanical scattering calculation for the benchmark system H(2)+D, and show that resonances can be moved substantially and that rate coefficients at cold and ultracold temperatures can be increased by several orders of magnitude.

Electromagnetically induced transparency in an entangled medium

We theoretically investigate light propagation and electromagnetically induced transparency in a quasi-one-dimensional gas in which atoms interact strongly via exchange interactions. We focus on the case in which the gas is initially prepared in a many-body state that contains a single excitation and conduct a detailed study of the absorptive and dispersive properties of such a medium. This scenario is achieved in interacting gases of Rydberg atoms with two relevant S states that are coupled through exchange. Of particular interest is the case in which the medium is prepared in an entangled spin-wave state. This, in conjunction with the exchange interaction, gives rise to a nonlocal susceptibility that--in comparison to conventional Rydberg electromagnetically induced transparency--qualitatively alters the absorption and propagation of weak probe light, leading to nonlocal propagation and enhanced absorption.

Two-photon dynamics in coherent Rydberg atomic ensemble

We study the interaction of two photons in a Rydberg atomic ensemble under the condition of electromagnetically induced transparency, combining a semiclassical approach for pulse propagation and a complete quantum treatment for quantum state evolution. We find that the blockade regime is not suitable for implementing photon-photon cross-phase modulation due to pulse absorption and dispersion. However, approximately ideal cross-phase modulation can be realized based on relatively weak interactions, with counterpropagating and transversely separated pulses.

Wigner crystallization of single photons in cold Rydberg ensembles

The coupling of weak light fields to Rydberg states of atoms under conditions of electromagnetically induced transparency leads to the formation of Rydberg polaritons which are quasiparticles with tunable effective mass and nonlocal interactions. Confined to one spatial dimension their low energy physics is that of a moving-frame Luttinger liquid which, due to the nonlocal character of the repulsive interaction, can form a Wigner crystal of individual photons. We calculate the Luttinger K parameter using density-matrix renormalization group simulations and find that under typical slow-light conditions kinetic energy contributions are too strong for crystal formation. However, adiabatically increasing the polariton mass by turning a light pulse into stationary spin excitations allows us to generate true crystalline order over a finite length. The dynamics of this process and asymptotic correlations are analyzed in terms of a time-dependent Luttinger theory.

Dark entangled steady states of interacting Rydberg atoms

We propose a scheme for rapid generation of high fidelity steady-state entanglement between a pair of atoms. A two-photon excitation process toward long-lived Rydberg states with finite pairwise interaction, a dark-state interference effect in the individual atoms, and spontaneous emission from their short-lived excited states lead to rapid, dissipative formation of an entangled steady state. We show that for a wide range of physical parameters, this entangled state is formed on a time scale given by the strengths of coherent Raman and Rabi fields applied to the atoms, while it is only weakly dependent on the Rydberg interaction strength.

Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps

The laser excitation of Rydberg atoms in ultracold gases is often described assuming that the atomic motion is frozen during the excitation time. We show that this frozen gas approximation can break down for atoms that are held in optical lattices or microtraps. In particular, we show that the excitation dynamics is in general strongly affected by mechanical forces among the Rydberg atoms as well as the spread of the atomic wave packet in the confining potential. This causes decoherence in the excitation dynamics-resulting in a dissipative blockade effect-that renders the Rydberg excitation inefficient even in the antiblockade regime. For a strongly off-resonant laser excitation-usually considered in the context of Rydberg dressing-these motional effects compromise the applicability of the Born-Oppenheimer approximation. In particular, our results indicate that they can also lead to decoherence in the dressing regime.

Sub-Poissonian statistics of Rydberg-interacting dark-state polaritons

We observe individual dark-state polaritons as they propagate through an ultracold atomic gas involving Rydberg states coupled via an electromagnetically induced transparency resonance. Strong long-range interactions between Rydberg excitations give rise to a blockade between polaritons, resulting in large optical nonlinearities and modified polariton number statistics. By combining optical imaging and high-fidelity detection of the Rydberg polaritons we investigate both aspects of this coupled atom-light system. We map out the full nonlinear optical response as a function of atomic density and follow the temporal evolution of polaritons through the atomic cloud. In the blockade regime, the statistical fluctuations of the polariton number drop well below the quantum noise limit. The low level of fluctuations indicates that photon correlations modified by the strong interactions have a significant backaction on the Rydberg atom statistics.

Dissipative many-body quantum optics in Rydberg media

We develop a theoretical framework for the dissipative propagation of quantized light under conditions of electromagnetically induced transparency in atomic media involving strongly interacting Rydberg states. The theory allows us to determine the peculiar spatiotemporal structure of the output of the recently demonstrated single-photon filter and the recently proposed single-photon subtractor, which, respectively, let through and absorb a single photon. In addition to being crucial for applications of these and other optical quantum devices, the theory opens the door to the study of exotic dissipative many-body dynamics of strongly interacting photons in nonlinear nonlocal media.

Three-photon electromagnetically induced transparency using Rydberg states

We demonstrate electromagnetically induced transparency in a four-level cascade system where the upper level is a Rydberg state. The observed spectral features are sub-Doppler and can be enhanced due to the compensation of Doppler shifts with AC Stark shifts. A theoretical description of the system is developed that agrees well with the experimental results, and an expression for the optimum parameters is derived.