Ravid Shaniv

Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite all atomic frequency references having more than two energy-levels, the commonly used model for evaluating their ultimate limits assumes a two-level atom. This leads to frequency interrogation protocols and theoretical stability bounds that are suboptimal for a true multi-level atom. The most fundamental stability bound assumes two noise sources - quantum projection noise and spontaneous decay from the excited state. In this work, we analyze a model that includes these noise types and is generalized beyond the two-level assumption, where spontaneous decay can branch to more than a single ground state. This model allows for detection and exclusion of atomic frequency interrogations in which the atom decayed, leading to a frequency stability improvement of up to $\approx 4.5 \text{ dB}$ compared with the two-level model. Furthermore, we identify an even greater stability enhancement of $\approx 5.4 \text{ dB}$ for frequency comparisons between atoms in an odd parity Bell state. These enhancements are particularly relevant for the numerous trapped-ion optical clock species that operate close to lifetime-limited stability. We calculate new stability limits for those cases and provide a detailed experimental protocol for frequency interrogation with an $^{27}\text{Al}^{+}$ optical ion clock.

The prevalent approach to executing quantum algorithms on quantum computers is to break-down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate sequences which are exponential in the qubit register size. Furthermore, gate fidelities tend to decrease when acting in larger qubit registers. Thus high-fidelity implementations in large qubit registers is still a prominent challenge. Here we propose and investigate multi-qubit entangling gates for trapped-ions. Our gates couple many qubits at once, allowing to decrease the total number of gates used while retaining a high gate fidelity. Our method employs all of the normal-modes of motion of the ion chain, which allows to operate outside of the adiabatic regime and at rates comparable to the secular ion-trapping frequency. Furthermore we extend our method for generating Hamiltonians which are suitable for quantum analog simulations, such as a nearest-neighbour spin Hamiltonian or the Su-Schrieffer-Heeger Hamiltonian.

Atomic isotope shifts (ISs) are the isotope-dependent energy differences in the atomic electron energy levels. These shifts serve an important role in atomic and nuclear physics, and particularly in the latter as signatures of nuclear structure. Recently ISs have been suggested as unique probes of beyond Standard Model (SM) physics, under the condition that they be determined significantly more precisely than current state of the art. In this work we present a simple and robust method for measuring ISs with ions in a Paul trap, by taking advantage of Hilbert subspaces that are insensitive to common-mode noise yet sensitive to the IS. Using this method we evaluate the IS of the $5S_{1/2}\leftrightarrow4D_{5/2}$ transition in $^{86}\text{Sr}^+$ and $^{88}\text{Sr}^+$ with a $1.6\times10^{-11}$ relative uncertainty to be 570,264,063.435(9) Hz. Furthermore, we detect a relative difference of $3.46(23)\times10^{-8}$ between the orbital g-factors of the electrons in the $4D_{5/2}$ level of the two isotopes. Our method is relatively easy to implement and is indifferent to element or isotope, paving the way for future tabletop searches for new physics and posing interesting prospects for testing quantum many-body calculations and for the study of nuclear structure.

We present a method that uses radio-frequency pulses to cancel the quadrupole shift in optical clock transitions. Quadrupole shifts are an inherent inhomogeneous broadening mechanism in trapped ion crystals, limiting current optical ion clocks to work with a single probe ion. Cancelling this shift at each interrogation cycle of the ion frequency allows the use of $N>1$ ions in clocks, thus reducing the uncertainty in the clock frequency by $\sqrt{N}$ according to the standard quantum limit. Our sequence relies on the tensorial nature of the quadrupole shift, and thus also cancels other tensorial shifts, such as the tensor ac stark shift. We experimentally demonstrate our sequence on three and seven $^{88}\mathrm{Sr}^{+}$ ions trapped in a linear Paul trap, using correlation spectroscopy. We show a reduction of the quadrupole shift difference between ions to $\approx20$ mHz's level where other shifts, such as the relativistic 2$^{\mathrm{nd}}$ order Doppler shift, are expected to limit our spectral resolution. In addition, we show that using radio-frequency dynamic decoupling we can also cancel the effect of 1$^{\mathrm{st}}$ order Zeeman shifts.

High-fidelity two-qubit entangling gates play an important role in many quantum information processing tasks and are a necessary building block for constructing a universal quantum computer. Such high-fidelity gates have been demonstrated on trapped-ion qubits, however, control errors and noise in gate parameters may still lead to reduced fidelity. Here we propose and demonstrate a general family of two-qubit entangling gates which are robust to different sources of noise and control errors. These gates generalize the celebrated Mølmer-Sørensen gate by using multi-tone drives. We experimentally implemented several of the proposed gates on $^{88}\text{Sr}^{+}$ ions trapped in a linear Paul trap, and verified their resilience.

Engineering entanglement between quantum systems often involves coupling through a bosonic mediator, which should be disentangled from the systems at the operation's end. The quality of such an operation is generally limited by environmental and control noise. One of the prime techniques for suppressing noise is by dynamical decoupling, where one actively applies pulses at a rate that is faster than the typical time scale of the noise. However, for boson-mediated gates, current dynamical decoupling schemes require executing the pulses only when the boson and the quantum systems are disentangled. This restriction implies an increase of the gate time by a factor of $\sqrt{N}$, with $N$ being the number of pulses applied. Here we propose and realize a method that enables dynamical decoupling in a boson mediated system where the pulses can be applied while spin-boson entanglement persists, resulting in an increase in time that is at most a factor of $\fracπ{2}$, independently of the number of pulses applied. We experimentally demonstrate the robustness of our fast dynamically decoupled entangling gate to $σ_z$ noise with ions in a Paul trap.

Force sensors are at the heart of different technologies such as atomic force microscopy or inertial sensing \cite{RMPforce2003, Rugar2004, YazdiIEEE}. These sensors often rely on the measurement of the displacement amplitude of mechanical oscillators under applied force. Examples for such mechanical oscillators include micro-fabricated cantilevers \cite{YazdiIEEE}, carbon nanotubes \cite{NanotubeForce} as well as single trapped ions \cite{Bollinger, Udem} . The best sensitivity is typically achieved when the force is alternating at the mechanical resonance frequency of the oscillator thus increasing its response by the mechanical quality factor. The measurement of low-frequency forces, that are below resonance, is a more difficult task as the resulting oscillation amplitudes are significantly lower. Here we use a single trapped $^{88}Sr^{+}$ ion as a force sensor. The ion is trapped in a linear harmonic trap, and is electrically driven at a frequency much lower than the trap resonance frequency. To be able to measure the small amplitude of motion we combine two powerful techniques. The force magnitude is determined by the measured periodic Doppler shift of an atomic optical clock transition and the Quantum Lock-in technique is used to coherently accumulate the phases acquired during different force half-cycles. We demonstrate force detection both when the oscillating force is phase-synchronized with the quantum lock-in sequence and when it is asynchronous and report frequency force detection sensitivity as low as $5.3\times10^{-19}\frac{\mathrm{N}}{\sqrt{\mathrm{Hz}}}$ .