Laser cooling to the zero-point energy of motion

Laser-type cooling with unfiltered sunlight

Cooling of systems to sub-Kelvin temperatures is usually done using either a cold bath of particles or spontaneous photon scattering from a laser field; in either case, cooling is driven by interaction with a well-ordered cold (i.e., low-entropy) system. However, there have recently been several schemes proposed for "cooling by heating," in which raising the temperature of some mode drives the cooling of the desired system faster. We discuss how to cool a trapped ion to its motional ground state using unfiltered sunlight at 5800K to drive the cooling. We show how to treat the statistics of thermal light in a single-mode fiber for delivery to the ion and show experimentally how the blackbody spectrum is strongly modified by being embedded in quasi-one-dimension. Quantitative estimates for the achievable cooling rate with our measured fiber-coupled low-dimensional sunlight show promise for demonstrating this implementation of cooling by heating.

Sideband cooling of a trapped ion in strong sideband coupling regime

Conventional theoretical studies on the ground-state laser cooling of a trapped ion have mostly focused on the weak sideband coupling (WSC) regime, where the cooling rate is inverse proportional to the linewidth of the excited state. In a recent work [New J. Phys.23, 023018 (2021)10.1088/1367-2630/abe273], we proposed a theoretical framework to study the ground state cooling of a trapped ion in the strong sideband coupling (SSC) regime, under the assumption of a vanishing carrier transition. Here we extend this analysis to more general situations with nonvanishing carrier transitions, where we show that by properly tuning the coupling lasers a cooling rate proportional to the linewidth can be achieved. Our theoretical predictions closely agree with the corresponding exact solutions in the SSC regime, which provide an important theoretical guidance for sideband cooling experiments.

Trapping and Ground-State Cooling of a Single H_{2}^{+}

We demonstrate co-trapping and sideband cooling of a H_{2}^{+}-^{9}Be^{+} ion pair in a cryogenic Paul trap. We study the chemical lifetime of H_{2}^{+} and its dependence on the apparatus temperature, achieving lifetimes of up to 11_{-3}^{+6}  h at 10 K. We demonstrate cooling of two of the modes of translational motion to an average phonon number of 0.07(1) and 0.05(1), corresponding to a temperature of 22(1) and 55(3)  μK, respectively. Our results provide a basis for quantum logic spectroscopy experiments of H_{2}^{+}, as well as other light ions such as HD^{+}, H_{3}^{+}, and He^{+}.

Predicting molecular vibronic spectra using time-domain analog quantum simulation

Spectroscopy is one of the most accurate probes of the molecular world. However, predicting molecular spectra accurately is computationally difficult because of the presence of entanglement between electronic and nuclear degrees of freedom. Although quantum computers promise to reduce this computational cost, existing quantum approaches rely on combining signals from individual eigenstates, an approach whose cost grows exponentially with molecule size. Here, we introduce a method for scalable analog quantum simulation of molecular spectroscopy: by performing simulations in the time domain, the number of required measurements depends on the desired spectral range and resolution, not molecular size. Our approach can treat more complicated molecular models than previous ones, requires fewer approximations, and can be extended to open quantum systems with minimal overhead. We present a direct mapping of the underlying problem of time-domain simulation of molecular spectra to the degrees of freedom and control fields available in a trapped-ion quantum simulator. We experimentally demonstrate our algorithm on a trapped-ion device, exploiting both intrinsic electronic and motional degrees of freedom, showing excellent quantitative agreement for a single-mode vibronic photoelectron spectrum of SO2.

Formation of Ultracold Molecules by Merging Optical Tweezers

We demonstrate the formation of a single RbCs molecule during the merging of two optical tweezers, one containing a single Rb atom and the other a single Cs atom. Both atoms are initially predominantly in the motional ground states of their respective tweezers. We confirm molecule formation and establish the state of the molecule formed by measuring its binding energy. We find that the probability of molecule formation can be controlled by tuning the confinement of the traps during the merging process, in good agreement with coupled-channel calculations. We show that the conversion efficiency from atoms to molecules using this technique is comparable to magnetoassociation.

Test of Causal Nonlinear Quantum Mechanics by Ramsey Interferometry with a Trapped Ion

Quantum mechanics requires the time evolution of the wave function to be linear. While this feature has been associated with the preservation of causality, a consistent causal nonlinear theory was recently developed. Interestingly, this theory is unavoidably sensitive to the full physical spread of the wave function, rendering existing experimental tests for nonlinearities inapplicable. Here, using well-controlled motional superpositions of a trapped ion, we set a stringent limit of 5.4×10^{-12} on the magnitude of the unitless scaling factor ε[over ˜]_{γ} for the predicted causal nonlinear perturbation.

Active impedance matching of a cryogenic radio frequency resonator for ion traps

A combination of direct current (DC) fields and high amplitude radio frequency (RF) fields is necessary to trap ions in a Paul trap. Such high electric RF fields are usually reached with the help of a resonator in close proximity to the ion trap. Ion trap based quantum computers profit from good vacuum conditions and low heating rates that cryogenic environments provide. However, an impedance matching network between the resonator and its RF source is necessary, as an unmatched resonator would require higher input power due to power reflection. The reflected power would not contribute to the RF trapping potential, and the losses in the cable induce additional heat into the system. The electrical properties of the matching network components change during cooling, and a cryogenic setup usually prohibits physical access to integrated components while the experiment is running. This circumstance leads to either several cooling cycles to improve the matching at cryogenic temperatures or the operation of poorly matched resonators. In this work, we demonstrate an RF resonator that is actively matched to the wave impedance of coaxial cables and the signal source. The active part of the matching circuit consists of a varactor diode array. Its capacitance depends on the DC voltage applied from outside the cryostat. We present measurements of the power reflection, the Q-factor, and higher harmonic signals resulting from the nonlinearity of the varactor diodes. The RF resonator is tested in a cryostat at room temperature and cryogenic temperatures, down to 4.3 K. A superior impedance matching for different ion traps can be achieved with this type of resonator.

Lifetime of the ^{2}F_{7/2} Level in Yb^{+} for Spontaneous Emission of Electric Octupole Radiation

We report a measurement of the radiative lifetime of the ^{2}F_{7/2} level of ^{171}Yb^{+} that is coupled to the ^{2}S_{1/2} ground state via an electric octupole transition. The radiative lifetime is determined to be 4.98(25)×10^{7}  s, corresponding to 1.58(8) yr. The result reduces the relative uncertainty in this exceptionally long excited state lifetime by 1 order of magnitude with respect to previous experimental estimates. Our method is based on the coherent excitation of the corresponding transition and avoids limitations through competing decay processes. The explicit dependence on the laser intensity is eliminated by simultaneously measuring the resonant Rabi frequency and the induced quadratic Stark shift. Combining the result with information on the dynamic differential polarizability permits a calculation of the transition matrix element to infer the radiative lifetime.

Cooling photon-pressure circuits into the quantum regime

Quantum control of electromagnetic fields was initially established in the optical domain and has been advanced to lower frequencies in the gigahertz range during the past decades extending quantum photonics to broader frequency regimes. In standard cryogenic systems, however, thermal decoherence prevents access to the quantum regime for photon frequencies below the gigahertz domain. Here, we engineer two superconducting LC circuits coupled by a photon-pressure interaction and demonstrate sideband cooling of a hot radio frequency (RF) circuit using a microwave cavity. Because of a substantially increased coupling strength, we obtain a large single-photon quantum cooperativity 𝒞_q0 ∼ 1 and reduce the thermal RF occupancy by 75% with less than one pump photon. For larger pump powers, the coupling rate exceeds the RF thermal decoherence rate by a factor of 3, and the RF circuit is cooled into the quantum ground state. Our results lay the foundation for RF quantum photonics.

Analog quantum simulation of chemical dynamics

Ultrafast chemical reactions are difficult to simulate because they involve entangled, many-body wavefunctions whose computational complexity grows rapidly with molecular size. In photochemistry, the breakdown of the Born-Oppenheimer approximation further complicates the problem by entangling nuclear and electronic degrees of freedom. Here, we show that analog quantum simulators can efficiently simulate molecular dynamics using commonly available bosonic modes to represent molecular vibrations. Our approach can be implemented in any device with a qudit controllably coupled to bosonic oscillators and with quantum hardware resources that scale linearly with molecular size, and offers significant resource savings compared to digital quantum simulation algorithms. Advantages of our approach include a time resolution orders of magnitude better than ultrafast spectroscopy, the ability to simulate large molecules with limited hardware using a Suzuki-Trotter expansion, and the ability to implement realistic system-bath interactions with only one additional interaction per mode. Our approach can be implemented with current technology; e.g., the conical intersection in pyrazine can be simulated using a single trapped ion. Therefore, we expect our method will enable classically intractable chemical dynamics simulations in the near term.

An ion trap apparatus with high optical access in multiple directions

Optical controls provided by lasers are the most important and essential techniques in trapped ion and cold atom systems. It is crucial to increase the optical accessibility of the setup to enhance these optical capabilities. Here, we present the design and construction of a new segmented-blade ion trap integrated with a compact glass vacuum cell, in place of the conventional bulky metal vacuum chamber. The distance between the ion and four outside surfaces of the glass cell is 15 mm, which enables us to install four high-numerical-aperture (NA) lenses (with two NA ⩽ 0.32 lenses and two NA ⩽ 0.66 lenses) in two orthogonal transverse directions, while leaving enough space for laser beams in the oblique and longitudinal directions. The high optical accessibility in multiple directions allows the application of small laser spots for addressable Raman operations, programmable optical tweezer arrays, and efficient fluorescence collection simultaneously. We have successfully loaded and cooled a string of ¹⁷⁴Yb⁺ and ¹⁷¹Yb⁺ ions in the trap, which verifies the trapping stability. This compact high-optical-access trap setup not only can be used as an extendable module for quantum information processing but also facilitates experimental studies on quantum chemistry in a cold hybrid ion-atom system.

Times of arrival and gauge invariance

We revisit the arguments underlying two well-known arrival-time distributions in quantum mechanics, viz., the Aharonov–Bohm–Kijowski (ABK) distribution, applicable for freely moving particles, and the quantum flux (QF) distribution. An inconsistency in the original axiomatic derivation of Kijowski’s result is pointed out, along with an inescapable consequence of the ‘negative arrival times’ inherent to this proposal (and generalizations thereof). The ABK free-particle restriction is lifted in a discussion of an explicit arrival-time set-up featuring a charged particle moving in a constant magnetic field. A natural generalization of the ABK distribution is in this case shown to be critically gauge-dependent. A direct comparison to the QF distribution, which does not exhibit this flaw, is drawn (its acknowledged drawback concerning the quantum backflow effect notwithstanding).

Ultra-low-vibration closed-cycle cryogenic surface-electrode ion trap apparatus

We describe the design, commissioning, and operation of an ultra-low-vibration closed-cycle cryogenic ion trap apparatus. One hundred lines for low-frequency signals and eight microwave/radio frequency coaxial feed-lines offer the possibility of implementing a small-scale ion-trap quantum processor or simulator. With all supply cables attached, more than 1.3 W of cooling power at 5 K is still available for absorbing energy from electrical pulses introduced to control ions. The trap itself is isolated from vibrations induced by the cold head using a helium exchange gas interface. The performance of the vibration isolation system has been characterized using a Michelson interferometer, finding residual vibration amplitudes on the order of 10 nm rms. Trapping of ⁹Be⁺ ions has been demonstrated using a combination of laser ablation and photoionization.

Enhanced observation time of magneto-optical traps using micro-machined non-evaporable getter pumps

We show that micro-machined non-evaporable getter pumps (NEGs) can extend the time over which laser cooled atoms can be produced in a magneto-optical trap (MOT), in the absence of other vacuum pumping mechanisms. In a first study, we incorporate a silicon-glass microfabricated ultra-high vacuum (UHV) cell with silicon etched NEG cavities and alumino-silicate glass (ASG) windows and demonstrate the observation of a repeatedly-loading MOT over a 10 min period with a single laser-activated NEG. In a second study, the capacity of passive pumping with laser activated NEG materials is further investigated in a borosilicate glass-blown cuvette cell containing five NEG tablets. In this cell, the MOT remained visible for over 4 days without any external active pumping system. This MOT observation time exceeds the one obtained in the no-NEG scenario by almost five orders of magnitude. The cell scalability and potential vacuum longevity made possible with NEG materials may enable in the future the development of miniaturized cold-atom instruments.

Efficient Ground-State Cooling of Large Trapped-Ion Chains with an Electromagnetically-Induced-Transparency Tripod Scheme

We report the electromagnetically-induced-transparency (EIT) cooling of a large trapped ^{171}Yb^{+} ion chain to the quantum ground state. Unlike conventional EIT cooling, we engage a four-level tripod structure and achieve fast sub-Doppler cooling over all motional modes. We observe simultaneous ground-state cooling across the complete transverse mode spectrum of up to 40 ions, occupying a bandwidth of over 3 MHz. The cooling time is observed to be less than 300  μs, independent of the number of ions. Such efficient cooling across the entire spectrum is essential for high-fidelity quantum operations using trapped ion crystals for quantum simulators or quantum computers.

Motional Sideband Asymmetry of a Nanoparticle Optically Levitated in Free Space

The hallmark of quantum physics is Planck's constant h, whose finite value entails the quantization that gave the theory its name. The finite value of h gives rise to inevitable zero-point fluctuations even at vanishing temperature. The zero-point fluctuation of mechanical motion becomes smaller with growing mass of an object, making it challenging to observe at macroscopic scales. Here, we transition a dielectric particle with a diameter of 136 nm from the classical realm to the regime where its zero-point motion emerges as a sizable contribution to its energy. To this end, we optically trap the particle at ambient temperature in ultrahigh vacuum and apply active feedback cooling to its center-of-mass motion. We measure an asymmetry between the Stokes and anti-Stokes sidebands of photons scattered by the levitated particle, which is a signature of the particle's quantum ground state of motion.

Gallium Phosphide as a Piezoelectric Platform for Quantum Optomechanics

Recent years have seen extraordinary progress in creating quantum states of mechanical oscillators, leading to great interest in potential applications for such systems in both fundamental as well as applied quantum science. One example is the use of these devices as transducers between otherwise disparate quantum systems. In this regard, a promising approach is to build integrated piezoelectric optomechanical devices that are then coupled to microwave circuits. Optical absorption, low quality factors, and other challenges have up to now prevented operation in the quantum regime, however. Here, we design and characterize such a piezoelectric optomechanical device fabricated from gallium phosphide in which a 2.9 GHz mechanical mode is coupled to a high quality factor optical resonator in the telecom band. The large electronic band gap and the resulting low optical absorption of this new material, on par with devices fabricated from silicon, allows us to demonstrate quantum behavior of the structure. This not only opens the way for realizing noise-free quantum transduction between microwaves and optics, but in principle also from various color centers with optical transitions in the near visible to the telecom band.

^{27}Al^{+} Quantum-Logic Clock with a Systematic Uncertainty below 10^{-18}

We describe an optical atomic clock based on quantum-logic spectroscopy of the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+} with a systematic uncertainty of 9.4×10^{-19} and a frequency stability of 1.2×10^{-15}/sqrt[τ]. A ^{25}Mg^{+} ion is simultaneously trapped with the ^{27}Al^{+} ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous ^{27}Al^{+} clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous ^{27}Al^{+} clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.

Entropy Exchange and Thermodynamic Properties of the Single Ion Cooling Process

A complete quantum cooling cycle may be a useful platform for studying quantum thermodynamics just as the quantum heat engine does. Entropy change is an important feature which can help us to investigate the thermodynamic properties of the single ion cooling process. Here, we analyze the entropy change of the ion and laser field in the single ion cooling cycle by generalizing the idea in Reference (Phys. Rev. Lett.2015, 114, 043002) to a single ion system. Thermodynamic properties of the single ion cooling process are discussed and it is shown that the Second and Third Laws of Thermodynamics are still strictly held in the quantum cooling process. Our results suggest that quantum cooling cycles are also candidates for the investigation on quantum thermodynamics besides quantum heat engines.

Near Ground-State Cooling of Two-Dimensional Trapped-Ion Crystals with More than 100 Ions

We experimentally study electromagnetically induced transparency cooling of the drumhead modes of planar two-dimensional arrays with up to N≈190 Be^{+} ions stored in a Penning trap. Substantial sub-Doppler cooling is observed for all N drumhead modes. Quantitative measurements for the center-of-mass mode show near ground-state cooling with motional quantum numbers of n[over ¯]=0.3±0.2 obtained within 200  μs. The measured cooling rate is faster than that predicted by single particle theory, consistent with a quantum many-body calculation. For the lower frequency drumhead modes, quantitative temperature measurements are limited by frequency instabilities, but near ground-state cooling of the full bandwidth is strongly suggested. This advance will greatly improve the performance of large trapped ion crystals in quantum information and metrology applications.

Carrier thermometry of cold ytterbium atoms in an optical lattice clock

The ultracold atomic gas serving as the quantum reference is a key part of an optical lattice clock, and the temperature of atoms in the optical lattice affects the uncertainty and instability of the optical lattice clocks. Since the carrier spectrum of the clock transition in the lattices reflects the thermal dynamics of cold atoms, the temperature of atoms can be extracted from the carrier spectrum in a non-magic wavelength lattice of ytterbium optical clocks. Furthermore, the temperatures obtained from the carrier spectra are in good agreement with the results obtained by the time-of-flight method and thermometry based on the sideband spectrum. In addition, the heating effects caused by the lattice laser are studied on the basis of the sample temperatures.

Revealing Quantum Statistics with a Pair of Distant Atoms

Quantum statistics have a profound impact on the properties of systems composed of identical particles. At the most elementary level, Bose and Fermi quantum statistics differ in the exchange phase, either 0 or π, which the wave function acquires when two identical particles are exchanged. In this Letter, we demonstrate that the exchange phase can be directly probed with a pair of massive particles by physically exchanging their positions. We present two protocols where the particles always remain spatially well separated, thus ensuring that the exchange contribution to their interaction energy is negligible and that the detected signal can only be attributed to the exchange symmetry of the wave function. We discuss possible implementations with a pair of trapped atoms or ions.

3D Sisyphus Cooling of Trapped Ions

Using a laser polarization gradient, we realize 3D Sisyphus cooling of ^{171}Yb^{+} ions confined in and near the Lamb-Dicke regime in a linear Paul trap. The cooling rate and final mean motional energy of a single ion are characterized as a function of laser intensity and compared to semiclassical and quantum simulations. Sisyphus cooling is also applied to a linear string of four ions to obtain a mean energy of 1-3 quanta for all vibrational modes, an approximately order of magnitude reduction below Doppler cooled energies. This is used to enable subsequent, efficient sideband laser cooling.

Optical angular momentum and atoms

Any coherent interaction of light and atoms needs to conserve energy, linear momentum and angular momentum. What happens to an atom's angular momentum if it encounters light that carries orbital angular momentum (OAM)? This is a particularly intriguing question as the angular momentum of atoms is quantized, incorporating the intrinsic spin angular momentum of the individual electrons as well as the OAM associated with their spatial distribution. In addition, a mechanical angular momentum can arise from the rotation of the entire atom, which for very cold atoms is also quantized. Atoms therefore allow us to probe and access the quantum properties of light's OAM, aiding our fundamental understanding of light-matter interactions, and moreover, allowing us to construct OAM-based applications, including quantum memories, frequency converters for shaped light and OAM-based sensors.This article is part of the themed issue 'Optical orbital angular momentum'.

Sympathetic Ground State Cooling and Time-Dilation Shifts in an ^{27}Al^{+} Optical Clock

We report on Raman sideband cooling of ^{25}Mg^{+} to sympathetically cool the secular modes of motion in a ^{25}Mg^{+}-^{27}Al^{+} two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -(1.9±0.1)×10^{-18} for an ^{27}Al^{+} clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous ^{27}Al^{+} clocks.

Hyperspherical coupled channel calculations of energy and structure of (4)He-(4)He-Li(+) and its isotopic combinations

The ground state vibrational energy and spatial features of (4)He-(4)He-Li(+) and its triatomic isotopic complexes are studied using the slow variable discretization (SVD) method in the hyperspherical coordinates for the zero total angular momentum. Our results show that the dominant structure of the system is an isosceles triangle with the shorter side associated with the two Li(+)-He distances using the sum-of-potential approximation. Corrections caused by the induced dipole-induced dipole interactions on the He atoms are also investigated. The effects are seen to be small and have a minor influence on the binding energy and the structure of present system. The results are also compared with the full ab initio calculations including all the three-body interactions and information of three-body corrections is obtained.

High-order corrections on the laser cooling limit in the Lamb-Dicke regime

We investigate corrections on the cooling limit of high-order Lamb-Dicke (LD) parameters in the double electromagnetically induced transparency (EIT) cooling scheme. Via utilizing quantum interferences, the single-phonon heating mechanism vanishes and the system evolves to a double dark state, from which we will obtain the mechanical occupation on the single-phonon excitation state. In addition, the further correction induced by two-phonon heating transitions is included to achieve a more accurate cooling limit. There exist two pathways of two-phonon heating transitions: direct two-phonon excitation from the dark state and further excitation from the single-phonon excited state. By adding up these two parts of correction, the obtained analytical predictions show a well consistence with numerical results. Moreover, we find that the two pathways can destructively interfere with each other, leading to the elimination of two-phonon heating transitions and achieving a lower cooling limit.

Continuous Quantum Nondemolition Measurement of the Transverse Component of a Qubit

Quantum jumps of a qubit are usually observed between its energy eigenstates, also known as its longitudinal pseudospin component. Is it possible, instead, to observe quantum jumps between the transverse superpositions of these eigenstates? We answer positively by presenting the first continuous quantum nondemolition measurement of the transverse component of an individual qubit. In a circuit QED system irradiated by two pump tones, we engineer an effective Hamiltonian whose eigenstates are the transverse qubit states, and a dispersive measurement of the corresponding operator. Such transverse component measurements are a useful tool in the driven-dissipative operation engineering toolbox, which is central to quantum simulation and quantum error correction.

Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space

The Kibble-Zurek mechanism is the paradigm to account for the nonadiabatic dynamics of a system across a continuous phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. We test the Kibble-Zurek mechanism in the quantum regime in the momentum space and find the measured scaling of excitations is in accordance with the theoretical prediction.

Optical gradient force assist maneuver

We describe an energy transfer process whereby a moving particle loses (or gains) kinetic energy upon interacting with the moving optical potential of a swept beam of light. This approach is akin to a gravitational assist maneuver for interplanetary satellite propulsion. Special consideration is given to the stopping condition. For analytical convenience, we examine the Rayleigh scattering regime, providing examples at small and large scattering angles. A 5% uncertainty in the initial particle speed and position has negligible effect on the slowing/speeding ability when the beam size is much larger than the particle.

Stability Diagrams for Paul Ion Traps Driven by Two-Frequencies

In this paper, we present and discuss stability diagrams for Paul traps driven by two ac voltages. In contrast to a typical Paul trap, here we suggest a secondary ac voltage whose frequency is twice the frequency of the primary one. The ratio between their amplitudes can be used to expand the region of stability and to access different states of motion of trapped ions. This provides a further mechanism to trap, cool, and manipulate single ions and also to improve the experimental framework where ion clouds and crystals can be prepared and controlled. Such approach opens the possibility of designing more sophisticated trapping architectures, leading to a wide variety of applications on ion trap research and mass analysis techniques.

Single atom detection in ultracold quantum gases: a review of current progress

The recent advances in single atom detection and manipulation in experiments with ultracold quantum gases are reviewed. The discussion starts with the basic principles of trapping, cooling and detecting single ions and atoms. The realization of single atom detection in ultracold quantum gases is presented in detail and the employed methods, which are based on light scattering, electron scattering, field ionization and direct neutral particle detection are discussed. The microscopic coherent manipulation of single atoms in a quantum gas is also covered. Various examples are given in order to highlight the power of these approaches to study many-body quantum systems.

Resolved-Sideband Laser Cooling in a Penning Trap

We report the laser cooling of a single ^{40}Ca^{+} ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole S_{1/2}↔D_{5/2} transition, broadened by a quench laser coupling the D_{5/2} and P_{3/2} levels. We find the final ground-state occupation to be 98(1)%. We measure the heating rate of the trap to be very low with n[over ¯][over ˙]≈0.3(2)  s^{-1} for trap frequencies from 150-400 kHz, consistent with the large ion-electrode distance.

Quantum Rabi Model with Trapped Ions

We propose the quantum simulation of the quantum Rabi model in all parameter regimes by means of detuned bichromatic sideband excitations of a single trapped ion. We show that current setups can reproduce, in particular, the ultrastrong and deep strong coupling regimes of such a paradigmatic light-matter interaction. Furthermore, associated with these extreme dipolar regimes, we study the controlled generation and detection of their entangled ground states by means of adiabatic methods. Ion traps have arguably performed the first quantum simulation of the Jaynes-Cummings model, a restricted regime of the quantum Rabi model where the rotating-wave approximation holds. We show that one can go beyond and experimentally investigate the quantum simulation of coupling regimes of the quantum Rabi model that are difficult to achieve with natural dipolar interactions.

Dynamical backaction cooling with free electrons

The ability to cool single ions, atomic ensembles, and more recently macroscopic degrees of freedom down to the quantum ground state has generated considerable progress and perspectives in fundamental and technological science. These major advances have been essentially obtained by coupling mechanical motion to a resonant electromagnetic degree of freedom in what is generally known as laser cooling. Here, we experimentally demonstrate the first self-induced coherent cooling mechanism that is not mediated by an electromagnetic resonance. Using a focused electron beam, we report a 50-fold reduction of the motional temperature of a nanowire. Our result primarily relies on the sub-nanometre confinement of the electron beam and generalizes to any delayed and spatially confined interaction, with important consequences for near-field microscopy and fundamental nanoscale dissipation mechanisms.

Cooling atoms and ions to the quantum ground state is generally achieved by resonantly coupling their mechanical motion to an electromagnetic wave. Here the authors report self-induced cooling based on sub-nanometre confinement with an electron beam, rather than an electromagnetic resonance.

Ground-State Cooling of a Trapped Ion Using Long-Wavelength Radiation

We demonstrate ground-state cooling of a trapped ion using radio-frequency (rf) radiation. This is a powerful tool for the implementation of quantum operations, where rf or microwave radiation instead of lasers is used for motional quantum state engineering. We measure a mean phonon number of n[over ¯]=0.13(4) after sideband cooling, corresponding to a ground-state occupation probability of 88(7)%. After preparing in the vibrational ground state, we demonstrate motional state engineering by driving Rabi oscillations between the |n=0⟩ and |n=1⟩ Fock states. We also use the ability to ground-state cool to accurately measure the motional heating rate and report a reduction by almost 2 orders of magnitude compared with our previously measured result, which we attribute to carefully eliminating sources of electrical noise in the system.

Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition

The dynamic structure factor is a central quantity describing the physics of quantum many-body systems, capturing structure and collective excitations of a material. In condensed matter, it can be measured via inelastic neutron scattering, which is an energy-resolving probe for the density fluctuations. In ultracold atoms, a similar approach could so far not be applied because of the diluteness of the system. Here we report on a direct, real-time and nondestructive measurement of the dynamic structure factor of a quantum gas exhibiting cavity-mediated long-range interactions. The technique relies on inelastic scattering of photons, stimulated by the enhanced vacuum field inside a high finesse optical cavity. We extract the density fluctuations, their energy and lifetime while the system undergoes a structural phase transition. We observe an occupation of the relevant quasi-particle mode on the level of a few excitations, and provide a theoretical description of this dissipative quantum many-body system.

Thermometry via light shifts in optical lattices

For atoms or molecules in optical lattices, conventional thermometry methods are often unsuitable due to low particle numbers or a lack of cycling transitions. However, a differential spectroscopic light shift can map temperature onto the line shape with a low sensitivity to trap anharmonicity. We study narrow molecular transitions to demonstrate precise frequency-based lattice thermometry, as well as carrier cooling. This approach should be applicable down to nanokelvin temperatures. We also discuss how the thermal light shift can affect the accuracy of optical lattice clocks.

Low-temperature kinetics and dynamics with Coulomb crystals

Coulomb crystals-as a source of translationally cold, highly localized ions-are being increasingly utilized in the investigation of ion-molecule reaction dynamics in the cold regime. To develop a fundamental understanding of ion-molecule reactions, and to challenge existing models that describe the rates, product branching ratios, and temperature dependence of such processes, investigators need to exercise full control over the experimental reaction parameters. This requires not only state selection of the reactants, but also control over the collision process (e.g., the collisional energy and angular momentum) and state-selective product detection. The combination of Coulomb crystals in ion traps with cold neutral-molecule sources is enabling the measurement of state-selective reaction rates in a diverse range of systems. With the development of appropriate product detection techniques, we are moving toward the ultimate goal of examining low-energy, state-to-state ion-molecule reaction dynamics.

Motional heating in a graphene-coated ion trap

Electric field noise originating from metal surfaces is a hindrance for a variety of microengineered systems, including for ions in microtraps, but is not well understood at the microscopic level. For trapped ions, it is manifested as motional-state decoherence inexplicable by thermal noise of electrodes alone, but likely surface-dependent. Here, we investigate the role of surface properties in motional heating by creating an ion trap with a unique exterior. Using single trapped-ion probes, we characterize copper electrodes covered in monolayer graphene, a material free of surface charge and dangling bonds. Surprisingly, we measure an average heating rate of 1020 ± 30 quanta/s, which is ∼100 times higher than typical for an uncoated trap operated under similar conditions. This may be related to hydrocarbon deposits on the surface, which could be monitored on graphene to potentially elucidate the mechanisms of motional heating on the atomic scale.

Scalable implementation of boson sampling with trapped ions

Boson sampling solves a classically intractable problem by sampling from a probability distribution given by matrix permanents. We propose a scalable implementation of boson sampling using local transverse phonon modes of trapped ions to encode the bosons. The proposed scheme allows deterministic preparation and high-efficiency readout of the bosons in the Fock states and universal mode mixing. With the state-of-the-art trapped ion technology, it is feasible to realize boson sampling with tens of bosons by this scheme, which would outperform the most powerful classical computers and constitute an effective disproof of the famous extended Church-Turing thesis.

A new epoch of quantum manipulation

The behavior of individual microscopic particles, such as an atom (or a photon), predicted using quantum mechanics, is dramatically different from the behavior of classical particles, such as a planet, determined using classical mechanics. How can the counter-intuitive behavior of the microscopic particle be verified and manipulated experimentally? David Wineland and Serge Haroche, who were awarded the Nobel Prize in physics in 2012, developed a set of methods to isolate the ions and photons from their environment to create a genuine quantum system. Furthermore, they also developed methods to measure and manipulate these quantum systems, which open a path not only to explore the fundamental principles of quantum mechanics, but also to develop a much faster computer: a quantum computer.

Micro-fabricated stylus ion trap

An electroformed, three-dimensional stylus Paul trap was designed to confine a single atomic ion for use as a sensor to probe the electric-field noise of proximate surfaces. The trap was microfabricated with the UV-LIGA technique to reduce the distance of the ion from the surface of interest. We detail the fabrication process used to produce a 150 μm tall stylus trap with feature sizes of 40 μm. We confined single, laser-cooled, (25)Mg(+) ions with lifetimes greater than 2 h above the stylus trap in an ultra-high-vacuum environment. After cooling a motional mode of the ion at 4 MHz close to its ground state (<n> = 0.34 ± 0.07), the heating rate of the trap was measured with Raman sideband spectroscopy to be 387 ± 15 quanta/s at an ion height of 62 μm above the stylus electrodes.

Ground-state cooling of a single atom at the center of an optical cavity

A single neutral atom is trapped in a three-dimensional optical lattice at the center of a high-finesse optical resonator. Using fluorescence imaging and a shiftable standing-wave trap, the atom is deterministically loaded into the maximum of the intracavity field where the atom-cavity coupling is strong. After 5 ms of Raman sideband cooling, the three-dimensional motional ground state is populated with a probability of (89±2)%. Our system is the first to simultaneously achieve quantum control over all degrees of freedom of a single atom: its position and momentum, its internal state, and its coupling to light.

No-go theorem for ground state cooling given initial system-thermal bath factorization

Ground-state cooling and pure state preparation of a small object that is embedded in a thermal environment is an important challenge and a highly desirable quantum technology. This paper proves, with two different methods, that a fundamental constraint on the cooling dynamic implies that it is impossible to cool, via a unitary system-bath quantum evolution, a system that is embedded in a thermal environment down to its ground state, if the initial state is a factorized product of system and bath states. The latter is a crucial but artificial assumption included in numerous tools that treat system-bath dynamics, such as master equation approaches and Kraus operator based methods. Adopting these approaches to address ground state and even approximate ground state cooling dynamics should therefore be done with caution, considering the fundamental theorem exposed in this work.

Sympathetic electromagnetically-induced-transparency laser cooling of motional modes in an ion chain

We use electromagnetically-induced-transparency laser cooling to cool motional modes of a linear ion chain. As a demonstration, we apply electromagnetically-induced-transparency cooling on 24Mg+ ions to cool the axial modes of a 9Be+-24Mg+ ion pair and a 9Be+-24Mg+-24Mg+-9Be+ ion chain, thereby sympathetically cooling the 9Be+ ions. Compared to previous implementations of conventional Raman sideband cooling, we achieve approximately an order-of-magnitude reduction in the duration required to cool the modes to near the ground state and significant reduction in required laser intensity.

Shot-noise-limited monitoring and phase locking of the motion of a single trapped ion

We perform a high-resolution real-time readout of the motion of a single trapped and laser-cooled Ba+ ion. By using an interferometric setup, we demonstrate a shot-noise-limited measurement of thermal oscillations with a resolution of 4 times the standard quantum limit. We apply the real-time monitoring for phase control of the ion motion through a feedback loop, suppressing the photon recoil-induced phase diffusion. Because of the spectral narrowing in the phase-locked mode, the coherent ion oscillation is measured with a resolution of about 0.3 times the standard quantum limit.