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Old Dog, New Trick: High Fidelity, Background-free State Detection of an Ytterbium Ion Qubit

Anthony Ransford

Published Jan 1, 2020• 1 citation
OpenAlex

Abstract

The highly popular ytterbium-171 ($^{171} \\mathrm{Yb}^+$) 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 $^{171} \\mathrm{Yb}^+$ 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 ($\\sim$ 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) $^2$F$_{7/2}$ state of $^{171}$Yb$^+$, functionally disconnected state. This is accomplished via narrow-band optical pumping on the $^2$S$_{1/2}$ to the $^2$D$_{5/2}$ quadrupole which has a leaky dipole channel into the $^2$F$_{7/2}$. 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 $^{171}\\mathrm{Yb}^+$ qubit.

Related papers

Background free high fidelity state preparation and measurement (SPAM) in a 171Yb+ qubit (Conference Presentation)

Conrad Roman, Anthony Ransford, Michael Ip +1 more

We present two novel approaches to state detection of qubits defined with trapped ions. The first uses simple pulse sequences from a mode-locked laser to induce state-dependent excitations in less than 1 ns. The resulting atomic fluorescence occurs in the dark, allowing the placement of non-imaging detectors right next to the atom to improve the qubit state detection efficiency and speed.The second employs the long lived F state in Yb+ which has been used in quantum information science almost exclusively for clocks and optical-frequency qubits. We describe how this resource can be used in conjunction with the ground state S1/2 manifold to aid in the scaling of trapped ion quantum information science. Narrow-band optical pumping into the 2F7/2 from one of the conventional 2S1/2 qubit states is projected to achieve a higher state preparation and measurement (SPAM) fidelity than any other demonstrated technique.

•Apr 24, 2020•1 citation

Development and implementation of an Yb+ ion trap experiment towards coherent manipulation and entanglement

James J. McLoughlin

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.

•Apr 20, 2012•1 citation

Coherent control for qubit state readout

Conrad Roman, Anthony Ransford, Michael Ip +1 more

Abstract Short pulses from mode-locked lasers can produce background-free atomic fluorescence by allowing temporal separation of the prompt incidental scatter from the subsequent atomic emission. We use this to improve our quantum state detection of optical-frequency and electron-shelved trapped ion qubits by more than two orders of magnitude. For direct detection of qubits defined on atomic hyperfine structure, however, the large bandwidth of short pulses is greater than the hyperfine splitting, and repeated excitation is not qubit state selective. Here, we show that the state resolution needed for projective quantum measurement of hyperfine qubits can be recovered by applying techniques from coherent control to the orbiting valence electron of the queried ion. We demonstrate electron wavepacket interference to allow readout of the original qubit state using broadband pulses, even in the presence of large amounts of background laser scatter.

arXiv:1911.10138•New Journal of Physics•Jun 4, 2020•15 citations

Manipulation and detection of a trapped Yb+ hyperfine qubit

Steven Olmschenk, Kelly Cooper Younge, David L. Moehring +3 more

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.

arXiv:0708.0657•Physical Review A•Nov 19, 2007•463 citations

High-fidelity operation of a radioactive trapped-ion qubit, $^{133}$Ba$^+$

Justin Christensen

$^{133}$Ba$^+$ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus, visible wavelength electronic transitions, and long D-state lifetimes ($\\tau\\sim $1~min). Using a microgram source of radioactive material, we trap and laser-cool the synthetic \\textit{A} = 133 radioisotope of barium II ($\\tau_{1/2} \\approx 10.5$~yr) in a radio-frequency ion trap. To demonstrate high fidelity qubit operations, a number of unknown state energies were needed. We measure the isotope shift and hyperfine structure of the 6$^2$P$_{1/2}\\leftrightarrow 5^2$D$_{3/2}$ electronic transition needed for laser cooling, state preparation, and state detection of the clock-state hyperfine and optical qubits. For high-fidelity operations with electron shelving, we report measurements of the 6$^2$P$_{3/2}$ and $5^2$D$_{5/2}$ hyperfine splittings, as well as the~6$^2$P$_{3/2}~\\leftrightarrow~6^2$S$_{1/2}$ and ~6$^2$P$_{3/2}~\\leftrightarrow~5^2$D$_{5/2}$ transition frequencies. Using these transitions, we demonstrate high-fidelity \\ba \\ hyperfine qubit manipulation with electron shelving detection to benchmark qubit state preparation and measurement (SPAM). Using single-shot, threshold discrimination, we measure an average SPAM fidelity of $\\mathcal{F} = 0.99971(3)$, a factor of $\\approx$ 2 improvement over the best reported performance of any qubit.Finally, we report the 6$^2$P$_{1/2}\\leftrightarrow 5^2$D$_{3/2}$ electronic transition isotope shift for the rare \\textit{A} = 130 and 132 barium nuclides, completing the spectroscopic characterization necessary for laser cooling all long-lived barium II isotopes.

•Jan 1, 2020•3 citations

Quantum computing with naturally trapped sub-nanometre-spaced ions

Lars Rippe

The main aim of this work, was to lay the foundations for the experimental realisation of a quantum mechanical controlled NOT gate in rare-earth-metal-ion-doped crystals. Small amounts of rare-earth elements, added during the growth of some inorganic crystals, will become substituted into the crystal lattice as trivalent ions. The trivalent rare-earth-metal ions between cerium, with atomic number 58, and ytterbium, with atomic number 70, have a partly filled 4f shell, which does not extend spatially outside the full 5s and 5p shells. The 4f vacancies make electronic inner shell transitions possible between spectroscopic 4f terms. Some of these optical transitions have coherence times of the order of milliseconds, when the crystals are cooled down to ~ 4 K. There are several reasons for these extraordinary coherence times, which are approximately 8 orders of magnitude greater than those typical for electronic transitions in solids. The most important one is the cage-like shield which the outer 5s and 5p shells provide for the 4f electrons. Furthermore, since these ions are naturally trapped inside the crystal lattice there is no Doppler broadening of the line-width. The coherence properties of these optical transitions is one of the features that makes these materials attractive for use as a solid-state platform for quantum computing, using these ions as qubits. Another appealing characteristic is the fact that different ions have different optical resonance frequencies, which means that ions belonging to different qubits, which only have nm separation, can still be addressed separately by using different laser frequencies. Since the inter-ion spacing is so small, it is possible to make two ions interact strongly, although they are well shielded, through a permanent dipole-dipole interaction. This interaction can be turned on and off by switching between two different ways of encoding the qubit, a most useful feature. When the qubit is represented as a superposition between two ground state hyperfine levels, the interaction is turned off. The interaction is turned on selectively by transferring this superposition to the optical transition with a pi-pulse, for the specific ions that are to interact. This thesis describes how peaks of ions, absorbing on a single transition, residing in spectral pits with no other ions, have been isolated. It is shown how these ions can be coherently transferred between hyperfine levels via the optically excited state, how the interaction between such peaks of ions representing qubits can be turned on and off, and how subgroups of ions with strong interaction can be distilled out. All the work described here has been performed using the ensemble approach. The ensemble approach will, however, be difficult to scale up to large numbers of qubits. A method employing a single ion in each qubit, using a specialised ion for readout, has therefore also been proposed. The rare-earth-metal-ion-based quantum computing experiments require a laser with coherence properties which at least match those of the material. To this end a frequency stabilisation system was developed for a dye laser. This system uses a transient spectral hole in a rare-earth-metal-ion-doped crystal, of the same kind that is used in the experiments, as frequency reference, and is to the authors knowledge the first demonstration of locking a dye laser to a spectral hole. This system provides a line-width of 1 kHz on a 10 microseconds timescale and a frequency drift below 1 kHz/s.

•Jan 1, 2006•7 citations
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 ($\\sim$ 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\\approxapprox5 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.
We present two novel approaches to state detection of qubits defined with trapped ions. The first uses simple pulse sequences from a mode-locked laser to induce state-dependent excitations in less than 1 ns. The resulting atomic fluorescence occurs in the dark, allowing the placement of non-imaging detectors right next to the atom to improve the qubit state detection efficiency and speed.The second employs the long lived F state in Yb+ which has been used in quantum information science almost exclusively for clocks and optical-frequency qubits. We describe how this resource can be used in conjunction with the ground state S1/2 manifold to aid in the scaling of trapped ion quantum information science. Narrow-band optical pumping into the 2F7/2 from one of the conventional 2S1/2 qubit states is projected to achieve a higher state preparation and measurement (SPAM) fidelity than any other demonstrated technique.
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.
Abstract Short pulses from mode-locked lasers can produce background-free atomic fluorescence by allowing temporal separation of the prompt incidental scatter from the subsequent atomic emission. We use this to improve our quantum state detection of optical-frequency and electron-shelved trapped ion qubits by more than two orders of magnitude. For direct detection of qubits defined on atomic hyperfine structure, however, the large bandwidth of short pulses is greater than the hyperfine splitting, and repeated excitation is not qubit state selective. Here, we show that the state resolution needed for projective quantum measurement of hyperfine qubits can be recovered by applying techniques from coherent control to the orbiting valence electron of the queried ion. We demonstrate electron wavepacket interference to allow readout of the original qubit state using broadband pulses, even in the presence of large amounts of background laser scatter.
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.
High-fidelity operation of a radioactive trapped-ion qubit, 133^{133}133Ba+^++
133^{133}133Ba+^++ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus, visible wavelength electronic transitions, and long D-state lifetimes ($\\tau\\sim 1 min).Usingamicrogramsourceofradioactivematerial,wetrapandlaser−coolthesynthetictextitA=133radioisotopeofbariumII(1~min). Using a microgram source of radioactive material, we trap and laser-cool the synthetic \\textit{A} = 133 radioisotope of barium II (1 min).Usingamicrogramsourceofradioactivematerial,wetrapandlaser−coolthesynthetictextitA=133radioisotopeofbariumII(\\tau_{1/2} \\approx 10.5 yr)inaradio−frequencyiontrap.Todemonstratehighfidelityqubitoperations,anumberofunknownstateenergieswereneeded.Wemeasuretheisotopeshiftandhyperfinestructureofthe6~yr) in a radio-frequency ion trap. To demonstrate high fidelity qubit operations, a number of unknown state energies were needed. We measure the isotope shift and hyperfine structure of the 6 yr)inaradio−frequencyiontrap.Todemonstratehighfidelityqubitoperations,anumberofunknownstateenergieswereneeded.Wemeasuretheisotopeshiftandhyperfinestructureofthe6^2PPP_{1/2}\\leftrightarrow 5^2DDD_{3/2}$ electronic transition needed for laser cooling, state preparation, and state detection of the clock-state hyperfine and optical qubits. For high-fidelity operations with electron shelving, we report measurements of the 62^22P3/2_{3/2}3/2​ and 525^252D5/2_{5/2}5/2​ hyperfine splittings, as well as the~62^22P3/2 leftrightarrow 62_{3/2}~\\leftrightarrow~6^23/2​ leftrightarrow 62S1/2_{1/2}1/2​ and ~62^22P3/2 leftrightarrow 52_{3/2}~\\leftrightarrow~5^23/2​ leftrightarrow 52D5/2_{5/2}5/2​ transition frequencies. Using these transitions, we demonstrate high-fidelity \\ba \\ hyperfine qubit manipulation with electron shelving detection to benchmark qubit state preparation and measurement (SPAM). Using single-shot, threshold discrimination, we measure an average SPAM fidelity of mathcalF=0.99971(3)\\mathcal{F} = 0.99971(3)mathcalF=0.99971(3), a factor of approx\\approxapprox 2 improvement over the best reported performance of any qubit.Finally, we report the 62^22P1/2leftrightarrow52_{1/2}\\leftrightarrow 5^21/2​leftrightarrow52D3/2_{3/2}3/2​ electronic transition isotope shift for the rare \\textit{A} = 130 and 132 barium nuclides, completing the spectroscopic characterization necessary for laser cooling all long-lived barium II isotopes.
The main aim of this work, was to lay the foundations for the experimental realisation of a quantum mechanical controlled NOT gate in rare-earth-metal-ion-doped crystals. Small amounts of rare-earth elements, added during the growth of some inorganic crystals, will become substituted into the crystal lattice as trivalent ions. The trivalent rare-earth-metal ions between cerium, with atomic number 58, and ytterbium, with atomic number 70, have a partly filled 4f shell, which does not extend spatially outside the full 5s and 5p shells. The 4f vacancies make electronic inner shell transitions possible between spectroscopic 4f terms. Some of these optical transitions have coherence times of the order of milliseconds, when the crystals are cooled down to ~ 4 K. There are several reasons for these extraordinary coherence times, which are approximately 8 orders of magnitude greater than those typical for electronic transitions in solids. The most important one is the cage-like shield which the outer 5s and 5p shells provide for the 4f electrons. Furthermore, since these ions are naturally trapped inside the crystal lattice there is no Doppler broadening of the line-width. The coherence properties of these optical transitions is one of the features that makes these materials attractive for use as a solid-state platform for quantum computing, using these ions as qubits. Another appealing characteristic is the fact that different ions have different optical resonance frequencies, which means that ions belonging to different qubits, which only have nm separation, can still be addressed separately by using different laser frequencies. Since the inter-ion spacing is so small, it is possible to make two ions interact strongly, although they are well shielded, through a permanent dipole-dipole interaction. This interaction can be turned on and off by switching between two different ways of encoding the qubit, a most useful feature. When the qubit is represented as a superposition between two ground state hyperfine levels, the interaction is turned off. The interaction is turned on selectively by transferring this superposition to the optical transition with a pi-pulse, for the specific ions that are to interact. This thesis describes how peaks of ions, absorbing on a single transition, residing in spectral pits with no other ions, have been isolated. It is shown how these ions can be coherently transferred between hyperfine levels via the optically excited state, how the interaction between such peaks of ions representing qubits can be turned on and off, and how subgroups of ions with strong interaction can be distilled out. All the work described here has been performed using the ensemble approach. The ensemble approach will, however, be difficult to scale up to large numbers of qubits. A method employing a single ion in each qubit, using a specialised ion for readout, has therefore also been proposed. The rare-earth-metal-ion-based quantum computing experiments require a laser with coherence properties which at least match those of the material. To this end a frequency stabilisation system was developed for a dye laser. This system uses a transient spectral hole in a rare-earth-metal-ion-doped crystal, of the same kind that is used in the experiments, as frequency reference, and is to the authors knowledge the first demonstration of locking a dye laser to a spectral hole. This system provides a line-width of 1 kHz on a 10 microseconds timescale and a frequency drift below 1 kHz/s.