Trapped atomic ensembles are convenient systems for quantum information storage in the long-lived sublevels of the electronic ground state and its conversion to propagating optical photons via stimulated Raman processes. Here we investigate a phase-matched emission of photons from a coherently prepared atomic ensemble. We consider an ensemble of cold atoms in an elongated harmonic trap with normal density distribution, and determine the parameters of paraxial optics to match the mode geometry of the emitted radiation and optimally collect it into an optical waveguide.
When two indistinguishable single photons are fed into the two input ports of a beam splitter, the photons will coalesce and leave together from the same output port. This is a quantum interference effect, which occurs because the two possible paths where the photons leave in different output ports interfere destructively. This effect was first observed in parametric downconversion by Hong, Ou and Mandel, and then with single photons produced one after the other by the same quantum emitter. With the recent development of quantum information, a lot of attention has been devoted to this coalesce…
Interference and coincidence detection of two photons emitted by two remote ions can lead to an entangled state which is a critical resource for scalable quantum information processing. Currently, the success probabilities of experimental realizations of this protocol are mainly limited by low coupling efficiency of a photon emitted by an ion into a single mode fiber. Here, we consider two strategies to enhance the collection probability of a photon emitted from a trapped Yb ion, using analytic methods that can be easily applied to other types of ion or neutral atoms. Our analysis shows that w…
Efficient collection of fluorescence from trapped ions is crucial for quantum optics and quantum computing applications, specifically, for qubit state detection and in generating single photons for ion-photon and remote ion entanglement. In a typical setup, only a few per cent of ion fluorescence is intercepted by the aperture of the imaging optics. We employ a simple metallic spherical mirror integrated with a linear Paul ion trap to achieve photon collection efficiency of at least 10% from a single Ba$^+$ ion. An aspheric corrector is used to reduce the aberrations caused by the mirror and a…
We investigate the emission of single photons from CdSe/CdS dot-in-rods which are optically trapped in the focus of a deep parabolic mirror. Thanks to this mirror, we are able to image almost the full 4$π$ emission pattern of nanometer-sized elementary dipoles and verify the alignment of the rods within the optical trap. From the motional dynamics of the emitters in the trap we infer that the single-photon emission occurs from clusters comprising several emitters. We demonstrate the optical trapping of rod-shaped quantum emitters in a configuration suitable for efficiently coupling an ensemble…
We present the design and implementation of a trapped ion cavity QED system. A single ytterbium ion is confined by a micron-scale ion trap inside a 2 mm optical cavity. The ion is coherently pumped by near resonant laser light while the cavity output is monitored as a function of pump intensity and cavity detuning. We observe a Purcell enhancement of scattered light into the solid angle subtended by the optical cavity, as well as a three-peak structure arising from strongly driving the atom. This system can be integrated into existing atom{photon quantum network protocols and is a pathway towa…
Analysis of the effects of decoherence on the radiative and squeezing properties of a coherently driven two-level atom trapped in a resonant cavity applying the corresponding master equation is presented. The atomic dynamics as well as the squeezing and statistical properties of the emitted radiation are investigated. It is found that the atom stays in the lower energy level more often at steady state irrespective of the strength of the coherent radiation and thermal fluctuations entering the cavity. Moreover, a strong external coherent radiation results the splitting of the line of the emissi…
We propose a method for scaling trapped ions for large-scale quantum computation and communication based on a probabilistic ion-photon mapping. Deterministic quantum gates between remotely located trapped ions can be achieved through detection of spontaneously-emitted photons, accompanied by the local Coulomb interaction between neighboring ions. We discuss gate speeds and tolerance to experimental noise for different probabilistic entanglement schemes.
We observe quantum interference of photons emitted by two continuously laser-excited single ions, independently trapped in distinct vacuum vessels. High contrast two-photon interference is observed in two experiments with different ion species, calcium and barium. Our experimental findings are quantitatively reproduced by Bloch equation calculations. In particular, we show that the coherence of the individual resonance fluorescence light field is determined from the observed interference.
We propose an optical scheme to generate an entangled state between a trapped ion and a solid state donor qubit through which-path erasure of identical photons emitted from the two systems. The proposed scheme leverages the similar transition frequencies between In donor bound excitons in ZnO and the $^2P_{1/2}$ to $^2S_{1/2}$ transition in Yb$^+$. The lifetime of the relevant ionic state is longer than that of the ZnO system by a factor of 6, leading to a mismatch in the temporal profiles of emitted photons. A detuned cavity-assisted Raman scheme weakly excites the donor with a shaped laser p…
Efficient collection and analysis of trapped ion qubit fluorescence is essential for robust qubit state detection in trapped ion quantum computing schemes. We discuss simple techniques of improving photon collection efficiency using high numerical aperture (N.A.) reflective optics. To test these techniques we placed a spherical mirror with an effective N.A. of about 0.9 inside a vacuum chamber in the vicinity of a linear Paul trap. We demonstrate stable and reliable trapping of single barium ions, in excellent agreement with our simulations of the electric field in this setup. While a large N.…
Trapped atomic ions are ideal single photon emitters with long lived internal states which can be entangled with emitted photons. Coupling the ion to an optical cavity enables efficient emission of single photons into a single spatial mode and grants control over their temporal shape. These features are key for quantum information processing and quantum communication. However, the photons emitted by these systems are unsuitable for long-distance transmission due to their wavelengths. Here we report the transmission of single photons from a single $^{40}\text{Ca}^{+}$ ion coupled to an optical …
By illuminating an individual rubidium atom stored in a tight optical tweezer with short resonant light pulses, we create an efficient triggered source of single photons with a well-defined polarization. The measured intensity correlation of the emitted light pulses exhibits almost perfect antibunching. Such a source of high rate, fully controlled single photon pulses has many potential applications for quantum information processing.
Quantum secure data transfer is an important topic for quantum cyber security. We propose a scheme to realize quantum secure data transfer in the basis of quantum secure direct communication (QSDC). In this proposal, the transmitted data is encoded in the pulse shape of a single optical qubit, which is emitted from a trapped atom owned by the sender and received by the receiver with another trapped atom. The encoding process can be implemented with high fidelity by controlling the time-dependent driving pulse on the trapped atom to manipulate the Rabi frequency in accordance with the target pu…
We collect the fluorescence from two trapped atomic ions, and measure quantum interference between photons emitted from the ions. The interference of two photons is a crucial component of schemes to entangle atomic qubits based on a photonic coupling. The ability to preserve the generated entanglement and to repeat the experiment with the same ions is necessary to implement entangling quantum gates between atomic qubits, and allows the implementation of protocols to efficiently scale to larger numbers of atomic qubits.
We develop a theory of quantum feedback cooling of a single ion trapped in front of a mirror. By monitoring the motional sidebands of the light emitted into the mirror mode we infer the position of the ion, and act back with an appropriate force to cool the ion. We derive a feedback master equation along the lines of the quantum feedback theory developed by Wiseman and Milburn, which provides us with cooling times and final temperatures as a function of feedback gain and various system parameters.
The development of efficient network nodes is a key element for the realisation of quantum networks which promise great capabilities as distributed quantum computing or provable secure communication. We report the realisation of a quantum network node using a trapped ion inside a fiber-based Fabry-Perot cavity. We show the generation of deterministic entanglement at a high fidelity of $ 91.2(2) $\,\% between a trapped Yb--ion and a photon emitted into the resonator mode. We achieve a success probability for generation and detection of entanglement for a single shot of $ 2.5 \cdot 10^{-3}$ resu…
Integration of fiber optics may play a critical role in the development of quantum information processors based on trapped ions and atoms by enabling scalable collection and delivery of light and coupling trapped ions to optical microcavities. We trap 24Mg+ ions in a surface-electrode Paul trap that includes an integrated optical fiber for detecting 280-nm fluorescence photons. The collection numerical aperture is 0.37 and total collection efficiency is 2.1 %. The ion can be positioned between 80 \mum and 100 \mum from the tip of the fiber by use of an adjustable rf-pseudopotential.
Trapped atomic ions are a leading platform for quantum information networks, with long-lived identical qubit memories that can be locally entangled through their Coulomb interaction and remotely entangled through photonic channels. However, performing both local and remote operations in a single node of a quantum network requires extreme isolation between spectator qubit memories and qubits associated with the photonic interface. We achieve this isolation and demonstrate the ingredients of a scalable ion trap network node by co-trapping $^{171}$Yb$^+\ $ and $^{138}$Ba$^+\ $ qubits, entangling …
We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven $Λ$-system based on electromagnetically induced transparency (EIT). In the ideal limit of unit collection efficiency this provides a quantum limited measurement with minimal backaction on the atomic motion. A feedback loop, which drives the atom with a force proportional to measured signal, provides a cooling mechanism for the atomic motion. We derive the master equation which describes the feedback cooling and show that in the Lamb-Dicke limit th…
We describe a simplified scheme for quantum logic with a collection of laser-cooled trapped atomic ions. Building on the scheme of Cirac and Zoller, we show how the fundamental controlled-NOT gate between a collective mode of ion motion and the internal states of a single ion can be reduced to a single laser pulse, and the need for a third auxiliary internal electronic state can be eliminated.
We analyze the performance of a quantum repeater protocol based on single trapped ions. At each node, single trapped ions embedded into high finesse cavities emit single photons whose polarization is entangled with the ion state. A specific detection of two photons at a central station located half-way between two nodes heralds the entanglement of two remote ions. Entanglement can be extended to long distances by applying successive entanglement swapping operations based on two-ion gate operations that have already been demonstrated experimentally with high precision. Our calculation shows tha…
Trapped, laser-cooled ions produce intense fluorescence. Detecting this fluorescence enables efficient measurement of quantum state of qubits based on trapped atoms. It is desirable to collect a large fraction of the photons to make the detection faster and more reliable. Additionally, efficient fluorescence collection can improve speed and fidelity of remote ion entanglement and quantum gates. Here we show a novel ion trap design that incorporates metallic spherical mirror as the integral part of the trap itself, being its RF electrode. The mirror geometry enables up to 35% solid angle collec…
We examine the viability of quantum repeaters based on two-species trapped ion modules for long distance quantum key distribution. Repeater nodes comprised of ion-trap modules of co-trapped ions of distinct species are considered. The species used for communication qubits has excellent optical properties while the other longer lived species serves as a memory qubit in the modules. Each module interacts with the network only via single photons emitted by the communication ions. Coherent Coulomb interaction between ions is utilized to transfer quantum information between the communication and me…
Quantum repeater segment with free-space coupled co-trapped ions using telecom photon interference
Universität des Saarlandes（萨尔兰大学）；Zentrum für Quantentechnologien (QuTe), Universität des Saarlandes（萨尔兰大学量子技术中心 (QuTe)）；Ruhr-Universität Bochum（波鸿鲁尔大学）
Qubit state detection is an important part of a quantum computation. As number of qubits in a quantum register increases, it is necessary to maintain high fidelity detection to accurately measure the multi-qubit state. Here we present experimental demonstration of high-fidelity detection of a multi-qubit trapped ion register with average single qubit detection error of 4.2(1.5) ppm and a 4-qubit state detection error of 17(2) ppm, limited by the decay lifetime of the qubit, using a novel single-photon-sensitive camera with fast data collection, excellent temporal and spatial resolution, and lo…
Fiber-based quantum networks require photons at telecommunications wavelengths to interconnect qubits separated by long distances. Trapped ions are leading candidates for quantum networking with high-fidelity two-qubit gates, long coherence times, and the ability to readily emit photons entangled with the ion's internal qubit states. However, trapped ions typically emit photons at wavelengths incompatible with telecommunications fiber. Here, we demonstrate frequency conversion of visible photons, emitted from the S-P dipole transition of a trapped Ba+ ion, into the telecommunications C-band. T…
Remote Gottesman-Kitaev-Preskill Entanglement Generation between Trapped Ions
School of Mathematical and Physical Sciences, Keio University（庆应义塾大学数理科学学院）；Department of Electronics and Electrical Engineering, Keio University（庆应义塾大学电子电气工程系）；Advanced ICT Research Institute, National Institute of Information and Communications Technology (NICT)（信息通信研究机构高级ICT研究所）
We present an optical scheme to detect the oscillations of a two-ion string confined in a linear Paul trap. The motion is detected by analyzing the intensity correlations in the fluorescence light emitted by one or two ions in the string. We present measurements performed under continuous Doppler cooling and under pulsed illumination. We foresee several direct applications of this detection method, including motional analysis of multi-ion species or coupled mechanical oscillators, and sensing of mechanical correlations.
The vibrations of a collection of ions in a microtrap array can be described in terms of hopping phonons. We show theoretically that the vibrational couplings may be tailored by using a gradient of the microtrap frequencies, together with a periodic driving of the trapping potential. These ingredients allow us to induce effective gauge fields on the vibrational excitations, such that phonons mimic the behavior of charged particles in a magnetic field. In particular, microtrap arrays are ideally suited to realize the famous Aharonov-Bohm effect, and observe the paradigmatic edge states typical …
A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin-spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how appropriate design of laser fields can provide for arbitrary multidimensional spin-spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently existing trap technology and…
Experimental results are presented on the efficiency limits for a quantum interface between a matter-based qubit and a photonic qubit. Using a trapped ion in an optical cavity, we obtain a single ion-entangled photon at the cavity output with a probability of 0.69(3). The performance of our system is shown to saturate the upper limit to photon-collection probability from a quantum emitter in a cavity, set by the emitter's electronic structure and by the cavity parameters. The probability for generating and detecting the ion-entangled fiber-coupled photon is 0.462(3), a five-fold increase over …
More than one hundred years ago Heinrich Hertz succeeded in transmitting signals over a few meters to a receiving antenna using an electromagnetic oscillator and thus proving the electromagnetic theory developed by James C. Maxwell[1]. Since then, technology has developed, and today a variety of oscillators is available at the quantum mechanical level. For quantized electromagnetic oscillations atoms in cavities can be used to couple electric fields[2, 3]. For mechanical oscillators realized, for example, with cantilevers[4, 5] or vibrational modes of trapped atoms[6] or ions[7, 8], a quantum …
The vast majority of physical objects we are dealing with are almost exclusively made of atoms. Due to their discrete level structure, single atoms have proved to be emitters of light which is incompatible with the classical description of electromagnetic waves. We demonstrate this incompatibility for atomic fluorescence when scaling up the size of the source ensemble, which consists of trapped atomic ions, by several orders of magnitude. The presented measurements of nonclassical statistics on light unconditionally emitted from ensembles containing up to more than a thousand ions promise furt…
Trapped ions are excellent candidates for quantum nodes, as they possess many desirable features of a network node including long-lifetimes, on-site processing capability and produce photonic flying qubits. However, unlike classical networks in which data may be transmitted in optical fibers and the range of communication readily extended with amplifiers, quantum systems often emit photons that have limited propagation range in optical fibers and, by virtue of the nature of a quantum state, cannot be noiselessly amplified. Here, we first describe a method to extract flying qubits from a Ba$^+$…
Stimulated Raman scattering of atoms with $Λ$-configuration of levels is a promising tool for transducing microwave photons to optical photons. We consider an atomic Bose-Einstein condensate whose large phase-space density highly amplifies the coupling to the microwave field. Due momentum transfer to the condensate, stimulated photon scattering can occur outside of the phase-matched direction, which can be used to separate the converted photons from the strong Raman readout pulse. Conversely, in the phase-matched direction, superradiant scattering due to bosonic enhancement leads to increased …
We observe a sixfold Purcell broadening of the D$_2$ line of an optically trapped $^{87}\text{Rb}$ atom strongly coupled to a fiber cavity. Under external illumination by a near-resonant laser, up to $90\%$ of the atom's fluorescence is emitted into the resonant cavity mode. The sub-Poissonian statistics of the cavity output and the Purcell enhancement of the atomic decay rate are confirmed by the observation of a strongly narrowed antibunching dip in the photon autocorrelation function. The photon leakage through the higher-transmission mirror of the single-sided resonator is the dominant con…
Long range quantum information processing will require the integration of different technologies to form hybrid architectures combining the strengths of multiple quantum systems. In this work, we propose a hybrid networking architecture designed to improve entanglement rates in quantum networks based on trapped ions. Trapped ions are excellent candidates as network nodes but photon losses make long-distance networking difficult. To overcome some losses and extend the range of trapped-ion-based networks, we propose including neutral-atom-based non-destructive single-photon detection and single …
Electric noise from metallic surfaces is a major obstacle towards quantum applications with trapped ions due to motional heating of the ions. Here, we discuss how the same noise source can also lead to pure dephasing of motional quantum states. The mechanism is particularly relevant at small ion-surface distances, thus imposing a new constraint on trap miniaturization. By means of a free induction decay experiment, we measure the dephasing time of the motion of a single ion trapped 50~$μ$m above a Cu-Al surface. From the dephasing times we extract the integrated noise below the secular frequen…
Australian National University（澳大利亚国立大学）；Institut für Experimentalphysik, Universität Innsbruck（因斯布鲁克大学实验物理研究所）；Department of Optics Palacký University（帕拉茨基大学光学系）；Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften（奥地利科学院量子光学与量子信息研究所）
Single atoms or atom-like emitters are the purest source of on-demand single photons, they are intrinsically incapable of multi-photon emission. To demonstrate this degree of purity we have realized a tunable, on-demand source of single photons using a single ion trapped at the common focus of high numerical aperture lenses. Our trapped-ion source produces single-photon pulses at a rate of 200 kHz with g$^2(0) = (1.9 \pm 0.2) \times 10^{-3}$, without any background subtraction. The corresponding residual background is accounted for exclusively by detector dark counts. We further characterize t…
We show that single-atoms can be trapped on the surface of a subwavelength-diameter silica-fiber, an optical nanofiber, without any external field, and that single photons spontaneously emitted from the atoms can be readily detected through the single guided-mode of the nanofiber. A key point of the work is our finding that atom trapping sites are created on the nanofiber surface by irradiating the atom cloud around the nanofiber with a violet laser radiation.
This review presents the Laser-Induced Fluorescence Spectroscopy (LIFS) of trapped gas-phase molecular ions. A brief description of the theory and experimental approaches involved in fluorescence spectroscopy, together with state-of-the-art LIFS experiments employing ion traps, is presented. Quadrupole ion traps are commonly used for spatial confinement of ions. One of the main challenges involved in such experiments is poor Signal-to-Noise Ratio (SNR) arising due to weak gas-phase fluorescence emission, high background noise, and small solid angle for the fluorescence collection optics. The e…
Ordered atomic arrays trapped in the vicinity of nanoscale waveguides offer original light-matter interfaces, with applications to quantum information and quantum non-linear optics. Here, we study the decay dynamics of a single collective atomic excitation coupled to a waveguide in different configurations. The atoms are arranged as a linear array and only a segment of them is excited to a superradiant mode and emits light into the waveguide. Additional atomic chains placed on one or both sides play a passive role, either reflecting or absorbing this emission. We show that when varying the geo…
A general bound on the Lyapunov exponent of a quantum system is given by $λ_L\leq2π\,T/\hbar$, where $T$ is the system temperature, as established by Maldacena, Shenker, and Stanford (MSS). This upper bound is saturated when the system under consideration is the exact holographic dual of a black hole. It has also been shown that an inverted harmonic oscillator (IHO) may exhibit the behavior of thermal energy emission, in close analogy to the Hawking radiation emitted by black holes. We demonstrate that the Lyapunov exponent of the IHO indeed saturates the MSS bound, with an effective temperatu…
We demonstrate a probabilistic entangling quantum gate between two distant trapped ytterbium ions. The gate is implemented between the hyperfine "clock" state atomic qubits and mediated by the interference of two emitted photons carrying frequency encoded qubits. Heralded by the coincidence detection of these two photons, the gate has an average fidelity of 90+-2%. This entangling gate together with single qubit operations is sufficient to generate large entangled cluster states for scalable quantum computing.
We demonstrate an optical frequency analysis method using the Fourier transform of detection times of fluorescence photons emitted from a single trapped 40Ca+ ion. The response of the detected photon rate to the relative laser frequency deviations is recorded within the slope of a dark resonance formed in the lambda-type energy level scheme corresponding to two optical dipole transitions. This approach enhances the sensitivity to the small frequency deviations and does so with reciprocal dependence on the fluorescence rate. The employed lasers are phase locked to an optical frequency comb, whi…
Future quantum networks will require the ability to produce matter-photon entanglement at photon frequencies not naturally emitted from the matter qubit. This allows for a hybrid network architecture, where these photons can couple to other tools and quantum technologies useful for tasks such as multiplexing, routing, and storage, but which operate at wavelengths different from that of the matter qubit source, while also reducing network losses. Here, we demonstrate entanglement between a trapped ion and a 780 nm photon, a wavelength which can interact with neutral-Rb-based quantum networking …
We study the collective radiation properties of cold, trapped ensembles of atoms. We consider the high density regime with the mean interatomic distance being comparable to, or smaller than, the wavelength of the resonant optical radiation emitted by the atoms. We find that the emission rate of a photon from an excited atomic ensemble is strongly enhanced for an elongated cloud. We analyze collective single-excitation eigenstates of the atomic ensemble and find that the absorption/emission spectrum is broadened and shifted to lower frequencies as compared to the non-interacting (low density) o…
Experiments with individual trapped ions are ideally suited to investigate fundamental issues of quantum mechanics such as the measurement process. At the same time electrodynamically trapped ions have been used with great success to demonstrate quantum logic operations and are a candidate for scalable quantum computing. In this article a brief introduction is given to the basic steps that constitute a quantum measurement; in particular, measurements on single quantum systems are considered. Then experiments with single Yb+ are reviewed demonstrating the quantum Zeno paradox, as well as an exp…
We describe a scheme to coherently convert a microwave photon of a superconducting co-planar waveguide resonator to an optical photon emitted into a well-defined temporal and spatial mode. The conversion is realized by a cold atomic ensemble trapped above the surface of the superconducting atom chip, near the antinode of the microwave cavity. The microwave photon couples to a strong Rydberg transition of the atoms that are also driven by a pair of laser fields with appropriate frequencies and wavevectors for an efficient wave-mixing process. With only few thousand atoms in an ensemble of moder…
Fast and efficient detection of the qubit state in trapped ion quantum information processing is critical for implementing quantum error correction and performing fundamental tests such as a loophole-free Bell test. In this work we present a simple qubit state detection protocol for a $^{171}$Yb$^+$ hyperfine atomic qubit trapped in a microfabricated surface trap, enabled by high collection efficiency of the scattered photons and low background photon count rate. We demonstrate average detection times of 10.5, 28.1 and 99.8\,$\upmu$s, corresponding to state detection fidelities of 99%, 99.85(1…
We perform a quantum simulation of the Ising model with a transverse field using a collection of three trapped atomic ion spins. By adiabatically manipulating the Hamiltonian, we directly probe the ground state for a wide range of fields and form of the Ising couplings, leading to a phase diagram of magnetic order in this microscopic system. The technique is scalable to much larger numbers of trapped ion spins, where phase transitions approaching the thermodynamic limit can be studied in cases where theory becomes intractable.
