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

Abstract

Efficient preparation and detection of the motional state of trapped ions is important in many experiments ranging from quantum computation to precision spectroscopy. We investigate the stimulated Raman adiabatic passage (STIRAP) technique for the manipulation of motional states in a trapped ion system. The presented technique uses a Raman coupling between two hyperfine ground states in 25 Mg + , implemented with delayed pulses, which removes a single phonon independent of the initial motional state. We show that for a thermal probability distribution of motional states the STIRAP population transfer is more efficient than a stimulated Raman Rabi pulse on a motional sideband. In contrast to previous implementations, a large detuning of more than 200 times the natural linewidth of the transition is used. This approach renders STIRAP suitable for atoms in which resonant laser fields would populate nearby fluorescing excited states and thus impede the STIRAP process. We use the technique to measure the wavefunction overlap of excited motional states with the motional ground state. This is an important application for force sensing applications using trapped ions, such as photon recoil spectroscopy, in which the signal is proportional to the depletion of motional ground state population. 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. It is usually implemented using Gaussian-shaped intensity profiles of two laser pulses with a fixed frequency difference that are delayed with respect to each other in time. It has been demonstrated for population transfer [34] and the generation of Dicke states [35], and suggested for efficient qubit detection of single ions [36] and Doppler-free efficient state transfer in multi-ion crystals [37].Here we demonstrate STIRAP between hyperfine qubit states in 25 Mg + involving a change in the motional state. The coupling strength of such sideband transitions is strongly dependent on the initial motional state of the ion [38]. We used the insensitivity of STIRAP to the coupling strength to perform a complete population transfer of motionally excited states to determine the motional ground state population. For thermal states the ground state population is a direct measure for the temperature [39]. Using this approach, good agreement with the expected Doppler cooling temperature is found.We implement STIRAP using a large detuning, which is in contrast to the near resonant STIRAP transfer typically discussed in the literature [25,40]. In this si...

Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions

“…At the beginning of the detection sequence the motional population {p n } is distributed over several motional Fock states n. (I). A blue sideband rapid adiabatic passage pulse (RAP) transfers the internal state to |↓ , while simultaneously taking out a quantum of motion, therefore keeping the ground state population untouched [24]. Averaging the number of |↓ and |↑ detection events after this mapping step provides the n = 0 population.…”

“…It is measured by mapping the overlap between initial and displaced state onto the atomic qubit (|↑ , |↓ , encoded in two hyperfine states of the 2 S 1/2 electronic ground state of 25 Mg + ), where state-readout is performed using state dependent fluorescence [23]. The mapping process is implemented by a sequence of sideband rapid adiabatic passage (RAP) [24] and microwave pulses and is described in more detail in the Methods section. Fig.…”

Corrigendum: Detection of motional ground state population using delayed pulses (2016New J. Phys.18 013037)

“…Δ 1 = Δ 2 ≡ Δ. In the following we will assume temporally Gaussian shapes of the Rabi frequencies and define the pulses according to the notation in the main paper [1]:…”

Photon-recoil spectroscopy: Systematic shifts and nonclassical enhancements

“…Both effects will contribute to the overlap integral in Eq. (19) generating an asymmetry in the measured resonance profile. For small g, this effect can be evaluated by a series expansion of the propagator for the Fokker-Planck equation (see Appendix B for details).…”