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arXiv:0708.0657 · Physical Review A

Manipulation and detection of a trapped Yb+ hyperfine qubit

Steven Olmschenk, Kelly Cooper Younge, David L. Moehring, Dzmitry Matsukevich, Peter Maunz, Christopher R. Monroe

Published Nov 19, 2007• 463 citations
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Abstract

We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of $^{171}\mathrm{Yb}^{+}$, with a measured coherence time of $2.5\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.

DOI
10.1103/physreva.76.052314

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We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of 171Yb+^{171}\mathrm{Yb}^{+}171Yb+, with a measured coherence time of 2.5s2.5\phantom{\rule{0.3em}{0ex}}\mathrm{s}2.5s. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.
Highly efficient, nearly deterministic, and isotope selective generation of Yb+{\mathrm{Yb}}^{+}Yb+ ions by one- and two-color photoionization is demonstrated. State preparation and state selective detection of hyperfine states in 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ is investigated in order to optimize the purity of the prepared state and to time-optimize the detection process. Linear laser-cooled Yb+{\mathrm{Yb}}^{+}Yb+ ion crystals confined in a Paul trap are demonstrated. Advantageous features of different previous ion trap experiments are combined, while at the same time the number of possible error sources is reduced by using a comparatively simple experimental apparatus. This opens a new path toward quantum state manipulation of individual trapped ions, and in particular, to scalable quantum computing.
Fast and efficient detection of the qubit state in trapped ion systems is critical for implementing quantum error correction and performing fundamental tests such as a loophole-free Bell test. In this work we present a simple qubit state detection protocol for a (171)Yb+ hyperfine atomic qubit trapped in a microfabricated surface trap, enabled by high collection efficiency of the scattered photons and low background photon count rate. We demonstrate average detection times of 10.5, 28.1, and 99.8 μs, corresponding to state detection fidelities of 99%, 99.856(8)%, and 99.915(7)%, respectively.
The highly popular ytterbium-171 (171mathrmYb+^{171} \\mathrm{Yb}^+171mathrmYb+) ion is commonly employed in quantum information research as a qubit whose excellent coherence time and fast, simple state preparation has allowed cutting edge work in quantum computation and simulation. Despite these large benefits, the demonstrated measurement fidelity of this ion has lagged the state preparation and gate fidelity achieved to date.In this thesis we investigate and realize methods of increasing the measurement fidelity of 171mathrmYb+^{171} \\mathrm{Yb}^+171mathrmYb+ in a scaleable way for large quantum systems. Using methods of coherent control, we implement a pulsed state detection scheme using a mode-locked laser to perform background-free spectroscopy of the ``bright'' state of the qubit. The small hyperfine splitting of the ion necessitates the use of multiple (two) pulses to manipulate time dynamics of the ion to excite a single transition. A Mach-Zehnder interferometer is constructed to control these pulse separations both coarsely (sim\\simsim 237 ps) and on a fine sub-femtosecond scale. These pulses cause destructive/constructive interference of the electron wave packet of a single ion levitated in vacuum and are engineered to state-selectively excite the qubit. This allows measurement of the qubit whose transition frequency is much smaller than the bandwidth of the interrogation laser.During this spectroscopy, mechanical forces from the mode-locked laser frequency comb can drive the ion into large coherent states of motion. This motion has been dubbed ``phonon lasing''. We investigate the phonon lasing affect and how the ion interacts with multiple comb teeth. The large number of teeth leads to a protection mechanism from runaway energy gain by near-by blue detuned teeth, allowing ions to be trapped and cooled by the mode-locked laser, regardless of its detuning. We further explore these discrete amplitude coherent states by injecting energy into the ion's motion and exciting higher-order oscillations.We, for the first time, implement an ``electron shelving'' of the hyperfine qubit, and incoherently transfer the bright state population in the extremely long-lived ($\\approx$5 yr) 2^22F7/2_{7/2}7/2​ state of 171^{171}171Yb+^++, functionally disconnected state. This is accomplished via narrow-band optical pumping on the 2^22S1/2_{1/2}1/2​ to the 2^22D5/2_{5/2}5/2​ quadrupole which has a leaky dipole channel into the 2^22F7/2_{7/2}7/2​. Narrow-band optical pumping is again used to rescue the ion at the end of the experiment with the aid of a 760 nm E2 transition back into the cooling cycle. Measurement with this scheme is no longer limited by off-resonant effects from the main cycling transition. Limits of this novel technique, as well as further directions using the F state as a utility for quantum information are explored. Finally, we combine the pulsed background-free spectroscopy with shelving and demonstrate high-fidelity, background free detection of a single trapped 171mathrmYb+^{171}\\mathrm{Yb}^+171mathrmYb+ qubit.
Trapped ions are currently one of the most promising architectures for realising the quantum information processor. The long lived internal states are ideal for representing qubit states and, through controlled interactions with electromagnetic radiation, ions can be manipulated to execute coherent logic operations. In this thesis an experiment capable of trapping Yb+ ions, including 171Yb+, is presented. Since ion energy can limit the coherence of qubit manipulations, characterisation of an ion trap heating rate is vital. Using a trapped 174Yb+ ion a heating rate consistent with previous measurements of other ion species in similar ion traps is obtained. This result shows abnormal heating of Yb+ does not occur, further solidifying the suitability of this species for quantum information processing. Efficient creation, and cooling of trapped ions requires exact wavelengths for the ionising, cooling and repump transitions. A simple technique to measure the 1S0 ? 1P1 transition wavelengths, required for isotope selective photoionisation of neutral Yb, is developed. Using the technique new wavelengths, accurate to 60 MHz, are obtained and differ from previously published results by 660 MHz. Through a simple modification the technique can also predict Doppler shifted transition frequencies, which may be required in non-perpendicular atom-laser interactions. Using trapped ions, the 2S1=2 ? 2P1/2 Doppler cooling and 2D3/2 ? 2D[3/2]1/2 repump transitions are also measured to a greater accuracy than previously reported. Many experiments require wavelengths which can only be obtained using complex expensive laser systems. To remedy this a simple cost effective laser is developed to enable laser diodes to be operated at sub zero temperatures, extending the range of obtainable wavelengths. Additional diode modulation capabilities allow for the manipulation of atoms and ions with hyperfine structures. The laser is shown to be suitable for manipulating Yb+ ions by cooling a diode from 372 nm to 369 nm and simultaneously generating 2.1 GHz frequency sidebands. Coherent manipulation such as arbitrary qubit rotations, motional coupling and ground state cooling, are required for trapped ion quantum computing. Two photon stimulated Raman transitions are identified as a suitable technique to implement all of these requirements and an investigation into implementing this technique with 171Yb+ is conducted. The possibility of exciting a Raman transition via either a dipole or quadrupole transitions in 171Yb+ is analysed, with dipole transitions preferred because quadrupole transitions are found to be too demanding experimentally. An inexpensive setup, utilising a dipole transition, is designed and tested. Although currently limited the setup shows potential to be an inexpensive, high fidelity method of exciting a Raman transition.
Fluorescence of single, trapped 171Yb^{171}\mathrm{Yb}171Yb+{}^{+}+ ions has been experimentally studied as a function of laser polarization, power, and detuning and as a function of magnetic field strength. The suppression of efficient fluorescence by coherent population trapping and the counteracting effect of the magnetic field are found to agree with theoretical predictions. For comparison, a fluorescence study has also been made of the isotope 174Yb^{174}\mathrm{Yb}174Yb+{}^{+}+ for which coherent population trapping is absent on the main fluorescence and laser cooling transition. Finally, state-sensitive fluorescence detection of the 171Yb^{171}\mathrm{Yb}171Yb+{}^{+}+ hyperfine qubit is studied, including the role of coherent population trapping in the optimization of detection parameters. A qubit detection fidelity of greater than 9797%97 is achieved.
We trap individual 171 Yb + ions in a surface trap microfabricated on a silicon substrate, and demonstrate a complete set of high fidelity single qubit operations for the hyperfine qubit. Trapping times exceeding 20 min without laser cooling, and heating rates as low as 0.8 quanta ms −1 , indicate stable trapping conditions in these microtraps. A coherence time of more than 1 s, high fidelity qubit state detection and single qubit rotations are demonstrated. The observation of low heating rates and demonstration of high quality single qubit gates at room temperature are critical steps toward scalable quantum information processing in microfabricated surface traps.