High-precision force sensing using a single trapped ion

We introduce quantum sensing schemes for measuring very weak forces with a single trapped ion. They use the spin-motional coupling induced by the laser-ion interaction to transfer the relevant force information to the spin-degree of freedom. Therefore, the force estimation is carried out simply by observing the Ramsey-type oscillations of the ion spin states. Three quantum probes are considered, which are represented by systems obeying the Jaynes-Cummings, quantum Rabi (in 1D) and Jahn-Teller (in 2D) models. By using dynamical decoupling schemes in the Jaynes-Cummings and Jahn-Teller models, our force sensing protocols can be made robust to the spin dephasing caused by the thermal and magnetic field fluctuations. In the quantum-Rabi probe, the residual spin-phonon coupling vanishes, which makes this sensing protocol naturally robust to thermally-induced spin dephasing. We show that the proposed techniques can be used to sense the axial and transverse components of the force with a sensitivity beyond the yN $/\sqrt{\text{Hz}}$ range, i.e. in the xN$/\sqrt{\text{Hz}}$ (xennonewton, $10^{-27}$). The Jahn-Teller protocol, in particular, can be used to implement a two-channel vector spectrum analyzer for measuring ultra-low voltages.Comment: 7 pages, 4 figure

Analytic approximations to the phase diagram of the Jaynes-Cummings-Hubbard model with application to ion chains

We discuss analytic approximations to the ground state phase diagram of the homogeneous Jaynes-Cummings-Hubbard (JCH) Hamiltonian with general short-range hopping. The JCH model describes e.g. radial phonon excitations of a linear chain of ions coupled to an external laser field tuned to the red motional sideband with Coulomb mediated hopping or an array of high-$Q$ coupled cavities containing a two-level atom and photons. Specifically we consider the cases of a linear array of coupled cavities and a linear ion chain. We derive approximate analytic expressions for the boundaries between Mott-insulating and superfluid phases and give explicit expressions for the critical value of the hopping amplitude within the different approximation schemes. In the case of an array of cavities, which is represented by the standard JCH model we compare both approximations to numerical data from density-matrix renormalization group (DMRG) calculations.Comment: 9 pages, 5 figures, extended and corrected second versio

Suppression of Excitation and Spectral Broadening Induced by Interactions in a Cold Gas of Rydberg Atoms

We report on the observation of ultralong range interactions in a gas of cold Rubidium Rydberg atoms. The van-der-Waals interaction between a pair of Rydberg atoms separated as far as 100,000 Bohr radii features two important effects: Spectral broadening of the resonance lines and suppression of excitation with increasing density. The density dependence of these effects is investigated in detail for the S- and P- Rydberg states with main quantum numbers n ~ 60 and n ~ 80 excited by narrow-band continuous-wave laser light. The density-dependent suppression of excitation can be interpreted as the onset of an interaction-induced local blockade

Quantum sensors assisted by spontaneous symmetry breaking for detecting very small forces

We propose a quantum-sensing scheme for measuring weak forces based on a symmetry-breaking adiabatic transition in the quantum Rabi model. We show that the system described by the Rabi Hamiltonian can serve as a sensor for extremely weak forces with sensitivity beyond the yoctonewton (yN) per sqrt (Hz) range. We propose an implementation of this sensing protocol using a single trapped ion. A major advantage of our scheme is that the force detection is performed by projective measurement of the population of the spin states at the end of the transition, instead of the far slower phonon number measurement used hitherto

A nano heat engine beyond the Carnot limit

Heat engines extract work by running cyclically between two heat reservoirs. When the two reservoirs are thermal and at different temperatures, the maximum efficiency of the engine is given by the Carnot limit. Here we consider a quantum Otto cycle for a time-dependent harmonic oscillator coupled to an engineered squeezed thermal reservoir. We show that the efficiency at maximum power increases with the degree of squeezing, exponentially approaching unity for large squeezing parameters $r$. Furthermore, we propose an experimental scheme to implement such a system by using a single trapped ion in a linear Paul trap with special geometry and coupled to engineered reservoirs. Our analytical investigations are supported with Monte Carlo simulations that demonstrate the feasibility of our proposal. For realistic trap parameters, an increase of up to a factor of four is reached, largely exceeding the classical limit

Focusing a deterministic single-ion beam

We focus down an ion beam consisting of single 40Ca+ ions to a spot size of a few mum using an einzel-lens. Starting from a segmented linear Paul trap, we have implemented a procedure which allows us to deterministically load a predetermined number of ions by using the potential shaping capabilities of our segmented ion trap. For single-ion loading, an efficiency of 96.7(7)% has been achieved. These ions are then deterministically extracted out of the trap and focused down to a 1sigma-spot radius of (4.6 \pm 1.3)mum at a distance of 257mm from the trap center. Compared to former measurements without ion optics, the einzel-lens is focusing down the single-ion beam by a factor of 12. Due to the small beam divergence and narrow velocity distribution of our ion source, chromatic and spherical aberration at the einzel-lens is vastly reduced, presenting a promising starting point for focusing single ions on their way to a substrate.Comment: 16 pages, 7 figure