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We present the experimental implementation of a two-qubit phase gate, using a radio frequency (RF) controlled trapped-ion quantum processor. The RFdriven gate is generated by a pulsed dynamical decoupling sequence applied to the ions’ carrier transitions only. It allows for a tunable phase shift with high-fidelity results. The conditional phase shift is measured using a Ramsey-type measurement with an inferred fringe contrast of up to 99+1 −2%. We also prepare a Bell state using this laser-free gate. The phase gate is robust against common sources of error. We investigate the effect of the excitation of the center-of-mass (COM) mode, errors in the axial trap frequency, pulse area errors and errors in sequence timing. The contrast of the phase gate is not significantly reduced up to a COM mode excitation < 20 phonons, trap frequency errors of +10%, and pulse area errors of -8%. The phase shift is not significantly affected up to < 10 phonons and pulse area errors of -2%. Both, contrast and phase shift are robust to timing errors up to -30% and +15%. The gate implementation is resource efficient, since only a single driving field is required per ion. Furthermore, it holds the potential for fast gate speeds (gate times on the order of 100 μs) by using two axial motional modes of a two-ion crystal through improved setups.

We report a detailed investigation on near-ground state cooling of one and two trapped atomic ions. We introduce a simple sideband cooling method for confined atoms and ions, using RF radiation applied to bare ionic states in a static magnetic field gradient, and demonstrate its application to ions confined at secular trap frequencies, $\omega_z \approx 2\pi\times 117 $kHz. For a single \ybplus ion, the sideband cooling cycle reduces the average phonon number, $\left\langle\,n\,\right\rangle$ from the Doppler limit to $\left\langle\,n\,\right\rangle =$ 0.30(12). This is in agreement with the theoretically estimated lowest achievable phonon number in this experiment. We extend this method of RF sideband cooling to a system of two \ybplus ions, resulting in a phonon number of $\left\langle\,n\,\right\rangle =$ 1.1(7) in the center-of-mass mode. Furthermore, we demonstrate the first realisation of sympathetic RF sideband cooling of an ion crystal consisting of two individually addressable identical isotopes of the same species., Comment: 8 pages, 7 figures

We report on a transportable and easy-to-operate optical clock utilizing the 2S1/2 - 2D3/2 transition of a single trapped 171Yb+ ion at 436 nm. Developed within a pilot project for quantum technology in Germany lead by industry, the clock is set up in two 19″ racks. In this way, transportation can easily be realized, and the large degree of automatization allows for operation outside highly specialized laboratories for applications beyond basic research. Comparisons to existing high-accuracy optical clock systems enable a verification of the clock's stability and uncertainty budget at the low 10−17 level. During these tests, operation with 99.8% availability over more than 14 days has been achieved.

We report a proof-of-principle experimental demonstration of the quantum speed-up for learning agents utilizing a small-scale quantum information processor based on radiofrequency-driven trapped ions. The decision-making process of a quantum learning agent within the projective simulation paradigm for machine learning is implemented in a system of two qubits. The latter are realized using hyperfine states of two frequency-addressed atomic ions exposed to a static magnetic field gradient. We show that the deliberation time of this quantum learning agent is quadratically improved with respect to comparable classical learning agents. The performance of this quantum-enhanced learning agent highlights the potential of scalable quantum processors taking advantage of machine learning., Comment: 21 pages, 7 figures, 2 tables. Author names now spelled correctly; sections rearranged; changes in the wording of the manuscript

Cold ions trapped in the vicinity of conductive surfaces experience heating of their oscillatory motion. Typically, the rate of this heating is orders of magnitude larger than expected from electric field fluctuations due to thermal motion of electrons in the conductors. This effect, known as anomalous heating, is not fully understood. One of the open questions is the heating rate's dependence on the ion-electrode separation. We present a direct measurement of this dependence in an ion trap of simple planar geometry. The heating rates are determined by taking images of a single $^{172}$Yb${^+}$ ion's resonance fluorescence after a variable heating time and deducing the trapped ion's temperature from measuring its average oscillation amplitude. Assuming a power law for the heating rate vs. ion-surface separation dependence, an exponent of -3.79 $\pm$ 0.12 is measured., 5 pages, 5 figures and 2 pages, 2 figures of supplemental material

An efficient scheme is proposed to carry out gate operations on an array of trapped Yb$^+$ ions, based on a previous proposal using both electronic and nuclear degrees of freedom in a magnetic field gradient. For this purpose we consider the Paschen-Back regime (strong magnetic field) and employ a high-field approximation in this treatment. We show the possibility to suppress the unwanted coupling between the electron spins by appropriately swapping states between electronic and nuclear spins. The feasibility of generating the required high magnetic field is discussed.

Novel ion traps that provide either a static or a dynamic magnetic gradient field allow for the use of radio frequency (rf) radiation for coupling internal and motional states of ions, which is essential for conditional quantum logic. We show that the coupling mechanism in the presence of a dynamic gradient is the same, in a dressed state basis, as in the case of a static gradient. Then, it is shown how demanding experimental requirements arising when using a dynamic gradient could be overcome. Thus, using dressed states in a dynamic gradient field could decisively reduce experimental complexity on the route towards a scalable device for quantum information science based on rf-driven trapped ions., Comment: 5 pages

Nature Communications 5: Article number: 4679 (2014); Published: 19 August 2014; Updated: 5 November 2015 In the original version of this Article, which was submitted to the journal on 28 March 2014, the submission date was incorrectly given as 28 March 2013. This has now been corrected in both the PDF and HTML versions of the Article.

Even though quantum systems in energy eigenstates do not evolve in time, they can exhibit correlations between internal degrees of freedom in such a way that one of the internal degrees of freedom behaves like a clock variable, and thereby defines an internal time, that parametrizes the evolution of the other degrees of freedom. This situation is of great interest in quantum cosmology where the invariance under reparametrization of time implies that the temporal coordinate dissapears and is replaced by the Wheeler-DeWitt constraint. Here we show that the emergent character of an internal time variable can be investigated experimentally using the exquisite control now available on moderate-size quantum systems. We describe in detail how to implement such an experimental demonstration using the spin and motional degrees of freedom of a single trapped ion.

Using trapped atomic ions we demonstrate a tailored and versatile effective spin-system suitable for quantum simulations and universal quantum computation. By simply applying microwave pulses, selected spins can be decoupled from the remaining system and thus can serve as a quantum memory, while simultaneously, other coupled spins perform conditional quantum dynamics. Also, microwave pulses can change the sign of spin-spin couplings, as well as their effective strength, even during the course of a quantum algorithm. Taking advantage of the simultaneous long-range coupling between three spins a coherent quantum Fourier transform -- an essential building block for many quantum algorithms -- is efficiently realized. This approach, which is based on microwave-driven trapped ions and is complementary to laser-based methods, opens a new route to overcoming technical and physical challenges in the quest for a quantum simulator and a quantum computer., Published version. 22 pages, 5 figures

For experiments with ions confined in a Paul trap, minimization of micromotion is often essential. In order to diagnose and compensate micromotion we have implemented a method that allows for finding the position of the radio-frequency (RF) null reliably and efficiently, in principle, without any variation of direct current (DC) voltages. We apply a trap modulation technique and focus-scanning imaging to extract 3d ion positions for various RF drive powers and analyze the power dependence of the equilibrium position of the trapped ion. In contrast to commonly used methods, the search algorithm directly makes use of a physical effect as opposed to efficient numerical minimization in a high-dimensional parameter space. Using this method we achieve a compensation of the residual electric field that causes excess micromotion in the radial plane of a linear Paul trap down to 0.09V/m. Additionally, the precise position determination of a single harmonically trapped ion employed here can also be utilized for the detection of small forces. This is demonstrated by determining light pressure forces with a precision of 135yN. As the method is based on imaging only, it can be applied to several ions simultaneously and is independent of laser direction and thus well-suited to be used with, for example, surface-electrode traps., 22 pages, 9 figures

A scheme for efficient correction of driving-field frequency drifts in Ramsey interferometry is proposed. The two off-resonant $\ensuremath{\pi}/2$ pulses of duration $T$ used in the traditional Ramsey setup are supplemented with an additional pulse of duration $2T$ (approximate $\ensuremath{\pi}$ pulse), which is applied midway between the Ramsey pulses and has a detuning of opposite sign to theirs. This scheme, which resembles a Hahn's spin-echo pulse embedded into the Ramsey setup, corrects small-to-moderate random errors in the detuning of the driving field. This allows the observation of Ramsey fringes of high contrast even with a noisy driving field or in inhomogeneously broadened atomic ensembles. The contrast is further improved by replacing the refocusing $2T$ pulse by a composite $\ensuremath{\pi}$ pulse. We demonstrate the validity of the concept by comparing experimental results from usual Ramsey measurements with Hahn-Ramsey measurements. These experimental results are obtained from microwave-optical double-resonance spectroscopy on $^{171}\mathrm{Yb}{}^{+}$ ions in a segmented linear Paul trap. In the same way, we verify qualitatively the predicted advantage from using a composite $\ensuremath{\pi}$ pulse for refocusing.

The evolution of a quantum system under observation becomes retarded or even impeded. We review this ``quantum Zeno effect'' in the light of the criticism that has been raised upon a previous attempt to demonstrate it, of later reexaminations of both the projection postulate and the significance of the observations, and of the results of a recent experiment on an individual cold atom. Here, the micro-state of the quantum system gets unveiled with the observation, and the effect of measurement is no longer mixed up with dephasing the object's wave function by the reactive effect of the detection. A procedure is outlined that promises to provide, by observation, an upper limit for the delay of even an exponential decay., Comment: 9 pages, 4 figures. Published version: Section VII sligthly changed

The peculiar ultra-fast trembling motion of a free electron — the Zitterbewegung predicted by Erwin Schrodinger in 1930 when he scrutinized the Dirac equation — has been simulated using a single trapped ion. The Dirac equation, proposed by Paul Dirac in 1928 to describe the behaviour of relativistic quantum particles, merges quantum mechanics with special relativity. A number of peculiar effects emerge from the equation, including a rapid quivering motion or 'Zitterbewegung', well established in theory but difficult to observe in real particles. Christian Roos and colleagues have developed a proof-of-principle quantum simulation of the Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. The high level of control of trapped-ion experimental parameters in this system makes it possible to simulate and study Zitterbewegung and other textbook examples of relativistic quantum physics.

The addressing of a particular qubit within a quantum register is a key prerequisite for scalable quantum computing. In general, executing a quantum gate with a single qubit, or a subset of qubits, affects the quantum states of all other qubits. This reduced fidelity of the whole quantum register could prevent the application of quantum error correction protocols and thus preclude scalability. We demonstrate addressing of individual qubits within a quantum byte (eight qubits) and measure the error induced in all non-addressed qubits (cross-talk) associated with the application of single-qubit gates. The quantum byte is implemented using microwave-driven hyperfine qubits of $^{171}$Yb$^+$ ions confined in a Paul trap augmented with a magnetic gradient field. The measured cross-talk is on the order of $10^{-5}$ and therefore below the threshold commonly agreed sufficient to efficiently realize fault-tolerant quantum computing. Hence, our results demonstrate how this threshold can be overcome with respect to cross-talk., Comment: 13 pages, 5 figures Version 2: Some parts of the text have been rephrased and provide more detail. One figure and additional references have been added. Version 2 of this preprint is similar to the published version

The quantum information carried by a two-level atom was transferred to a high- $Q$ cavity and, after a delay, to another atom. We realized in this way a quantum memory made of a field in a superposition of 0 and 1 photon Fock states. We measured the ``holding time'' of this memory corresponding to the decay of the field intensity or amplitude at the single photon level. This experiment implements a step essential for quantum information processing operations.

Pairs of atoms have been prepared in an entangled state of the Einstein-Podolsky-Rosen (EPR) type. They were produced by the exchange of a single photon between the atoms in a high $Q$ cavity. The atoms, entangled in a superposition involving two different circular Rydberg states, were separated by a distance of the order of 1 cm. At variance with most previous EPR experiments, this one involves massive particles. It can be generalized to three or more atoms and opens the way to new tests of nonlocality in mesoscopic quantum systems.

We investigate the dissociation dynamics of molecules exposed to intense laser fields that induce electronic Rabi frequencies comparable to the frequency of nuclear vibration. A fast, mass selected beam of the simply structured model molecule ${\mathrm{Ar}}_{2}^{+}$ was prepared in low vibrational levels and crossed with a dye laser beam (532 nm, $\ensuremath{\le}5\ifmmode\times\else\texttimes\fi{}{10}^{12}\mathrm{W}/{\mathrm{cm}}^{2}$). The absolute number of photofragments has been measured as a function of intensity. A clear experimental signature of light-induced potential curves is observed: enhanced dissociation by tunneling through a light-induced potential barrier. This is deduced from a quantitative comparison with theoretical predictions.

We have studied the interaction between intense laser fields (⩽ 7 × 10 12 W/cm 2 ) and molecules. For the diatomic molecular ion Ar + 2 the number of photofragments as a function of laser intensity can be quantitatively explained in terms of light-induced adiabatic molecular potentials. The effects predicted by this model tend to cancel under realistic experimental conditions with a thermal distribution of the rovibrational populations. This molecular beam experiment allows for a fully quantitative comparison with theory, since only one dissociation channel is operative and all parameters relevant for a computational simulation have been determined.

We adopt thick-film technology to produce ultra high vacuum compatible interfaces for electrical signals. These interfaces permit voltages of hundreds of Volts and currents of several Amperes and allow for very compact vacuum setups, useful in quantum optics in general, and especially for quantum information and quantum simulations using miniaturized traps for ions or neutral atoms. Such printed circuits can also be useful as pure in-vacuum devices. We demonstrate a specific interface, which provides eleven current feedthroughs, more than 70 dc feedthroughs and a feedthrough for radio frequencies. We achieve a pressure in the low 1e-11mbar range and demonstrate the full functionality of the interface by trapping chains of cold ytterbium ions, which requires all of the signals mentioned above being present. In addition, a versatile multi-channel device for supplying precise time-dependent voltages has been developed., 8 pages, 7 figures added references to recent literature about microwave anipulated ions and fast shuttling

We present a laser cooling scheme for trapped ions and atoms using a combination of laser couplings and a magnetic gradient field. In a Schrieffer–Wolff transformed picture, this setup cancels the carrier and blue sideband terms completely (up to first order in the Lamb–Dicke parameter), resulting in an improved cooling behaviour compared to standard cooling schemes in the Lamb–Dicke regime (e.g. sideband cooling) and allowing cooling to the vibrational ground state. A condition for optimal cooling rates is presented and the cooling behaviour for different Lamb–Dicke parameters and spontaneous decay rates is discussed. Cooling rates of one order of magnitude less than the trapping frequency are achieved using the new cooling method. Furthermore, the scheme exhibits fast rates and low final populations, even for significant deviations from the optimal parameters, and provides good cooling rates also in the multi-particle case., publishedVersion

We discuss the experimental feasibility of quantum simulation with trapped ion crystals, using magnetic field gradients. We describe a micro structured planar ion trap, which contains a central wire loop generating a strong magnetic gradient of about 20 T/m in an ion crystal held about 160 \mu m above the surface. On the theoretical side, we extend a proposal about spin-spin interactions via magnetic gradient induced coupling (MAGIC) [Johanning, et al, J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 154009]. We describe aspects where planar ion traps promise novel physics: Spin-spin coupling strengths of transversal eigenmodes exhibit significant advantages over the coupling schemes in longitudinal direction that have been previously investigated. With a chip device and a magnetic field coil with small inductance, a resonant enhancement of magnetic spin forces through the application of alternating magnetic field gradients is proposed. Such resonantly enhanced spin-spin coupling may be used, for instance, to create Schr\"odinger cat states. Finally we investigate magnetic gradient interactions in two-dimensional ion crystals, and discuss frustration effects in such two-dimensional arrangements., Comment: 20 pages, 13 figures

We present results of lifetime measurements of rotational substates of the E 2Π state in the Rydberg molecules 40ArH and 40ArD. We find reasonable agreement between our result and theoretical predictions in the case of ArH. However, for ArD we obtain a distinctively longer lifetime than for the lighter isotopic molecule, ArH, which is not unusual for hydrides but is not accounted for by theory. In addition, different lifetimes measured for the Q and R,P‐branch, respectively, emitting levels of the E 2Π state in ArD, give interesting insight into the interaction between excited Rydberg states of this molecule. The dependence of the lifetime of levels emitting the Q‐branch on the rotational quantum number N for N≳19 is also investigated. Furthermore, the lifetime of the state(s) responsible for the continuous emission in the ultraviolet (UV) region was measured at discrete wavelengths for each of the molecules 40ArH and 40ArD. Our results, together with theoretical predictions, clearly favor the assignment of the UV continuum to two electronic states, namely B 2Π and E 2Π.

In the positive ion current extracted from a 120 MHz H/He gas discharge, we have observed intermittent behavior as some source control parameters were varied. When the rf power is varied, the average temporal length 〈τ I 〉 of stable intermissions follows a simple power-law dependence with exponent −2.05±0.09. When an axial magnetic field is varied, however, we find 〈τ I 〉 to decrease linearly with the logarithm of this control parameter. Embedding analysis of a fully chaotic state of the discharge shows its dynamics to be associated with a correlation dimension near four.

The control of internal and motional quantum degrees of freedom of laser cooled trapped ions has been subject to intense theoretical and experimental research for about three decades. In the realm of quantum information science the ability to deterministically prepare and measure quantum states of trapped ions is unprecedented. This expertise may be employed to investigate physical models conceived to describe systems that are not directly accessible for experimental investigations. Here, we give an overview of current theoretical proposals and experiments for such quantum simulations with trapped ions. This includes various spin models (e.g., the quantum transverse Ising model, or a neural network), the Bose-Hubbard Hamiltonian, the Frenkel-Kontorova model, and quantum fields and relativistic effects., 50 pages, submitted on 10 March to J. Phys. B, Special issue on Modern Applications of Trapped Ions

We present schemes to prepare two-dimensional cluster states [H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. {\bf 86}, 910 (2001)] with atomic ions confined in a micro-structured linear ion trap and coupled by an engineered spin-spin interaction. In particular, we show how to prepare a $n \times 2$ cluster state by creating a linear cluster state and adding third-neighbor entanglement using selective recoupling techniques. The scheme is based on the capabilities provided by segmented linear Paul traps to confine ions in local potential wells and to separate and transport ions between these wells. Furthermore, we consider creating 3 and 4-qubit cluster states by engineering the coupling matrix such that through the periodicity of the time evolution unwanted couplings are canceled. All entangling operations are achieved by switching of voltages and currents, and do not require interaction with laser light., Comment: Polished and published version, amended author list, amended list of references

Neutral Ytterbium (YbI) and singly ionized Ytterbium (YbII) is widely used in experiments in quantum optics, metrology and quantum information science. We report on the investigation of isotope selective two-photoionisation of YbI that allows for efficient loading of ion traps with YbII. Results are presented on two-colour (399 nm and 369 nm) and single-colour (399 nm) photoionisation and their efficiency is compared to electron impact ionisation. Nearly deterministic loading of a desired number of YbII ions into a linear Paul trap is demonstrated., 9 pages. Considerably extended and revised version including new data

This study presents single qubit gates with trapped ions that are robust against experimental imperfections over a wide range of parameters. In particular it is shown that errors caused by an inaccurate setting of either frequency, amplitude, or duration of the driving field, or of a combination of these errors are tolerable when a suitable sequence of radiation pulses, or a shaped pulse is applied instead of, for instance, a single rectangular pi-pulse. Thus an essential prerequisite for scalable quantum computation with trapped ions is demonstrated.

We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit one to store information distributed over the whole system. The storage capacity of such network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential. We analyze the implementation of error resistant universal quantum information processing in such systems., Comment: 4 pages, 2 figures; Has overlap with cond-mat/0512606; v2: published version

Summary form only given. The temporal evolution of a quantum system is retarded by repeated measurements of the observable involved in the evolution. This impediment, the "quantum Zeno effect", has been proven indistinguishable from the effect of dephasing the system's wave function, except in an individual quantum system. We have demonstrated the retardation of the light-driven quantum evolution on the line S/sub 1/2/-D/sub 6/2/ of a single cooled /sup 172/Yb ion placed in the node of the electric field of a 2-mm Paul trap.

Publisher Summary This chapter discusses quantum measurements and new concepts for experiments with trapped ions. Quantum mechanics is a tremendously successful theory playing a central role in natural sciences even beyond physics, and has been verified in countless experiments, some of which were carried out with very high precision. Quantum theory predicts correlations between two or more quantum systems once an entangled state of these systems has been generated. The chapter introduces experiments with 171 Yb + ions demonstrating the precise manipulation of hyperfine states of single ions essentially free of longitudinal and transverse relaxation. A new concept for ion traps is described that allows for experiments requiring individual addressing of ions and conditional dynamics with several ions even with radiation in the radio frequency (rf) or microwave (mw) regime. It is shown how an additional magnetic field gradient applied to an electrodynamic trap individually shifts ionic qubit resonances making them distinguishable in frequency space. Thus, individual addressing for the purpose of single qubit operations becomes possible using long-wavelength radiation. At the same time, a coupling term between internal and motional states arises even when rf or mw radiation is applied to drive qubit transitions. Thus, conditional quantum dynamics can be carried out in this modified electrodynamic trap and in such a new type of trap all schemes originally devised for optical QIP in ion traps can be applied in the rf or mw regime, too.

In order to faithfully detect the state of an individual two-state quantum system (qubit) realized using, for example, a trapped ion or atom, state selective scattering of resonance fluorescence is well established. The simplest way to read out this measurement and assign a state is the threshold method. The detection error can be decreased by using more advanced detection methods like the time-resolved method or the $\pi$-pulse detection method. These methods were introduced to qubits with a single possible state change during the measurement process. However, there exist many qubits like the hyperfine qubit of $^{171}Yb^+$ where several state change are possible. To decrease the detection error for such qubits, we develope generalizations of the time-resolved method and the $\pi$-pulse detection method for such qubits. We show the advantages of these generalized detection methods in numerical simulations and experiments using the hyperfine qubit of $^{171}Yb^+$. The generalized detection methods developed here can be implemented in an efficient way such that experimental real time state discrimination with improved fidelity is possible., Comment: 22 pages, 9 figures

Quantum information processing (QIP) requires thorough assessment of decoherence. Atoms or ions prepared for QIP often become addressed by radiation within schemes of alternating microwave-optical double resonance. A welldefined amount of decoherence may be applied to the system when spurious resonance light is admitted simultaneously with the driving radiation. This decoherence is quantified in terms of longitudinal and transverse relaxation. It may serve for calibrating observed decoherence as well as for testing errorcorrecting quantum codes.

Digital information processing builds upon elementary physical elements (“bits”) that may occupy either one of two possible states labeled 0 and 1, respectively. If a quantum system, for example, an individual atom having discrete energy eigenstates is chosen as an elementary switch (“qubit”), then the general state of this system will be a superposition of the two computational basis states, i.e. the states chosen to represent the logic 0 and 1. When applying the superposition principle to a register comprising N qubits, one immediately sees that such a register can exist in a superposition of 2 N states thus representing 2 N binary encoded numbers simultaneously. Any operation on this register will act on all states at once, effecting parallel processing on an exponentially growing (with N) number of states. The outcome of a measurement on this register after such an operation will, of course, yield just one out of 2 N possible results with a certain probability.

A quantum information processor is proposed that combines experimental techniques and technology successfully demonstrated either in nuclear magnetic resonance experiments or with trapped ions. An additional inhomogenenous magnetic field applied to an ion trap i) shifts individual ionic resonances (qubits), making them distinguishable by frequency, and, ii) mediates the coupling between internal and external degrees of freedom of trapped ions. This scheme permits one to individually address and coherently manipulate ions confined in an electrodynamic trap using radiation in the radiofrequency or microwave regime., Comment: 4 pages, no figures, replaced with published version (wording and grammar have been slightly changed)

This article reports on development of a multichannel arbitrary waveform generator (MAWG), which simultaneously generates arbitrary voltage waveforms on 24 independent channels with a dynamic update rate of up to 25 Msps. A real-time execution of a single waveform and/or sequence of multiple waveforms in succession, with a user programmable arbitrary sequence order is provided under the control of a stand-alone sequencer circuit implemented using an FPGA. The device is operated using an internal clock and can be synced to other devices by means of the TTL pulses. The device can be used for output voltages in the range of up to +-9 V with a drift rate below +-10 uV/min and a maximum deviation less than +-300 uVpp over a period of two hours., Comment: 12 pages, 12 figures

A mesoscopic superposition of quantum states involving radiation fields with classically distinct phases was created and its progressive decoherence observed. The experiment involved Rydberg atoms interacting one at a time with a few photon coherent field trapped in a high $Q$ microwave cavity. The mesoscopic superposition was the equivalent of an `` $\mathrm{atom}+\mathrm{measuring}\mathrm{apparatus}$'' system in which the ``meter'' was pointing simultaneously towards two different directions---a ``Schr\"odinger cat.'' The decoherence phenomenon transforming this superposition into a statistical mixture was observed while it unfolded, providing a direct insight into a process at the heart of quantum measurement.

Summary form only given. The preparation of simple entangled quantum systems and the demonstration of their nonclassical properties has been a challenging goal since the early days of quantum mechanics and the famous Einstein Poldolsky Rosen (ERR) paper. Using "circular Rydberg atoms" strongly interacting with a zero or one-photon field stored in a microwave superconducting cavity, we have been able to prepare a new kind of EPR pair involving two entangled massive particles. The entanglement originates from the Rabi oscillation of a single excited atom emitting a photon in an initially empty cavity on a transition between two adjacent Rydberg levels.