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arXiv:1509.03444 · Physical Review A

Long-range quantum gate via Rydberg states of atoms in a thermal microwave cavity

L. Sárkány, József Fortágh, David Petrosyan

Published Sep 21, 2015• 42 citations
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Abstract

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.

DOI
10.1103/physreva.92.030303

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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.
High-fidelity two-qubit gates in neutral-atom arrays rely on the Rydberg blockade, which is intrinsically short ranged and requires long range connectivity to be achieved through atom shuttling. We propose a four level architecture, where the typical ground state qubit can be leveraged for its long lifetime and the Rydberg states couple to a microwave cavity, allowing for long range cavity mediated gates. We first find the thermal dependence of two established protocols, the dispersive iSWAP native to the Tavis-Cummings model and the Controlled phase gate generated from driving the cavity. We simulate them under the presence of Rydberg decay, thermal photons, finite cavity linewidth and find fidelities which accompany closed form bounds. We then introduce the bichromatic Raman gate, which only virtually populates the Rydberg states and cancels dispersive shifts to mitigate both atomic and cavity decay, achieving a fidelity of F=0.997F = 0.997F=0.997. Finally, we consider a full optical tweezer array in a microwave cavity, and show that using a cavity mediated gate to close the periodic boundaries of the toric code shortens an error correction round by a factor of 2.3 for realistic array sizes. This was then applied to the wider family of Bivariate bicycle codes, and we find that it shortens a round of the gross code by a factor of 4.8.
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.
This thesis intends to give a concise yet meaningful overview about the progress in the physical realization of quantum information processing using hybrid systems of ultracold atoms and superconducting microwave resonators, describing our own theoretical and experimental contributions to advancing. Ultracold atoms in their ground states are well-isolated quantum systems offering long coherence times, and therefore are prime candidates for quantum memory applications. Their performance is limited by their sensitivity on external magnetic-field noises and inhomogeneous Zeeman shifts inherently present in magnetic traps. We have developed an efficient method to eliminate the magnetic-field dependence of the differential Zeeman shift between the magnetically trappable clock-states up to second order around an arbitrarily chosen offset field, hence rendering atom-based quantum memory insensitive to magnetic noises. We describe two protocols to mediate long-range interactions between Rydberg atoms using a thermally populated microwave cavity, realizing universal 2-bit quantum gates. This is of great practical interest, since in existing hybrid atom-superconducting resonator experiments the attainable temperature is not low enough to reach the vacuum state of the cavity mode. The first method relies on active mode cooling using an auxiliary reservoir of atoms. The second method makes use of a destructive quantum interference between different excitation paths, making the scheme insensitive to the actual photon state of the cavity. We also report on a new laboratory for optical lattice clocks that we have established in parallel with this work. We present a novel concept for continuously operated atomic clocks, along with the steps we have taken towards its experimental realization.
We propose a scheme for implementing quantum gates for two atoms trapped in distant cavities connected by an optical fiber. The effective long-distance coupling between the two distributed qubits is achieved without excitation and transportation of photons through the optical fiber. Since the cavity modes and fiber mode are never populated and the atoms undergo no transitions, the gate operation is insensitive to the decoherence effect when the thermal photons in the environment are negligible. The scheme opens promising perspectives for networking quantum information processors and implementing distributed and scalable quantum computation.
We consider state transfer between two qubits---effective two-level systems represented by Rydberg atoms---via a common mode of a microwave cavity at finite temperature. We find that when both qubits have the same coupling strength to the cavity field, at large enough detuning from the cavity mode frequency, quantum interference between the transition paths makes the swap of the excitation between the qubits largely insensitive to the number of thermal photons in the cavity. When, however, the coupling strengths are different, the photon-number-dependent differential Stark shift of the transition frequencies precludes efficient transfer. Nevertheless, using an auxiliary cooling system to continuously extract the cavity photons, we can still achieve a high-fidelity state transfer between the qubits.
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.