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arXiv:1607.08323 · Journal of Physics B Atomic Molecular and Optical Physics

Cavity polaritons with Rydberg blockade and long-range interactions

Marina Litinskaya, Edoardo Tignone, Guido Pupillo

Published Aug 1, 2016• 10 citations
arXivHTMLPDF

Abstract

Abstract We study interactions between polaritons, arising when photons strongly couple to collective excitations in an array of two-level atoms trapped in an optical lattice inside a cavity. We consider two types of interactions between atoms: dipolar forces and atomic saturability, which range from hard-core repulsion to Rydberg blockade. We show that, in spite of the underlying repulsion in the subsystem of atomic excitations, saturability induces a broadband bunching of photons for two-polariton scattering states. We interpret this bunching as a result of interference, and trace it back to the mismatch of the quantization volumes for atomic excitations and photons. We also examine bound bipolaritonic states: these include states created by dipolar forces, as well as a gap bipolariton, which forms solely due to saturability effects in the atomic transition. Both types of bound states exhibit strong bunching in the photonic component. We discuss the dependence of bunching on experimentally relevant parameters.

DOI
10.1088/0953-4075/49/16/164006

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Abstract We study interactions between polaritons, arising when photons strongly couple to collective excitations in an array of two-level atoms trapped in an optical lattice inside a cavity. We consider two types of interactions between atoms: dipolar forces and atomic saturability, which range from hard-core repulsion to Rydberg blockade. We show that, in spite of the underlying repulsion in the subsystem of atomic excitations, saturability induces a broadband bunching of photons for two-polariton scattering states. We interpret this bunching as a result of interference, and trace it back to the mismatch of the quantization volumes for atomic excitations and photons. We also examine bound bipolaritonic states: these include states created by dipolar forces, as well as a gap bipolariton, which forms solely due to saturability effects in the atomic transition. Both types of bound states exhibit strong bunching in the photonic component. We discuss the dependence of bunching on experimentally relevant parameters.
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.
Controllably producing optical photons and making them interact are two key requirements for the development of long-distance quantum communications, and more generally for photonic quantum information processing. This thesis presents experimental studies on possible solutions to these two problems, using the conversion of the photons into collective excitations (polaritons) in a cold atomic cloud, inside the mode of a low-finesse optical cavity (~100). Firstly, ground-state polaritons are used to store a single excitation in the cloud memory. This polariton is then efficiently converted into a single photon, whose field is characterized via homodyne tomography. The single photon state’s Wigner function is reconstructed from the experimental data and exhibits negative values, demonstrating that the photon’s degrees of freedom (spatio-temporal mode and quantum state) are well controlled. Secondly, photons can be coupled to polaritons involving Rydberg states. The strong dipolar interactions between these give rise to very strong optical dispersive nonlinearities, that are characterized in a classical excitation regime. These nonlinearities can be amplified until a single photon is enough to modify the entire system’s response, allowing in principle for the generation of effective photon-photon interactions.
Abstract We investigate the coherent manipulation of interacting Rydberg atoms placed inside a high-finesse optical cavity for the deterministic preparation of strongly coupled light-matter systems. We consider a four-level diamond scheme with one common Rydberg level for N interacting atoms. One side of the diamond is used to excite the atoms into a collective ‘superatom’ Rydberg state using either π -pulses or stimulated Raman adiabatic passage (STIRAP) pulses. The upper transition on the other side of the diamond is used to transfer the collective state to one that is coupled to a field mode of an optical cavity. Due to the strong interaction between the atoms in the Rydberg level, the Rydberg blockade mechanism plays a key role in the deterministic quantum state synthesis of the atoms in the cavity. We use numerical simulation to show that non-classical states of light can be generated and that the state that is coupled to the cavity field is a collective one. We also investigate how different decay mechanisms affect this interacting many-body system. We also analyze our system in the case of two Rydberg excitations within the blockade volume. The simulations are carried out with parameters corresponding to realizable high-finesse optical cavities and alkali atoms like rubidium.
We investigate the interaction of weak light fields with two-dimensional lattices of atoms with high lying atomic Rydberg states. This system features different interactions that act on disparate length scales, from zero-range defect scattering of atomic excitations and finite-range dipole exchange processes to long-range Rydberg-state interactions, which span the entire array and can block multiple Rydberg excitations. Analyzing their interplay, we identify conditions that yield a nonlinear quantum mirror which coherently splits incident fields into correlated photon-pairs in a single transverse mode, while transmitting single photons unaffected. In particular, we find strong anti-bunching of the transmitted light with equal-time pair correlations that decrease exponentially with an increasing range of the Rydberg blockade. Such strong photon-photon interactions in the absence of photon losses open up promising avenues for the generation and manipulation of quantum light, and the exploration of many-body phenomena with interacting photons.
We propose a new type of spatially periodic structure, i.e. polaritonic crystal (PolC), to observe a "slow"/"stopped" light phenomenon due to coupled atom-field states (polaritons) in a lattice. Under the tightbinding approximation, such a system realizes an array of weakly coupled trapped two-component atomic ensembles interacting with optical field in a tunnel-coupled one dimensional cavity array. We have shown that the phase transition to the superfluid Bardeen-Cooper-Schrieffer state, a so-called (BCS)-type state of low branch polaritons, occurs under the strong coupling condition. Such a transition results in the appearance of a macroscopic polarization of the atomic medium at non-zero frequency. The principal result is that the group velocity of polaritons depends essentially on the order parameter of the system, i.e. on the average photon number in the cavity array.
We discuss electromagnetically induced transparency in a cold ensemble of atoms optically excited to the Rydberg states. Strong dipole-dipole or van der Waals interactions between the atomic Rydberg states translate into large nonlocal nonlinearities for a propagating probe field. In the case of weak quantum fields, this can be used to attain a conditional phase shift of π between pairs of single photons realizing a deterministic photonic phase gate. For stronger fields, long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our calculations reproduce and interpret the results of recent experiments.