Adiabatic passage in the presence of noise

Abstract

We report on an experimental investigation of rapid adiabatic passage (RAP) in a trapped barium ion system. RAP is implemented on the transition from the 6S 1/2 ground state to the metastable 5D 5/2 level by applying a laser at 1.76 µm. We focus on the interplay of laser frequency noise and laser power in shaping the effectiveness of RAP, which is commonly assumed to be a robust tool for high efficiency population transfer. However, we note that reaching high state transfer fidelity requires a combination of small laser linewidth and large Rabi frequency.PACS numbers: 32.80. Xx, 32.80.Qk, 37.10.Ty Adiabatic passage has been used for coherent population transfer in many fields [1][2][3][4]. Nuclear magnetic resonance (NMR) was the first system in which adiabatic passage was implemented [1]. In an NMR system, slowly varying the magnetic field frequency or direction can transfer population between nuclear spin states. The technique has since been applied to infrared and optical transitions in atomic and molecular systems [2,3]. In such systems the frequency of a laser is swept across a transition, effecting population transfer between the ground state and an excited state. More recently, adiabatic passage has been applied in trapped singly ionized alkali earth element systems similar to ours. This has enabled high fidelity (≥ 0.99) readout of ionic qubit states [5,6]. Using adiabatic passage for state detection has several important advantages over a simple π-pulse of resonant light. First, small drifts in laser frequency do not cause a dramatic change in transfer fidelity. Similarly, adiabatic passage is mostly insensitive to frequency shifts caused by magnetic field fluctuations. Additionally, adiabatic passage efficiency is not strongly dependent on laser power, and so obviates the need for laser intensity stabilization. On the other hand, adiabatic passage is necessarily slower than a π-pulse and still requires optical coherence of a sufficient degree that Rabi oscillations can be observed. Previous experiments on RAP were done with sufficiently high Rabi frequency and low driving field noise that the role of noise processes was not investigated. There is considerable interest in the role that noise plays in adiabatic processes for applications in adiabatic quantum computing [7][8][9]. Here we present a detailed study of the dependence of adiabatic passage efficiency on laser noise and other relevant parameters.The theory behind adiabatic passage has been described in several papers and books [5,[10][11][12][13], so we will only sketch the idea in broad strokes. Consider a Hamiltonian H, which describes two states whose energies cross as a function of a parameter ∆. Now add to this Hamiltonian a term which couples the two states, yielding a new Hamiltonian H ′ . The eigenstates of H ′ will exhibit an avoided crossing as a function of ∆. Consider such a coupled system initially in an eigenstate of H with ∆ set such that the energy splitting between the states is much larger than the coupling energy. If ∆ is n...

Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors

“…As a consequence the range of possible parameters is vast. As an example we use here parameters close to a recent experiment on adiabatic passage for trapped ions in the presence of laser-frequency noise [21]. There is much interest in the role that noise plays in adiabatic processes with trapped ions for quantum-computing applications.…”

Detection of motional ground state population of a trapped ion using delayed pulses

“…Furthermore, a determination of the ground state population enables a simple measurement of the ionʼs temperature.OPEN ACCESS RECEIVED has a Gaussian shape, whereas the frequency is varied linearly in time across an atomic resonance. RAP has been used in optical qubits on carrier transitions for robust internal state preparation [27][28][29][30], and on sideband transitions, to prepare Fock [31] and Dicke [32,33] states. The STIRAP technique is typically realized in Λ-systems and relies on an adiabatic evolution from an initial to a final state without populating a short-lived intermediate state.…”

Ion–photon entanglement and Bell inequality violation with ^138Ba^+

“…Ionic qubit state detection was accomplished by the use of a stabilized 1762 nm fiber laser to drive the "shelving" transition from the 6S 1/2 (m J = − 1 2 ) ground state sublevel (defined as | ↓>) to the 5D 5/2 (m J = − 5 2 ) metastable sublevel (lifetime ≈ 30 s) using adiabatic rapid passage sweeps [28,29]. Once excited to the 5D 5/2 shelved state, the ion is removed from the cooling cycle and will appear "dark" while the cooling lasers are incident on the ion, whereas an unshelved ion will be "bright."…”