Decoherence of a single-ion qubit immersed in a spin-polarized atomic bath

Reducing Effective System Dimensionality with Long-Range Collective Dipole-Dipole Interactions

Dimensionality plays a crucial role in long-range dipole-dipole interactions (DDIs). We demonstrate that a resonant nanophotonic structure modifies the apparent dimensionality in an interacting ensemble of emitters, as revealed by population decay dynamics. Our measurements on a dense ensemble of interacting quantum emitters in a resonant nanophotonic structure with long-range DDIs reveal an effective dimensionality reduction to d[over ¯]=2.20(12), despite the emitters being distributed in 3D. This contrasts with the homogeneous environment, where the apparent dimension is d[over ¯]=3.00. Our work presents a promising avenue to manipulate dimensionality in an ensemble of interacting emitters.

Observation of Chemical Reactions between a Trapped Ion and Ultracold Feshbach Dimers

We measure chemical reactions between a single trapped ^{174}Yb^{+} ion and ultracold Li_{2} dimers. This produces LiYb^{+} molecular ions that we detect via mass spectrometry. We explain the reaction rates by modeling the dimer density as a function of the magnetic field and obtain excellent agreement when we assume the reaction to follow the Langevin rate. Our results present a novel approach towards the creation of cold molecular ions and point to the exploration of ultracold chemistry in ion molecule collisions. What is more, with a detection sensitivity below molecule densities of 10^{14}  m^{-3}, we provide a new method to detect low-density molecular gases.

Observation of Feshbach resonances between a single ion and ultracold atoms

The control of physical systems and their dynamics on the level of individual quanta underpins both fundamental science and quantum technologies. Trapped atomic and molecular systems, neutral¹ and charged², are at the forefront of quantum science. Their extraordinary level of control is evidenced by numerous applications in quantum information processing^3,4 and quantum metrology^5,6. Studies of the long-range interactions between these systems when combined in a hybrid atom-ion trap^7,8 have led to landmark results^9-19. However, reaching the ultracold regime-where quantum mechanics dominates the interaction, for example, giving access to controllable scattering resonances^20,21-has so far been elusive. Here we demonstrate Feshbach resonances between ions and atoms, using magnetically tunable interactions between ¹³⁸Ba⁺ ions and ⁶Li atoms. We tune the experimental parameters to probe different interaction processes-first, enhancing three-body reactions^22,23 and the related losses to identify the resonances and then making two-body interactions dominant to investigate the ion's sympathetic cooling¹⁹ in the ultracold atomic bath. Our results provide deeper insights into atom-ion interactions, giving access to complex many-body systems^24-27 and applications in experimental quantum simulation^28-30.

Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an ²⁷Al⁺ clock to enable a total fractional systematic uncertainty below 10^-18. For this clock, with 38(19) nPa of room-temperature H₂ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order 10^-16 at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be -0.6(2.4) × 10^-19, where the shift is due to collisional heating time dilation and the uncertainty is dominated by the worst case ±π/2 bound used for collisional phase shift of the ²⁷Al⁺ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

State-selective coherent motional excitation as a new approach for the manipulation, spectroscopy and state-to-state chemistry of single molecular ions

We present theoretical and experimental progress towards a new approach for the precision spectroscopy, coherent manipulation and state-to-state chemistry of single isolated molecular ions in the gas phase. Our method uses a molecular beam for creating packets of rotationally cold neutrals from which a single molecule is state-selectively ionized and trapped inside a radiofrequency ion trap. In addition to the molecular ion, a single co-trapped atomic ion is used to cool the molecular external degrees of freedom to the ground state of the trap and to detect the molecular state using state-selective coherent motional excitation from a modulated optical-dipole force acting on the molecule. We present a detailed discussion and theoretical characterization of the present approach. We simulate the molecular signal experimentally using a single atomic ion, indicating that different rovibronic molecular states can be resolved and individually detected with our method. The present approach for the coherent control and non-destructive detection of the quantum state of a single molecular ion opens up new perspectives for precision spectroscopies relevant for, e.g., tests of fundamental physical theories and the development of new types of clocks based on molecular vibrational transitions. It will also enable the observation and control of chemical reactions of single particles on the quantum level. While focusing on N2+ as a prototypical example in the present work, our method is applicable to a wide range of diatomic and polyatomic molecules.

Signature of the s-Wave Regime High above Ultralow Temperatures

Resonant exchange is a general process playing a key role in many-body dynamics and transport phenomena, such as spin, charge, or excitation diffusion. The underlying process is described by the resonant exchange cross section. We show that the s-wave scattering, generally thought to contribute mainly in the ultracold (or Wigner) regime, dictates the overall cross section over a broad range of energies. We derive an analytical expression and explain its applicability high above the Wigner regime. In particular, we demonstrate its relationship to the classical capture (Langevin) cross section and apply it to three very different resonant processes: namely, resonant charge transfer, spin flip, and excitation exchange. This expression explains large variations for different isotopes that cannot otherwise be accounted for by the small change in mass. The s-wave signature also allows us to gain information about the Wigner regime from data obtained at much higher temperatures, which is especially advantageous for systems where the ultracold regime is not reachable.

Phase Locking between Different Partial Waves in Atom-Ion Spin-Exchange Collisions

We present a joint experimental and theoretical study of spin dynamics of a single ^{88}Sr^{+} ion colliding with an ultracold cloud of Rb atoms in various hyperfine states. While spin exchange between the two species occurs after 9.1(6) Langevin collisions on average, spin relaxation of the Sr^{+} ion Zeeman qubit occurs after 48(7) Langevin collisions, which is significantly slower than in previously studied systems due to a small second-order spin-orbit coupling. Furthermore, a reduction of the endothermic spin-exchange rate is observed as the magnetic field is increased. Interestingly, we find that while the phases acquired when colliding on the spin singlet and triplet potentials vary largely between different partial waves, the singlet-triplet phase difference, which determines the spin-exchange cross section, remains locked to a single value over a wide range of partial waves, which leads to quantum interference effects.

Quantum Spin Dynamics of Individual Neutral Impurities Coupled to a Bose-Einstein Condensate

We report on spin dynamics of individual, localized neutral impurities immersed in a Bose-Einstein condensate. Single cesium atoms are transported into a cloud of rubidium atoms and thermalize with the bath, and the ensuing spin exchange between localized impurities with quasispin F_{i}=3 and bath atoms with F_{b}=1 is resolved. Comparing our data to numerical simulations of spin dynamics, we find that, for gas densities in the Bose-Einstein condensate regime, the dynamics is dominated by the condensed fraction of the cloud. We spatially resolve the density overlap of impurities and gas by the spin population of impurities. Finally, we trace the coherence of impurities prepared in a coherent superposition of internal states when coupled to a gas of different densities. For our choice of states, we show that, despite high bath densities and, thus, fast thermalization rates, the impurity coherence is not affected by the bath, realizing a regime of sympathetic cooling while maintaining internal state coherence. Our work paves the way toward the nondestructive probing of quantum many-body systems via localized impurities.

Controlling Qubit Networks in Polynomial Time

Future quantum devices often rely on favorable scaling with respect to the number of system components. To achieve desirable scaling, it is therefore crucial to implement unitary transformations in a time that scales at most polynomial in the number of qubits. We develop an upper bound for the minimum time required to implement a unitary transformation on a generic qubit network in which each of the qubits is subject to local time dependent controls. Based on the developed upper bound, the set of gates is characterized that can be implemented polynomially in time. Furthermore, we show how qubit systems can be concatenated through controllable two body interactions, making it possible to implement the gate set efficiently on the combined system. Finally, a system is identified for which the gate set can be implemented with fewer controls.

Spin-controlled atom-ion chemistry

Quantum control of chemical reactions is an important goal in chemistry and physics. Ultracold chemical reactions are often controlled by preparing the reactants in specific quantum states. Here we demonstrate spin-controlled atom–ion inelastic (spin-exchange) processes and chemical (charge-exchange) reactions in an ultracold Rb-Sr⁺ mixture. The ion’s spin state is controlled by the atomic hyperfine spin state via spin-exchange collisions, which polarize the ion’s spin parallel to the atomic spin. We achieve ~ 90% spin polarization due to the absence of strong spin-relaxation channel. Charge-exchange collisions involving electron transfer are only allowed for (RbSr)⁺ colliding in the singlet manifold. Initializing the atoms in various spin states affects the overlap of the collision wave function with the singlet molecular manifold and therefore also the reaction rate. Our observations agree with theoretical predictions.

Chemical reactions with ultracold atoms and ions are explored so far with the atom–ion interactions. Here the authors discuss spin-exchange process and show that the spin state of an ensemble of neutral Rb atoms can be used to control the final spin of an imbedded Sr⁺ ion in the collisions.

Unraveling the Structure of Ultracold Mesoscopic Collinear Molecular Ions

We present an in-depth many-body investigation of the so-called mesoscopic molecular ions that can buildup when an ion is immersed into an atomic Bose-Einstein condensate in one dimension. To this end, we employ the multilayer multiconfiguration time-dependent Hartree method for mixtures of ultracold bosonic species for solving the underlying many-body Schrödinger equation. This enables us to unravel the actual structure of such massive charged molecules from a microscopic perspective. Laying out their phase diagram with respect to atom number and interatomic interaction strength, we determine the maximal number of atoms bound to the ion and reveal spatial densities and molecular properties. Interestingly, we observe a strong interaction-induced localization, especially for the ion, that we explain by the generation of a large effective mass, similarly to ions in liquid Helium. Finally, we predict the dynamical response of the ion to small perturbations. Our results provide clear evidence for the importance of quantum correlations, as we demonstrate by benchmarking them with wave function ansatz classes employed in the literature.

Superstatistical Energy Distributions of an Ion in an Ultracold Buffer Gas

An ion in a radio frequency ion trap interacting with a buffer gas of ultracold neutral atoms is a driven dynamical system which has been found to develop a nonthermal energy distribution with a power law tail. The exact analytical form of this distribution is unknown, but has often been represented empirically by q-exponential (Tsallis) functions. Based on the concepts of superstatistics, we introduce a framework for the statistical mechanics of an ion trapped in an rf field subject to collisions with a buffer gas. We derive analytic ion secular energy distributions from first principles both neglecting and including the effects of the thermal energy of the buffer gas. For a buffer gas with a finite temperature, we prove that Tsallis statistics emerges from the combination of a constant heating term and multiplicative energy fluctuations. We show that the resulting distributions essentially depend on experimentally controllable parameters paving the way for an accurate control of the statistical properties of ion-atom hybrid systems.

Dynamics of a Ground-State Cooled Ion Colliding with Ultracold Atoms

Ultracold atom-ion mixtures are gaining increasing interest due to their potential applications in ultracold and state-controlled chemistry, quantum computing, and many-body physics. Here, we studied the dynamics of a single ground-state cooled ion during few, to many, Langevin (spiraling) collisions with ultracold atoms. We measured the ion's energy distribution and observed a clear deviation from the Maxwell-Boltzmann distribution, characterized by an exponential tail, to a power-law distribution best described by a Tsallis function. Unlike previous experiments, the energy scale of atom-ion interactions is not determined by either the atomic cloud temperature or the ion's trap residual excess-micromotion energy. Instead, it is determined by the force the atom exerts on the ion during a collision which is then amplified by the trap dynamics. This effect is intrinsic to ion Paul traps and sets the lower bound of atom-ion steady-state interaction energy in these systems. Despite the fact that our system is eventually driven out of the ultracold regime, we are capable of studying quantum effects by limiting the interaction to the first collision when the ion is initialized in the ground state of the trap.

Spin-Orbit Interactions and Quantum Spin Dynamics in Cold Ion-Atom Collisions

We present accurate ab initio and quantum scattering calculations on a prototypical hybrid ion-atom system Yb^{+}-Rb, recently suggested as a promising candidate for the experimental study of open quantum systems, quantum information processing, and quantum simulation. We identify the second-order spin-orbit (SO) interaction as the dominant source of hyperfine relaxation in cold Yb^{+}-Rb collisions. Our results are in good agreement with recent experimental observations [L. Ratschbacher et al., Phys. Rev. Lett. 110, 160402 (2013)] of hyperfine relaxation rates of trapped Yb^{+} immersed in an ultracold Rb gas. The calculated rates are 4 times smaller than is predicted by the Langevin capture theory and display a weak T^{-0.3} temperature dependence, indicating significant deviations from statistical behavior. Our analysis underscores the deleterious nature of the SO interaction and implies that light ion-atom combinations such as Yb^{+}-Li should be used to minimize hyperfine relaxation and decoherence of trapped ions in ultracold atomic gases.

Dissipative dynamics in a finite chaotic environment: Relationship between damping rate and Lyapunov exponent

We consider the energy flow between a classical one-dimensional harmonic oscillator and a set of N two-dimensional chaotic oscillators, which represents the finite environment. Using linear response theory we obtain an analytical effective equation for the system harmonic oscillator, which includes a frequency dependent dissipation, a shift, and memory effects. The damping rate is expressed in terms of the environment mean Lyapunov exponent. A good agreement is shown by comparing theoretical and numerical results, even for environments with mixed (regular and chaotic) motion. Resonance between system and environment frequencies is shown to be more efficient to generate dissipation than larger mean Lyapunov exponents or a larger number of bath chaotic oscillators.

Neutral gas sympathetic cooling of an ion in a Paul trap

A single ion immersed in a neutral buffer gas is studied. An analytical model is developed that gives a complete description of the dynamics and steady-state properties of the ions. An extension of this model, using techniques employed in the mathematics of economics and finance, is used to explain the recent observation of non-Maxwellian statistics for these systems. Taken together, these results offer an explanation of the long-standing issues associated with sympathetic cooling of an ion by a neutral buffer gas.

Dissipative dynamics of a driven quantum spin coupled to a bath of ultracold fermions

We explore the dynamics and the steady state of a driven quantum spin coupled to a bath of fermions, which can be realized with a strongly imbalanced mixture of ultracold atoms using currently available experimental tools. Radio-frequency driving can be used to induce tunneling between the spin states. The Rabi oscillations are modified due to the coupling of the quantum spin to the environment, which causes frequency renormalization and damping. The spin-bath coupling can be widely tuned by adjusting the scattering length through a Feshbach resonance. When the scattering potential creates a bound state, by tuning the driving frequency it is possible to populate either the ground state, in which the bound state is filled, or a metastable state in which the bound state is empty. In the latter case, we predict an emergent inversion of the steady-state magnetization. Our work shows that different regimes of dissipative dynamics can be explored with a quantum spin coupled to a bath of ultracold fermions.

Emulating solid-state physics with a hybrid system of ultracold ions and atoms

We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of high fidelity operations and detection offered by trapped ion systems with ultracold atomic systems. It also features close analogies to natural solid-state systems, as the atomic degrees of freedom couple to phonons of the ion lattice, thereby emulating a solid-state system. Starting from the microscopic many-body Hamiltonian, we derive the low energy Hamiltonian, including the atomic band structure, and give an expression for the atom-phonon coupling. We discuss possible experimental implementations such as a Peierls-like transition into a period-doubled dimerized state.

Motional coherence of fermions immersed in a Bose gas

We prepare a superposition of two motional states by addressing lithium atoms immersed in a Bose-Einstein condensate of sodium with a species-selective potential. The evolution of the superposition state is characterized by the populations of the constituent states as well as their coherence. The latter we extract employing a novel scheme analogous to the spin-echo technique. Comparing the results directly to measurements on freely evolving fermions allows us to isolate the decoherence effects induced by the bath. In our system, the decoherence time is close to the maximal possible value since the decoherence is dominated by population relaxation processes. The measured data are in good agreement with a theoretical model based on Fermi's golden rule.