Resonant enhancement of three-body loss between strongly interacting photons
Marcin Kalinowski, Yidan Wang, Przemysław Bienias, Michael J. Gullans, Dalia Ornelas-Huerta, Alexander N. Craddock, S. L. Rolston, J. V. Porto, Hans Peter Büchler, Alexey Vyacheslavovich Gorshkov
Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong as or even stronger than two-body interactions.The three-body interactions can be either dispersive or dissipative, with both types possibly giving rise to exotic, strongly interacting, and topological phases of matter.Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored.Using a renormalization group technique to solve the quantum three-body problem, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons.We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiments.
Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong as or even stronger than two-body interactions.The three-body interactions can be either dispersive or dissipative, with both types possibly giving rise to exotic, strongly interacting, and topological phases of matter.Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored.Using a renormalization group technique to solve the quantum three-body problem, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons.We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiments.
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.
Photons are elementary particles of light, and their interactions in vacuum are extremely weak. The seclusion of photons makes them perfect carriers of classical and quantum information, but also poses difficulties for employing them in quantum information technologies. Recent years have seen tremendous experimental progress in the development of synthetic quantum systems where strong and controllable coupling between single photons is achieved. In a variety of solid-state and optical platforms, propagating photons are coupled with local emitters such as atoms, quantum dots, NV centers, or superconducting qubits. Despite the different nature of the platforms, many of these systems can be described using the same theoretical framework called waveguide quantum electrodynamics (WQED). Dissipation is an inevitable ingredient of many synthetic quantum systems and is a source of error in quantum information applications. Despite its important role in experimental systems, the implications of dissipation in scattering theory havenot been fully explored. Chapter 2 discusses our discovery of the dissipation-induced bound states in WQED systems. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission. We also formulate a dissipative version of Levinson's theorem by looking at the relation between the number of bound states and the winding number of the transmission phases. In Chapter 3, we study three-body loss in Rydberg polaritons. Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored. Using a renormalization group technique to solve the quantum three-body problem, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons. We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiments. The high level of control of the synthetic quantum systems behind WQED offers many inspirations for theoretical studies. In Chapter 4 of this dissertation, we explore a new direction of scattering theory motivated by the controllability of dispersion relations in synthetic quantum systems. We study single-particle scattering in one dimension when the dispersion relation is E(k)=k^m, where m>= 2 is an integer. For a large class of interactions, we discover that the S-matrix evaluated at an energy E->0 converges to a universal limit that is only dependent on m. We also give a generalization of Levinson's theorem for these more general dispersion relations in WQED systems.
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.
Designing materials with specific properties has been a long-time goal of the physics community. Optical photons have recently emerged as a promising candidate for such metamaterials due to their fast dynamics and available manipulation toolkit. In conjunction with carefully engineered optical resonators, it is possible to precisely control the properties of individual photons through the resonator Hamiltonian. The only missing ingredient to photonic materials is strong photon-photon interactions. This thesis describes the characterization of cavity Rydberg polaritons and the emergence of strong interactions in such a system. Electromagnetically induced transparency (EIT) is used to create quasiparticles that inherit the properties of both photons and Rydberg atoms: fast dynamics and trapping from the photons and long-range dipole-dipole interactions from the Rydberg atoms. The emergent polaritonic properties are characterized and controlled through the dark-state rotation angle and agree very well with theoretical predictions. We then expand upon this understanding of polaritons by putting them inside a zerodimensional quantum dot. Confining the polaritons in such an object allows for strong interparticle interactions to manifest. We observe these interactions through the temporal auto-correlation intensity function g2(t) and verify the dimensionality of the quantum dot itself by measure the polariton Rabi oscillations. With the experimental demonstration of strong photonic interactions, a complete understanding of Rydberg atoms and polaritons is needed to allow for better control of the system. To this effect, the properties of Rydberg atoms are analytically and numerically understood and the full formalism needed to describe resonator Rydberg polaritons is developed, along with their interactions and various sources of decoherence. Furthermore, a renormalized effective field theory for single mode cavities is developed and tested against full numerical models, paving the way for the simulation of the physical phenomena of manybody states in multi-mode cavities. Strongly interacting cavity polaritons can be utilized in quantum gate and repeater protocols for quantum information processing. Furthermore, combining the experimental and theoretical work here with non-planar resonators presents a clear path to non-trivial topological synthetic materials and strongly correlated quantum states.
Abstract Photonic materials are an emerging platform to explore quantum matter (Carusotto and Ciuti 2013 Rev. Mod. Phys. 85 299; Sommer et al 2015 arXiv: 1506.00341 ) and quantum dynamics (Peyronel et al 2012 Nature 488 57). The development of Rydberg electromagnetically induced transparency (Weatherill et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 201002; Petrosyan et al 2011 Phys. Rev. Lett. 107 213601) provided a clear route to strong interactions between individual optical photons. In conjunction with carefully designed optical resonators, it is now possible to achieve extraordinary control of the properties of individual photons, introducing tunable gauge fields (Schine et al 2016 Nature 534 671) whilst imbuing the photons with mass and embedding them on curved spatial manifolds (Sommer et al 2016 New J. Phys. 18 035008). Building on work formalizing Rydberg mediated interactions between propagating photons (Gorshkov et al 2011 Phys. Rev. Lett. 107 133602; Gullans et al 2016 Phys. Rev. Lett. 117 113601), we develop a theory of interacting Rydberg polaritons in multimode optical resonators, where the strong interactions are married with tunable single particle properties to build and probe exotic matter. In the presence of strong coupling between the resonator field and a Rydberg-dressed atomic ensemble, a quasiparticle called the ‘cavity Rydberg polariton’ emerges. We investigate its properties, finding that it inherits both the fast dynamics of its photonic constituents and the strong interactions of its atomic constituents. We develop tools to properly renormalize the interactions when polaritons approach each other, and investigate the impact of atomic motion on the coherence of multi-mode polaritons, showing that most channels for atom-polariton cross-thermalization are strongly suppressed. Finally, we propose to harness the repeated diffraction and refocusing of the optical resonator to realize interactions which are local in momentum-space. This work points the way to efficient modeling of polaritonic quantum materials in properly renormalized strongly interacting effective theories, thereby enabling experimental studies of photonic fractional quantum Hall fluids and crystals (Sommer et al 2015 arXiv: 1506.00341 ; Umucalılar et al 2014 Phys. Rev. A 89 023803; Grusdt and Fleischhauer 2013 Phys. Rev. A 87 043628), plus photonic quantum information processors and repeaters (Jaksch et al 2000 Phys. Rev. Lett. 85 2208; Saffman et al 2010 Rev. Mod. Phys. 82 2313; Han et al 2010 Phys. Rev. A 81 , 052311).
Interacting Rydberg excitations in cold atomic ensembles can exhibit large quantum nonlinearities that enable engineering of strong interactions between individual photons. Consequently, Rydberg ensembles are a promising platform for quantum information applications and the study of more fundamental physics of few- and many-body phenomena with interacting photons. This thesis presents a series of experiments that study and exploit different regimes of Rydberg-mediated interactions. We report the realization of an efficient on-demand single-photon source. The strong long-range Rydberg interactions allow the excitation of only a single collective Rydberg state within the entire atomic medium. The collective excitation can be subsequently retrieved as a single-photon. We use this scheme to generate highly pure and highly indistinguishable photons, which are suitable for scalable quantum information applications. These photons can be compatible with other atomic systems due to their narrow bandwidth, which makes building practical hybrid quantum systems feasible. Here, we demonstrate high visibility two-photon quantum interference between our Rydberg-produced photons, and photons emitted by a remote single-trapped ion. We also study Rydberg atoms under electromagnetically induced transparency conditions, where coherent superpostions of photons and Rydberg excitations propagate through the atomic medium as lossless dark-state polaritons. In the experiment, we use the external control fields to tune the interactions to a many-body regime where we can observe resonant scattering of dark-state polaritons to lossy channels. We show that the enhanced scattering process arises as a pure three-body effect.