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Frontiers of Physics

Quantum state manipulation of single-Cesium-atom qubit in a micro-optical trap

Zhi‐Hui Wang, Gang Li, Yali Tian, Tiancai Zhang

Published Aug 4, 2014• 9 citations
Publisher

Abstract

Based on single Cesium atoms trapped in a 1064 nm microscopic optical trap we have exhibited a single qubit encoded in the Cesium “clock states”. The single qubit initialization, detection and the fast state rotation with high efficiencies are demonstrated and this state manipulation is crucial for quantum information processing. The ground states Rabi flopping rate of 229.0 ± 0.6 kHz is realized by a two-photon Raman process. A clock states dephasing time of 3.0±0.7 ms is measured, while an irreversible homogeneous dephasing time of 124±17 ms is achieved by using the spin-echo technique. This well-controlled single atom provides an idea quantum qubit and quantum node for quantum information processing.

DOI
10.1007/s11467-014-0442-0

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Based on single Cesium atoms trapped in a 1064 nm microscopic optical trap we have exhibited a single qubit encoded in the Cesium “clock states”. The single qubit initialization, detection and the fast state rotation with high efficiencies are demonstrated and this state manipulation is crucial for quantum information processing. The ground states Rabi flopping rate of 229.0 ± 0.6 kHz is realized by a two-photon Raman process. A clock states dephasing time of 3.0±0.7 ms is measured, while an irreversible homogeneous dephasing time of 124±17 ms is achieved by using the spin-echo technique. This well-controlled single atom provides an idea quantum qubit and quantum node for quantum information processing.
We demonstrate the initialization, readout, and high-speed manipulation of a qubit stored in a single 87Rb^{87}\mathrm{Rb}87Rb atom trapped in a submicrometer-sized optical tweezer. Single-qubit rotations are performed on a time scale below 100ns100\phantom{\rule{0.3em}{0ex}}\mathrm{ns}100ns using two-photon Raman transitions. Using the spin-echo technique, we measure an irreversible dephasing time of 34ms34\phantom{\rule{0.3em}{0ex}}\mathrm{ms}34ms. The readout of the single atom qubit is at the quantum projection noise limit when averaging up to 1000 individual events.
Two-photon Raman process (TPRP) is an important technique in controlling the atomic internal states. It plays an important role in quantum manipulation and quantum information process. A reliable Raman laser for specific atom is the first step to demonstrate TPRP and quantum manipulation of an atom. In this paper, we theoretically analyze the two-photon Raman process regarding to Cesium “clock states” |6S1/2, F=4, mF=0 and |6S1/2, F=3, mF=0, and we obtain the dependences of the corresponding Rabi frequency on one-and two-photon detunings and one-photon Rabi frequencies in a realistic multi-level Cesium atom system. We find that to obtain an atom state flopping efficiency of 0.99 the Raman laser power fluctuation should be controlled to be smaller than 3.2%. We also report our simple experimental Raman laser system for TPRP of Cesium atom based on a fiber waveguide phase modulator. The phase modulator is driven by a 4.6 GHz microwave source and the two first-order sidebands with a frequency difference of 9.19 GHz are filtered out by a Fabry-Pérot cavity with a finesse of 48. After an amplitude-modulator-based intensity stabilization system, a total power of 73 μupW with a fluctuation of 2.2% within 90 min is obtained. By applying this Raman laser to a single Cesium atom trapped in a micrometer size far-off resonant trap (FORT), we obtain Raman spectra between Cesium “clock states” |6S1/2, F=4, mF=0 and |6S1/2, F=3, mF=0. The discrepancy between the two-photon resonance frequency and the defined clock frequency 9.192631770 GHz is due to the differential Stark shifts by FORT beam and Raman beams as well as the inaccuracy of the microwave source. By varying the Raman pulse length we also show the corresponding Rabi flopping with a rate of 153 kHz, which is consistent with the theoretical calculation. The obtained state transfer efficiency of 0.75 is much smaller than theoretical expectation 0.99, which is mainly limited by the state initialization efficiency. The Raman laser system reported in this paper is simple and reliable to realize and it provides a reliable method to manipulate the Cesium internal state. Moreover it could also be easily extended to other system for quantum manipulation of other species of atom.
Single-atom-based single-photon source has several advantages, such as narrow bandwidth, wavelength matching with the absorption line of the same atomic ensemble, and insensitivity to the environment disturbing, and it is very important not only for basic researches in quantum optic field but also for applications in quantum information processing. In this paper, we report the generation of a 10-MHz-repetition-rate triggered single-photon source at 852 nm based on a trapped single cesium atom in a far-off-resonance microscopic optical dipole trap (FORT). To generate an optical dipole trap, a far-red-detuned 1064 nm laser beam is tightly focused by using a high numerical aperture lens, a typical trap depth is 2 mK and trap waist is 2.3 m. To obtain a maximum probability of pulsed excitation, the frequency of the pulsed laser should be resonant with the atomic energy levels and the trapped single atom must be excited with a -pulse. However, the interaction between the FORT laser and the atoms causes AC Stark shifts of the atomic energy levels. Thus, in order to demonstrate the resonant pulsed excitation, it is important to calculate and measure the shift of 6S1/2|Fg=4,mF=+4-6P3/2|Fe=5,mF=+5 cyclical transition in the FORT. For a two-level system, the probability of pulsed excitation can be described by Rabi oscillations with a characteristic Rabi frequency . With an optimized time sequence, we experimentally demonstrate the Rabi oscillation between the ground state and the excited state, and the peak power of -pulse laser is about 1.25 mW. We also measure the temporal envelope of single photons after a -pulse excitation. A gated pulsed excitation and cooling technique are used to reduce the possibility that atoms are heated by -pulse laser. The typical trapping lifetime of single cesium atom is extended from~108 ups to~2536 ms. The corresponding number of excitations is improved from 108 to 360000. The second-order intensity correlations of the emitted single-photon are characterized by implementing Hanbury Brown-Twiss setup. The statistics shows a strong anti-bunching with a value of 0.09 for the second-order correlation at zero delay. In the future, we will perform a Hong-Ou-Mandel two-photon interference experiment to analyze the indistinguishability of the single photons. We will also trap single atoms in a magic-wavelength optical dipole trap where the ground and the excited states have the same shift.
This work deals with the cooling and trapping of single cesium (Cs) atoms in a large-magnetic-gradient magneto-optical trap (MOT) and the confinement of single Cs atoms in a far-off-resonance optical dipole trap (FORT). The experiment setup is based on two large-numerical-aperture lens assemblies which allow us to strongly focus a 1064-nm TEM00-mode Gaussian laser beam to a 1/e2 radius of ~ 2.3 μm to form a microscopic FORT for isolating single atom with environment and to efficiently collect the laser-induced-fluorescence photons emitted by single atoms for detecting and recognizing single atom’s internal state. We have tried both of “bottom-up” and “top-down” loading schemes to confine single atoms in the microscopic FORT. In the “bottom-up” scheme, we have successfully prepared single Cs atoms in the MOT and transferred it into FORT with a probability of almost 100%. In the “top-down” scheme, we have achieved ~ 74% of single atom loading probability in the FORT using light-assisted collisions induced by blue detuning laser and with prepared many Cs atoms in the MOT. The relaxation time in hyperfine level of ground state of trapped single Cs atom is measured to be ~5.4 s. To coherently manipulate atomic quantum bits (qubit) encoded in the clock states (mF = 0 states in Fg = 3 and 4 hyperfine levels) of single Cs atom via the two-photon simulated Raman adiabatic passage (STIRAP), we have prepared two phase-locked laser beams with a frequency difference of ~ 9.192 GHz by optically injecting an 852-nm master laser to lock the +1-order sideband of a 9-GHz current-modulated slave diode laser. The two phase-locked laser beams are used to drive STIRAP process in the Λ-type three-level system consists of Cs |6S1/2 Fg = 4, mF = 0> and |6S1/2 Fg = 3, mF = 0< long-lived clock states and Cs |6S1/2 Fe = 4, mF = +1 > excited state with the single-photon detuning of ~ -20 GHz. Rabi flopping experiments are in progress.
We demonstrate the implementation of a spin qubit with a single 40 Ca + ion in a micro ion trap. The qubit is encoded in the Zeeman ground state levels m J = +1/2 and m J = −1/2 of the S 1/2 state of the ion. We show sideband cooling close to the vibrational ground state and demonstrate the initialization and readout of the qubit levels with 99.5% efficiency. We employ a Raman transition close to the S 1/2 –P 1/2 resonance for coherent manipulation of the qubit. We observe single qubit rotations with 96% fidelity and gate times below 5 µs. Rabi oscillations on the blue motional sideband are used to extract the phonon number distribution. The dynamics of this distribution is analysed to deduce the trap-induced heating rate of 0.3(1) phonons ms −1 .