Coupling Rydberg atoms to superconducting qubits via nanomechanical resonator

II. ATOM-RESONATOR COUPLING
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As shown in Fig. 1, the proposed system includes three parts: a disk nanomechanical resonator of radius R and thickness b and an atom trapped at a distance L above the nanomechanical resonator, which is capacitively coupled to a SCQ. The resonator consists of a piezoelectric film sandwiched between two metal electrodes. It has a fundamental dilatational resonance frequency ωm /2π of a few gigahertz [17] and can be cooled to its quantum ground state with conventional cryogenic ˆ †a ˆ (¯ h = 1) with refrigeration [1]. The Hamiltonian is ωm a ˆ † (a ˆ ), and mechanical the creation (annihilation) operator a oscillation generates, through the piezoelectric effect, a charge ˆ +a ˆ † ) on the electrodes, where σ0 is the magnitude σ ˆ = σ0 (a ˆ with of the charge. The charge creates an electric field E the magnitude E outside the resonator. The atom is trapped above the center of the upper disk where the electric field is perpendicular to the disk (along the z axis), so the atom-resonator coupling via the electric field is given by ˆz,a , where d ˆ a −m = E ˆ zd ˆz,a is the z component of the atomic H dipole moment operator. When the atom is in its ground state, the interaction between the electric field and the atom can be neglected due to the negligibly small dipole moments. Therefore, the atom can be excited to the Rydberg states to
dipole moments and choosing appropriate parameters of the resonator, we can make the atom-resonator coupling large enough. Recent experiments have shown that the SCQ can be coupled to a piezoelectric nanomechanical resonator [17]. Thus, a quantized mechanical resonator can be coupled to both the SCQs and the atoms. This hybrid system can be used to obtain an effective interaction between the SCQ and the atom via adiabatically eliminating the dynamics of the resonator and then allowing reversible quantum-state transfer between two systems. The idea of hybrid quantum systems has been proposed in recent years [18,19]. However, our study can combine scalable SCQ systems [20] with quantum memory realized by the neutral atoms. In contrast to the cavity-mediated schemes [21], the system here is a mechanical analog and has significantly smaller dimensions, which may provide a truly scalable approach.
PHYSICAL REVIEW A 83, 022309 (2011)
Coupling Rydberg atoms to superconducting qubits via nanomechanical resonator
Ming Gao,1,2 Yu-xi Liu,3 and Xiang-Bin Wang1,*
The Key Laboratory of Atomic and Molecular Nanosciences, Ministry of Education, Tsinghua University, Beijing, 100084, China 2 Department of Physics, National University of Defense Technology, Changsha, 410073, China 3 Institute of Microelectronics, Tsinghua University, Beijing 100084, China (Received 19 October 2010; published 11 February 2011) We propose a hybrid system to realize long information storage and fast quantum operation via Rydberg atoms and superconducting qubits (SCQs). The internal states of a Rydberg atom are coupled to a nanomechanical resonator. The atom-resonator coupling is achieved via an electric field generated by the quantized motions of the resonator and temporarily exciting the atom to Rydberg states. The coupling can be made large enough to allow quantum manipulation and measurement of the resonator via the atom. The resonator can also be coupled to a SCQ, and therefore the tripartite system can provide a quantum interface between the SCQ and the atom via the nanomechanical resonator. DOI: 10.1103/PhysRevA.83.022309 PACS number(s): 03.67.Lx, 03.67.Mn, 42.50.Ex, 85.85.+j
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I. INTRODUCTION
ቤተ መጻሕፍቲ ባይዱ
Recently there has been great experimental progress in cooling micromechanical and nanomechanical resonators to their quantum ground states [1–3]. Coupling a quantized resonator to other quantum systems enables us to explore quantum mechanics at the mesoscopic scale. This can also be used for quantum-limited measurements and quantuminformation processing. Several hybrid systems have been studied, for example, the coupling of the nanomechanical resonator to photons via radiation pressure [4], to an atomic vapor via magnetic field [5], to a Bose-Einstein condensate via surface potentials [6], and to a superconducting qubit (SCQ) via electrical signals [1,7]. A few proposals also have been put forward to couple the nanomechanical resonators to the motions of ions [8] or molecules [9], to spins in solid-state systems [10], and to the displacements of a single atom in the cavity [11]. Experimental studies have shown that neutral atoms and SCQs are very good candidates for quantum-information processing. Neural atoms can be trapped with high precision at a distance of a few micrometers from the resonator by magnetic microtraps [12]. Atomic internal states can be easily manipulated and have long coherence time. Atomic Rydberg states are used to realize controlled interaction between the atoms [13,14]. The Rabi oscillations between the atomic ground state and the Rydberg state have been demonstrated [15]. On the other hand, the SCQ is one of the well-developed solid-state quantum devices; it can be easily controlled and has fast quantum operation time. However, its coherence time is relatively short [16]. Here we first study a method that enables a strong and switchable coupling between individual atomic internal states and a piezoelectric nanomechanical resonator. This atomresonator coupling can be switched off when the atom is in its ground state since the dipole moment of the ground state is small and the coupling can be neglected. Through temporarily exciting the atom into a Rydberg state with large transition