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International Journal of Quantum Information

QUANTUM PHASE GATES WITH TRAPPED ATOMS COUPLING TO A SUPERCONDUCTING TRANSMISSION LINE RESONATOR

Fuli Li

Published Feb 1, 2011• 3 citations
Publisher

Abstract

We propose a hybrid approach with atoms trapped above the surface of a microwave superconducting transmission line resonator to implement a universal two-qubit phase gate based on geometric or dynamical phase shifts. These proposals exploit the Rydberg excitation blockade mechanism that results from the effective long-range dipole–dipole interactions mediated by the stripline cavity mode. The geometric one relies on the stimulated Raman adiabatic passage techniques involving only the ground states of the trapped atoms, while the dynamical phase gate employs the pulse area techniques. These proposals may provide interesting applications in the field of on-chip quantum computations.

DOI
10.1142/s0219749911007654

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We propose a hybrid approach with atoms trapped above the surface of a microwave superconducting transmission line resonator to implement a universal two-qubit phase gate based on geometric or dynamical phase shifts. These proposals exploit the Rydberg excitation blockade mechanism that results from the effective long-range dipole–dipole interactions mediated by the stripline cavity mode. The geometric one relies on the stimulated Raman adiabatic passage techniques involving only the ground states of the trapped atoms, while the dynamical phase gate employs the pulse area techniques. These proposals may provide interesting applications in the field of on-chip quantum computations.
Rydberg blockaded gate is a fundamental ingredient for scalable quantum computation with neutral Rydberg atoms. However the fidelity of such a gate is intrinsically limited by a blockade error coming from a Rydberg level shift that forbids its extensive use. Based on a dark-state adiabatic passage, we develop a novel protocol for realizing a two-atom blockade-error-free quantum gate in a hybrid system with simultaneous van der Waals (vdWsI) and resonant dipole-dipole interactions (DDI). The basic idea relies on converting the roles of two interactions, which is, the DDI serves as one time-dependent tunable pulse and the vdWsI acts as a negligible middle level shift, as long as the adiabatic condition is preserved. We adopt an optimized super-Gaussian optical pulse with kπ(k ≫ 1) area accompanied by a smooth tuning for the DDI, composing a circular stimulated Raman adiabatic passage, which can robustly ensure a faster operation time ∼ 80ns as well as a highly-efficient gate fidelity ∼ 0.9996. This theoretical protocol offers a flexible treatment for hybrid interactions in complex Rydberg systems, enabling on-demand design of new types of effective Rydberg quantum gate devices.
Hybrid quantum systems involving cold atoms and microwave resonators can enable cavity-mediated infinite-range interactions between atomic spin systems and realize atomic quantum memories and transducers for microwave-to-optical conversion. To achieve strong coupling of atoms to on-chip microwave resonators, it was suggested to use atomic Rydberg states with strong electric-dipole transitions. Here we report on the experimental realization of coherent coupling of a Rydberg transition of ultracold atoms, trapped on an integrated superconducting atom chip, to the microwave field of an on-chip coplanar waveguide resonator. Close to the chip surface, stray electric fields lead to inhomogeneous Rydberg level shifts, which would hinder coherent interactions of atoms in a cloud with the Rydberg excitation lasers and the microwave cavity field. We, however, use optical excitation of a Rydberg state of atoms in a narrow layer with nearly constant electric field, which allows for resonant coupling of the atoms to the cavity microwave field on an appropriate Rydberg transition. We also achieve state-selective detection of the energetically close Rydberg states. We then observe and characterize cavity-driven Rabi oscillations between a pair of atomic Rydberg states. The residual damping of the oscillations is dominated by the spread of Rabi frequencies of atoms in different positions of the resonant cavity mode, as revealed by our model. Despite the technical challenges, our studies demonstrate the feasibility of coherent-state manipulation of Rydberg atoms interacting with superconducting circuits, paving the way for realization of capable hybrid quantum systems.
We present schemes for geometric phase compensation in an adiabatic passage which can be used for the implementation of quantum logic gates with atomic ensembles consisting of an arbitrary number of strongly interacting atoms. Protocols using double sequences of stimulated Raman adiabatic passage (STIRAP) or adiabatic rapid passage (ARP) pulses are analyzed. Switching the sign of the detuning between two STIRAP sequences, or inverting the phase between two ARP pulses, provides state transfer with well-defined amplitude and phase independent of atom number in the Rydberg blockade regime. Using these pulse sequences we present protocols for universal single-qubit and two-qubit operations in atomic ensembles containing an unknown number of atoms.
We propose an implementation of a universal quantum gate between pairs of spatially separated atoms in a microwave cavity at finite temperature. The gate results from reversible laser excitation of Rydberg states of atoms interacting with each other via exchange of virtual photons through a common cavity mode. Quantum interference of different transition paths between the two-atom ground and double-excited Rydberg states makes both the transition amplitude and resonance largely insensitive to the excitations in the microwave cavity quantum bus which can therefore be in any superposition or mixture of photon number states. Our scheme for attaining ultra-long-range interactions and entanglement also applies to mesoscopic atomic ensembles in the Rydberg blockade regime and is scalable to many ensembles trapped within a centimeter-sized microwave resonator.
We show that pairs of atoms optically excited to the Rydberg states can strongly interact with each other via effective long-range dipole-dipole or van der Waals interactions mediated by their nonresonant coupling to a common microwave field mode of a superconducting coplanar waveguide cavity. These cavity mediated interactions can be employed to generate single photons and to realize in a scalable configuration a universal phase gate between pairs of single photon pulses propagating or stored in atomic ensembles in the regime of electromagnetically induced transparency.