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arXiv:0902.3964 · Physical Review A

Single-photon nonlinearities using arrays of cold polar molecules

R.M.G. Rajapakse, T. Bragdon, Ana María Rey, Tommaso Calarco, Susanne F. Yelin

Published Jul 15, 2009• 26 citations
arXivHTMLPDF

Abstract

We model single-photon nonlinearities resulting from the dipole-dipole interactions of cold polar molecules. We propose utilizing ``dark state polaritons'' to effectively couple photon and molecular states; through this framework, coherent control of the nonlinearity can be expressed and potentially used in an optical quantum computation architecture. Due to the dipole-dipole interaction the photons pick up a measurable nonlinear phase even in the single-photon regime. A manifold of protected symmetric eigenstates is used as basis. Depending on the implementation, major sources of decoherence result from nonsymmetric interactions and phonon dispersion. We discuss the strength of the nonlinearity per photon and the feasibility of this system.

DOI
10.1103/physreva.80.013810

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We model single-photon nonlinearities resulting from the dipole-dipole interactions of cold polar molecules. We propose utilizing ``dark state polaritons'' to effectively couple photon and molecular states; through this framework, coherent control of the nonlinearity can be expressed and potentially used in an optical quantum computation architecture. Due to the dipole-dipole interaction the photons pick up a measurable nonlinear phase even in the single-photon regime. A manifold of protected symmetric eigenstates is used as basis. Depending on the implementation, major sources of decoherence result from nonsymmetric interactions and phonon dispersion. We discuss the strength of the nonlinearity per photon and the feasibility of this system.
Most phenomena around us can be explained by classical optics since photons interact weakly with atoms. When the interaction is strong enough where one photon affects the properties of other photons, we go to the regime of quantum photon-photon nonlinear optics. The work in this thesis explores this regime of physics. This paves the path to exploring strongly interacting many-body physics with photons which is still a largely unexplored domain. The ability to control strongly interacting photons is also of central importance in quantum science and engineering. We use the approach of Electromagnetically Induced Transparency (EIT) in atomic ensembles to create strong interactions and demonstrate coherent control between single photons. Using EIT, we coherently map single photons onto the atoms which travel as coupled excitations of light and matter called dark-state polaritons. When the medium is optically dense, the polariton propagates as a massive particle with a velocity that is much smaller than the speed of light. These polaritons interact with each other via their atomic component. In this thesis, we show robust symmetry-protected collisions between photons that imprint a large phase of π/2 with little loss and extend the nature of photon-photon interactions to the repulsive regime, which are essential for quantum communication and metrology. We use the technique of photon blockade to make a fast optical detector of Rydberg states, directly demonstrating the use of quantum nonlinear optics for quantum computation. We also study the extensions of the attractive and repulsive photons for three particles shedding light into the formation of bound states and crystals of photons and paving the way to studying many-body physics of 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.
Quantum entanglement and coherence are both essential physical resources in quantum theory. Cold polar molecules have long coherence time and strong dipole-dipole interaction and thus have been suggested as a platform for quantum information processing. In this paper, we employ the pendular states of the polar molecules trapped in static electric fields as the qubits, and put forward several theoretical schemes to generate the entanglement and coherence for two coupled dipoles by using optimal control theory. Through the designs of appropriate laser pulses, the transitions from the ground state to the Bell state and maximally coherent state can be realized with high fidelities 0.9906 and 0.9943 in the two-dipole system, respectively. Meanwhile, we show that the degrees of entanglement and coherence between the two pendular qubits are effectively enhanced with the help of optimized control fields. Furthermore, our schemes are generalized to the preparation of the Hardy state and even to the creation of arbitrary two-qubit states. Our findings can shed some light on the implementation of quantum information tasks with the molecular pendular states.
We present a theoretical scheme to study optical cavity quantum electrodynamics using dark-state polaritons. Exploiting the highly tunable lifetimes of the photons in the form of cavity dark-state polaritons, we push the strong coupling of single optical photons to an effective two-level emitter in a Rydberg-blockade atomic ensemble to an unprecedented regime. The resulting Jaynes--Cummings model with extremely strong coupling is of fundamental interest. We discuss applications in controlled quantum Rabi oscillation, nonlinear spectroscopy of the Jaynes-Cummings ladder, as well as the generation of nonclassical states, all based on light-matter interactions in the optical domain.
Microwave shielding has recently emerged as a powerful tool for engineering interactions in ultracold polar molecules, yet its potential for controlling cavity quantum electrodynamics remains largely unexplored. Here, we investigate a molecular cavity quantum electrodynamics platform in which two microwave-shielded polar molecules are coupled to a single optical cavity mode and demonstrate that shielding-induced interactions provide a unified mechanism for both photon blockade and Bell-state protection. The anisotropic interaction reshapes the few-excitation spectrum by enhancing its anharmonicity, thereby suppressing multiphoton transitions and improving the single-photon purity by more than three orders of magnitude. The enhanced blockade is accompanied by the emergence of negative longitudinal spin correlations, revealing the interaction-induced suppression of simultaneous molecular excitations. We further show that the photon statistics are highly sensitive to the relative molecular configuration, with positional variations on the scale of the relative zero-point fluctuation substantially modifying the blockade performance. Beyond few-photon nonlinear optics, the same interaction protects an initially prepared molecular Bell state by dispersively decoupling molecular excitations from the lossy cavity mode, thereby suppressing cavity-mediated dissipation and slowing the fidelity decay. Our results establish microwave-shielded interactions as a unified interaction resource for engineering few-photon nonlinearities and protecting quantum states in molecular cavity-QED systems.
We analyse recently proposed physical implementations of a quantum computer based on polar molecules. A set of general requirements for a molecular system is presented, which would provide an optimal combination of quantum gate times, coherence times, number of operations, high gate accuracy and experimental feasibility. We proceed with a detailed analysis of a scheme utilizing switchable dipole-dipole interactions between polar molecules. Switchable dipole-dipole interaction is an efficient tool for realization of two-qubit quantum gates, necessary to construct a universal set of gates. We consider three possible realizations of a phase gate using specific molecules, such as CO, NF, alkali dimers and alkaline-earth monohalides. We suggest suitable electronic states and ransitions and investigate requirements for the pulses driving them. Finally, we analyse possible sources of decoherence.