Shlomi Kotler

Single-ion quantum lock-in amplifier

Quantum metrology uses tools from quantum information science to improve measurement signal-to-noise ratios. The challenge is to increase sensitivity while reducing susceptibility to noise, tasks that are often in conflict. Lock-in measurement is a detection scheme designed to overcome this difficulty by spectrally separating signal from noise. Here we report on the implementation of a quantum analogue to the classical lock-in amplifier. All the lock-in operations—modulation, detection and mixing—are performed through the application of non-commuting quantum operators to the electronic spin state of a single, trapped Sr+ ion. We significantly increase its sensitivity to external fields while extending phase coherence by three orders of magnitude, to more than one second. Using this technique, we measure frequency shifts with a sensitivity of 0.42 Hz Hz−1/2 (corresponding to a magnetic field measurement sensitivity of 15 pT Hz−1/2), obtaining an uncertainty of less than 10 mHz (350 fT) after 3,720 seconds of averaging. These sensitivities are limited by quantum projection noise and improve on other single-spin probe technologies by two orders of magnitude. Our reported sensitivity is sufficient for the measurement of parity non-conservation, as well as the detection of the magnetic field of a single electronic spin one micrometre from an ion detector with nanometre resolution. As a first application, we perform light shift spectroscopy of a narrow optical quadrupole transition. Finally, we emphasize that the quantum lock-in technique is generic and can potentially enhance the sensitivity of any quantum sensor.

Measurement of the magnetic interaction between two bound electrons of two separate ions

Electrons have an intrinsic, indivisible, magnetic dipole aligned with their internal angular momentum (spin)1. The magnetic interaction between two electrons can therefore impose a change in their spin orientation. Similar dipolar magnetic interactions exists between other spin systems and were studied experimentally. Examples include the interaction between an electron and its nucleus or between several multi-electron spin complexes2–8. The process for two electrons, however, was never observed in experiment. The challenge is two-fold. At the atomic scale, where the coupling is relatively large, the magnetic interaction is often overshadowed by the much larger coulomb exchange counterpart2. In typical situations where exchange is negligible, magnetic interactions are also very weak and well below ambient magnetic noise. Here we report on the first measurement of the magnetic interaction between two electronic spins. To this end, we used the ground state valence electrons of two Sr ions, co-trapped in an electric Paul trap and separated by more than two micrometers. We measured the weak, millihertz scale (alternatively 10−18 eV or 10−14 K), magnetic interaction between their electronic spins. This, in the presence of magnetic noise that was six ∗Current address: Physical Measurement Laboratory, National Institute of Science and Technology, Boulder CO, 80305, USA. †Current address: Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB30HE, United Kingdom.

Nonlinear single-spin spectrum analyzer.

A qubit can be used as a sensitive spectrum analyzer of its environment. Here we show how the problem of spectral analysis of noise induced by a strongly coupled environment can be solved for discrete spectra. Our analytical model shows non-linear signal dependence on noise power, as well as possible frequency mixing, both are inherent to quantum evolution. This model enabled us to use a single trapped ion as a sensitive probe for strong, non-Gaussian, discrete magnetic field noise. To overcome ambiguities arising from the non-linear character of strong noise, we develop a three step noise characterization scheme: peak identification, magnitude identification and fine-tuning. Finally, we compare experimentally equidistant versus Uhrig pulse schemes for spectral analysis. The method is readily available to any quantum probe which can be coherently manipulated.

Single-ion nonlinear mechanical oscillator

We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

Universal gate-set for trapped-ion qubits using a narrow linewidth diode laser

We report on the implementation of a high fidelity universal gate-set on optical qubits based on trapped 88Sr+ ions for the purpose of quantum information processing. All coherent operations were performed using a narrow linewidth diode laser. We employed a master-slave configuration for the laser, where an ultra low expansion glass Fabry–Perot cavity is used as a stable reference as well as a spectral filter. We characterized the laser spectrum using the ions with a modified Ramsey sequence which eliminated the affect of the magnetic field noise. We demonstrated high fidelity single qubit gates with individual addressing, based on inhomogeneous micromotion, on a two-ion chain as well as the Molmer–Sorensen two-qubit entangling gate.

High-fidelity state detection and tomography of a single-ion Zeeman qubit

We demonstrate high-fidelity Zeeman qubit state detection in a single trapped 88Sr+ ion. Qubit readout is performed by shelving one of the qubit states to a metastable level using a narrow linewidth diode laser at 674 nm, followed by state-selective fluorescence detection. The average fidelity reached for the readout of the qubit state is 0.9989(1). We then measure the fidelity of state tomography, averaged over all possible single-qubit states, which is 0.9979(2). We also fully characterize the detection process using quantum process tomography. This readout fidelity is compatible with recent estimates of the detection error threshold required for fault-tolerant computation, whereas high-fidelity state tomography opens the way for high-precision quantum process tomography.

Constraints on Exotic Dipole-Dipole Couplings between Electrons at the Micrometer Scale.

New constraints on exotic dipole-dipole interactions between electrons at the micrometer scale are established, based on a recent measurement of the magnetic interaction between two trapped 88Sr(+) ions. For light bosons (mass≤0.1  eV) we obtain a 90% confidence interval for an axial-vector-mediated interaction strength of |g(A)(e)g(A)(e)/4πℏc|≤1.2×10(-17). Assuming CPT invariance, this constraint is compared to that on anomalous electron-positron interactions, derived from positronium hyperfine spectroscopy. We find that the electron-electron constraint is 6 orders of magnitude more stringent than the electron-positron counterpart. Bounds on pseudoscalar-mediated interaction as well as on torsion gravity are also derived and compared with previous work performed at different length scales. Our constraints benefit from the high controllability of the experimental system which contained only two trapped particles. It therefore suggests a useful new platform for exotic particle searches, complementing other experimental efforts.

Addressing two-level systems variably coupled to an oscillating field.

We propose a simple method to spectrally resolve an array of identical two-level systems coupled to an inhomogeneous oscillating field. The addressing protocol uses a dressing field with a spatially dependent coupling to the atoms. We validate this scheme experimentally by realizing single-spin addressing of a linear chain of trapped ions that are separated by ~3 μm, dressed by a laser field that is resonant with the micromotion sideband of a narrow optical transition.

Measurements of trapped-ion heating rates with exchangeable surfaces in close proximity

Electric-field noise from the surfaces of ion-trap electrodes couples to the ions charge causing heating of the ions motional modes. This heating limits the fidelity of quantum gates implemented in quantum information processing experiments. The exact mechanism that gives rise to electric-field noise from surfaces is not well-understood and remains an active area of research. In this work, we detail experiments intended to measure ion motional heating rates with exchangeable surfaces positioned in close proximity to the ion, as a sensor to electric-field noise. We have prepared samples with various surface conditions, characterized in situ with scanned probe microscopy and electron spectroscopy, ranging in degrees of cleanliness and structural order. The heating-rate data, however, show no significant differences between the disparate surfaces that were probed. These results suggest that the driving mechanism for electric-field noise from surfaces is due to more than just thermal excitations alone.

Quantum process tomography of a Mølmer-Sørensen interaction

We report the quantum process tomography of a M