Probing surface charge densities on optical fibers with a trapped ion
Florian R. Ong, Klemens Schüppert, Pierre Jobez, Markus Teller, Ben Ames, Dario A. Fioretto, Konstantin Friebe, Moonjoo Lee, Yves Colombe, Rainer Blatt, Tracy E. Northup
We describe a novel method to measure the surface charge densities on optical fibers placed in the vicinity of a trapped ion, where the ion itself acts as the probe. Surface charges distort the trapping potential, and when the fibers are displaced, the ion's equilibrium position and secular motional frequencies are altered. We measure the latter quantities for different positions of the fibers and compare these measurements to simulations in which unknown charge densities on the fibers are adjustable parameters. Values ranging from $-10$ to $+50$ e/$μ$m$^2$ were determined. Our results will benefit the design and simulation of miniaturized experimental systems combining ion traps and integrated optics, for example, in the fields of quantum computation, communication and metrology. Furthermore, our method can be applied to any setup in which a dielectric element can be displaced relative to a trapped charge-sensitive particle.
We demonstrate an all-fiber cavity QED system with a trapped single atom in the strong coupling regime. We use a nanofiber Fabry-Perot cavity, that is, an optical nanofiber sandwiched by two fiber-Bragg-grating mirrors. Measurements of the cavity transmission spectrum with a single atom in a state-insensitive nanofiber trap clearly reveal the vacuum Rabi splitting.
The demonstration of an optical fiber based probe for efficiently exciting the waveguide modes of high-index contrast planar photonic crystal (PC) slabs is presented. Utilizing the dispersion of the PC, fiber taper waveguides formed from standard silica single-mode optical fibers are used to evanescently couple light into the guided modes of a patterned silicon membrane. A coupling efficiency of approximately 95% is obtained between the fiber taper and a PC waveguide mode suitably designed for integration with a previously studied ultra-small mode volume high-Q PC resonant cavity [1]. The micr…
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.
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…
Tapered optical fibers with a nanofiber waist are versatile tools for interfacing light and matter. In this context, laser-cooled atoms trapped in the evanescent field surrounding the optical nanofiber are of particular interest: They exhibit both long ground-state coherence times and efficient coupling to fiber-guided fields. Here, we demonstrate electromagnetically induced transparency, slow light, and the storage of fiber-guided optical pulses in an ensemble of cold atoms trapped in a nanofiber-based optical lattice. We measure a slow-down of light pulses to group velocities of 50 m/s. More…
In this work we present a platform for testing the device performance of a cavity-emitter system, using an ensemble of emitters and a tapered optical fiber. This method provides high-contrast spectra of the cavity modes, selective detection of emitters coupled to the cavity, and an estimate of the device performance in the single- emitter case. Using nitrogen-vacancy (NV) centers in diamond and a GaP optical microcavity, we are able to tune the cavity onto the NV resonance at 10 K, couple the cavity-coupled emission to a tapered fiber, and measure the fiber-coupled NV spontaneous emission deca…
We show that a chain of trapped ions embedded in microtraps generated by an optical lattice can be used to study oscillator models related to dry friction and energy transport. Numerical calculations with realistic experimental parameters demonstrate that both static and dynamic properties of the ion chain change significantly as the optical lattice power is varied. Finally, we lay out an experimental scheme to use the spin degree of freedom to probe the phase space structure and quantum critical behavior of the ion chain.
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…
We demonstrate that the quantum phase transition (QPT) of the Rabi model and critical dynamics near the QPT can be probed in the setup of a single trapped ion. We first show that there exists equilibrium and non-equilibrium universal functions of the Rabi model by finding a proper rescaling of the system parameters and observables. We then propose a scheme that can faithfully realize the Rabi model in the limit of a large ratio of the effective atomic transition frequency to the oscillator frequency using a single trapped-ion and therefore the QPT. It is demonstrated that the predicted univers…
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…
We study a system of periodic Bose condensed atoms coupled to cavity photons using the input-output formalism. We show that the cavity will either act as a through pass Lorentzian filter when the superfluid fraction of the condensate is minimum or completely reflect the input field when the superfluid fraction is maximum. We show that by monitoring the ratio between the transmitted field and the reflected field, one can estimate the superfluid fraction.
A method for gaining information about the phonon-number moments and the generalized nonlinear and linear quadratures in the motion of trapped ions (in particular, position and momentum) is proposed, valid inside and outside the Lamb-Dicke regime. It is based on the measurement of first time derivatives of electronic populations, evaluated at the motion-probe interaction time t=0. In contrast to other state-reconstruction proposals, based on measuring Rabi oscillations or dispersive interactions, the present scheme can be performed resonantly at infinitesimal short motion-probe interaction tim…
In this chapter, we illustrate how a trapped ion system can be used for the experimental study of quantum thermodynamics, in particular, quantum fluctuation of work. As technology of nano/micro scale develops, it becomes critical to understand thermodynamics at the quantum mechanical level. The trapped ion system is a representative physical platform to experimentally demonstrate quantum phenomena with excellent control and precision. We provide a basic introduction of the trapped ion system and present the theoretical framework for the experimental study of quantum thermodynamics. Then we bri…
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…
We propose a scheme for implementing quantum gates for two atoms trapped in distant cavities connected by an optical fiber. The effective long-distance coupling between the two distributed qubits is achieved without excitation and transportation of photons through the optical fiber. Since the cavity modes and fiber mode are never populated and the atoms undergo no transitions, the gate operation is insensitive to the decoherence effect when the thermal photons in the environment are negligible. The scheme opens promising perspectives for networking quantum information processors and implementi…
A theoretical model for driving a two qubit system to a stable long-lived entanglement is discussed. The entire system is represented by two atoms, initially in ground states and disentangled, each one coupled to a separate cavity with the cavities connected by a fiber. The cavities and fiber exchange energy with their individual thermal environments. Under these conditions, we apply the theory of microscopic master equation developed for the dynamics of the open quantum system. Deriving the density operator of the two-qubit system we found that stable long-lived quantum correlations are gener…
We present a novel technique for measuring the characteristics of a magneto-optical trap for cold atoms by monitoring the spontaneous emission from trapped atoms coupled into the guided mode of a tapered optical nanofiber. We show that the nanofiber is highly sensitive to very small numbers of atoms close to its surface. The size and shape of the MOT, determined by translating the cold atom cloud across the tapered fiber, is in excellent agreement with measurements obtained using the conventional method of fluorescence imaging using a CCD camera. The coupling of atomic fluorescence into the ta…
We devise a phase-coherent three-pulse protocol to probe the polariton dynamics in a trapped-ion quantum simulation. In contrast to conventional nonlinear signals, the presented scheme does not change the number of excitations in the system, allowing for the investigation of the dynamics within an $N$-excitation manifold. In the particular case of a filling factor one ($N$ excitations in an $N$-ion chain), the proposed interaction induces coherent transitions between a delocalized phonon superfluid and a localized atomic insulator phase. Numerical simulations of a two-ion chain demonstrate tha…
Dissipation is often considered as a detrimental effect in quantum systems for unitary quantum operations. However, it has been shown that suitable dissipation can be useful resources both in quantum information and quantum simulation. Here, we propose and experimentally simulate a dissipative phase transition (DPT) model using a single trapped ion with an engineered reservoir. We show that the ion's spatial oscillation mode reaches a steady state after the alternating application of unitary evolution under a quantum Rabi model Hamiltonian and sideband cooling of the oscillator. The average ph…
We present and characterize fiber mirrors and a miniaturized ion-trap design developed to integrate a fiber-based Fabry-Perot cavity (FFPC) with a linear Paul trap for use in cavity-QED experiments with trapped ions. Our fiber-mirror fabrication process not only enables the construction of FFPCs with small mode volumes, but also allows us to minimize the influence of the dielectric fiber mirrors on the trapped-ion pseudopotential. We discuss the effect of clipping losses for long FFPCs and the effect of angular and lateral displacements on the coupling efficiencies between cavity and fiber. Op…
We propose a scheme where strongly correlated photons generated inside a hollow-core one-dimensional fiber filled with two cold atomic species can be used to simulate the BCS-BEC crossover. We first show how stationary light-matter excitations (polaritons) in the system can realize an optically tunable two component Bose-Hubbard model, and then analyze the optical parameters regime necessary to generate an effective Fermi-Hubbard model of photons exhibiting Cooper pairing. The characteristic correlated phases of the system can be efficiently observed due to the {\it in situ} accessibility of t…
We demonstrate an optical tweezer based single atom trapping on an optical nanofiber cavity. We show that the fluorescence of single atoms trapped on the nanofiber cavity can be readily observed in real-time through the fiber guided modes. The photon correlation measurements further clarify the atom number and the dynamics of the trap. The trap lifetime is measured to be 52$\pm$5 ms. From the photon statistics measured for different cavity decay rates, the effective coupling rate of the atom-cavity interface is estimated to be 34$\pm$2 MHz. This yields a cooperativity of 5.4$\pm$0.6 and a cavi…
We demonstrate polarisation-preserving frequency conversion of single-photon-level light at 854 nm, resonant with a trapped-ion transition and qubit, to the 1550-nm telecom C band. A total photon in / fiber-coupled photon out efficiency of $\sim$ 30 % is achieved, for a free-running photon noise rate of $\sim$ 60 Hz. This performance would enable telecom conversion of 854-nm polarisation qubits, produced in existing trapped-ion systems, with a signal-to-noise ratio greater than 1. In combination with near-future trapped-ion systems, our converter would enable the observation of entanglement be…
Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, …
We present the realization of a combined trapped-ion and optical cavity system, in which a single Yb^+ ion is confined by a micron-scale ion trap inside a 230 mum-long optical fiber cavity. We characterize the spatial ion-cavity coupling and measure the ion-cavity coupling strength using a cavity-stimulated Lambda-transition. Owing to the small mode volume of the fiber resonator, the coherent coupling strength between the ion and a single photon exceeds the natural decay rate of the dipole moment. This system can be integrated into ion-photon quantum networks and is a step towards cavity quant…
Probing excited-state quantum phase transitions with trapped cold ions
Czech Academy of Sciences, Institute of Scientific Instruments（捷克科学院科学仪器研究所）；Charles University, Faculty of Mathematics and Physics, Institute of Theorertical Physics（查理大学数学物理学院理论物理研究所）
We use a string of confined $^{40}$Ca$^+$ ions to measure perturbations to a trapping potential which are caused by light-induced charging of an anti-reflection coated window and of insulating patches on the ion-trap electrodes. The electric fields induced at the ions' position are characterised as a function of distance to the dielectric, and as a function of the incident optical power and wavelength. The measurement of the ion-string position is sensitive to as few as $40$ elementary charges per $\sqrt{\mathrm{Hz}}$ on the dielectric at distances of order millimetres, and perturbations are o…
We present an ion trap with an integrated fiber cavity, designed for strong coupling at the level of single ions and photons. The cavity is aligned to the axis of a miniature linear Paul trap, enabling simultaneous coupling of multiple ions to the cavity field. We simulate how charges on the fiber mirrors affect the trap potential, and we test these predictions with an ion trapped in the cavity. Furthermore, we measure micromotion and heating rates in the setup.
The generating functional of a self-interacting scalar quantum field theory (QFT), which contains all the relevant information about real-time dynamics and scattering experiments, can be mapped onto a collection of multipartite-entangled two-level sensors via an interferometric protocol that exploits a specific set of source functions. Although one typically focuses on impulsive delta-like sources, as these give direct access to $n$-point Feynman propagators, we show in this work that using always-on harmonic sources can simplify substantially the sensing protocol. In a specific regime, the ef…
A technique based on using optical fiber taper waveguides for probing single emitters embedded in thin dielectric membranes is assessed through numerical simulations. For an appropriate membrane geometry, photoluminescence collection efficiencies in excess of 10 % are predicted, exceeding the efficiency of standard free-space collection by an order of magnitude. Our results indicate that these fiber taper waveguides offer excellent prospects for performing efficient spectroscopy of single emitters embedded in thin films, such as a single self-assembled quantum dot in a semiconductor membrane.
We investigate the position oscillation of a particle that models the center of mass quantum state of a trapped Bose-Einstein condensate coupled to the zero-point fluctuations of the gravitational field. A semiclassical analysis is performed that allows to calculate the mean square amplitude of the oscillation. In analogy with the Lamb shift in quantum electrodynamics, this gives rise to an upshift of the energy of the trapped condensates. We show that for an elongated trap, the energy shift scales quadratically with the length as well as cubically with the total number of atoms.
We experimentally study the ground state coherence properties of cesium atoms in a nanofiber-based two-color dipole trap, localized 200 nm away from the fiber surface. Using microwave radiation to coherently drive the clock transition, we record Ramsey fringes as well as spin echo signals and infer a reversible dephasing time $T_2^\ast=0.6$ ms and an irreversible dephasing time $T_2^\prime=3.7$ ms. By theoretically modelling the signals, we find that, for our experimental parameters, $T_2^\ast$ and $T_2^\prime$ are limited by the finite initial temperature of the atomic ensemble and the heatin…
We propose a method to construct a classical analog of an open quantum system, namely a single quantum particle confined in a potential well and immersed in a thermal bath. The classical analog is made out of a collection of identical wells where classical particles of mass $m$ are trapped. The distribution $n(x,t)$ of the classical positions is used to reconstruct the quantum Bohm potential $V_{\rm Bohm} = -\frac{\hbar^2}{2 m} \frac{Δ\sqrt{n}}{\sqrt{n}}$, which in turn acts on the shape of the potential wells. As a result, the classical particles experience an effective "quantum" force. This …
We present a novel method of machining optical fiber surfaces with a CO${}_2$ laser for use in Fiber-based Fabry-Perot Cavities (FFPCs). Previously FFPCs were prone to large birefringence and limited to relatively short cavity lengths ($\le$ 200 $μ$m). These characteristics hinder their use in some applications such as cavity quantum electrodynamics with trapped ions. We optimized the laser machining process to produce large, uniform surface structures. This enables the cavities to achieve high finesse even for long cavity lengths. By rotating the fibers around their axis during the laser mach…
We discuss the low energy shape oscillations of a magnetic trapped atomic condensate including the spin dipole interaction. When the nominal isotropic s-wave interaction strength becomes tunable through a Feshbach resonance (e.g. as for $^{85}$Rb atoms), anisotropic dipolar effects are shown to be detectable under current experimental conditions [E. A. Donley {\it et al.}, Nature {\bf 412}, 295 (2001)].
The generation of atomic entanglement is discussed in a system that atoms are trapped in separate cavities which are connected via optical fibers. Two distant atoms can be projected to Bell-state by synchronized turning off the local laser fields and then performing a single quantum measurement by a distant controller. The distinct advantage of this scheme is that it works in a regime that $Δ\approxκ\gg g$, which makes the scheme insensitive to cavity strong leakage. Moreover, the fidelity is not affected by atomic spontaneous emission.
Taking recent experiments as examples, we discuss the conditions for sub-wavelength probing of optical field structures by single trapped atoms. We calculate the achievable resolution, highlighting its connection to the fringe visibility in an interference experiment. We show that seemingly different physical pictures, such as spatial averaging, phase modulation, and which-way information, describe the situation equally and lead to identical results. The connection to Bohr's moving slit experiment is pointed out.
We propose an approach to sensitively probe the chirality of molecules by measuring their coherent optical absorption spectra. It is shown that quantum dynamics of the cyclic three-level chiral molecules driven by appropriately-designed external fields is total-phase dependent. This will result in chirality-dependent absorption spectra for the probe field. As a consequence, these absorption spectra can be utilized to identify molecular chirality and determinate enantiomer excess. The feasibility of the proposal with chiral molecules confined in hollow-core photonic crystal fiber (HC-PCF) is al…
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$^+$…
We measure the temporal pair correlation function $g^{(2)}(τ)$ of a trapped gas of bosons above and below the critical temperature for Bose-Einstein condensation. The measurement is performed {\it in situ} using a local, time-resolved single-atom sensitive probing technique. Third and fourth order correlation functions are also extracted. We develop a theoretical model and compare it with our experimental data, finding good quantitative agreement and highlighting the role of interactions. Our results promote temporal correlations as new observables to study the dynamics of ultracold quantum ga…
We evaluate the feasibility of the implementation of two quantum repeater protocols with an existing experimental platform based on a $^{40}$Ca$^+$-ion in a segmented micro trap, and a third one that requires small changes to the platform. A fiber cavity serves as an ion-light interface. Its small mode volume allows for a large coupling strength of $g_c = 2 π20$ MHz despite comparatively large losses $κ= 2 π36.6$ MHz. With a fiber diameter of 125 mu m, the cavity is integrated into the microstructured ion trap, which in turn is used to transport single ions in and out of the interaction zone i…
Trapped atomic ions enable a precise quantification of the flow of information between internal and external degrees of freedom by employing a non-Markovianity measure [H.-P. Breuer et al., Phys. Rev. Lett. 103, 210401 (2009)]. We reveal that the nature of projective measurements in quantum mechanics leads to a fundamental, nontrivial bias in this measure. We observe and study the functional dependence of this bias to permit a demonstration of applications of local quantum probing. An extension of our approach can act as a versatile reference, relevant for understanding complex systems.
We propose a driven optical cavity quantum electrodynamics (QED) set up aimed at directly probing energy transport dynamics in photosynthetic biomolecules. We show that detailed information concerning energy transfer paths and delocalization of exciton states can be inferred (and exciton energies estimated) from the statistical properties of the emitted photons. This approach provides us with a novel spectroscopic tool for the interrogation of biological systems in terms of quantum optical phenomena which have been usually studied for atomic or solid-state systems, e.g. trapped atoms and semic…
We propose a scheme to prepare a maximally entangled state for two Lambda-type atoms trapped in separate optical cavities coupled through an optical fiber based on the combined effect of the unitary dynamics and the dissipative process. Our work shows that the fiber loss, as well as the atomic spontaneous emission and the cavity decay, is no longer undesirable, but requisite to prepare the distributed entanglement, which is meaningful for the long distance quantum information processing tasks. Originating from an arbitrary state, the desired state could be prepared without precise time control…
We demonstrate how optical nanofibers can be used to manipulate and probe single-atom fluorescence. We show that fluorescence photons from a very small number of atoms, average atom number of less than 0.1, around the nanofiber can readily be observed through single-mode optical fiber under resonant laser irradiation. We show also that optical nanofibers enable us to probe the van der Waals interaction between atoms and surface with high precision by observing the fluorescence excitation spectrum.
We show that a system of three trapped ultracold and strongly interacting atoms in one-dimension can be emulated using an optical fiber with a graded-index profile and thin metallic slabs. While the wave-nature of single quantum particles leads to direct and well known analogies with classical optics, for interacting many-particle systems with unrestricted statistics such analoga are not straightforward. Here we study the symmetries present in the fiber eigenstates by using discrete group theory and show that, by spatially modulating the incident field, one can select the atomic statistics, i.…
