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

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

Phonon lasing from optical frequency comb illumination of a trapped ion

An atomic transition can be addressed by a single tooth of an optical frequency comb if the excited state lifetime ($\tau$) is significantly longer than the pulse repetition period ($T_\mathrm{r}$). In the crossover regime between fully-resolved and unresolved comb teeth ($\tau \lessapprox T_\mathrm{r}$), we observe Doppler cooling of a pre-cooled trapped atomic ion by a single tooth of a frequency-doubled optical frequency comb. We find that for initially hot ions, a multi-tooth effect gives rise to lasing of the ion's harmonic motion in the trap, verified by acoustic injection locking. The gain saturation of this phonon laser action leads to a comb of steady-state oscillation amplitudes, allowing hot ions to be loaded directly into the trap and laser cooled to crystallization despite the presence of hundreds of blue-detuned teeth.Comment: 5 pages, 4 figure

Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer

Calculating the equilibrium properties of condensed matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude $\langle \psi| e^{-i \hat H t}|\psi \rangle$ from initial states $|\psi\rangle$ and a time evolution under the Hamiltonian $\hat H$ up to short times $t$. In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a $16$-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm.Comment: 18 pages, 12 figure

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

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

Phonon Lasing from Optical Frequency Comb Illumination of Trapped Ions.

We demonstrate the use of a frequency-doubled optical frequency comb to load, cool, and crystallize trapped atomic ions as an alternative to ultraviolet (UV) or even deep UV continuous-wave lasers. We find that the Doppler shift from the atom's oscillation in the trap, driven by the blue-detuned comb teeth, introduces additional cooling and amplification which gives rise to steady-state phonon lasing of the ion's harmonic motion in the trap. The phonon laser's gain saturation keeps the optical frequency comb from continually adding energy without bound. This protection allows us to demonstrate loading and crystallization of hot ions directly with the comb, eliminating the need for a continuous-wave cooling laser, a technique that is extendable to the deep UV